http://nanowiki.no/api.php?action=feedcontributions&feedformat=atom&user=StorsetNanoWiki - Brukerbidrag [nb]2026-04-18T14:30:45ZBrukerbidragMediaWiki 1.44.2http://nanowiki.no/index.php?title=Prosjektoppgave&diff=4725Prosjektoppgave2010-12-29T23:50:55Z<p>Storset: /* Materialer */</p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
Under følger rapporter skrevet av studenter på innen de forskjellige fordypningsretningene på nano. Disse kan være nyttige å kikke på før man begynner å skrive sin egen oppgave, og også underveis i prosessen.<br />
==Høst 2010==<br />
===Bio===<br />
* [[Media:SigmundBio2010.pdf|Photochemical Internalization of Chitosan/pDNA Nanoparticles]] av Sigmund Østtveit Størset. Sammarbeid mellom Institutt for Fysikk ved NTNU (Catharina de Lange Davies) og Institutt for Strålingsbiologi ved Radiumhospitalet (Kristian Berg).<br />
<br />
===Elektro===<br />
===Materialer===<br />
* [[Media:CNC-project.pdf|Carbon Nanocones as Anode Material in Lithium Ion Batteries]] av [[Bruker:Mariusuv|mariusuv]]. IMT prosjekt av ypperste klasse, godt veiledet av Fride Vullum-Bruer og med Morten Onsrud som støttespiller i de hardeste stunder på laben.<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=Prosjektoppgave&diff=4720Prosjektoppgave2010-12-22T23:56:00Z<p>Storset: /* Bio */</p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
Under følger rapporter skrevet av studenter på innen de forskjellige fordypningsretningene på nano. Disse kan være nyttige å kikke på før man begynner å skrive sin egen oppgave, og også underveis i prosessen.<br />
==Høst 2010==<br />
===Bio===<br />
* [[Media:SigmundBio2010.pdf|Photochemical Internalization of Chitosan/pDNA Nanoparticles]] av Sigmund Østtveit Størset. Sammarbeid mellom Institutt for Fysikk ved NTNU (Catharina de Lange Davies) og Institutt for Strålingsbiologi ved Radiumhospitalet (Kristian Berg).<br />
<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=Finansminister&diff=4719Finansminister2010-12-22T23:50:45Z<p>Storset: </p>
<hr />
<div>== Stillingsbeskrivelse ==<br />
Finansminister holder styr på foreningens økonomi og legger frem revidert regnskap for <br />
Generalvorsamlingen. <br />
* All støtte til undergrupper, refundering av utgifter og lignende blir utbetalt av <br />
finansministeren, men kun på grunnlag av kvitteringer og bilag. <br />
* Finansminister har ansvar for å overholde de økonomiske lover og regler som til enhver tid <br />
er gjeldende. <br />
* Det er nødvendig med en mer grundig erfaringsoverføring enn for øvrige stillinger i Styret, <br />
og finansminister bør derfor å ha opplæring i tre (3) måneder etter avtredelse. <br />
* Finansminister har ansvar for søknader om økonomisk støtte, det som er spesielt aktuelt her <br />
er repromidler og kulturcash.<br />
<br />
==Buckministere gjennom tidene==<br />
<br />
* 2006 og 2007: Sigmund Østtveit Størset<br />
* 2008: Vidar Fausek<br />
* 2009: Line Rude Jakobsen<br />
* 2010: Stian Gulla<br />
* 2011: Raymond Luneng</div>Storsethttp://nanowiki.no/index.php?title=Finansminister&diff=4718Finansminister2010-12-22T23:49:27Z<p>Storset: </p>
<hr />
<div>== Stillingsbeskrivelse ==<br />
Finansminister holder styr på foreningens økonomi og legger frem revidert regnskap for <br />
Generalvorsamlingen. <br />
* All støtte til undergrupper, refundering av utgifter og lignende blir utbetalt av <br />
finansministeren, men kun på grunnlag av kvitteringer og bilag. <br />
* Finansminister har ansvar for å overholde de økonomiske lover og regler som til enhver tid <br />
er gjeldende. <br />
* Det er nødvendig med en mer grundig erfaringsoverføring enn for øvrige stillinger i Styret, <br />
og finansminister bør derfor å ha opplæring i tre (3) måneder etter avtredelse. <br />
* Finansminister har ansvar for søknader om økonomisk støtte, det som er spesielt aktuelt her <br />
er repromidler og kulturcash.<br />
<br />
Buckministere gjennom tidene<br />
<br />
2006 og 2007: Sigmund Østtveit Størset<br />
2008: Vidar Fausek<br />
2009: Line Rude Jakobsen<br />
2010: Stian Gulla<br />
2011: Raymond Luneng</div>Storsethttp://nanowiki.no/index.php?title=Prosjektoppgave&diff=4717Prosjektoppgave2010-12-22T23:42:31Z<p>Storset: /* Bio */</p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
Under følger rapporter skrevet av studenter på innen de forskjellige fordypningsretningene på nano. Disse kan være nyttige å kikke på før man begynner å skrive sin egen oppgave, og også underveis i prosessen.<br />
==Høst 2010==<br />
===Bio===<br />
* [[Media:SigmundBio2010.pdf|Photochemical Internalization of Chitosan/pDNA Nanoparticles]] av Sigmund Østtveit Størset. Sammarbeid mellom institutt for Fysikk ved NTNU (Catharina de Lange Davies) og Institutt for Strålingsbiologi ved Radiumhospitalet (Kristian Berg).<br />
<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=Prosjektoppgave&diff=4716Prosjektoppgave2010-12-22T23:41:00Z<p>Storset: /* Bio */</p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
Under følger rapporter skrevet av studenter på innen de forskjellige fordypningsretningene på nano. Disse kan være nyttige å kikke på før man begynner å skrive sin egen oppgave, og også underveis i prosessen.<br />
==Høst 2010==<br />
===Bio===<br />
[[Media:SigmundBio2010.pdf|Photochemical Internalization of Chitosan/pDNA Nanoparticles]] av Sigmund Østtveit Størset. Sammarbeid mellom institutt for Fysikk ved NTNU (Catharina de Lange Davies) og Institutt for Strålingsbiologi ved Radiumhospitalet.<br />
<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=Fil:SigmundBio2010.pdf&diff=4715Fil:SigmundBio2010.pdf2010-12-22T23:36:28Z<p>Storset: </p>
<hr />
<div></div>Storsethttp://nanowiki.no/index.php?title=Prosjektoppgave&diff=4714Prosjektoppgave2010-12-22T23:35:26Z<p>Storset: </p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
Under følger rapporter skrevet av studenter på innen de forskjellige fordypningsretningene på nano. Disse kan være nyttige å kikke på før man begynner å skrive sin egen oppgave, og også underveis i prosessen.<br />
==Høst 2010==<br />
===Bio===<br />
<br />
<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=Master&diff=4713Master2010-12-22T23:31:46Z<p>Storset: Ny side: Master- eller diplomoppgaven skrives i 10. semester, dvs. på våren i 5. klasse. Vanligvis er masteren en fortsettelse av prosjektoppgaven i 9. semester.</p>
<hr />
<div>Master- eller diplomoppgaven skrives i 10. semester, dvs. på våren i 5. klasse. Vanligvis er masteren en fortsettelse av [[Prosjektoppgave|prosjektoppgaven]] i 9. semester.</div>Storsethttp://nanowiki.no/index.php?title=Prosjektoppgave&diff=4712Prosjektoppgave2010-12-22T23:30:23Z<p>Storset: Ny side: I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning...</p>
<hr />
<div>I 9. semester (dvs. høst i 5. klasse etter vanlig studieprogresjon) skal alle studenter gjennomføre en prosjektoppgave verdt 15 studiepoeng. Venligvis er oppgavene praktiske (i motsetning til teoretiske oppgaver eller literaturstudier). På slutten av semester skriver man en rapport som er den delen av arbeidet som legges til grunnlag for sensur av hele oppgaven.\\<br />
Prosjektet kan enten gjøres ved et institutt på NTNU eller eksternt ved andre institusjoner (dette gjelder også [[Master|masteren]] i 10. semester. Eksempler på institutter som nanostudenter har skrevet prosjekt hos er IFY, IMT og IVT. Av eksterne institusjoner kan IFE og Radiumhospitalet nevnes.<br />
<br />
<br />
<br />
=Rapporter=<br />
==Høst 2010==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Vår 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===<br />
<br />
<br />
==Høst 2011==<br />
===Bio===<br />
===Elektro===<br />
===Materialer===</div>Storsethttp://nanowiki.no/index.php?title=MOL3014_-_Nanomedisin_I_-_Bioanalyse&diff=4710MOL3014 - Nanomedisin I - Bioanalyse2010-12-10T16:11:29Z<p>Storset: </p>
<hr />
<div>{{Infobox<br />
|Fakta høst 2009<br />
|*Foreleser: Øyvind Halaas m.f.<br />
*Vurderingsform: Prosjektarbeid (25%) og skriftlig eksamen (75%)<br />
*Eksamensdato: 14.12.09<br />
}}<br />
<br />
== Faglig innhold ==<br />
Emnet vil ta for seg grunnleggende metoder i bioanalyse og integrering av moduler for anvendelser. I detalj skal<br />
emnet inneholde: Protein-konjugerings-kjemi. DNA-hybridiserings-kjemi. Metoder for kvantitering og<br />
idenfisering av DNA/RNA og protein med fokus på tekniske løsninger og kommende nanoteknologier. Bruk av<br />
bildedannelse i nanoskala biomedisinsk forskning. Mikrofluidikk. Prinispper for og konstruksjon av lab-on-a-chip<br />
og biosensorer. Nevrosensorer. In vivo diagnostikk ved bruk av nanoteknologi.<br />
<br />
== Læringsformer og aktiviteter ==<br />
Timeplanen bestemmes av læringsmål. Emnet baserer seg på forelesninger gitt av forskere med<br />
spesialkompetanse. I emnet inngår en obligatorisk semesteroppgave som blir et dypdykk i originallitteraturen fra<br />
en selvvalgt forelesning og som teller 25% av karakteren. Undervisningen holdes på engelsk.<br />
<br />
== Læringsmål ==<br />
Studententene skal erverve innsikt i teknologisk integrasjon av kjemi, fysikk og molekylærbiologi til bruk i<br />
bioanalyse relevant for biomedisinsk forskning og diagnostikk. Studentene skal videre forstå prinsippene for og<br />
konstruksjon av analytiske og strukturelle moduler som kan inngå i mikro- og nanoverktøy. Studentene skal<br />
fordype seg i et emne fra forelesningene gjennom en semesteroppgave.<br />
<br />
= Prosjektoppgaver =<br />
Prosjektoppgavene i faget skrives om et selvvalgt tema fortrinnsvis med utgangspunkt i et tema tatt opp i forelesningene. En øvre grense på 5 sider og noen retningslinjer blir gitt, og prosjektet er et litteraturprosjekt som skal ta utgangspunkt i forskningsartikler om temaet. <br />
<br />
Et utvalg av prosjekter:<br />
<br />
*[[Media:Nanomedicine_project_Kai_Beckwith_-_Nanoparticles_for_neuroscientific_imaging_applications.pdf|Nanoparticles for neuroscientific imaging applications]] av Kai Beckwith.<br />
*[[Media:Creation_and_applications_of_nanoarrays_of_biomolecules_through_Dip-Pen_Nanotechnology.doc|Creation and applications of nanoarrays of biomolecules through Dip-Pen Nanolithography]] av Sigmund Ø. Størset.<br />
<br />
<br />
<br />
== Eksterne linker ==<br />
<br />
*[http://www.ntnu.no/studier/emner?emnekode=MOL3014 NTNUs fagbeskrivelse]<br />
*[http://timeplan.medisin.ntnu.no/timetable_show.php Timeplan ved DMF]<br />
<br />
[[Kategori:Obligatoriske emner]]<br />
[[Kategori:Fag 7. semester]]<br />
[[Kategori:Fag]]</div>Storsethttp://nanowiki.no/index.php?title=Buckminister&diff=4709Buckminister2010-12-10T13:22:35Z<p>Storset: </p>
<hr />
<div>== Stillingsbeskrivelse ==<br />
Buckminister er leder av Timini, sjef for Styret, og skal være Timinis ansikt utad. Buckminister har <br />
til oppgave å: <br />
* Administrere den daglige driften av foreningen. <br />
* Sørge for at foreningens lover følges og medlemmenes interesser ivaretas. <br />
* Kalle inn til og lede styremøter. <br />
* Ha generell oversikt over det som skjer i Timini.<br />
<br />
== Buckministere gjennom tidene ==<br />
* 2006 og 2007: Lotte Maria Beate Skolem<br />
* 2008: Kai Beckwith<br />
* 2009: Marianne Sandvold<br />
* 2010: Ida Marie Høyås<br />
* 2011: Anne Brit Lello</div>Storsethttp://nanowiki.no/index.php?title=Bruker:Storset&diff=4409Bruker:Storset2010-03-30T05:44:49Z<p>Storset: </p>
<hr />
<div>Er i USA på [[University of Colorado at Boulder (CU Boulder)]]. Her prøver han å være ute og gjøre uteting så mye som mulig, men av en aller annen grunn driver foreleserne og gir ham lekser slik at han må være inne. Det liker han bare sånn passe godt.</div>Storsethttp://nanowiki.no/index.php?title=Bruker:Storset&diff=4408Bruker:Storset2010-03-30T05:42:18Z<p>Storset: </p>
<hr />
<div>Er i USA på University of Colorado at Boulder. Her prøver han å være ute og gjøre uteting så mye som mulig, men av en aller annen grunn driver foreleserne og gir ham lekser slik at han må være inne. Det liker han bare sånn passe godt.</div>Storsethttp://nanowiki.no/index.php?title=University_of_Colorado_at_Boulder_(CU_Boulder)&diff=4407University of Colorado at Boulder (CU Boulder)2010-03-30T05:34:07Z<p>Storset: /* Hjemmeside */</p>
<hr />
<div>==Hjemmeside==<br />
[http://www.colorado.edu University of Colorado at Boulder]<br />
<br />
[[Kategori:Utveksling]]</div>Storsethttp://nanowiki.no/index.php?title=University_of_Colorado_at_Boulder_(CU_Boulder)&diff=4406University of Colorado at Boulder (CU Boulder)2010-03-30T05:17:27Z<p>Storset: Ny side: ==Hjemmeside== [http://www.colorado.edu University of Colorado at Boulder]</p>
<hr />
<div>==Hjemmeside==<br />
[http://www.colorado.edu University of Colorado at Boulder]</div>Storsethttp://nanowiki.no/index.php?title=Utveksling&diff=4405Utveksling2010-03-30T05:15:17Z<p>Storset: /* Utvekslingssteder */</p>
<hr />
<div>== Standard ting ==<br />
<br />
Det kan være greit å finne ut hvor man vil, og hva man vil ved å dra ut.<br />
Når man vet hvor, så er det litt greiere å finne ut hva man vil; lære et språk, finne et sted med bedre kompetanse, høste kulturerfaring, unngå Trondheimsklimaet, skaffe kontakter eller bare få seg et år borte fra de andre på linja.<br />
<br />
Uansett er det visse ting man må finne ut:<br />
<br />
*Noe om universitetet: Gå på hjemmesida til universitet, eller søk etter informasjon hos [http://www.ntnu.no/studier/studier_i_utlandet/land internasjonal seksjon].<br />
*Få [http://www.ntnu.no/eksternweb/multimedia/archive/00031/Forh_ndsgodkjennings_31079a.pdf godkjenning] hos fakultetet når du har funnet ut av fagene.<br />
*Søk om støtte hos [http://www.lanekassen.no/templates/Page____5505.aspx Lånekassa] og hos [https://www.intersek.ntnu.no/soknadsskjema/ Internasjonal seksjon].<br />
<br />
Ellers er Internajsonalt Hus på Gløshaugen et sted å gå for å få mer informasjon og det finner du på [http://www.ntnu.no/ntnukart//no/gloshaugen.gif dette kartet] (øverst i venstre hjørne).<br />
<br />
<br />
Ved utveksling utenom 4. året, da med tanke på masteroppgaven, eventuelt Ph.D, så er det viktigste å kontakte faglærere og finne ut av hvem som har kontakter hvor, for da går det mye på hvem som kjenner hvem.<br />
<br />
<br />
== Praktiske ting ==<br />
<br />
Det kan i mange tilfeller være greit å være litt tidlig ute med følgende ting:<br />
*Forsikring - skaff en spesialforsikring for studenter i utlandet enten via ANSA eller ditt forsikringsselskap<br />
*Enkelte steder er det knot å få seg en plass i faget, men bare besøk professorens kontor, etter litt korrespondanse via mail, og snakk med ham/henne så ordner slikt seg.<br />
*Velg deg ut en hel haug med fag! Er ikke alltid du er like heldig med fagvalgenes ledighet og tilgjengelighet...<br />
*Kom ned litt tidlig slik at du har tid til å skaffe bolig, da det er litt kjedelig å bo på hostell når du begynner med undervisninga. Dette kan selvfølgelig i noen tilfeller ordnes hjemme fra Norge, men det er greiere å se hva du får før du sier ja.<br />
<br />
== Utvekslingssteder ==<br />
<br />
Her er en oversikt over noen forslag til universiteter rundt om i verden, en del av dem med tanke på at de bedriver litt med nanoteknologi på noen av sine fakulteter og muligens har programmer for utdanning innen vårt fagfelt:<br />
<br />
{| class="wikitable sortable"<br />
|- <br />
! Institusjon<br />
! Land<br />
! Beliggenhet<br />
! Avtale med NTNU<br />
|-<br />
| [[Universitetet i Oslo]]<br />
| Norge<br />
| Oslo<br />
| ?<br />
|-<br />
| [[University of California, Berkeley]]<br />
| USA<br />
| Berkeley, California<br />
| Delvis<br />
|-<br />
| [[University of Waterloo]]<br />
| Canada<br />
| Waterloo, Ontario<br />
| Ja<br />
|-<br />
| [[California Institute of Technology]]<br />
| USA<br />
| Pasadena, California<br />
| Nei<br />
|-<br />
| [[Seoul National University]]<br />
| Korea<br />
| Seoul<br />
| Ja<br />
|-<br />
| [[Osaka Prefecture University]]<br />
| Japan<br />
| Osaka<br />
| Ja<br />
|-<br />
| [[Tokyo Instuitute of Technology]]<br />
| Japan<br />
| Tokyo<br />
| Ja<br />
|-<br />
| [[Waseda University]]<br />
| Japan<br />
| Shinjuku, Tokyo<br />
| Ja<br />
|-<br />
| [[University of Alberta]]<br />
| Canada<br />
| Edmonton, Alberta<br />
| Ja<br />
|-<br />
| [[Cornell University]]<br />
| USA<br />
| Ithaca, New York<br />
| Nei<br />
|-<br />
| [[University of California, San Diego]]<br />
| USA<br />
| San Diego, California<br />
| Ja(?)<br />
|-<br />
| [[University of Guelph]]<br />
| Canada<br />
| Guelph, Ontario<br />
| Nei<br />
|-<br />
| [[Penn State University]]<br />
| USA<br />
| Centre County, Pennsylvania<br />
| Ja (Bare lærerutdanning?)<br />
|-<br />
| [[Korea Advanced Institute of Science and Technology]] (KAIST)<br />
| Korea<br />
| Yuseong, Deajeon<br />
| Ja<br />
|-<br />
| [[TU Delft]]<br />
| Nederland<br />
| Delft<br />
| Ja, Erasmus<br />
|-<br />
| [[Massachusetts Institute of Technology (MIT)]]<br />
| USA<br />
| Cambridge, Massachusetts<br />
| Nei<br />
|-<br />
| [[University of Colorado at Boulder (CU Boulder)]]<br />
| USA<br />
| Boulder, Colorado<br />
| Nei<br />
|}<br />
<br />
Det at NTNU har avtale med universitet kan bety litt forskjellig. Det kan variere fra at man får totalt fritak av betaling av skolepenger til at man bare får et lite avslag i prisen. For mer informasjon bes det tas kontakt med Internasjonal Seksjon.<br />
<br />
== Finansiering av utdanning ==<br />
<br />
* [http://www.lanekassen.no/templates/Page____9098.aspx Lånekassen]<br />
* [https://www.intersek.ntnu.no/soknadsskjema/ Stipend fra NTNU]<br />
* [http://www.legathandboken.no/ Legathåndboken]<br />
* [http://www.fulbright.no/Fulbright_Grants/Norwegians_to_the_US/Fulbright+stipend+for+norske+studenter+til+USA.E3p1MY7.ips Fullbright-stipend (kun USA)]<br />
* [http://www.noram.no/index.php?side_id=75&vis=1 NORAM-stipend (kun USA og Canada)]<br />
<br />
== Utvekslingsrapporter ==<br />
Mange studenter fra NTNU får utvekslingsstipend fra Internasjonal Seksjon. For å få utbetalt stipendet må man skrive en rapport som legges inn i [https://www.intersek.ntnu.no/rapport/FMPro?-db=Rapport.fp5&-lay=www&-format=search.htm&-view database]. Nedenfor er ei liste med utvekslingsrapporter skrevet av nanoteknologistudenter.<br />
<br />
===Nederland===<br />
===Singapor===<br />
===Sveits===<br />
===USA===<br />
[https://www.intersek.ntnu.no/rapport/FMPro?-db=rapport.fp5&-format=record_detail.htm&-lay=www&-sortfield=-none-&-op=cn&City=Boulder&-max=10&-recid=40002&-find= University of Colorado at Boulder] vår 2010, skrevet av Sigmund Østtveit Størset, [[Bionanoteknologi]]<br />
<br />
== Nyttige lenker ==<br />
<br />
*[http://www.ntnu.no/studier/studier_i_utlandet Internasjonal seksjon, NTNU]<br />
*[http://www.ntnu.no/intersek/tilutlandet123 Til utlandet på 123]<br />
*[http://www.ansa.no/ Mye nyttig informasjon om utdanning i utlandet fra ANSA]<br />
*[http://ed.sjtu.edu.cn/ARWU-FIELD2008/ENG2008.htm De 100 beste teknologiuniversitetene]<br />
*[http://www.ifs.tuwien.ac.at/~silvia/research-tips/times_top100_technologie_2005.pdf Times rangering av de 100 beste tekniske universitetene] <br />
*[http://colleges.usnews.rankingsandreviews.com/college Rangeringer inne mange kategorier i USA]<br />
*[http://www.ntnu.no/international/usa/visa.pdf Informasjon om prosedyren for å søke visum til USA]<br />
*[http://www.ntnu.no/international/recommendations Informasjon om letters of recommendation]<br />
*[http://www.ntnu.no/international/statementofpurpose.pdf Informasjon om å skrive statement of purpose (motivasjonsbrev)]<br />
*[http://www.ansa.no/upload/Dokumenter/Infosenteret/Landbrosjyrer/usa07.pdf ANSA's brosjyre om utdanning i USA]<br />
<br />
[[Kategori:Utveksling]]</div>Storsethttp://nanowiki.no/index.php?title=Utveksling&diff=4404Utveksling2010-03-30T05:14:51Z<p>Storset: /* Utvekslingssteder */</p>
<hr />
<div>== Standard ting ==<br />
<br />
Det kan være greit å finne ut hvor man vil, og hva man vil ved å dra ut.<br />
Når man vet hvor, så er det litt greiere å finne ut hva man vil; lære et språk, finne et sted med bedre kompetanse, høste kulturerfaring, unngå Trondheimsklimaet, skaffe kontakter eller bare få seg et år borte fra de andre på linja.<br />
<br />
Uansett er det visse ting man må finne ut:<br />
<br />
*Noe om universitetet: Gå på hjemmesida til universitet, eller søk etter informasjon hos [http://www.ntnu.no/studier/studier_i_utlandet/land internasjonal seksjon].<br />
*Få [http://www.ntnu.no/eksternweb/multimedia/archive/00031/Forh_ndsgodkjennings_31079a.pdf godkjenning] hos fakultetet når du har funnet ut av fagene.<br />
*Søk om støtte hos [http://www.lanekassen.no/templates/Page____5505.aspx Lånekassa] og hos [https://www.intersek.ntnu.no/soknadsskjema/ Internasjonal seksjon].<br />
<br />
Ellers er Internajsonalt Hus på Gløshaugen et sted å gå for å få mer informasjon og det finner du på [http://www.ntnu.no/ntnukart//no/gloshaugen.gif dette kartet] (øverst i venstre hjørne).<br />
<br />
<br />
Ved utveksling utenom 4. året, da med tanke på masteroppgaven, eventuelt Ph.D, så er det viktigste å kontakte faglærere og finne ut av hvem som har kontakter hvor, for da går det mye på hvem som kjenner hvem.<br />
<br />
<br />
== Praktiske ting ==<br />
<br />
Det kan i mange tilfeller være greit å være litt tidlig ute med følgende ting:<br />
*Forsikring - skaff en spesialforsikring for studenter i utlandet enten via ANSA eller ditt forsikringsselskap<br />
*Enkelte steder er det knot å få seg en plass i faget, men bare besøk professorens kontor, etter litt korrespondanse via mail, og snakk med ham/henne så ordner slikt seg.<br />
*Velg deg ut en hel haug med fag! Er ikke alltid du er like heldig med fagvalgenes ledighet og tilgjengelighet...<br />
*Kom ned litt tidlig slik at du har tid til å skaffe bolig, da det er litt kjedelig å bo på hostell når du begynner med undervisninga. Dette kan selvfølgelig i noen tilfeller ordnes hjemme fra Norge, men det er greiere å se hva du får før du sier ja.<br />
<br />
== Utvekslingssteder ==<br />
<br />
Her er en oversikt over noen forslag til universiteter rundt om i verden, en del av dem med tanke på at de bedriver litt med nanoteknologi på noen av sine fakulteter og muligens har programmer for utdanning innen vårt fagfelt:<br />
<br />
{| class="wikitable sortable"<br />
|- <br />
! Institusjon<br />
! Land<br />
! Beliggenhet<br />
! Avtale med NTNU<br />
|-<br />
| [[Universitetet i Oslo]]<br />
| Norge<br />
| Oslo<br />
| ?<br />
|-<br />
| [[University of California, Berkeley]]<br />
| USA<br />
| Berkeley, California<br />
| Delvis<br />
|-<br />
| [[University of Waterloo]]<br />
| Canada<br />
| Waterloo, Ontario<br />
| Ja<br />
|-<br />
| [[California Institute of Technology]]<br />
| USA<br />
| Pasadena, California<br />
| Nei<br />
|-<br />
| [[Seoul National University]]<br />
| Korea<br />
| Seoul<br />
| Ja<br />
|-<br />
| [[Osaka Prefecture University]]<br />
| Japan<br />
| Osaka<br />
| Ja<br />
|-<br />
| [[Tokyo Instuitute of Technology]]<br />
| Japan<br />
| Tokyo<br />
| Ja<br />
|-<br />
| [[Waseda University]]<br />
| Japan<br />
| Shinjuku, Tokyo<br />
| Ja<br />
|-<br />
| [[University of Alberta]]<br />
| Canada<br />
| Edmonton, Alberta<br />
| Ja<br />
|-<br />
| [[Cornell University]]<br />
| USA<br />
| Ithaca, New York<br />
| Nei<br />
|-<br />
| [[University of California, San Diego]]<br />
| USA<br />
| San Diego, California<br />
| Ja(?)<br />
|-<br />
| [[University of Guelph]]<br />
| Canada<br />
| Guelph, Ontario<br />
| Nei<br />
|-<br />
| [[Penn State University]]<br />
| USA<br />
| Centre County, Pennsylvania<br />
| Ja (Bare lærerutdanning?)<br />
|-<br />
| [[Korea Advanced Institute of Science and Technology]] (KAIST)<br />
| Korea<br />
| Yuseong, Deajeon<br />
| Ja<br />
|-<br />
| [[TU Delft]]<br />
| Nederland<br />
| Delft<br />
| Ja, Erasmus<br />
|-<br />
| [[Massachusetts Institute of Technology (MIT)]]<br />
| USA<br />
| Cambridge, Massachusetts<br />
| Nei<br />
| [[University of Colorado at Boulder (CU Boulder)]]<br />
| USA<br />
| Boulder, Colorado<br />
| Nei<br />
|}<br />
<br />
Det at NTNU har avtale med universitet kan bety litt forskjellig. Det kan variere fra at man får totalt fritak av betaling av skolepenger til at man bare får et lite avslag i prisen. For mer informasjon bes det tas kontakt med Internasjonal Seksjon.<br />
<br />
== Finansiering av utdanning ==<br />
<br />
* [http://www.lanekassen.no/templates/Page____9098.aspx Lånekassen]<br />
* [https://www.intersek.ntnu.no/soknadsskjema/ Stipend fra NTNU]<br />
* [http://www.legathandboken.no/ Legathåndboken]<br />
* [http://www.fulbright.no/Fulbright_Grants/Norwegians_to_the_US/Fulbright+stipend+for+norske+studenter+til+USA.E3p1MY7.ips Fullbright-stipend (kun USA)]<br />
* [http://www.noram.no/index.php?side_id=75&vis=1 NORAM-stipend (kun USA og Canada)]<br />
<br />
== Utvekslingsrapporter ==<br />
Mange studenter fra NTNU får utvekslingsstipend fra Internasjonal Seksjon. For å få utbetalt stipendet må man skrive en rapport som legges inn i [https://www.intersek.ntnu.no/rapport/FMPro?-db=Rapport.fp5&-lay=www&-format=search.htm&-view database]. Nedenfor er ei liste med utvekslingsrapporter skrevet av nanoteknologistudenter.<br />
<br />
===Nederland===<br />
===Singapor===<br />
===Sveits===<br />
===USA===<br />
[https://www.intersek.ntnu.no/rapport/FMPro?-db=rapport.fp5&-format=record_detail.htm&-lay=www&-sortfield=-none-&-op=cn&City=Boulder&-max=10&-recid=40002&-find= University of Colorado at Boulder] vår 2010, skrevet av Sigmund Østtveit Størset, [[Bionanoteknologi]]<br />
<br />
== Nyttige lenker ==<br />
<br />
*[http://www.ntnu.no/studier/studier_i_utlandet Internasjonal seksjon, NTNU]<br />
*[http://www.ntnu.no/intersek/tilutlandet123 Til utlandet på 123]<br />
*[http://www.ansa.no/ Mye nyttig informasjon om utdanning i utlandet fra ANSA]<br />
*[http://ed.sjtu.edu.cn/ARWU-FIELD2008/ENG2008.htm De 100 beste teknologiuniversitetene]<br />
*[http://www.ifs.tuwien.ac.at/~silvia/research-tips/times_top100_technologie_2005.pdf Times rangering av de 100 beste tekniske universitetene] <br />
*[http://colleges.usnews.rankingsandreviews.com/college Rangeringer inne mange kategorier i USA]<br />
*[http://www.ntnu.no/international/usa/visa.pdf Informasjon om prosedyren for å søke visum til USA]<br />
*[http://www.ntnu.no/international/recommendations Informasjon om letters of recommendation]<br />
*[http://www.ntnu.no/international/statementofpurpose.pdf Informasjon om å skrive statement of purpose (motivasjonsbrev)]<br />
*[http://www.ansa.no/upload/Dokumenter/Infosenteret/Landbrosjyrer/usa07.pdf ANSA's brosjyre om utdanning i USA]<br />
<br />
[[Kategori:Utveksling]]</div>Storsethttp://nanowiki.no/index.php?title=Utveksling&diff=4403Utveksling2010-03-30T04:53:54Z<p>Storset: /* Utvekslingsrapporter */</p>
<hr />
<div>== Standard ting ==<br />
<br />
Det kan være greit å finne ut hvor man vil, og hva man vil ved å dra ut.<br />
Når man vet hvor, så er det litt greiere å finne ut hva man vil; lære et språk, finne et sted med bedre kompetanse, høste kulturerfaring, unngå Trondheimsklimaet, skaffe kontakter eller bare få seg et år borte fra de andre på linja.<br />
<br />
Uansett er det visse ting man må finne ut:<br />
<br />
*Noe om universitetet: Gå på hjemmesida til universitet, eller søk etter informasjon hos [http://www.ntnu.no/studier/studier_i_utlandet/land internasjonal seksjon].<br />
*Få [http://www.ntnu.no/eksternweb/multimedia/archive/00031/Forh_ndsgodkjennings_31079a.pdf godkjenning] hos fakultetet når du har funnet ut av fagene.<br />
*Søk om støtte hos [http://www.lanekassen.no/templates/Page____5505.aspx Lånekassa] og hos [https://www.intersek.ntnu.no/soknadsskjema/ Internasjonal seksjon].<br />
<br />
Ellers er Internajsonalt Hus på Gløshaugen et sted å gå for å få mer informasjon og det finner du på [http://www.ntnu.no/ntnukart//no/gloshaugen.gif dette kartet] (øverst i venstre hjørne).<br />
<br />
<br />
Ved utveksling utenom 4. året, da med tanke på masteroppgaven, eventuelt Ph.D, så er det viktigste å kontakte faglærere og finne ut av hvem som har kontakter hvor, for da går det mye på hvem som kjenner hvem.<br />
<br />
<br />
== Praktiske ting ==<br />
<br />
Det kan i mange tilfeller være greit å være litt tidlig ute med følgende ting:<br />
*Forsikring - skaff en spesialforsikring for studenter i utlandet enten via ANSA eller ditt forsikringsselskap<br />
*Enkelte steder er det knot å få seg en plass i faget, men bare besøk professorens kontor, etter litt korrespondanse via mail, og snakk med ham/henne så ordner slikt seg.<br />
*Velg deg ut en hel haug med fag! Er ikke alltid du er like heldig med fagvalgenes ledighet og tilgjengelighet...<br />
*Kom ned litt tidlig slik at du har tid til å skaffe bolig, da det er litt kjedelig å bo på hostell når du begynner med undervisninga. Dette kan selvfølgelig i noen tilfeller ordnes hjemme fra Norge, men det er greiere å se hva du får før du sier ja.<br />
<br />
== Utvekslingssteder ==<br />
<br />
Her er en oversikt over noen forslag til universiteter rundt om i verden, en del av dem med tanke på at de bedriver litt med nanoteknologi på noen av sine fakulteter og muligens har programmer for utdanning innen vårt fagfelt:<br />
<br />
{| class="wikitable sortable"<br />
|- <br />
! Institusjon<br />
! Land<br />
! Beliggenhet<br />
! Avtale med NTNU<br />
|-<br />
| [[Universitetet i Oslo]]<br />
| Norge<br />
| Oslo<br />
| ?<br />
|-<br />
| [[University of California, Berkeley]]<br />
| USA<br />
| Berkeley, California<br />
| Delvis<br />
|-<br />
| [[University of Waterloo]]<br />
| Canada<br />
| Waterloo, Ontario<br />
| Ja<br />
|-<br />
| [[California Institute of Technology]]<br />
| USA<br />
| Pasadena, California<br />
| Nei<br />
|-<br />
| [[Seoul National University]]<br />
| Korea<br />
| Seoul<br />
| Ja<br />
|-<br />
| [[Osaka Prefecture University]]<br />
| Japan<br />
| Osaka<br />
| Ja<br />
|-<br />
| [[Tokyo Instuitute of Technology]]<br />
| Japan<br />
| Tokyo<br />
| Ja<br />
|-<br />
| [[Waseda University]]<br />
| Japan<br />
| Shinjuku, Tokyo<br />
| Ja<br />
|-<br />
| [[University of Alberta]]<br />
| Canada<br />
| Edmonton, Alberta<br />
| Ja<br />
|-<br />
| [[Cornell University]]<br />
| USA<br />
| Ithaca, New York<br />
| Nei<br />
|-<br />
| [[University of California, San Diego]]<br />
| USA<br />
| San Diego, California<br />
| Ja(?)<br />
|-<br />
| [[University of Guelph]]<br />
| Canada<br />
| Guelph, Ontario<br />
| Nei<br />
|-<br />
| [[Penn State University]]<br />
| USA<br />
| Centre County, Pennsylvania<br />
| Ja (Bare lærerutdanning?)<br />
|-<br />
| [[Korea Advanced Institute of Science and Technology]] (KAIST)<br />
| Korea<br />
| Yuseong, Deajeon<br />
| Ja<br />
|-<br />
| [[TU Delft]]<br />
| Nederland<br />
| Delft<br />
| Ja, Erasmus<br />
|-<br />
| [[Massachusetts Institute of Technology (MIT)]]<br />
| USA<br />
| Cambridge, Massachusetts<br />
| Nei<br />
|}<br />
<br />
Det at NTNU har avtale med universitet kan bety litt forskjellig. Det kan variere fra at man får totalt fritak av betaling av skolepenger til at man bare får et lite avslag i prisen. For mer informasjon bes det tas kontakt med Internasjonal Seksjon.<br />
<br />
== Finansiering av utdanning ==<br />
<br />
* [http://www.lanekassen.no/templates/Page____9098.aspx Lånekassen]<br />
* [https://www.intersek.ntnu.no/soknadsskjema/ Stipend fra NTNU]<br />
* [http://www.legathandboken.no/ Legathåndboken]<br />
* [http://www.fulbright.no/Fulbright_Grants/Norwegians_to_the_US/Fulbright+stipend+for+norske+studenter+til+USA.E3p1MY7.ips Fullbright-stipend (kun USA)]<br />
* [http://www.noram.no/index.php?side_id=75&vis=1 NORAM-stipend (kun USA og Canada)]<br />
<br />
== Utvekslingsrapporter ==<br />
Mange studenter fra NTNU får utvekslingsstipend fra Internasjonal Seksjon. For å få utbetalt stipendet må man skrive en rapport som legges inn i [https://www.intersek.ntnu.no/rapport/FMPro?-db=Rapport.fp5&-lay=www&-format=search.htm&-view database]. Nedenfor er ei liste med utvekslingsrapporter skrevet av nanoteknologistudenter.<br />
<br />
===Nederland===<br />
===Singapor===<br />
===Sveits===<br />
===USA===<br />
[https://www.intersek.ntnu.no/rapport/FMPro?-db=rapport.fp5&-format=record_detail.htm&-lay=www&-sortfield=-none-&-op=cn&City=Boulder&-max=10&-recid=40002&-find= University of Colorado at Boulder] vår 2010, skrevet av Sigmund Østtveit Størset, [[Bionanoteknologi]]<br />
<br />
== Nyttige lenker ==<br />
<br />
*[http://www.ntnu.no/studier/studier_i_utlandet Internasjonal seksjon, NTNU]<br />
*[http://www.ntnu.no/intersek/tilutlandet123 Til utlandet på 123]<br />
*[http://www.ansa.no/ Mye nyttig informasjon om utdanning i utlandet fra ANSA]<br />
*[http://ed.sjtu.edu.cn/ARWU-FIELD2008/ENG2008.htm De 100 beste teknologiuniversitetene]<br />
*[http://www.ifs.tuwien.ac.at/~silvia/research-tips/times_top100_technologie_2005.pdf Times rangering av de 100 beste tekniske universitetene] <br />
*[http://colleges.usnews.rankingsandreviews.com/college Rangeringer inne mange kategorier i USA]<br />
*[http://www.ntnu.no/international/usa/visa.pdf Informasjon om prosedyren for å søke visum til USA]<br />
*[http://www.ntnu.no/international/recommendations Informasjon om letters of recommendation]<br />
*[http://www.ntnu.no/international/statementofpurpose.pdf Informasjon om å skrive statement of purpose (motivasjonsbrev)]<br />
*[http://www.ansa.no/upload/Dokumenter/Infosenteret/Landbrosjyrer/usa07.pdf ANSA's brosjyre om utdanning i USA]<br />
<br />
[[Kategori:Utveksling]]</div>Storsethttp://nanowiki.no/index.php?title=Utveksling&diff=4402Utveksling2010-03-30T04:50:50Z<p>Storset: </p>
<hr />
<div>== Standard ting ==<br />
<br />
Det kan være greit å finne ut hvor man vil, og hva man vil ved å dra ut.<br />
Når man vet hvor, så er det litt greiere å finne ut hva man vil; lære et språk, finne et sted med bedre kompetanse, høste kulturerfaring, unngå Trondheimsklimaet, skaffe kontakter eller bare få seg et år borte fra de andre på linja.<br />
<br />
Uansett er det visse ting man må finne ut:<br />
<br />
*Noe om universitetet: Gå på hjemmesida til universitet, eller søk etter informasjon hos [http://www.ntnu.no/studier/studier_i_utlandet/land internasjonal seksjon].<br />
*Få [http://www.ntnu.no/eksternweb/multimedia/archive/00031/Forh_ndsgodkjennings_31079a.pdf godkjenning] hos fakultetet når du har funnet ut av fagene.<br />
*Søk om støtte hos [http://www.lanekassen.no/templates/Page____5505.aspx Lånekassa] og hos [https://www.intersek.ntnu.no/soknadsskjema/ Internasjonal seksjon].<br />
<br />
Ellers er Internajsonalt Hus på Gløshaugen et sted å gå for å få mer informasjon og det finner du på [http://www.ntnu.no/ntnukart//no/gloshaugen.gif dette kartet] (øverst i venstre hjørne).<br />
<br />
<br />
Ved utveksling utenom 4. året, da med tanke på masteroppgaven, eventuelt Ph.D, så er det viktigste å kontakte faglærere og finne ut av hvem som har kontakter hvor, for da går det mye på hvem som kjenner hvem.<br />
<br />
<br />
== Praktiske ting ==<br />
<br />
Det kan i mange tilfeller være greit å være litt tidlig ute med følgende ting:<br />
*Forsikring - skaff en spesialforsikring for studenter i utlandet enten via ANSA eller ditt forsikringsselskap<br />
*Enkelte steder er det knot å få seg en plass i faget, men bare besøk professorens kontor, etter litt korrespondanse via mail, og snakk med ham/henne så ordner slikt seg.<br />
*Velg deg ut en hel haug med fag! Er ikke alltid du er like heldig med fagvalgenes ledighet og tilgjengelighet...<br />
*Kom ned litt tidlig slik at du har tid til å skaffe bolig, da det er litt kjedelig å bo på hostell når du begynner med undervisninga. Dette kan selvfølgelig i noen tilfeller ordnes hjemme fra Norge, men det er greiere å se hva du får før du sier ja.<br />
<br />
== Utvekslingssteder ==<br />
<br />
Her er en oversikt over noen forslag til universiteter rundt om i verden, en del av dem med tanke på at de bedriver litt med nanoteknologi på noen av sine fakulteter og muligens har programmer for utdanning innen vårt fagfelt:<br />
<br />
{| class="wikitable sortable"<br />
|- <br />
! Institusjon<br />
! Land<br />
! Beliggenhet<br />
! Avtale med NTNU<br />
|-<br />
| [[Universitetet i Oslo]]<br />
| Norge<br />
| Oslo<br />
| ?<br />
|-<br />
| [[University of California, Berkeley]]<br />
| USA<br />
| Berkeley, California<br />
| Delvis<br />
|-<br />
| [[University of Waterloo]]<br />
| Canada<br />
| Waterloo, Ontario<br />
| Ja<br />
|-<br />
| [[California Institute of Technology]]<br />
| USA<br />
| Pasadena, California<br />
| Nei<br />
|-<br />
| [[Seoul National University]]<br />
| Korea<br />
| Seoul<br />
| Ja<br />
|-<br />
| [[Osaka Prefecture University]]<br />
| Japan<br />
| Osaka<br />
| Ja<br />
|-<br />
| [[Tokyo Instuitute of Technology]]<br />
| Japan<br />
| Tokyo<br />
| Ja<br />
|-<br />
| [[Waseda University]]<br />
| Japan<br />
| Shinjuku, Tokyo<br />
| Ja<br />
|-<br />
| [[University of Alberta]]<br />
| Canada<br />
| Edmonton, Alberta<br />
| Ja<br />
|-<br />
| [[Cornell University]]<br />
| USA<br />
| Ithaca, New York<br />
| Nei<br />
|-<br />
| [[University of California, San Diego]]<br />
| USA<br />
| San Diego, California<br />
| Ja(?)<br />
|-<br />
| [[University of Guelph]]<br />
| Canada<br />
| Guelph, Ontario<br />
| Nei<br />
|-<br />
| [[Penn State University]]<br />
| USA<br />
| Centre County, Pennsylvania<br />
| Ja (Bare lærerutdanning?)<br />
|-<br />
| [[Korea Advanced Institute of Science and Technology]] (KAIST)<br />
| Korea<br />
| Yuseong, Deajeon<br />
| Ja<br />
|-<br />
| [[TU Delft]]<br />
| Nederland<br />
| Delft<br />
| Ja, Erasmus<br />
|-<br />
| [[Massachusetts Institute of Technology (MIT)]]<br />
| USA<br />
| Cambridge, Massachusetts<br />
| Nei<br />
|}<br />
<br />
Det at NTNU har avtale med universitet kan bety litt forskjellig. Det kan variere fra at man får totalt fritak av betaling av skolepenger til at man bare får et lite avslag i prisen. For mer informasjon bes det tas kontakt med Internasjonal Seksjon.<br />
<br />
== Finansiering av utdanning ==<br />
<br />
* [http://www.lanekassen.no/templates/Page____9098.aspx Lånekassen]<br />
* [https://www.intersek.ntnu.no/soknadsskjema/ Stipend fra NTNU]<br />
* [http://www.legathandboken.no/ Legathåndboken]<br />
* [http://www.fulbright.no/Fulbright_Grants/Norwegians_to_the_US/Fulbright+stipend+for+norske+studenter+til+USA.E3p1MY7.ips Fullbright-stipend (kun USA)]<br />
* [http://www.noram.no/index.php?side_id=75&vis=1 NORAM-stipend (kun USA og Canada)]<br />
<br />
== Utvekslingsrapporter ==<br />
Mange studenter fra NTNU får utvekslingsstipend fra Internasjonal Seksjon. For å få utbetalt stipendet må man skrive en rapport som legges inn i database. Nedenfor er ei liste med utvekslingsrapporter skrevet av nanoteknologistudenter.<br />
<br />
===Nederland===<br />
===Singapor===<br />
===Sveits===<br />
===USA===<br />
[http:// University of Colorado at Boulder] vår 2010, skrevet av Sigmund Østtveit Størset, [[Bionanoteknologi]]<br />
<br />
<br />
== Nyttige lenker ==<br />
<br />
*[http://www.ntnu.no/studier/studier_i_utlandet Internasjonal seksjon, NTNU]<br />
*[http://www.ntnu.no/intersek/tilutlandet123 Til utlandet på 123]<br />
*[http://www.ansa.no/ Mye nyttig informasjon om utdanning i utlandet fra ANSA]<br />
*[http://ed.sjtu.edu.cn/ARWU-FIELD2008/ENG2008.htm De 100 beste teknologiuniversitetene]<br />
*[http://www.ifs.tuwien.ac.at/~silvia/research-tips/times_top100_technologie_2005.pdf Times rangering av de 100 beste tekniske universitetene] <br />
*[http://colleges.usnews.rankingsandreviews.com/college Rangeringer inne mange kategorier i USA]<br />
*[http://www.ntnu.no/international/usa/visa.pdf Informasjon om prosedyren for å søke visum til USA]<br />
*[http://www.ntnu.no/international/recommendations Informasjon om letters of recommendation]<br />
*[http://www.ntnu.no/international/statementofpurpose.pdf Informasjon om å skrive statement of purpose (motivasjonsbrev)]<br />
*[http://www.ansa.no/upload/Dokumenter/Infosenteret/Landbrosjyrer/usa07.pdf ANSA's brosjyre om utdanning i USA]<br />
<br />
[[Kategori:Utveksling]]</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4398Storset2010-03-17T16:34:35Z<p>Storset: Tømmer siden</p>
<hr />
<div></div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4397Storset2010-03-12T17:52:59Z<p>Storset: </p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
The plasma concentration of the drug is modeled by<br />
<br />
(1)<math>\begin{equation} {dc_1(t) \over dt} = -(k_1 + k_{12}) \cdot c_1(t) + {u(t) \over V_1} \end{equation}</math><br />
<br />
where k<sub>1</sub> and k<sub>12</sub> are rate constants as define in figure 1 (k<sub>12</sub> is the link between plasma and active state of the drug and k<sub>1</sub> is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V<sub>1</sub> is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2)<math>\begin{equation}{dc_2(t) \over dt} = k_{12} \cdot {V_1 \over v_2} cdot c_1(t)- k_2 cdot c_2(t) \end{equation}</math> <br />
<br />
where k<sub>2</sub> is the elimination rate constant of active drug and V<sub>2</sub> is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) <math\>begin{equation}c_1(0) = 0, c_2(0) = 0 \end{equation}</math><br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) <math>\begin{equation}{dn(t) \over dt} = \lambda cdot n(t) cdot ln[\theta/n(t)]-k cdot [c_2(t) - c_{MIN}] cdot n(t) cdot H[c_2(t) - C_{MIN}, n(0) = n_0 \end{equation}</math><br />
<br />
The first term is the tumor growth term modeled using a [http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve Gompertz curve] growth type, which has previously been showed to fit cancer growth data quite accurate<ref></ref>. Here n(t) donates the number of cancer cells at time t and n<sub>0</sub> is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the [http://en.wikipedia.org/wiki/Volume_of_distribution Heaviside step function], which leads to the cell-loss term equaling zero at all values of c<sub>2</sub>(t) < C<sub>MIN</sub>. C<sub>MIN</sub> is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the [http://en.wikipedia.org/wiki/Fractional_kill constant-cell-kill hypothesis] expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) <math>\begin{equation}{dw(t) \over dt} = r_c - v cdot w(t) - \mu cdot w(t) cdot c_1(t-\tau) \end{equation}</math><br />
<br />
where r<sub>c</sub> is constant production rate of white blood cells (with dimension volume<sup>-1</sup>*time<sup>-1</sup>), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w<sub>0</sub> = r<sub>c</sub>/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions concentration<sup>-1</sup>*time<sup>-1</sup>.<br />
<br />
==Constraints==<br />
Several constraints are put on the model to insure that the patient can handle the toxic side effects of the drug. Firstly, the maximum plasma drug concentration must never exceed a given value:<br />
<br />
(6) <math>\begin{equation}c_1(t_i) <= C_{MAX} \end{equation}</math><br />
<br />
where t<sub>i</sub> represents the time interval of maximum plasma drug concentration in one given administration protocol. Also, a maximum drug exposure is introduced, meaning that the total amount of drug introduced to the patient over the whole treatment period must not exceed a given limit. This can be expressed by<br />
<br />
(7) <math>\begin{equation}{da(t) \over dt} = c_1(t), a(0) = 0 \end{equation}</math><br />
<br />
This is commonly known as area under the curve, AUC, because a(t) equals the integral from 0 to infinity over the concentration distribution of c<sub>1</sub>(t). Equation (7) leads to<br />
<br />
(8) <math>\begin{equation}a(T) <= A_{MAX} \end{equation}</math><br />
<br />
where T is at time point where all drug is completely eliminated from the body (the integral is zero from point T until infinity, and therefore the integration can be stopped at this point). Also constraints on the white blood cell counts are introduced. First, a minimum value of w(t) is defined, under which the white blood cell count never can fall:<br />
<br />
(9) <math>\begin{equation} w(t_j) >= W_D \end{equation}</math><br />
<br />
where t<sub>j</sub> represents the time interval of lowest white blood cell count. The second constraint puts a limit on how long the white blood cell count can stay under a given upper value, W<sub>U</sub>. The time t<sub>U</sub>(T) over which the white blood cell count is under W<sub>U</sub> must be less or equal to T<sub>U</sub>:<br />
<br />
(10) <math>\begin{equation}t_u(T) <= T_u \end{equation}</math><br />
<br />
==Drug delivery==<br />
The optimization problem considers how to best infuse the drug over a period of time, t<sub>N</sub>, divided into N time treatment intervals, such that the tumor size is minimized without violating any of the given constraints. The infusion rates can vary between each of the time intervals such that<br />
<br />
(11) <math>\begin{equation} u(t) = {d_i \over t_i} for 0 <= t < t_1, u(t) = {d_i \over t_i} for t_{i-1}<= t < t_i, i = 2,...,N, \end{equation}</math><br />
<br />
is fulfilled. d<sub>i</sub> donates the total amount of drug infused in the time interval from t<sub>i-1</sub> to t<sub>i</sub>. By examining different drug regimens, the optimal drug delivery scheme can be found using this given model.<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4396Storset2010-03-12T17:45:14Z<p>Storset: /* Drug delivery */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
The plasma concentration of the drug is modeled by<br />
<br />
(1)<math> {dc_1(t) \over dt} = -(k_1 + k_{12}) \cdot c_1(t) + {u(t) \over V_1} </math><br />
<br />
where k<sub>1</sub> and k<sub>12</sub> are rate constants as define in figure 1 (k<sub>12</sub> is the link between plasma and active state of the drug and k<sub>1</sub> is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V<sub>1</sub> is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2)<math>{dc_2(t) \over dt} = k_{12} \cdot {V_1 \over v_2} cdot c_1(t)- k_2 cdot c_2(t)</math> <br />
<br />
where k<sub>2</sub> is the elimination rate constant of active drug and V<sub>2</sub> is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) <math>c_1(0) = 0, c_2(0) = 0 </math><br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) <math>{dn(t) \over dt} = \lambda cdot n(t) cdot ln[\theta/n(t)]-k cdot [c_2(t) - c_{MIN}] cdot n(t) cdot H[c_2(t) - C_{MIN}, n(0) = n_0</math><br />
<br />
The first term is the tumor growth term modeled using a [http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve Gompertz curve] growth type, which has previously been showed to fit cancer growth data quite accurate<ref></ref>. Here n(t) donates the number of cancer cells at time t and n<sub>0</sub> is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the [http://en.wikipedia.org/wiki/Volume_of_distribution Heaviside step function], which leads to the cell-loss term equaling zero at all values of c<sub>2</sub>(t) < C<sub>MIN</sub>. C<sub>MIN</sub> is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the [http://en.wikipedia.org/wiki/Fractional_kill constant-cell-kill hypothesis] expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) <math>{dw(t) \over dt} = r_c - v cdot w(t) - \mu cdot w(t) cdot c_1(t-\tau)</math><br />
<br />
where r<sub>c</sub> is constant production rate of white blood cells (with dimension volume<sup>-1</sup>*time<sup>-1</sup>), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w<sub>0</sub> = r<sub>c</sub>/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions concentration<sup>-1</sup>*time<sup>-1</sup>.<br />
<br />
==Constraints==<br />
Several constraints are put on the model to insure that the patient can handle the toxic side effects of the drug. Firstly, the maximum plasma drug concentration must never exceed a given value:<br />
<br />
(6) <math>c_1(t_i) <= C_{MAX}</math><br />
<br />
where t<sub>i</sub> represents the time interval of maximum plasma drug concentration in one given administration protocol. Also, a maximum drug exposure is introduced, meaning that the total amount of drug introduced to the patient over the whole treatment period must not exceed a given limit. This can be expressed by<br />
<br />
(7) <math>{da(t) \over dt} = c_1(t), a(0) = 0</math><br />
<br />
This is commonly known as area under the curve, AUC, because a(t) equals the integral from 0 to infinity over the concentration distribution of c<sub>1</sub>(t). Equation (7) leads to<br />
<br />
(8) <math>a(T) <= A_{MAX}</math><br />
<br />
where T is at time point where all drug is completely eliminated from the body (the integral is zero from point T until infinity, and therefore the integration can be stopped at this point). Also constraints on the white blood cell counts are introduced. First, a minimum value of w(t) is defined, under which the white blood cell count never can fall:<br />
<br />
(9) <math>w(t_j) >= W_D</math><br />
<br />
where t<sub>j</sub> represents the time interval of lowest white blood cell count. The second constraint puts a limit on how long the white blood cell count can stay under a given upper value, W<sub>U</sub>. The time t<sub>U</sub>(T) over which the white blood cell count is under W<sub>U</sub> must be less or equal to T<sub>U</sub>:<br />
<br />
(10) <math>t_u(T) <= T_u</math><br />
<br />
==Drug delivery==<br />
The optimization problem considers how to best infuse the drug over a period of time, t<sub>N</sub>, divided into N time treatment intervals, such that the tumor size is minimized without violating any of the given constraints. The infusion rates can vary between each of the time intervals such that<br />
<br />
(11) <math>u(t) = </math><br />
<br />
is fulfilled. di donates the total amount of drug infused in the time interval from t<sub>i-1</sub> to t<sub>i</sub>. By examining different drug regimens, the optimal drug delivery scheme can be found using this given model.<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4395Storset2010-03-12T17:40:36Z<p>Storset: /* Constraints */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
The plasma concentration of the drug is modeled by<br />
<br />
(1)<math> {dc_1(t) \over dt} = -(k_1 + k_{12}) \cdot c_1(t) + {u(t) \over V_1} </math><br />
<br />
where k<sub>1</sub> and k<sub>12</sub> are rate constants as define in figure 1 (k<sub>12</sub> is the link between plasma and active state of the drug and k<sub>1</sub> is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V<sub>1</sub> is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2)<math>{dc_2(t) \over dt} = k_{12} \cdot {V_1 \over v_2} cdot c_1(t)- k_2 cdot c_2(t)</math> <br />
<br />
where k<sub>2</sub> is the elimination rate constant of active drug and V<sub>2</sub> is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) <math>c_1(0) = 0, c_2(0) = 0 </math><br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) <math>{dn(t) \over dt} = \lambda cdot n(t) cdot ln[\theta/n(t)]-k cdot [c_2(t) - c_{MIN}] cdot n(t) cdot H[c_2(t) - C_{MIN}, n(0) = n_0</math><br />
<br />
The first term is the tumor growth term modeled using a [http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve Gompertz curve] growth type, which has previously been showed to fit cancer growth data quite accurate<ref></ref>. Here n(t) donates the number of cancer cells at time t and n<sub>0</sub> is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the [http://en.wikipedia.org/wiki/Volume_of_distribution Heaviside step function], which leads to the cell-loss term equaling zero at all values of c<sub>2</sub>(t) < C<sub>MIN</sub>. C<sub>MIN</sub> is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the [http://en.wikipedia.org/wiki/Fractional_kill constant-cell-kill hypothesis] expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) <math>{dw(t) \over dt} = r_c - v cdot w(t) - \mu cdot w(t) cdot c_1(t-\tau)</math><br />
<br />
where r<sub>c</sub> is constant production rate of white blood cells (with dimension volume<sup>-1</sup>*time<sup>-1</sup>), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w<sub>0</sub> = r<sub>c</sub>/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions concentration<sup>-1</sup>*time<sup>-1</sup>.<br />
<br />
==Constraints==<br />
Several constraints are put on the model to insure that the patient can handle the toxic side effects of the drug. Firstly, the maximum plasma drug concentration must never exceed a given value:<br />
<br />
(6) <math>c_1(t_i) <= C_{MAX}</math><br />
<br />
where t<sub>i</sub> represents the time interval of maximum plasma drug concentration in one given administration protocol. Also, a maximum drug exposure is introduced, meaning that the total amount of drug introduced to the patient over the whole treatment period must not exceed a given limit. This can be expressed by<br />
<br />
(7) <math>{da(t) \over dt} = c_1(t), a(0) = 0</math><br />
<br />
This is commonly known as area under the curve, AUC, because a(t) equals the integral from 0 to infinity over the concentration distribution of c<sub>1</sub>(t). Equation (7) leads to<br />
<br />
(8) <math>a(T) <= A_{MAX}</math><br />
<br />
where T is at time point where all drug is completely eliminated from the body (the integral is zero from point T until infinity, and therefore the integration can be stopped at this point). Also constraints on the white blood cell counts are introduced. First, a minimum value of w(t) is defined, under which the white blood cell count never can fall:<br />
<br />
(9) <math>w(t_j) >= W_D</math><br />
<br />
where t<sub>j</sub> represents the time interval of lowest white blood cell count. The second constraint puts a limit on how long the white blood cell count can stay under a given upper value, W<sub>U</sub>. The time t<sub>U</sub>(T) over which the white blood cell count is under W<sub>U</sub> must be less or equal to T<sub>U</sub>:<br />
<br />
(10) <math>t_u(T) <= T_u</math><br />
<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4394Storset2010-03-12T17:23:19Z<p>Storset: /* Differential equations */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
The plasma concentration of the drug is modeled by<br />
<br />
(1)<math> {dc_1(t) \over dt} = -(k_1 + k_{12}) \cdot c_1(t) + {u(t) \over V_1} </math><br />
<br />
where k<sub>1</sub> and k<sub>12</sub> are rate constants as define in figure 1 (k<sub>12</sub> is the link between plasma and active state of the drug and k<sub>1</sub> is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V<sub>1</sub> is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2)<math>{dc_2(t) \over dt} = k_{12} \cdot {V_1 \over v_2} cdot c_1(t)- k_2 cdot c_2(t)</math> <br />
<br />
where k<sub>2</sub> is the elimination rate constant of active drug and V<sub>2</sub> is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) <math>c_1(0) = 0, c_2(0) = 0 </math><br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) <math>{dn(t) \over dt} = \lambda cdot n(t) cdot ln[\theta/n(t)]-k cdot [c_2(t) - c_{MIN}] cdot n(t) cdot H[c_2(t) - C_{MIN}, n(0) = n_0</math><br />
<br />
The first term is the tumor growth term modeled using a [http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve Gompertz curve] growth type, which has previously been showed to fit cancer growth data quite accurate<ref></ref>. Here n(t) donates the number of cancer cells at time t and n<sub>0</sub> is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the [http://en.wikipedia.org/wiki/Volume_of_distribution Heaviside step function], which leads to the cell-loss term equaling zero at all values of c<sub>2</sub>(t) < C<sub>MIN</sub>. C<sub>MIN</sub> is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the [http://en.wikipedia.org/wiki/Fractional_kill constant-cell-kill hypothesis] expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) <math>{dw(t) \over dt} = r_c - v cdot w(t) - \mu cdot w(t) cdot c_1(t-\tau)</math><br />
<br />
where r<sub>c</sub> is constant production rate of white blood cells (with dimension volume<sup>-1</sup>*time<sup>-1</sup>), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w<sub>0</sub> = r<sub>c</sub>/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions concentration<sup>-1</sup>*time<sup>-1</sup>.<br />
<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4393Storset2010-03-12T17:17:13Z<p>Storset: /* Differential equations */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
The plasma concentration of the drug is modeled by<br />
<br />
(1)<math> {dc_1(t) \over dt} = -(k_1 + k_{12}) \cdot c_1(t) + {u(t) \over V_1} </math><br />
<br />
where k<sub>1</sub> and k<sub>12</sub> are rate constants as define in figure 1 (k<sub>12</sub> is the link between plasma and active state of the drug and k<sub>1</sub> is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V<sub>1</sub> is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2)<math>{dc_2(t) \over dt} = k_{12} \cdot {V_1 \over v_2} cdot c_1(t)- k_2 cdot c_2(t)</math> <br />
<br />
where k<sub>2</sub> is the elimination rate constant of active drug and V<sub>2</sub> is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) <math>c_1(0) = 0, c_2(0) = 0 </math><br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) <math>{dn(t) \over dt} = \lambda cdot n(t) cdot ln[\theta/n(t)]-k cdot [c_2(t) - c_{MIN}] cdot n(t) cdot H[c_2(t) - C_{MIN}, n(0) = n_0</math><br />
<br />
The first term is the tumor growth term modeled using a [http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve Gompertz curve] growth type, which has previously been showed to fit cancer growth data quite accurate<ref></ref>. Here n(t) donates the number of cancer cells at time t and n<sub>0</sub> is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the [http://en.wikipedia.org/wiki/Volume_of_distribution Heaviside step function], which leads to the cell-loss term equaling zero at all values of c<sub>2</sub>(t) < CMIN. CMIN is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the [http://en.wikipedia.org/wiki/Fractional_kill constant-cell-kill hypothesis] expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) M4<br />
<br />
where rc is constant production rate of white blood cells (with dimension (volume)-1*(time)-1), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w0 = rc/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions (concentration)-1*(time)-1.<br />
<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4392Storset2010-03-12T16:48:59Z<p>Storset: </p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
When a chemotherapeutic agent (a drug) is introduced into the blood stream, both cancer cells and normal, healthy cells are affected and killed. Because of this it is important to monitor the delivery of the drug to the patient, since overexposure could lead to dramatic side effects and death of the patient. Since the drug is highly present in the blood stream of the patient, monitoring the white blood cell concentration in plasma as a function of time, drug concentration and drug infusion rate could give a good idea of at which level of risk the patient is at each given time during the treatment. Also, by using this approach, a drug delivery regimen can be optimized such that cancer cell count is minimized at the end of treatment without putting the patient at risk during the cure.<br />
<br />
=History=<br />
Chemotherapy of cancer is a field which have been studied extensively over the past decades. Cancer is very complex group of diseases which strikes numerous people around the world each year, and the wish to find a good and effective cure has driven research forward in this field. Chemotherapy of cancer is a way of killing cancer cells by introducing poison to the body. This poison mainly effect proliferating cells, which the bulk of most cancer tumors consists of. The poisons introduced can attack the cancer cells in many different ways. One method is to induce DNA-damage to activate the p53-pathway and induce apoptosis in the cells<ref></ref>. Other pathways can interact with the cell cycle and result in cell cycle arrest<ref></ref>. Common for all chemotherapeutic schemes is that they do not influence cancer cells alone. The chemotherapeutic poison is often introduced intravenously leading to a poison distribution throughout the body. This gives cell death of healthy cells around the body leading to severe side effects<ref></ref> often leading to great suffering of the patient. Because of this, research within chemotherapy have also been focused on how to distribute the chemotherapeutic in a best possible way such that side effects are minimized and tumor regression is maximized. Thus has been done using several constraints such as maximum drug exposure, maximum injection rate etc. Here, the constraints investigated are instead the white blood cell count per unit volume as a function of time, drug concentration and drug infusion rate.<br />
<br />
=Mathematical model=<br />
==Outline==<br />
The model is designed to give information of the chemotherapy's effect on both tumor cells and white blood cells. To do this, a compartment model is used to illustrate the stages the drug can be in in the body (figure 1). The model consists of four compartments. On the side of pharmacokinetics, the plasma drug concentration, c<sub>1</sub>(t), and the active drug concentration, c<sub>2</sub>(t) is present, with [http://en.wikipedia.org/wiki/Volume_of_distribution volumes of distribution] V<sub>1</sub> and V<sub>2</sub>. The active drug concentration is the portion of the drug which can affect the tumor cells, while the drug in plasma will affect the white blood cells. The two other compartments in the model are the white blood cell count per unit volume, w(t), and the tumor cell count per unit volume, n(t). These compartments constitute the phamacodynamics of the model.<br />
<br />
==Differential equations==<br />
<nowiki><br />
The plasma concentration of the drug is modeled by<br />
<br />
(1) M1<br />
<br />
where k1 and k12 are rate constants as define in figure 1 (k12 is the link between plasma and active state of the drug and k1 is general elimination of the drug from the plasma through other pathways), u(t) is the drug infusion rate function, and V1 is the plasma volume of distribution (the total volume of plasma in the body). The active drug concentration is modeled by<br />
<br />
(2) M2<br />
<br />
where k2 is the elimination rate constant of active drug and V2 is the volume of distribution of the cancer tumor. For both these equations it is important to remember that an interaction between the drug and a cancer or white blood cell does not lead to elimination of the drug. The drug affects the cell merely by its presence in the given volume of distribution. For both equations (2) and (3) the initial drug concentrations are set to zero:<br />
<br />
(3) c1(0) = 0, c2(0) = 0<br />
<br />
The tumor count is modeled by the following differential equation:<br />
<br />
(4) M3<br />
<br />
The first term is the tumor growth term modeled using a Gompertz curve(link to wikipedia, http://en.wikipedia.org/wiki/Gompertz_curve#Growth_of_tumors_and_Gompertz_curve ) growth type, which has previously been showed to fit cancer growth data quite accurate[4]. Here n(t) donates the number of cancer cells at time t and n0 is the number of cancer cells at time 0. θ is the carrying capacity of the tumor, that is the maximal size the tumor can achieve at any time. When θ=n(t) we see that the growth term of equation (4) equals zero. λ is a constant modeling the proliferation ability of the cancer cells. The second term is the tumor cell-loss term, which is dependent of active drug concentration. H is the Heaviside step function(http://en.wikipedia.org/wiki/Volume_of_distribution ), which leads to the cell-loss term equaling zero at all values of c2(t) < CMIN. CMIN is set as a threshold value of the active drug concentration. The drug will have no effect on the cancer cells under this active concentration. The cell-loss term is also proportional with the tumor cell count, n(t), and k is a proportionality constant which expresses the constant-cell-kill hypothesis (http://en.wikipedia.org/wiki/Fractional_kill) expected to be valid when cells are sensitive to the drug. The white blood cell count is modeled by<br />
<br />
(5) M4<br />
<br />
where rc is constant production rate of white blood cells (with dimension (volume)-1*(time)-1), and v is the fraction of white blood cells which dies per time. The steady state of this system with no drug present gives the initial white blood cell count w(0) = w0 = rc/v. The last term in equation (5) represents the loss of white blood cells because of drug present in the blood plasma. White blood cells are all produced from stem cells in the bone marrow and not by cell division during circulation. Because of this, it is reasonable to assume a constant production rate. This phenomenon will also introduce a delay from the white blood cells are produced in the bone marrow until they have matured and been transported into circulation in the blood system were they are susceptible for the drug. These considerations result in the last term of equation (5) where a delay, τ, is introduced into the plasma drug concentration. The interpretation of this would be that the white blood cells produced at time t, will not be susceptible for drug until a time t + τ in the future. Therefor is the delayed plasma drug concentration used. The total drug induced white blood cell-loss term is then proportional to the number of white blood cells, and the delayed drug concentration. μ is a proportionality constant with dimensions (concentration)-1*(time)-1.<br />
</nowiki><br />
<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4391Storset2010-03-12T16:36:05Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! V<sub>1</sub><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! V<sub>2</sub><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! CL<br />
| 50<br />
| L/day<br />
| <br />
|- <br />
!_k<sub>1</sub>+k<sub>12</sub><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! k<sub>1</sub><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! k<sub>12</sub><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! k<sub>2</sub><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! n<sub>0</sub><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! C<sub>MIN</sub><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! k<br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! r<sub>c</sub><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! W<sub>0</sub><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! v<br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! C<sub>MAX</sub><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! W<sub>D</sub><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! T<sub>U</sub><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta</math> t<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! A<sub>MAX</sub><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! t<sub>N</sub><br />
| 21<br />
| days<br />
|<br />
|-<br />
! T<br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4390Storset2010-03-12T16:28:09Z<p>Storset: /* Summary */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta t</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4389Storset2010-03-12T16:24:20Z<p>Storset: /* Summary */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta t</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4388Storset2010-03-12T16:21:32Z<p>Storset: /* Summary */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<ref><br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta t</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4387Storset2010-03-11T23:51:43Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>\theta</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>\lambda</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>\mu</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>\tau</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>\delta t</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4386Storset2010-03-11T23:45:57Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! θ<br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! λ<br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! μ<br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! τ<br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! Δt<br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4385Storset2010-03-11T23:41:47Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>θ</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>λ</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>μ</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>τ</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>Δt</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
|-<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4384Storset2010-03-11T23:40:34Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>θ</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>λ</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>μ</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>τ</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <math>W_0</math><br />
| 8*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>v</math><br />
| 0.15<br />
| /day<br />
| <br />
|-<br />
! <math>C_MAX</math><br />
| 10<br />
| μg/mL<br />
| <br />
|-<br />
! <math>W_D</math><br />
| 2*10^9<br />
| /L<br />
| <br />
|-<br />
! <math>T_U</math><br />
| 7<br />
| days<br />
| <br />
|-<br />
! <math>Δt</math><br />
| 0.52<br />
| days<br />
| <br />
|-<br />
! <math>A_MAX</math><br />
| 30<br />
| μg*day/mL<br />
| <br />
|-<br />
! <math>t_N</math><br />
| 21<br />
| days<br />
|<br />
! <math>T</math><br />
| 31 <br />
| days<br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4383Storset2010-03-11T23:28:50Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>θ</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>λ</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>r_c</math><br />
| 1.2*10^9<br />
| /(L*day)<br />
| <br />
|-<br />
! <math>μ</math><br />
| 80<br />
| L/(g*day)<br />
| <br />
|-<br />
! <math>τ</math><br />
| 5<br />
| days<br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4382Storset2010-03-11T23:25:31Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Volume of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! <math>θ</math><br />
| 10^12<br />
| cells<br />
| <br />
|-<br />
! <math>n_0</math><br />
| 30*10^9<br />
| cells<br />
| <br />
|-<br />
! <math>λ</math><br />
| 3*10^-3<br />
| /day<br />
| <br />
|-<br />
! <math>C_MIN</math><br />
| 0.1<br />
| μg/mL<br />
| <br />
|-<br />
! <math>k</math><br />
| 30<br />
| L/(g*day)<br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4381Storset2010-03-11T23:11:07Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| Amount of plasma in adult human<br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <math>CL</math><br />
| 50<br />
| L/day<br />
| <br />
|- <br />
! <math>k_1+k_12</math><br />
| 2<br />
| /day <br />
|<br />
|-<br />
! <math>k_1</math><br />
| 1.6<br />
| /day<br />
| <br />
|-<br />
! <math>k_12</math><br />
| 0.4<br />
| /day<br />
| <br />
|-<br />
! <math>k_2</math><br />
| 0.8<br />
| /day<br />
| <br />
|-<br />
! θ<br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4380Storset2010-03-11T23:05:38Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: center;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| <br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
|<br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4379Storset2010-03-11T23:04:52Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: right;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <math>V_1</math><br />
| 25 <br />
| L <br />
| <br />
|- <br />
! <math>V_2</math><br />
| 15 <br />
| L <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
|<br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4378Storset2010-03-11T23:03:45Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: right;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="1000" | Comment<br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|- <br />
!<br />
| <br />
| <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
| <br />
|- <br />
! <br />
| <br />
| <br />
|<br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|-<br />
! <br />
| <br />
| <br />
| <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4377Storset2010-03-11T23:01:35Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: right;" <br />
! width="50" | Parameter<br />
! width="50" | Value<br />
! width="100" | Dimension<br />
! width="100" | Comment<br />
|-<br />
! 0,0<br />
| 0,50000 <br />
| 0,50399 <br />
| 0,50798 <br />
|- <br />
! 0,1<br />
| 0,53983 <br />
| 0,54380 <br />
| 0,54776 <br />
|- <br />
! 0,2<br />
| 0,57926 <br />
| 0,58317 <br />
| 0,58706 <br />
|- <br />
! 0,3<br />
| 0,61791 <br />
| 0,62172 <br />
| 0,62552 <br />
|}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4376Storset2010-03-11T22:58:27Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
{| class="wikitable" style="text-align: right;" <br />
! width="37" | z<br />
! width="53" | 0<br />
! width="53" | 1<br />
! width="53" | 2<br />
! width="53" | 3<br />
! width="53" | 4<br />
! width="53" | 5<br />
! width="53" | 6<br />
! width="53" | 7<br />
! width="53" | 8<br />
! width="53" | 9<br />
|-<br />
! 0,0<br />
| 0,50000 <br />
| 0,50399 <br />
| 0,50798 <br />
| 0,51197 <br />
| 0,51595 <br />
| 0,51994 <br />
| 0,52392 <br />
| 0,52790 <br />
| 0,53188 <br />
| 0,53586 <br />
|- <br />
! 0,1<br />
| 0,53983 <br />
| 0,54380 <br />
| 0,54776 <br />
| 0,55172 <br />
| 0,55567 <br />
| 0,55962 <br />
| 0,56356 <br />
| 0,56749 <br />
| 0,57142 <br />
| 0,57535 <br />
|- <br />
! 0,2<br />
| 0,57926 <br />
| 0,58317 <br />
| 0,58706 <br />
| 0,59095 <br />
| 0,59483 <br />
| 0,59871 <br />
| 0,60257 <br />
| 0,60642 <br />
| 0,61026 <br />
| 0,61409 <br />
|- <br />
! 0,3<br />
| 0,61791 <br />
| 0,62172 <br />
| 0,62552 <br />
| 0,62930 <br />
| 0,63307 <br />
| 0,63683 <br />
| 0,64058 <br />
| 0,64431 <br />
| 0,64803 <br />
| 0,65173 <br />
|- <br />
! 0,4<br />
| 0,65542 <br />
| 0,65910 <br />
| 0,66276 <br />
| 0,66640 <br />
| 0,67003 <br />
| 0,67364 <br />
| 0,67724 <br />
| 0,68082 <br />
| 0,68439 <br />
| 0,68793 <br />
|- <br />
! 0,5<br />
| 0,69146 <br />
| 0,69497 <br />
| 0,69847 <br />
| 0,70194 <br />
| 0,70540 <br />
| 0,70884 <br />
| 0,71226 <br />
| 0,71566 <br />
| 0,71904 <br />
| 0,72240 <br />
|- <br />
! 0,6<br />
| 0,72575 <br />
| 0,72907 <br />
| 0,73237 <br />
| 0,73565 <br />
| 0,73891 <br />
| 0,74215 <br />
| 0,74537 <br />
| 0,74857 <br />
| 0,75175 <br />
| 0,75490 <br />
|- <br />
! 0,7<br />
| 0,75804 <br />
| 0,76115 <br />
| 0,76424 <br />
| 0,76730 <br />
| 0,77035 <br />
| 0,77337 <br />
| 0,77637 <br />
| 0,77935 <br />
| 0,78230 <br />
| 0,78524 <br />
|- <br />
! 0,8<br />
| 0,78814 <br />
| 0,79103 <br />
| 0,79389 <br />
| 0,79673 <br />
| 0,79955 <br />
| 0,80234 <br />
| 0,80511 <br />
| 0,80785 <br />
| 0,81057 <br />
| 0,81327 <br />
|- <br />
! 0,9<br />
| 0,81594 <br />
| 0,81859 <br />
| 0,82121 <br />
| 0,82381 <br />
| 0,82639 <br />
| 0,82894 <br />
| 0,83147 <br />
| 0,83398 <br />
| 0,83646 <br />
| 0,83891 <br />
|- <br />
! 1,0<br />
| 0,84134 <br />
| 0,84375 <br />
| 0,84614 <br />
| 0,84849 <br />
| 0,85083 <br />
| 0,85314 <br />
| 0,85543 <br />
| 0,85769 <br />
| 0,85993 <br />
| 0,86214 <br />
|- <br />
! 1,1<br />
| 0,86433 <br />
| 0,86650 <br />
| 0,86864 <br />
| 0,87076 <br />
| 0,87286 <br />
| 0,87493 <br />
| 0,87698 <br />
| 0,87900 <br />
| 0,88100 <br />
| 0,88298 <br />
|- <br />
! 1,2<br />
| 0,88493 <br />
| 0,88686 <br />
| 0,88877 <br />
| 0,89065 <br />
| 0,89251 <br />
| 0,89435 <br />
| 0,89617 <br />
| 0,89796 <br />
| ;0,89973 <br />
| 0,90147 <br />
|- <br />
! 1,3<br />
| 0,90320 <br />
| 0,90490 <br />
| 0,90658 <br />
| 0,90824 <br />
| 0,90988 <br />
| 0,91149 <br />
| 0,91309 <br />
| 0,91466 <br />
| 0,91621 <br />
| 0,91774 <br />
|- <br />
! 1,4<br />
| 0,91924 <br />
| 0,92073 <br />
| 0,92220 <br />
| 0,92364 <br />
| 0,92507 <br />
| 0,92647 <br />
| 0,92785 <br />
| 0,92922 <br />
| 0,93056 <br />
| 0,93189 <br />
|- <br />
! 1,5<br />
| 0,93319 <br />
| 0,93448 <br />
| 0,93574 <br />
| 0,93699 <br />
| 0,93822 <br />
| 0,93943 <br />
| 0,94062 <br />
| 0,94179 <br />
| 0,94295 <br />
| 0,94408 <br />
|- <br />
! 1,6<br />
| 0,94520 <br />
| 0,94630 <br />
| 0,94738 <br />
| 0,94845 <br />
| 0,94950 <br />
| 0,95053 <br />
| 0,95154 <br />
| 0,95254 <br />
| 0,95352 <br />
| 0,95449 <br />
|- <br />
! 1,7<br />
| 0,95543 <br />
| 0,95637 <br />
| 0,95728 <br />
| 0,95818 <br />
| 0,95907 <br />
| 0,95994 <br />
| 0,96080 <br />
| 0,96164 <br />
| 0,96246 <br />
| 0,96327 <br />
|- <br />
! 1,8<br />
| 0,96407 <br />
| 0,96485 <br />
| 0,96562 <br />
| 0,96638 <br />
| 0,96712 <br />
| 0,96784 <br />
| 0,96856 <br />
| 0,96926 <br />
| 0,96995 <br />
| 0,97062 <br />
|- <br />
! 1,9<br />
| 0,97128 <br />
| 0,97193 <br />
| 0,97257 <br />
| 0,97320 <br />
| 0,97381 <br />
| 0,97441 <br />
| 0,97500 <br />
| 0,97558 <br />
| 0,97615 <br />
| 0,97670 <br />
|- <br />
! 2,0<br />
| 0,97725 <br />
| 0,97778 <br />
| 0,97831 <br />
| 0,97882 <br />
| 0,97932 <br />
| 0,97982 <br />
| 0,98030 <br />
| 0,98077 <br />
| 0,98124 <br />
| 0,98169 <br />
|- <br />
! 2,1<br />
| 0,98214 <br />
| 0,98257 <br />
| 0,98300 <br />
| 0,98341 <br />
| 0,98382 <br />
| 0,98422 <br />
| 0,98461 <br />
| 0,98500 <br />
| 0,98537 <br />
| 0,98574 <br />
|- <br />
! 2,2<br />
| 0,98610 <br />
| 0,98645 <br />
| 0,98679 <br />
| 0,98713 <br />
| 0,98745 <br />
| 0,98778 <br />
| 0,98809 <br />
| 0,98840 <br />
| 0,98870 <br />
| 0,98899 <br />
|- <br />
! 2,3<br />
| 0,98928 <br />
| 0,98956 <br />
| 0,98983 <br />
| 0,99010 <br />
| 0,99036 <br />
| 0,99061 <br />
| 0,99086 <br />
| 0,99111 <br />
| 0,99134 <br />
| 0,99158 <br />
|- <br />
! 2,4<br />
| 0,99180 <br />
| 0,99202 <br />
| 0,99224 <br />
| 0,99245 <br />
| 0,99266 <br />
| 0,99286 <br />
| 0,99305 <br />
| 0,99324 <br />
| 0,99343 <br />
| 0,99361 <br />
|- <br />
! 2,5<br />
| 0,99379 <br />
| 0,99396 <br />
| 0,99413 <br />
| 0,99430 <br />
| 0,99446 <br />
| 0,99461 <br />
| 0,99477 <br />
| 0,99492 <br />
| 0,99506 <br />
| 0,99520 <br />
|- <br />
! 2,6<br />
| 0,99534 <br />
| 0,99547 <br />
| 0,99560 <br />
| 0,99573 <br />
| 0,99585 <br />
| 0,99598 <br />
| 0,99609 <br />
| 0,99621 <br />
| 0,99632 <br />
| 0,99643 <br />
|- <br />
! 2,7<br />
| 0,99653 <br />
| 0,99664 <br />
| 0,99674 <br />
| 0,99683 <br />
| 0,99693 <br />
| 0,99702 <br />
| 0,99711 <br />
| 0,99720 <br />
| 0,99728 <br />
| 0,99736 <br />
|- <br />
! 2,8<br />
| 0,99744 <br />
| 0,99752 <br />
| 0,99760 <br />
| 0,99767 <br />
| 0,99774 <br />
| 0,99781 <br />
| 0,99788 <br />
| 0,99795 <br />
| 0,99801 <br />
| 0,99807 <br />
|- <br />
! 2,9<br />
| 0,99813 <br />
| 0,99819 <br />
| 0,99825 <br />
| 0,99831 <br />
| 0,99836 <br />
| 0,99841 <br />
| 0,99846 <br />
| 0,99851 <br />
| 0,99856 <br />
| 0,99861 <br />
|- <br />
!<br />
! 0<br />
! 1<br />
! 2<br />
! 3<br />
! 4<br />
! 5<br />
! 6<br />
! 7<br />
! 8<br />
! 9<br />
|}<br />
<br />
[[Kategori:Statistikk]]<br />
<br />
[[sv:Tabell över den kumulativa normalfördelningsfunktionen]]<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4375Storset2010-03-11T22:53:40Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<math><br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
</math><br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4374Storset2010-03-11T22:53:27Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<math><br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
</math><br />
<math>V_{1}</math><br />
<math>V_{1}</math><br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4373Storset2010-03-11T22:51:59Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<math><br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
</math><br />
<math>V_{1}</math><br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4372Storset2010-03-11T22:49:30Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<math><br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
</math><br />
<math>V_exp{1}</math><br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4371Storset2010-03-11T22:48:25Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
<math><br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
</math><br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4370Storset2010-03-11T22:47:50Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
1 & 25L & 3 \\ \hline<br />
2 & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storsethttp://nanowiki.no/index.php?title=Storset&diff=4369Storset2010-03-11T22:47:06Z<p>Storset: /* Parameter values */</p>
<hr />
<div>Til eventuelle webmastere eller lignende: Jeg skriver et prosjekt på ei wikiside i Boulder for tida, men sida er ikke oppe enda, så jeg lager den her foreløpig, så jeg kan skrive den i wikiformat, og så flytter jeg denne sida seinere (innen fredag 19. mars) og sletter den. Håper det er greit. Sigmund<br />
<br />
=Summary=<br />
<br />
=Biological background=<br />
<br />
=History=<br />
<br />
=Mathematical model=<br />
==Outline==<br />
==Differential equations==<br />
==Constraints==<br />
==Drug delivery==<br />
<br />
=The model and results=<br />
==Parameter values==<br />
There are quite many parameters involved with this model, and to get accurate results, it is important to chose values as close to reality as possible. The values used in this simulation is mainly taken from literature, but assumptions on some of the parameter values are done as well. Table 1 includes all parameter values with comments on each value.<br />
<br />
\begin{center}<br />
\begin{tabular}{| l | l | l | }<br />
\hline<br />
<math>V_exp{1}</math> & 25L & 3 \\ \hline<br />
<math>V_exp{2}</math> & 15L & 6 \\ \hline<br />
7 & 8 & 9 \\<br />
\hline<br />
\end{tabular}<br />
\end{center}<br />
<br />
==Clinical protocols==<br />
==Optimized protocols==<br />
<br />
=Analysis=<br />
==Inspection of problem 1==<br />
==Inspection of problem 2==<br />
==Discussion==<br />
<br />
=External links=</div>Storset