Team:Slovenia/ModelingPK

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<li>average concentration: C<sub>avg</sub> = 350 ng/ml</li><br><br>
<li>average concentration: C<sub>avg</sub> = 350 ng/ml</li><br><br>
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<center>Figure 6. Multi-compartmental model for anakinra. For local therapy model, we added one additional compartment (shown in purple color) inside the heart compartment. This represents the affected area, where microencapsulated cells would be administered to. In standard therapy, the whole heart, both infarcted and undamaged tissue, are represented as one, since standard treatments can not target selected area specifically. </center><br><br>
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<center>Figure 6. Multi-compartmental model for anakinra. For local therapy model, we added one additional compartment (shown in purple color) inside the heart compartment. This represents the affected area, where microencapsulated cells would be administered to. In conventional therapy model, the whole heart, both infarcted and undamaged tissue, are represented as one, since standard treatments can not target selected area specifically. </center><br><br>
<br><br><p>We calculated following partition coefficients according to a study on drug distribution in rodents.</p>
<br><br><p>We calculated following partition coefficients according to a study on drug distribution in rodents.</p>

Revision as of 19:03, 24 October 2012


Pharmacokinetic model

Distribution of drugs throughout tissues is very important for the effective therapy. We built pharmacokinetic models to simulate distribution of biological drugs produced by the engineered microencapsulated cells which would be implanted into the liver to treat hepatitis C and into the heart for the therapy of myocardial ischaemia, in comparison to the standard therapy.

Pharmacokinetic models suggest that the proposed type of delivery should decrease the systemic side effects and the required dose of biological drugs.

We developed a 3D visualization of pharmacokinetic model data representing our findings in that aspect.

Introduction

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.




Figure 1. Multi-compartmental physiologically based pharmacokinetic model, customized for different Interferon therapies. Main difference is the route of administration - for each administration, there is different compartment from which drug enters the body. Blue blocks are used in modeling for intravenous administration, green blocks are specific for subcutaneous administration and red blocks represent continuous production of the drug, in this case in the liver compartment. Therapies of course don't differ only in drug entry points, but also in absorption or production processes, percent of drug that enters the blood stream and so on.



Parameters

Types of parameters used:

1.) Species specific

Qi – blood flows to tissues
Vi – organ volumes

Blood flows
Cardiac output Qc Qc = 5.58 L/min = 335L/h
Comparment Parameter name Percent cardiac output
lung Qlung 100% Qc
venous blood Qven 100% Qc
arterial blood Qart 100% Qc
liver Qliver 25% Qc
kidney Qkidney 19% Qc
rapidly perfused tissue Qrpt 18% Qc
slowly perfused tissue Qspt 38% Qc

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

Tissue Volumes
Body Weight BW BW = 70 kg => *BV = 70 L
Comparment Parameter name Percent body volume
lung Vlung 0.8% BV
venous blood Vven 5.57% BV
arterial blood Vart 2.43% BV
liver Vliver 2.60% BV
kidney Vkidney 0.44% BV
rapidly perfused tissue Vrpt 5.16% BV
slowly perfused tissue Vspt 83% BV

* 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.) Chemical 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:

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 throughout 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

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.

Subcutaneous administration

In subcutaneous administration, more than 80% of the initial dose enters systemic circulation. This percentage is defined as bioavailability and can reach up to 95% for interferon alpha given subcutaneously.
Time to peak Tmax
The absorption half-life is approximately 2.3 h

Relying on the available studies, we specified the absorption as a two phase process:

1.) At the beginning, when the drug concentration at the injection site is highest, only a limited amount of drug can be absorbed into the blood - the rate of absorption is maximal. This is described by a zero order process from t=0 to t=tk.
Zero order process equation:


2.) At t=tk the concentration drops to a level where rate of absorption is proportional to local concentration. Absorption follows first order kinetics from t= tk until the bioavailable drug is completely absorbed.
First order process equation:


Constant ka was taken from literature and the value of k0 was calculated using paramteres from the same source. Fz denotes the portion of the drug that is absorbed by zero order process.


Distribution

Estimating partition coefficients

Distribution process is usually modelled indirectly with the use of partition coefficients, which are drug and tissue specific. We derived partition coefficients according to the available literature. However, these values do differ from study to study (e.g. that kidney concentration is 1-9x times that of plasma), but they overall agree that interferon concentration is highest in the kidney, very high in the liver and lungs and to some extent in other rapidly perfused tissues, but lower in the adipose and other slowly perfused tissues.


Comparment Parameter name Value
lung Pblood:lung 2.5
liver Pblood:liver 2.8
kidney Pblood:kidney 8.5
rapidly perfused tissue Pblood:rpt 2.2
slowly perfused tissue Pblood:spt 0.7

Elimination

In the literature the terminal half-life for interferon alpha is from 3-8 h, with a mean around 5 h. Interferon alpha is detectable in the plasma for 4-8 h after the rapid intravenous injection and for 16-30h after subcutaneous administration.
The elimination constant for the kidneys was determined by curve fitting to data from the obtained studies.

Simulation data for different therapies

Modeling subcutaneous therapy

We simulated common type of interferon administration:

  • 3 times per week, subcutaneous administration
  • 3 MU = 11100 ng, dose
  • F = 93%, bioavailability
  • Ko, Ka - zero and first order absorption
  • t1/2 = 5h, half life

  • We constructed the model according to data from the literature. Results are shown in graph below.


    Figure 2. Standard subcutaneous therapy: high peaks right after administration, followed by rapid concentration decrease.


    Calculating desired drug production

    Our model assumes no cell divisions and therefore a constant therapeutical cell count in the body. In this case, cell production of a drug is mathematically equivallent to a continuous infusion of a drug into the tissue, where cells are located. To calculate the desired concentration level in the target tissue, we calculated AUC * of liver concentrations for subcutaneous administration over a period of one week. This allowed us to estimate the average concentration in the liver which corresponds to the therapeutic level we wish to reach and maintain with cellular drug production. The combination of kidney elimination and constant production leads to stable drug levels in tissues. After about four half-lives, drug concentrations rise to final levels and remain steady as long as the production rate stays the same.



    Figure 3. Drug distribution troughout tissues with Switch-IT therapy.


    Results and conclusions

    If we compare result of different treatments it clearly shows that local therapy with drug producing cells does not result in concentration fluctuations, which are present in common therapies.
    Concentrations never reach levels as high as in subcutaneous or intravenous administration. On the other hand, concentrations do not drop to a point wich would prevent the drug from becoming therapeutically inefficient.

    When the drug is produced at the target site, concentration levels between target tissues and other organs are inclined in favor of the target tissue - although kidneys show a substantial uptake of the drug in subcutaneous administration, the relative difference between kidney and liver concentrations are smaller with localized therapy.



    Figure 4. Comparison of subcutaneous and Switch-IT therapy. We can see the new therapy results in stable concentration levels, without peaks and lows.


    From model to implementation

    When we calculate the desired steady concentration in the target tissue, it was possible to estimate how many cells would need to be implanted. From the required production rate, which is thought to be linearly proportional to the cell count, we can calculate the total number of cells needed. Considering the average number of cells per microcapsule and mean capsule size, we can calculate the amount of microcapsules we would need to inject in order to attain the wanted therapeutic effect.

    Modeling anakinra

    For modeling the local application of anakinra-producing microencapsulated cells in the ischaemic muscle tissue we adopted slightly different approach. Liver is perfused by sinusoid capillaries which allow for passage of macromolecules to the tissue, therefore even protein therapeutics can be rapidly equilibrated with blood and distributed around the organism. Muscle tissue, however, is perfused with continuous capillaries, which prevents fast passage of macromolecules from the tissue to the blood. Protein molecules pass the continuous capillaries only through slow trans-pinocytosis. Consequently this increases the local concentration of therapeutics permitting the achievement of high local concentration with relatively little loss to the system and elimination by kidneys.


    Figure 5. Different capillary types in muscle tissue (continuous capillary, left) and in liver (sinusoid capillary, right). Image from: (Mescher, 2009)


    Therefore we took this feature of the tissue into account when calculating partition coefficients between tissue and blood compartment. Myoglobin has similar molecular weight to anakinra, therefore we assumed its partition coefficient to be the same(Hall, 2010). We have calculated the therapeutic concentration of anakinra to be 25 ng/mL, which we derived from the anakinra IC_50 value (Dahlén et al., 2008).

    Compartmental model and parameters

    According to a study of anakinra distribution and elimination after subcutaneous injection, we calculated relevant compartments for physiological model. At first, we modeled standard regime for anakinra therapy: 100 mg per day subcutaneously with next parameters:

  • bioavailability: F = 95%
  • half life: T1/2 = 5h
  • time to maximum concentration: Tmax = 4h
  • maximum concentration: Cmax = 780 ng/ml
  • average concentration: Cavg = 350 ng/ml


  • Figure 6. Multi-compartmental model for anakinra. For local therapy model, we added one additional compartment (shown in purple color) inside the heart compartment. This represents the affected area, where microencapsulated cells would be administered to. In conventional therapy model, the whole heart, both infarcted and undamaged tissue, are represented as one, since standard treatments can not target selected area specifically.




    We calculated following partition coefficients according to a study on drug distribution in rodents.

    tissuepercent of dose
    kidney 11 %
    liver 9 %
    gut 6 %
    lung 2 %
    muscle 43 %
    plasma 26%

    Dose distribution plot, fitted to literature data, which was used to determine the partition coefficients for the listed tissues.


    Comparment Parameter name Value
    lung Pblood:lung 0.4
    liver Pblood:liver 0.8
    kidney Pblood:kidney 9
    rapidly perfused tissue Pblood:rpt 2.2
    slowly perfused tissue Pblood:spt 0.23
    muscle Pblood:muscle 0.25
    heart Pblood:heart 0.2
    target tissue Pblood:target 33





    We achieved significantly better results with our proposed therapy comparing with conventional treatment.

    References

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    Chatelut, E., Rostaing, L., Grégoire, N., Payen, J. L., Pujol, a, Izopet, J., Houin, G., et al. 1999. A pharmacokinetic model for alpha interferon administered subcutaneously. British journal of clinical pharmacology 47,365–71.

    Johns, T. G., Kerry, J. A., Veitch, B. A. J., Johns, T. G., Kerry, J. A., Veitch, B. A. J., Mackay, I. R., et al. 1990. Pharmacokinetics, Tissue Distribution , and Cell Localization of [ 35 S ] Methionine-labeled Recombinant Human and Murine α Interferons in Mice 4718–4723.

    Kim, D.-C., Reitz, B., Carmichael, D. F., Bloedow, D. C. 1995. Kidney as a major clearance organ for recombinant human interleukin-1 receptor antagonist. Journal of Pharmaceutical Sciences 84,575–580.

    Lavoie, T. B., Kalie, E., Crisafulli-Cabatu, S., Abramovich, R., DiGioia, G., Moolchan, K., Pestka, S., et al. 2011. Binding and activity of all human alpha interferon subtypes. Cytokine 56,282–9.

    Levitt, D. G., Schoemaker, R. C. 2006. Human physiologically based pharmacokinetic model for ACE inhibitors: ramipril and ramiprilat. BMC clinical pharmacology 6,1.

    Marcellin, P., Boyer, N. 2003. Chronic viral hepatitis 17,259–275.

    ROFERON -A. n.d.

    Roy, A., Georgopoulos, P. G. 1997. Mechanistic Modeling of Transport and Metabolism in Physiological Systems Towards a Framework for an Exposure and Dose Modeling and Analysis System.

    Thitinan, S., McConville, J. T. 2009. Interferon alpha delivery systems for the treatment of hepatitis C. International journal of pharmaceutics 369,121–35. Yang, B.-B., Baughman, S., Sullivan, J. T. 2003. Pharmacokinetics of anakinra in subjects with different levels of renal function. Clinical pharmacology and therapeutics 74,85–94.


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