Computational Biology Final Project, Bar-Ilan

UniversityAugust 2004

(Administered for Treating Thrombocytopenia and Various Diseases)

Smadar Horowitz & Moran Elishmereni

Guidance:

Prof. Zvia Agur Dr. Hila Harpak

Yuri Kheiffez

IMBM

Modeling the Atrial Fibrillation Side Effects of

Interleukin-11

Chemotherapy-Induced Thrombocytopenia

Reason - chemotherapeutic agents eliminate megakaryocytes and platelet precursors that are part of thrombopoiesis (platelet production).

Side effects - abnormal bleeding, bruising, spots on the skin, headaches.

Introduction

A low level of platelet formation or platelets in plasma due to administration of

chemotherapy.

Thrombocytopenia is a dose-limiting side

effect of chemotherapy.

How do we treat it?

Transfusion of Platelets

Introduction

Treatment

Chemotherapy-Induced Thrombocytopenia

Most common treatment.

Required every few days.

Risk of infections and immunologic reaction.

Expensive.

Platelet Growth Factors

Interleukin 11

A protein of 178 amino acids, molecular mass of 19 kDa.Secreted by bone marrow & intestine.Main biological activity : stimulation of megakaryocyte proliferation and increased platelet production.

Introduction

Interleukin 11 (IL-11)A pleiotropic cytokine / growth factor.

A protein of 179 amino acids, molecular mass of 19 kDa.Secreted by bone marrow & intestine.Main biological activity : stimulation of megakaryocyte proliferation and increased platelet production.

Introduction

Interleukin 11 (IL-11)A pleiotropic cytokine / growth factor.

A protein of 179 amino acids, molecular mass of 19 kDa.Secreted by bone marrow & intestine.Main biological activity : stimulation of megakaryocyte proliferation and increased platelet production.

Introduction

Interleukin 11 (IL-11)A pleiotropic cytokine / growth factor.

megakaryocyte

platelets

RBC

WBC

IL-11

Introduction

Interleukin 11 (IL-11)

Succeeds in

elevating platelet count!

Great Solution!

So what’s

the catch?

Side effects

Edema (59%)

Asthenia (50%)

Dyspnea (48%)

Conjunctival redness (19%)

Anemia (<15%)

Pleural effusion (<15%)

Interleukin 11 (IL-11)

Introduction

Common Adverse Events

Usually manageable and reversible with

drug discontinuation, but may become

severe

AF- Atrial Fibrillation (<15%)

Side-effects

Edema (59%)

Asthenia (50%)

Dyspnea (48%)

Conjunctival redness (19%)

Anemia (<15%)

Pleural effusion (<15%)

Interleukin 11 (IL-11)

Introduction

AF- Atrial Fibrillation (<15%)

Less-common Adverse Event

Usually severe, life-threatening, and

irreversible

What is Atrial

Fibrillation?

Normal Sinus Rhythm

Introduction

Electrical impulses are fired through the heart, creating a predictable wave of stimulation and contraction.

Heart beat:

60-100 bpm

regular

Introduction

Multiple atrial sites fire impulses in a random fashion, creating many uncoordinated contractions.

Heart beat:

120-180 bpm

erratic, ineffective and rapid

Atrial Fibrillation (AF)

Atrial Fibrillation (AF)

Introduction

The most common

arrhythmic disorder

Atrial Fibrillation (AF)

Introduction

Leads to serious complications such as heart

failure and blood clots.

Causes 15% of all strokes.

Prevalence rises with advanced

age or history of cardiac disorder.

The Problem

IL-11 is rarely administered due to all of the side-effects.

IL-11 is not administered at all in elderly or cardiac

impaired patients due to risk of AF .

IL-11 Induces AF

IL-11 AF

life-threatening side-effect

The Problem

IL-11 Induces AF

IL-11 AF

Major Problem!

The Problem

IL-11 Induces AF

IL-11 AF

How can we allow the safe use of IL-11

anyway?

Purpose of the Project

Mathematical Model

Creation of a

Simulating IL-11

induced AFI. Treatment protocol- dosage & time of administration.

II. Personal characteristics of the patient.

Risk of AF (%) in a specific patient

treated with IL-11

InputOutput

Purpose of the Project

Mathematical Model

Creation of a

Simulating IL-11

induced AF

Phases:

I. Understand the Physiological Mechanism of IL-11-induced AF.

II. Adjust the Mechanism & Write Appropriate Equations.

III. Analyze the Equations and Find Parameters.

Mathematical Model: (I) Physiological Mechanism

IL-11 Na+ & Fluid

Retention

Atrial Enlargement and Stretch

AF

Activation of Stretch-

Dependant Channels &

Faster Depolarization

IL-11 Induces AF: How?

Direct Effect on Kidney or

Compensatory Response of

Kidney (RAAS)

IL-11 Na+ & Fluid

Retention

Atrial Enlargement and Stretch

AF

Mathematical Model: (II) Adjusting Mechanism

IL-11 plasma concentration = IL-11 dosage.

IL-11 Dose

IL-11 Conc.

X

IL-11 Na+ & Fluid

Retention

Atrial Enlargement and Stretch

AF

IL-11 plasma concentration = IL-11 dosage.

IL-11 Dose

IL-11 Conc.

X

We don’t know how Fluid Retention occurs: Assume a mediating factor Y formed as a result of IL-11 activity and leading to FR.

Mathematical Model: (II) Adjusting Mechanism

IL-11 Na+ & Fluid

Retention FR

Atrial Enlargement and Stretch

AF

IL-11 plasma concentration = IL-11 dosage.

IL-11 Dose

IL-11 Conc.

X

We don’t know how Fluid Retention occurs: Assume a mediating factor Y formed as a result of IL-11 activity and leading to FR.

Factor Y

Mathematical Model: (II) Adjusting Mechanism

IL-11 AF

IL-11 plasma concentration = IL-11 dosage.

IL-11 Dose

IL-11 Conc.

X

We don’t know how Fluid Retention occurs: Assume a mediating factor Y formed as a result of IL-11 activity and leading to FR.

Factor Y

Fluid Retention (or Atrial Volume) highly correlate with occurrence of AF.

Na+ & Fluid

Retention FR

Atrial Enlargement and Stretch

Mathematical Model: (II) Adjusting Mechanism

IL-11 AF

IL-11 plasma concentration = IL-11 dosage.

IL-11 Dose

IL-11 Conc.

X

We don’t know how Fluid Retention occurs: Assume a mediating factor Y formed as a result of IL-11 activity and leading to FR.

Factor Y

Fluid Retention (or Atrial Volume) highly correlate with occurrence of AF.

Na+ & Fluid

Retention FR

Mathematical Model: (II) Adjusting Mechanism

IL-11 AFIL-11 Dose

IL-11 Conc.

X

Factor Y

Na+ & Fluid

Retention FR

Mathematical Model: (II) Adjusting Mechanism

Personalized Data entered:

Age

History of cardiac disorder

History of alcohol use

Obesity

Personalized Parameters

IL-11 AFIL-11 Dose

IL-11 Conc.

X

Factor Y

Na+ & Fluid

Retention FR

1 2 4

1

2

3

4

3Adm(X)

Mathematical Model: (II) Writing Equations

Personalized Parameters

)),(()(

)()(21

rsedParametePersonaliztFRftAF

tYftFR

YXX

X

dt

dY

XXAdmdt

dX

mm

m

)),(()(

)()(21

rsedParametePersonaliztFRftAF

tYftFR

YXX

X

dt

dY

XXAdmdt

dX

mm

m

1

2

3

4

How

Mathematical Model: (III) Analysis of Equations and Parameters

Deriving the Analytical Solutions:

FR (t)

Y (t)

How?

X (t)

Mathematical Model: (III) Analysis of Equations and Parameters

XXAdmdt

dX

)24(24

)1(24

1

1)(

nt

n

ee

etX

Initial Dose of IL-11 is

known

Day (0,1,2…

)

1

2

Mathematical Model: (III) Analysis of Equations and Parameters

YXX

X

dt

dYmm

m

21

24

)1(24)24(

1

1)(

e

eeuX

nnu

t

mm

mut du

XuX

uXeetY

021)(

)()(

Values of m X1/2

are unknown!

3

Mathematical Model: (III) Analysis of Equations and Parameters

)()( tYftFR

normFRtkYtFR )()(

normFRtFRtkY )()(

A B

H = (A – B)2 0

Solution: Curve

fitting (Aspire H to a

minimal value)

We want to find the

parameters of A so

that A and B are close

First Phase: Linear

Mathematical Model: (III) Analysis of Equations and Parameters

To find minimum of H we use a numerical method:

Steepest Descent Method

X(n+1) = X(n) - f (X(n))

nniii

i

xxfxxxxxf

x

f ,...,,...,,,,..., 1111

Start at random point.

Get direction of steepest descent.

Move in this direction.

Repeat until minimum is found.

Mathematical Model: (III) Analysis of Equations and Parameters

H

Iterations

H reaches

minimum value!

Parameter values of Y(t)

are: 9984.2

7496.0

8444.0

0375.0

21

X

Mathematical Model: (III) Analysis of Equations and Parameters

normFRtkYtFR )()(

We found parameters- function is known!

Defined by normal plasma

volume- 5.5 L

Not enough data - we cannot use interpolation to define FR(t).

First Phase: Linear

Later Phase: Unknown

We remain only with linear equation.

Mathematical Model: Achievements

1 32

X (t) Y (t) FR (t)

Deriving the Analytical Solutions:

Future studies will allow us to create a more complete and accurate model…

In Conclusion

Cancer

Interleukin-11

Chemotherapy

Chemotherapy-Induced

Thrombocytopenia

AFMathematica

l Modelfor IL-11 induced AF

DISEASE TREATMENT

We wish to thank the following people for their contribution to the

project:

... תודה על ההקשבה

Prof. Zvia Agur Dr. Hila

Harpak Yuri Kheiffez

Dr. Ron Unger Dr. Yehudit Sonn

Dr. Nethaniel Horowitz Dr. Yitzhak Kehatt Prof. Amir Pelleg

References

1. Age-dependent atrial remodeling induced by recombinant human interleukin-11: implications for atrial flutter/fibrillation. Jiang Xu, 2002.

2. A randomized placebo-controlled trial of recombinant human interleukin-11 in cancer patients with severe thrombocytopenia due to chemotherapy. Tepler I, 1996.

3. A phase I trial of recombinant human interleukin-11 (neumega rhIL-11 growth factor) in women with breast cancer receiving chemotherapy. Gordon MS, 1996.

4. Tolerability and side-effect profile of rhIL-11. Smith J.

5. Hematopoietic, immunomodulatory and epithelial effects of interleukin-11. Shwertzshlag US, 1999.

6. Mechanism and amelioration of recombinant human interleukin-11 (rhIL-11)-induced anemia in healthy subjects. Dykstra KH, 2000.

7. Pharmacokinetics of [125I]-recombinant human interleukin-11: 1. Absorption, distribution and excretion after subcutaneous administration to male rats. Uchida T, 1998.

8. Pharmaco-economic analysis of oprelvekin solid tumor patients receiving chemotherapy. Scott B. Cantor, Ph.D.