Modeling the Atrial Fibrillation Side Effects of Interleukin-11

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.


Introduction



Introduction


megakaryocyte

platelets

RBC

WBC

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%)


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%)


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)


Introduction

The most common

arrhythmic disorder


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


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


AF


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.


IL-11 Na+ & Fluid

Retention FR


AF


IL-11 Dose

IL-11 Conc.

X


Factor Y


IL-11 AF


IL-11 Dose

IL-11 Conc.

X


Factor Y

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

Na+ & Fluid

Retention FR



IL-11 AFIL-11 Dose

IL-11 Conc.

X

Factor Y

Na+ & Fluid

Retention FR


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)


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


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


)()( 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


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.


H

Iterations

H reaches

minimum value!

Parameter values of Y(t)

are: 9984.2

7496.0

8444.0

0375.0

21

X


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.

Modeling the Atrial Fibrillation Side Effects of Interleukin-11

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