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kprod – production rate constant</p>
kprod – production rate constant</p>
<h3>General mass-balance equations<h3>
<h3>General mass-balance equations</h3>
<p>The equation below describes the change in concentration over time in non-eliminating tissues. The equation has the same form for both rapidly and slowly perfused tissue. Each compartment is then described with it's distinctive values for blood flow, concentration and partition coefficient.</p>
<p>The equation below describes the change in concentration over time in non-eliminating tissues. The equation has the same form for both rapidly and slowly perfused tissue. Each compartment is then described with it's distinctive values for blood flow, concentration and partition coefficient.</p>

Revision as of 21:22, 26 September 2012

Pharmacokinetic model


The major downsides of standard interferon treatment are substantial side effects that to a large degree are the consequence of very high drug concentrations, occuring shortly after drug administration. If high concentration peaks could be avoided and lower levels maintained steadily over time, this would result in reduced side effects without compromising therapeutical effectiveness. This idea is currently being tested in clinical trials using the interferon infusion pump (COPE-HCV: Phase 2, randomized, open-label, active-control, dose-ranging study of interferon alfa-2b given via continuous sub-Q infusion; trial by Medronic Inc.)

One of our goals is to show that therapy with drug-producing cells is more beneficial than standard treatments based on drug injections, which are in use today. We predict that if the drug is constantly produced inside the body, it could reach a steady concentration at almost any desired level. We believe localization of therapeutical cells would also decrease the proportionate drug concentrations in non-target tissues, thus further reducing the side effects.

We tested this hypothesis and compared standard therapies with our proposed treatment.
Because of complex physiological mechanisms and an extensive set of biological parameters that can not be accurately measured for either ethical or technical reasons, we developed a model that covers the most crucial aspects and processes. At the same time, computer simulation provides simpler and faster option than in vivo research.

A physiologically based pharmacokinetic model

A pharmacokinetic model is a quantitative description of drug absorption, distribution, metabolism and elimination from the body. A model is defined by a system of ordinary differential equations to represent essential drug kinetics.
We took into account the neccessary biological parameters and based the simulated processes on actual physiological mechanisms to construct a physiologically plausible model.

Selecting the optimal physiological model

A physiologically based model is composed of multiple compartments which represent organs of the body. Parts were chosen in accordance with drug and tissue specifics, so that the relevant organs are represented as separate compartments, while other tissues were merged on the basis of common characteristics.

Determing compartments

We used the following characteristics as a criteria for splitting and merging organs:

  • Liver is the target organ of therapy.
  • Interferon alpha is widely distributed into body tissues – highest concentrations occur in kidney, liver and lung.
  • Interferon is a water-soluble molecule; it is only poorly distributed in adipose tissue.
  • Interferon alpha does not cross the blood-brain barrier.
  • Skin and muscle tissues do not seem to have much higher concentrations of the drug in comparison to adipose tissue.
  • Skin, musle and adipose tissue have similar, slow blood perfusion.
  • Gut, spleen and heart are all rapidly perfused tissues.
  • Interferon is mainly eliminated via renal catabolism, while hepatic metabolism accounts only for a minor pathway of elimination.

We decided to define separate compartments for the liver, kidney and lungs. All other rapidly perfused tissues are grouped together as one part. Since venous blood enters the lungs and arterial blood flows into all other organs, we separately simulate venous and arterial blood. Because interferon does not cross the blood-brain barrier it is not necessary for the brain to be modelled separately. Skin, muscle, fat and other slowly perfused tissues are merged together into one compartment.

We constructed three final models - two for standard interferon treatments and a third for a prospective therapy with drug-producing microencapsulated cells. The fundamental design is the same in all models, they are only modified for specific entry points of the drug and the corresponding absorption or production processes. On the diagram, blocks representing different administrations are shown in distinct colors: blue for the intravenous bolus, green for the subcutaneous injection and red for the interferon production by microencapsulated cells that are implanted into liver.


Types of parameters used:

1.) Species specific

Qi – blood flows to tissues
Vi – organ volumes

Blood flows

Sum of blood flows through liver, kidney, rapidly and slowly perfused tissue must always equal total cardiac output.

Tissue volumes

* average body density = 1 kg /L

2.) Individual specific

BW - body weight
Qc - cardiac output
varying percents of tissue volumes (e.g. percent body fat)

The variability of parameters

Parameter values can range significantly between individuals, depending on factors such as age, sex, renal function, activity level and diet.
For instance, cardiac output can vary significantly even in one individual, depending on the current activity (sleeping, sitting, running etc.). There can be substantial differences in, for example, the percent of body fat (accounted for in slowly perfused tissue) comparing individuals with an otherwise similar profile (same age, sex, etc.).
Values used in our model present an average adult male, weighing 70 kg, with mean cardiac output and normal renal function.

3.) Drug specific

t1/2 - drug half life
kel - elimination rate (kidney)
Pblood:tissue - partition coefficient

Interferon is expected to be found only in the plasma and not in red blood cells, therefore we can conclude that the amount of interferon found in plasma is equal to the amount in blood. Since blood is comprised of four parts plasma and three parts red blood cells, we can calculate the blood to plasma ratio to be:

The equation has the same form for each kind of tissue:

Partition coefficients

Uncertainty of partition coefficients

A critical element in human PBPK modelling is the uncertainty of values of the partition coefficients. Partition coefficients are an important aspect of pharmacokinetic modeling, because they denote how the drug distributes troughout body tissues. The value of each coefficient has a complex dependence on solubility, permeability, pH, binding affinity of the drug to the receptor receptor and many other factors. The difference in a few amino acids between subtypes of interferon alpha can impact values of coefficients quite noticably. Even so, there are deviations of evaluated drug distribution of the same subtype of interferon alpha, depending on the detection method (radioactivity, ELISA).

For legal and ethical reasons these values cannot be directly measured in humans. We had to rely on various studies of interferon tissue distribution in rodents to calculate partition coefficients. It is generally assumed that animal and human partition coefficients are similiar for the same kind of tissue.

Chemical and ROA* specific

* ROA - route of administration

D – dose
k0 – absorption rate constant (zero-order process)
ka – absorption rate constant (first-order process)
F – bioavailability (percent of absorbed dose)
kprod – production rate constant

General mass-balance equations

The equation below describes the change in concentration over time in non-eliminating tissues. The equation has the same form for both rapidly and slowly perfused tissue. Each compartment is then described with it's distinctive values for blood flow, concentration and partition coefficient.

We can use the same form for the liver compartment, since the metabolism of interferon is negligible.

Although the lungs also represent a non-eliminating tissue in this model, the equation is slightly different, since venous and not arterial blood flows into the tissue.

The kidneys represent a site of elimination, so we had to include this process as well.

In the equation describing the change of concentration in venous blood, there is a sum of blood flows which flows in from multiple compartments. These include liver, kidney, rapidly and slowly perfused tissue.

Blood flow from the lungs is accounted for in the equation for the arterial blood compartment.

Modeling pharmacokinetic processes


Absorption processes depend on the route of administration,

Intravenous administration

The drug is injected directly into the blood stream, so there is no special absorption process. The dose is bolus and enters the system completely.