Verify or refute the use of Non Linear Mixed

Effect Model for Interferon effect on HCV

Hila DavidShimrit Vashdi

Project Advisors: Prof. Avidan NeumannDr. Rachel Levy Drummer

Introduction

Biomathematical Model is a valuable tool for science and it has implications on medicine and economy.

It is often used to characterize diseases and drug’s behavior at the human body.

Finding the right model for HCV treatment will have a great medical and economic influence.

Hepatitis C Virus

HCV is a Single Strand Ribonucleic acid (RNA), belongs to the Flaviviridae family.

Its genome is 9.6 kb size, and encoding to a polyprotein of 3,000 amino acids, produced by cellular and viral proteases.

Interferon α

IFN- α is an anti-viral treatment for HCV. It’s a Glycoprotein, naturally secreted from cells in a response to viral infection.

The Glycoprotein attach to membrane receptors which starts a cellular signals sequence. Those signals cause expression of anti-viral genes.

Pegylated-Interferon α

Polyethylen glycol (peg) is a polymer which improves the pharmacokinetiks & pharmacodynamics of proteins its attached to.

Two variants of pegylated-IFN α were tested, pegasys and pegIntron, differ each other with three features which effect their behavior:

• average molecular weight. • branching. • Link to the Interferon.

PharmacoKinetics Study of the absorption, spreading, metabolism and elimination of a

drug. Its important to understand the IFN-α pharmacokinetics in order to

efficiently predict the patients response to the treatment, since it’s a critical stage of the disease.

The equations describes the concentration of the drug as a function of time.

The first relates to the bolus and the second to the serum. Bifn- the drug concentration at the bolus. Inj- the drug dose. Kbs- spreading drug rate.

Sifn- drug concentration at the serum.Cifn- drug elimination rate.

Project Goal

Running a simulation with virtual patients, using Non-Linear Mixed Effect Model in order to verify or refute the use of the individual

model for IFN-α effect on HCV.

Individual PK

The data is blood samples collected for each

patient separately and the estimation of the

parameters is done for each patient

specifically.

Attributes:

• Independency of the patients.

• More complicated to implement.

Population PK

Estimation of population parameters by

treating all data as if it arose from homogeneous

population. It can also identify the sources of

variability that explain differences in the

parameters between patients.

Attributes:• More objective.• Easier to implement.• More powerful (under some assumptions).

Non Linear Mixed Effect Modelfor PK

A method based on population PK. NLME makes a one stage analysis and evaluate

the population parameters that enable determine the PK and PD simultaneously.

The NLME combine both approaches, the

individual and population PK.

It fits the best model under statistic population assumptions and can combine together parameters with different influence.

MONOLIX PROGRAM

Monolix is a new software for the analysis of

Non-linear mixed effect models, used

especially at clinical experiments and

pharmacokinetics processes.

Monolix requires to define the data and the

model and to fix some parameters used for

the algorithms.

The output is the estimation of the individual

parameters, the maximal likelihood and the

residuals.

Working process

Analysis of Individual Experimental Data• Kinetics graphs.• Individual parameters.

Creating data for virtual patients• Simulated Individual kinetic profiles.• Adding noise to the simulated Individual kinetic profiles.

Running the population approach NLME• Individual parameters out of population parameters.

Comparison of the methods• Comparing the two methods individual parameters results.

*The working process was done for each treatment group of patients.

Step 1 – kinetics graphs

• pegIntron • pegasysPegIntron kinetics

0

0.5

1

1.5

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2.5

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3.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

time (days)

conc

entr

atio

n (lo

g)

PegIntron kinetics

Pegasys Kinetics

0

0.5

1

1.5

2

2.5

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3.5

4

4.5

0 2 4 6 8 10 12 14 16

time(days)

con

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trat

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(lo

g p

g/m

l)

The drug concentration was measured during the first week of the treatment at 21 patients treated with pegasys and 10 patients treated with pegintron.

Step 2 - individual parameters

Running the real data with the model equations at the Madonna.

Finding the combination of the parameters values that will make the best fit of the real data to the model for each patient. pegIntron pegasys

Step 3- creating virtual patients

• Creating 100 combinations of parameters for each treatment.

• Simulating the kinetic profiles according to the parameters of the individual patients.

• Adding noise (uniform distribution) on the data outcomes from the kinetic profiles.

Step 4 - virtual patient’s individual fit

Running the virtual patients data at the

Madonna and finding the individual fit and

parameters to every patient.

pegIntron pegasys

pegasys pegIntron

Cifn Kbs inj Cifn Kbs inj

Mean 0.499 0.498 83,280.4 11.711 0.423 51,506.6

s.d. 0.328 0.261 54,875.2 7.1912 0.186 34,591.8

Minimum 1.367E-7 0.088 8,089.73 1.4614 0.01838 9,850.33

maximum 1.362 1.301 240,315 57.6864 0.8315 293,502

median 0.438 0.431 67,146.7 11.4427 0.435 51,172.2

Virtual parameters according to the individual approach

Cifn Histogram

pegasys pegIntron

Inj Histogram

pegasys pegIntron

Kbs Histogram

pegIntronPegasys

Step 5 – population fit

Running the simulated data in monolix

program in order to estimate the population

parameters and the outcomes individual

parameters

Individual fit-Individual approach vs. population

approach

pegIntron pegasys

Red- individual approachBlue- population approach

Blue- individualPink- population

conclusions

• At the dynamic model, we can see clear differences at Cifn and Inj between the treatments, while the absorption from the bolus to the serum (Kbs) is similar.

• Under the restriction of running the programs for only one injection and for limited number of patients, the model used at the monolix succeed predicting the individual fits, but still the individual approach find a better fit.

Thanks

• Prof. Avidan Neumann

• Dr. Rachel Levy Drummer