l33b physiological modelling

8/2/2019 L33b Physiological Modelling

1/23

PHYSIOLOGICAL

MODELING


2/23

INTRODUCTION

Physiological model is a mathematical

representation that approximates the behavior of

an actual physiological system.

Physiological systems are generally dynamic and

characterize by differential equations.


3/23

GOALS

Generation of new knowledge

Prediction of observation before they occur

Assistance in designing new experiments


4/23

STEPS

OF

MODELING

Conjecture

Initial

Hypothesis

Obtain Data

Test Hypothesis

State Solution

Has

Objective

Been

reached

ModifyHypothesis

No

Yes


5/23

TYPES OF MODELS

Deterministic Model

Stochastic Model


6/23

DETERMINISTIC MODEL

It has exact solution that relates the independent

variables of the model to each other and to the

dependent variable.

For a given set of initial conditions a

deterministic model yields the same solution each

and every time.

All deterministic model includes a measurement

error which introduces a probabilistic element.


7/23

STOCHASTIC MODEL

Stochastic Model involves random variables that

are functions of time and include probabilistic

considerations.

For a given set of initial conditions Stochastic

Model yields a different solution each and every

time.

Stochastic Model are generally preferred over

deterministic models.


8/23

TYPES OF SOLUTIONS

Closed form Solution: Models that can be

solved by analytic technique such as solving a

differential equation

Numerical/simulation Solution: Models that

have no closed form solution such as

approximation of an integral by trapezoidal

method or solving non linear differential

equations


9/23

COMPARTMENTAL MODEL

Bodily systems are characterized by transfer ofsolute from one compartment to other.

It is possible to describe the system as a series of

compartment for eg. respiratory and circulatorysystems.

Variable of compartmental analysis: quantity

and concentration of solute, temp. , pressure etc.

Model predicts concentration/quantity in eachcompartment as a function of time.


10/23

BASICS OF COMPARTMENTAL MODEL

Describe system with finite number of

compartments each connected with a flow of

solute from one to another.

Solute can be exogenous, (such as drug

,radioactive tracer) or endogenous (such as

glucose, an enzyme, hormone, oxygen, CO2).

Compartmental model can be linear, non-linear,

continuous, discrete, and can have time varying

or stochastic parameters.


11/23

ASSUMPTIONS

Volume of each compartment remains constant

throughout the time.

Any solute q entering a compartment isinstantaneous mixed throughout the entire

compartment.

Rate of loss of a solute from a compartment isproportional to amount of solute in the

compartment times the transfer rate.


12/23

TRANSFER OF SUBSTANCE BETWEEN TWO

COMPARTMENTS SEPARATED BY A THIN

MEMBRANE

Flick law of diffusion

q: quantity of solute

A: membrane surface areac: concentration

D: diffusion coefficient

dx: membrane thickness


13/23

CONT

V

q

c

x

Here, q can be quantity ofIodine, and K1 and K2 are

transfer rates.

Here input = 0

Output = K1q + K2q

Rate of change of Iodine q

From conservation of mass:

q1+q2=Q

V1c1+V2c2=VCBy solving this equation we get:

K1K2


14/23

MULTICOMPARTMENTAL MODEL

Real models of body involve many more

compartments such as cell volume interstitial

volume and plasma volume etc. and each of these

volumes can be further compartmentalized.

Method describe before can be applied to model

each compartment.


15/23

CONT

V1

q1

c1

V2

q2

c2

x

Rate of change of solute incompartment one is given by:

From conservation of mass:

q1+q2=Q

V1c1+V2c2=VC

By solving these equations we

get:


16/23

INFECTIOUS DISEASE MODELS

Model the progress of an epidemic in a large

population, comprising many different individuals in

various fields

In 1760, D. Bernoulli studied the population

dynamics of smallpox with mathematical modeling.

Kermack-McKendrick Model (continuous)

Reed Frost Model (discrete)


17/23

STEPS

Theories regarding how patterns of disease are

generated in populations.

Observations relevant to those theories.

Methods that link theory and observation.


18/23

APPLICATIONS

Determining of cause or etiology of a disease

Controlling the spread of a disease

Prediction and Prevention of a disease in an area


19/23

SIR MODEL


20/23

MUSCLE MODELING


21/23

BIO ELECTRICAL MODELING

Modeling of action potentials and their

propagation

e. g. HodgkinHuxley model, FitzHugh-Nagumo

model, Morris Lecar Model, Hindmarse Rose

Model to model action potentian in neurons


22/23

REFERENCE

Introduction to biomedical Engineering by John

Enderle, Susan Blanchard, Joseph Bronzino


23/23

Thank you

Queries ????

l33b physiological modelling

Documents