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= Core Curriculum =
== Toxicokinetics ==

===Definitions===
''Xenobiotic'' (X.): A chemical that is not native in the body, or is present in much higher concentration than normal.

''Toxic effect'': A change in physiological conditions caused by an effect of xenobiotics on the cellular level creating a decrease in health or behavior.

''Toxicodynamics'': Mechanism of the toxic effect, reactivity, receptors and organ types.

''Toxicokinetics'': Uptake, transport and lingering time/concentration of X.

''Absorption'': Transport from the place of disposition to blood with a rate constant <math>k_a</math>.

''Bolus'': A dosage of X. administered directly into the plasma.

''Elimination'': Biotransformation, exhalation or excretion of X. X. does not need to be removed from the body, only made unavailable in its original form.

''First pass metabolism'': The metabolism of a X that occurs in liver during the first passage.

''Bioavailability (F)'': The fraction of a given dose D (X-parent compound) that reaches circulation in an unchanged form.

''Enteroheptic circulation'': Absorption from small intestine to blood --> liver --> conjugate --> bile --> small intestine --> hydrolyzed --> parent compound --> reasorbed into blood

''Distribution Equilibrium'': A state where consenstrations of a substanse in different organs are in equilibrium with each other.

===Introduction===
There are two main ways to model toxicokinetics: Compartmental models and physiological models. The compartmental models are described more in detail below, and involve modeling organ systems by simple relations without involving physiology, i.e. the rate constants used are acquired from measurements alone. The physiological model looks at theoretical, or physiological, models to predict rate constants of the organs in the body. This involves factors such as:
*Blood flow through organs
*Absorption of the small intestine
**Villi and microvilli in the intestine: These greatly increase the intestinal area, so absorption into the blood for selected X. is greatly enhanced here.
**Active and passive diffusion: Some substances can diffuse directly across tissues, but most require some form of transport proteins. The mechanisms of these proteins determine how effectively and selectively xenobiotics are absorbed.
**There is also metabolism in the intestine, by e.g. the cytochrome P450 3A4 (CYP3A4) enzyme which can activate many prodrugs.
**Drug export from cells via P-glycoprotein is a very important mechanism which greatly reduces the amount of many xenobiotics that are absorbed.
*The portal vein collects blood from the intestine and goes directly to the liver, where many substances are metabolized and their bioavailability is reduced. This is called first-pass metabolism, where the drugs are metabolized before reaching general systemic circulation. 
*After being metabolized in the liver many xenobiotics are conjugated and marked for excretion into the bile. The bile is excreted in the small intestine, where the drugs can be un-conjugated and reabsorbed, passing into the liver again. This is called the entero-hepatic circulation, and keeps plasma concentration of xenobiotics low in general.
*Other special barriers, such as the blood-brain barrier and the placenta also greatly effect the distribution of xenobiotics.

===Compartmental models===
A model often used to model toxicokinetics is the compartmental model. In the compartmental model there is a central compartment representing the blood plasma and rapidly equilibrating tissues (e.g. liver and kidney), and side-compartments of more slowly equilibrating tissues. The simplest such model is the one-compartment model. Here there is only one compartment, which means all the modeled tissues are rapidly equilibrating. In this model a bolus will decay exponentially, i.e. measuring the logarithm of the plasma concentration over time gives a linear plot. Conversely, if experimental data holds with this description, it can be modeled by the one-compartment model. The decay is elimination, and elimination happens from the central compartment. 

=== Rate constants and elimination ===
There are several rate constants involved in toxicokinetics. There are elimination and absorption rate constant, <math>k_e</math> and <math>k_a</math>, which describes elimination from and absorption into the central compartment (see below) if the dose is administered e.g. orally. In multi-compartment models there are also distribution and redistribution constants, e.g. <math>k_{12}</math> and <math>k_{21}</math>, which describes rates between the compartments.

An example of a rate constant is the excretion rate constant through the kidney, <math>k_r</math>. In the kidney, glomerular filtration has a certain rate, tubular excretion another, and and reabsorption into the tubules a third. Thus, the excretion from the kidneys is given by <math>k_r=k_{f}+k_{ts}-k_{tr}</math>, where <math>f</math> - feces, <math>ts </math>- tubular secretion and <math>tr</math>- tubular reabsorption. Similar models can be made for other organs, both absorbative and eliminative. 

The elimination rates can follow different rate laws. Generally, in a one-compartment model, there is a first-order rate law, e.g. <math>-\frac{d C(t)}{dt}=k_e * C(t)</math>. Other rate laws hold if e.g. the elimination system is saturated, then <math>-\frac{d C(t)}{dt}=const.</math>.

Integrating the formula above gives

<math>C(t)=C_0 e^{-k_{el} t}</math>,

and further manipulation gives e.g. the half-life of X. in the blood to be <math>t_{1/2}=\frac{ln 2}{k_e}</math>.

Often the concentration is plotted on a semilogarithmic plot versus time. If this yields a straight line, we have a one-compartment model. <math>k_e</math> can be predicted from the slope, and <math>C_0</math> by extrapolation. 

If the semilogarithmic plot of plasma concentration of X. versus time does not yield a straight line, higher compartmental models must be used. In the higher-compartment model the tissues connected to the plasma equilibrate more slowly with the plasma, so the plasma concentration falls off more rapidly in the beginning, in what is called the ''distribution phases'', before the concentration profile again is as for the one-compartment model above. If there are two phases, one distribution phase and one linear phase (the eliminiation phase), we have a two-compartment model, which usually can be modeled by:

<math>C(t)=A e^{-\alpha t}+B e^{-\beta t}</math>,

where <math>\beta</math> corresponds to <math>k_{e}</math> above, and can be treated the same way.

If C is measured for e.g. an orally distributed drug there is also an absorption phase where the concentration increases over a certain time.

=== Toxicokinetic Parameters ===
There are several parameters that can be used to describe the models in more experiment-friendly terms. At the heart is C(t), the plasma concentration of X. at a given time. X is the total amount of X. in the body. The parameter V, called the volume of distribution, which relates X and C. V tells how large a volume is needed to distribute the total amount of the xenobiotic (X), so the concentration of X. in V is the same as in the blood (C). Mathematically, this gives <math>V=\frac{X}{C}</math>.

D is the administered dosage. AUC is the area under the concentration/time curve from 0 to infinity. The bioavailability of X. is given as <math>F=\frac{AUC_{a}}{AUC_{i.v.}}</math>, which gives the fraction in plasma when administered e.g. orally compared to intra venously. This gives another relation: <math>V=\frac{D \times F}{k_{el} \times AUC}</math> for a non-i.v. delivered drug. The denominator term is the plasma concentration. For a one-compartment model this can often be approxomated as <math>V=\frac{D \times F}{C_0}</math>, or <math>V=\frac{X}{C}</math> as above for an i.v. delivered dosage (D=X).

Clearance (Cl) is a term the that describes the volume of plasma that is cleared of X. per unit time, and can be given as the sum of clearances from each of the eliminating organs (<math>Cl_{total}=Cl_{renal}+Cl_{hepatic}+...</math>). The total body clearance is given by <math>Cl=\frac{D_{i.v.}}{AUC}</math>, which gives units of volume/time. Using the relations from above this can be seen to be equivalent to <math>Cl_t=V \times k_{el}</math> for a one-compartment model.

If more than one dose is given, the dosage interval is given by <math>\tau</math>. Giving a dose either continuously, or with a certain interval, allows one to reach a steady state concentration, where there is a balance between absorption and elimination. By definition, this is equal to <math>5 \times C\left(t_{1/2}\right)</math>. Equivalent equations for this is:
*<math>C_{ss}=\frac{F\times D}{Cl_t \times \tau}=\frac{F\times D}{k_e\times V \times \tau}</math>

If the steady state is reached by a dosage D every <math>\tau</math>, there is naturally an oscillation of steady state values, given by <math>\frac{C_{ss}^{max}}{C_{ss}^{min}}=e^{k_e \tau}</math>. By replacing the bioavailable dosage per time <math>\left(\frac{F \times D}{\tau}\right)</math> with an constant infusion rate <math>k_0</math> on obtains <math> C_{ss}=\frac{k_0}{Cl_t}</math>. Often it is desirable to reach steady state concentration as quickly as possible. In this case a bolus dose that immediately gives <math>C_{ss}</math> in the plasma. This dose is then given by <math>D_{bolus}=C_{ss}\times V</math>.

==Metabolism of xenobiotics==
The biotransformation and metabolism of xenobiotics is of great importance in maintaining homeostasis. Some enzymes are very important for these metabolic reactions. There are several types of enzymes, responsible for oxidation, reduction, hydrolysis and conjugation of xenobiotics. These reaction are divided into two phases: Phase I and phase II.

===Phase I reactions===

Phase I reactions are the primary biotransformation of xenobiotics. This includes oxidation, hydrolysis or reduction, and generally introduces or reveals a functional group that increases the hydrophilicity of the xenobiotic a small amount. One very important oxidase is the cytochrome P-450 (CYP) family which are found in most lifeforms. CYP is a heme-containing enzyme family involved in electron transport. The most common reaction is oxidation of an organic substrate by using molecular oxygen as an electron acceptor, i.e. <math>RH + O_2 + 2H^+ + 2e^- \rightarrow ROH + H_2 O</math>. During the oxidation of certain compounds such as aliphatic alkenes and aromatic hydrocarbonds by CYP highly reactive species called epoxides can be formed. This is called activation of the xenobiotic, in which the metabolite form of the xenobiotic is more reactive than the original form. Epoxides can bind to DNA and are possibly mutagenic or carcinogenic. Therefore, in virtually all cells there are CYP-dependent oxidations there is enzyme called ''epoxide hydrolase'' which reacts the epoxide group with water to produce diols. CYP enzymes are especially prevalent in the liver, and play a vital role in regulating the toxicity of a number of compounds that pass trough the liver. Important members of the CYP family are CYP3A4, which metabolises a great variety of compounds, and is present at high concentrations in the liver, CYP1A2 and CYP2D6, which metabolise a many different drugs, among them caffeine. CYP2E1 is less prevalent enzyme, but important since it metabolises small polar molecules such as ethanol.

=== Phase II reactions ===
Conjugation with various groups, such as acetylation, methylation, sulfonation, conjugation with glutathion and glucuronidation are the phase II reactions. In general (with the exception of acetylation and methylation) these cause a large increase in hydrophilicity of the conjugate, which allows the xenobiotic to be easily eliminated. These reactions generally proceed much quicker than the phase I reactions, and can either follow a phase I reaction or proceed directly. 

Glucuronidation is a major pathway of biotransformation of xenobiotics in humans. In glucoronidation the xenobiotic is conjugated with the cofactor uride diphosphate-glucuronic acid, creating a highly water soluble molecule, which can be excreted in urine or bile, depending on the total size of the molecule. This reaction is catalyzed by UDP-glucuronosyltransferase, and requires a hydroxyl, carboxyl or thiol group (roughly), so this will often follow a phase I reaction that provides such groups. Other important pathways are glutathione conjugation (catalyzed by glutathione -S-transferase) and GSH (glycine-cysteine-glutamic acid) conjugation. 

''GAH, kan noen som faktisk var på denne forelesningen skrive noe her, notatene hans er forferdelige!''

== Risk assessment ==
In addition to the knowledge about toxicokinetics and toxicodynamics, there is a whole greater field of risk assessment to see if a given xenobiotic represents a threat in certain situation. There are two main ways to determine toxicity in general, the epidemiological and toxilogical methods. Epidemology is the study of toxicity of substances in man. The disadvantage of this method is that it only can be performed post-exposure. Toxicology is the study of substances working in cells and animals. This can be done pre-exposure, but requires extrapolations to be applicable to humans. 

The general system for risk assessment is as follows:
*Hazard identification
*Expose assessment to determine total daily exposure (TDE)
*Effect assessment of the TDE
*Risk characterization and action

===Hazard identification===
Questions asked: 1. Can people be exposed? This is answered by checking individual habitats, work places, etc to see if there is any exposure risk at all. If yes, the next question is: Can toxic effects occur? This is answered by knowledge of toxicity, structure, like compounds, etc. If the answer is yes, one proceeds to exposure assessment.

===Exposure assessment===
There are standardized rules for TDE depending on form of exposure. Formulas for this can be:
*<math>\text{TDE}_{environment}=\text{inhale} + \text{eat}=\frac{C_{air}[mg/m^3]\times V_{inhale} [20m^3/day]}{W_{body} [70 kg]} + \sum_{i=1}^n \frac{intake/day [kg] \times C_i [mg/kg]}{W}</math>
*<math>\text{TDE}_{work}=\text{inhale} + \text{skin}=\frac{C_{air}[mg/m^3]\times V_{inhale} [0.8m^3/hour]\times WT[8h]}{W_{body} [70 kg]} + \frac{A_{skin}[2000cm^2]\times Th_{matrix}[0.01cm]\times C_{subst. in matrix}[mg/cm^3]\times n}{W}, n=1...10</math>

===Effect assessment===
Firstly, more detailed toxicology data is acquired. For substances that are produced more than one ton per year this data is required, for lesser substances it might not be available. Many tests can be done to acquire this type of data:
*Acute toxicity -> dose vs. percentage of test animals dead.
**Dead animals get a full pathology, with target organ and type of toxicity present.
**The dosage is a single dosage, then wait 14 days and monitor behavior, GI trouble, cramps, etc.
**<math>\text{LD}_{50}</math>is the dose at which 50% of the animals die within 14 days, this is an important number.
*Irritation/sensitization, often done one guinea pigs or rabbits.
*No observed adverse effect limits (NOAELs) are calculated from 28 days repeated administration.
*In vitro testing of cell, genetic testing (Ames test), chromosomal tests and toxicokinetics.
*If the substance has a distribution of more than 1000 tons per year, the studies are larger, including fertility and long term effects.

===Risk characterization===
After the exposure and effects have been characterized, the total risk is assessed. This includes:
*Relevance and quality of previous testing
**Choice of animal, are the results applicable to humans?
**Is the toxicokinetic data of sufficient quality?
*Extrapolation of the acquired data
**Total daily exposure (TDE) compared to acceptable daily input (ADI) over a lifetime
**Calculated by <math>\text{ADI}=\frac{\text{NOAEL}}{\text{Uncertainty factors (UF)}}</math>, where UF is 10 for animal to man and man to man (!). If lowest adverse effect limit (LOAEL) is used instead, another factor of ten is added.
**Certain factor can modify the equation, e.g. if the metabolism of the specific xenobiotic is identical in the animal and human.

If the results give that <math>\text{TDE}\geq \text{ADI}</math>, action is taken to reduce the TDE.

An example of the importance of the quality of data is well known in the case of thalomide, which was tested, but tested on the wrong animals so the extrapolations where not valid. Another example is for <math>\beta</math>-naphthylamine, a drug that caused many cases of urinary bladder infection. In the liver this substance is not particularly harmful, and is oxidised by a CYP enzyme, producing and active and carcinogen form of the drug. But in the liver it is immediately conjugated with glucuronic acid, which makes it soluble and allows it to be secreted into the urine, and does not bind to DNA. In rats and mice this is the end result, and the substance is excreted and no adverse effects are observed. Dogs, on the other hand, contain <math>\beta</math>-glucuronidase, an enzyme in the bladder that hydrolyses the bond to glucuronic acid, redeeming the active and carcinogenic form of the drug. Since there are no UDP glucuronosyltransferase enzymes in the bladder, the drug stays in this activated form and binds to DNA, causing urinary bladder cancer. Initially, this drug was only tested on rats and mice and other animals that do not have <math>\beta</math>-glucuronidase in the bladder, this was not discovered. Humans do have this enzyme, which lead to many cases of urinary bladder cancer due to the use of the "wrong" test animals.


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