BME 580.223 Models and Simulation Part 2
Introduction to Nonlinear Dynamical Systems Modeling
Raimond L. Winslow Department of Biomedical Engineering The Johns Hopkins University School of Medicine
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Table of
Biological Models & Simulations Quiz #1
NAME:
EN580.223 BIOLOGICAL MODELS AND SIMULATIONS
The Johns Hopkins University
February 17, 2010
Name (print; also put your name on top-right of every page):
Number of pages, including the face page:
Use pen
(30 min
Biological Models & Simulations Quiz #1
EN580.223 BIOLOGICAL MODELS AND SIMULAnONS
The Johns Hopkins University
February 18, 2009
Name (print; also put your name on top-right of every page):
Number of pages, including the face page:
Use pen
QUIZ #1
Closed
Biological Models & Simulations Exam #1
EN580.223 BIOLOGICAL MODELS AND SIMULATIONS
The Johns Hopkins University
February 23, 2009
Name (print; also put your name on top-right of every page):
Number of pages, including the face page:
Use pen only. Closed
Biological Models & Simulations Quiz #1
NAME:
EN580.223 BIOLOGICAL MODELS AND SIMULATIONS
The Johns Hopkins University
February 17,2010
Name (print; also put your name on top-right of every page):
Number of pages, including the face page:
Use pen
QUIZ #1
EN580.223 BIOLOGICAL MODELS AND SIMULATIONS
The Johns Hopkins University
Name (print; print your name on each page):
March 10, 2008
EN580.223, SPRING, 2008
Midterm Exam
Misterm Exam
Scores (to be filled in by graders)
Problem 1
/25
Problem 2
/25
Problem 3
Alex Mathews
Section 5
Lab #9
Part 1 - Snells Law
1. Describe the method for verifying Snells law.
The method we used for verifying Snells law was to align multiple pins in a cork board,
two on each side of an acrylic block. When the pins were lined up, t
Alex Mathews
Section 5
Lab #9
Part 1 - Snells Law
1. Describe the method for verifying Snells law.
The method we used for verifying Snells law was to align multiple pins in a cork board,
two on each side of an acrylic block. When the pins were lined up, t
We can see that as t
,B t
R
, G(t )
ke
R
ka
sustained release when R>0
Free Diffusion Spatial Concentration Distribution
At finite temperature molecules in a system move randomly colliding with each other (thermal
fluctuations). Brownian motion is a manif
Biological Oscillators
Membrane potential 10ms 10s
Cardiac Rhythms 1s
Smooth Muscle s hr
Calcium Oscillations s-min
Circadian Rhythm 24h
Electrical Oscillators
Capacitor and Inductor in series
(1) I = C dV/dt
(2) V = L dI/dt
Take the derivative of (1) =>
Receptor-Ligand interactions
Consider this simple geometric situation where cells are in a dish.
Solution is placed on top containing glucose, growth factors, and a ligand
What are the kinetics of binding?
1 Receptor, 1 Ligand is the simplest case
The num
Dimensional Analysis
For a special case of hydrodynamic resistor,
Where delta P = P1 P2
L is length of vessel
Q is volumetric flow rate
R is radius
And is dynamic viscosity
Since delta P is proportional to length of tube,
Delta P/L (i.e. pressure per unit
Receptors are macromolecules involved
in chemical signaling between and
within cells; they may be located on the
cell surface membrane or within the
cytoplasm.
QO2
jw
Molecules that bind to a receptor are
called ligands (eg, growth factors,
hormones, neur
580.223
Spring 2009
Pharmacokinetics
Pharmacokinetics is the study of processes that affect the drug distribution and rate of
change of drug concentrations within various regions of the body.
Pharmacodynamics is the study of the time course of the treatme
Lecture 9 & 10
2010.3.1, 2010.3.3
Diffusion Examples
Diffusion in a slab (flat muscle) with a first order reaction
2h
x
The differential equation for diffusion with a first order reaction and concentrati
580.223 Biological Models and Simulations
Spring 2008
Free Diffusion Concentration distribution in Space
At finite temperature molecules in a system move randomly colliding with each other
(thermal fluctuations). Brownian motion is a manifestation of this
580.223
Spring 2008
Pharmacokinetics
Pharmacokinetics is the study of processes that affect the drug distribution and rate of
change of drug concentrations within various regions of the body.
Pharmacodynamics is the study of the time course of the treatme
Lecture 4 Mechanical Oscillator
Fes =- k ( Ls - Lo )
F
[cfw_]
"units of"
=
kg m
kg
;[ k ] = 2
2
s
s
Figure 1: Mass on a compliant string.
Newtons 1st Law:
Lo is strings free length, Ls is the
At rest, net applied force is zero:
loaded length at steady sta
580.223 Biological Models and Simulations
Reading material for Lectures 2 and 3: Linear circuit theory and differential equations
(adapted from notes by Dr. Eric Young, BME)
These notes will review the basics of linear discrete-element modeling, which can
Lecture 8
2010.2.24
Compartmental Models and drug dynamics
Consider the case of a drug taken orally, the drug gets into the GI tract and then absorbed by the
epithelial cells lining the GI tract into the body.
Lecture notes
2/15/10
Dr. Popel
Models & Simulations
Poisieulles Law
Apply a force to drive fluid through the pipe.
The heart generates a force to pump blood through the body through pressure
differences.
Lecture 7
2010.2.22
;
vs. B; eliminate [L]
Skatchard Plot: from experimental data we can get values for
, and Ro.
Mass Balance Chemical Kinetics
Let us start with a description of a simple system
Inpu
Lecture 6
2010.02.17
Receptor/Ligand interactions
Consider this simple geometric situation where cells are in a dish.
Solution is placed on top containing glucose, growth factors, and a ligand
What are
Lecture 1. The Art of Mathematical Modeling
The course goals:
(1) To learn how to analyze a biological system or process for specific conditions and describe it
in mathematical terms, i.e. to formulate a mathematical model;
(2) Where possible, to derive a
580.223 Biological Models and Simulations
Spring 2009
Free Diffusion Concentration distribution in Space
At finite temperature molecules in a system move randomly colliding with each other
(thermal fluctuations). Brownian motion is a manifestation of this
Lecture notes
2/1/10
Dr. Popel
Models & Simulations
In this lecture we expand the analytical solution developed for stepwise voltage, by
considering cases where the constant coefficient assumption is relaxed.
Lecture notes
1/28/09
Class 2 Models & Simulations
Dr. Popel
In the next two lectures we will consider the analogy between
electrical circuits and mechanical systems.
Kirchhoffs Laws
KCL = Kirchhoffs Cu