BMED3510
Types of Models
Book Chapters 1 and 2
Recall:GenericApproachofCSB
www.alternativecancer.net/
science.nationalgeographic.com
dX 12
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f
f
f 51
f
f
0 ,12 X 24 ,12 , 24 X 300 ,12 , 30 51 ,12 X 1251 ,12 ,12 X 28 ,12 , 28 X 5151 ,12 ,51 X 5251 ,12 ,52
BMED3510
Parameter Estimation
Book Chapter 5
RecapModelDevelopment
Define the problem:
processes
variables
Construct a network diagram
birth, infection, recover,
S, I, R

vBirth
vInfection
S
vDeath
I
vImmunity
vSusceptibility
Convert the scheme into mat
BMED3510
Discrete, Recursive Models
Book Chapter 4
ClassificationofDynamicModels
Deterministic
Stochastic
Continuous
ODEs
Stochastic
Diff. Eqs.
Discrete
Recursive models
SPs
2
Example:GrowthbyCellDivision
(InitialPhase)
Typically modeled as ODE:
dX
X a X
BMED3510
Analysis of Dynamic Models
Book Chapter 4
RecapModelDevelopment
Define the problem:
processes
variables
Construct a network diagram
birth, infection, recover,
S, I, R

vBirth
vInfection
S
vDeath
I
vImmunity
vSusceptibility
Convert the scheme in
Exam 1 BMED 3510 Name:
September 25, 2014 Signature:
Please use back sides if needed
1. Use the following matrices for the following problems (8 points)
3 0 . .
i 1 4 0
.4: ~12 .13: . . ; gawk.
, . 5 0 ~12 4 PM
i l
(i) Compute AB or state that it is not d
Qo [W304 Wide.
Signature:
BMED 3520
June 10, 2015
Quiz 2
This quiz is a closed book, ciosed notes exam. You can use a calculator. Feel free to
write on the back of these pages if you need more space just make sure to indicate
which problem your work is fo
An Introduction to
Copyright: Antnio E.N. Ferreira 20012012
Eberhard O. Voit
Georgia Tech
http:/enzymology.fc.ul.pt/software
Download PLAS and Create Shortcut
Start by clicking
Shortcut button to PLAS
Solve
Cut
Open File
Copy
Steady State
Paste
Save File
BMED3510
Book Chapters 3
Static Network Models
Dynamic vs. Static
Dynamic model

We can simulate its behavior and dynamics
We can evaluate it at any time point
S 3 0.01R 0.0005 S I
S 0 990
I 0.0005 S I 0.05 I 0.02 I I 0 10
R0 0
R 0.05 I 0.01 R
Why static
SIR_Model / Name: SIR_Model
SIR_HW3_Problem3 / Name of the file

Definition of differential equations  MANDATORY
x' = y  2 x^p / for p = 0, a powerlawed sine function
y' = 2 x^p  x / for p = 0, a powerlawed cosine function

Initial values, one per
Projects
1. Metabolic Pathways
The pathways below are quite similar. Nevertheless, they differ with respect to the reversibility
of two reactions. The objective of the project is to learn to make predictions regarding system
responses and checking them wi
BMED 3520 Biomedical Systems and Modeling
Credit: 233
Prerequisites: BMED 3100, BMED 2210, MATH 2403
Instructors:
Barbara McCord (Section A)
Peng Qiu (Section B)
Paul Benkeser (Section C)
Overview:
Aug 17: First day of classes
Sept 7: Labor Day
Oct 101
BMED 3520
Biomedical Systems and Modeling
Mo: Clough144
Tu/Th: MS&E G011 (A)
ES&T L1125 (B)
ES&T L1105 (C)
BMED 3520: Cast of Characters
Dr. Barbara McCord
Erik Reinertsen
Dr. Peng Qiu
Meredith Fay
Dr. Paul Benkeser
?
Mac Merritt
2
BMED 3520: Purpose
Biom
Review: Linear Algebra
Material Taken from: KREYSZIGs Advanced Engineering Mathematics, 9th edition
BMED3520B: Biomedical Systems & Modeling
August 17th, 2015
Topics to Review for BMED3520
Vectors & Matrices addition, scalar multiplication, matrix
multip
BMED 3520
Mathematical Models
for
Biological Systems
Textbook Chapters 1 and 2
Recall: Generic Approach of CSB
www.alternativecancer.net/
dX 12
f0
f
f
f 51
f
f
0 ,12 X 24 ,12 , 24 X 300 ,12 , 30 51,12 X 1251 ,12 ,12 X 28 ,12 , 28 X 5151 ,12 ,51 X 5251 ,1
BMED 3520 (Summer 2015)
Below are examples of questions from previous exams:
1. Compute the Taylor series of exp(X), using X=0 as an operating point.
2. Define the range of values of X for which exp(ln(X) is defined.
3. Compute the Taylor series of sin(X)
Topics to be discussed in the week of Jan. 13
Theory
1. Components of a model (15mins)
Dependent, independent vars (conversion back and forth);
time is mathematically the indep. var.
Parameters (vs. independent vars)
Constants
Different fluxes (material,
Topics to be discussed in the week of March 31
Theory:
Review details of PhasePlane Analysis
What do the various arrows mean? Where do they come from? How general is this
representation? How do the steady states differ?
Projects:
1. Download file Pop1.pl
Topics to be discussed in the week of Feb. 17
Theory
Types of dynamic analysis
Types of static analysis
Practice
1. Load the system (Lin_Pathway.plc), describing the system below, from tsquare into PLAS.
Lin_Pathway
X1'
X2'
X3'
X4'
X1
X2
X3
X4
=
=
=
=
=
Topics to be discussed in the week of March 10
Theory
1. Two ways of looking at chemical reactions:
1.1. Thermodynamics
Main currency: energy
What is energetically feasible?
Coupling of energyconsuming and energygenerating reactions
Role of enzymes
1.2.
Topics to be discussed in the week of March 24
Theory:
1. What does signaling or signal transduction mean? List generic components, processes,
and features of a signal transduction process.
2. What is network inference?
3. What is bistability? Where does
Topics to be discussed in the week of Jan. 20
Theory
1. Steps of a typical analysis (Table 2.1; p. 23)
What is done in each step and why?
What does it take to introduce a new variable (e.g., asymptomatics)?
Goals,
Inputs,
and Initial
Exploration
Model
Sel
Topics to be discussed in the week of Feb. 10
Theory
Linearity: Example of ODE system (linear) for sine and cosine (nonlinear)
Halflife in exponential decay
Linearization: 1d and 2d
Jacobian
Powerlaw approximation (1d and 2d)
Variables must be posit
Topics to be discussed in the week of Feb. 24
Theory
Why is linear regression easy and nonlinear is not?
Types of parameter estimation algorithms
Advantages and limitations
Practice
Parameter estimation in Excel
1.
2.
3.
4.
5.
Import or type data into Exc
Topics to be discussed in the week of Jan. 27
Theory
Components of a network
Do networks permit regulation?
Directed and undirected graphs
Adjacency matrix: what does it convey?
Cluster coefficient: what does it convey?
Degree distribution
Smallworld net
TEST 1
To know (from slides):
Biomaterial: A material intended to interface with biological systems to evaluate, treat, augment or
replace any tissue, organ or function of the body
Biomaterials Science: Study of biomaterials and their interaction with the
To know (from slides):
Biomaterial: A material intended to interface with biological systems to evaluate, treat, augment or
replace any tissue, organ or function of the body
Biomaterials Science: Study of biomaterials and their interaction with the biolog
Example problems from previous exams in BMED 3510
Spring 2015
Exam 1
4. Discuss similarities and differences between an adjacency matrix and a stoichiometric matrix.
5.
(i) For the undirected graph below, compute the clustering coefficients for the three
BMED 3510
Types of Models
Book Chapters 1 and 2
Recall: Generic Approach of CSB
www.alternativecancer.net/
dX 12
f
f
f
f
f
f
0 ,12 X 240 ,12, 24 X 300 ,12, 30 51,12 X 1251,12,1 2 X 2851,1 2, 28 X 5151,12,51 X 5251,12,52
dt
science.nationalgeographic.com
BMED 3520
Analysis of Dynamic Models
Book Chapter 4
Recap Model Development
Identify the key players:
 Processes (i.e., flows, signals)
 Variables (stocks)
birth, infection, recover,
S, I, R

Construct a diagrammatical
representation of how these
pl