BME 6716: Mathematical Modeling of Cellular Systems
Spring 2005
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INSTRUCTOR: Nikolaos
Tsoukias
OFFICE: EAS
2674 PHONE: 305 348-7291
Office
Hours
EMAIL:
Textbooks: Required
Mathematical Physiologyby; by Keener and Sneyd.
Recommended
Receptors; by Lauffenburger
and Linderman
Physiology, by
Introduction
to Matlab 6, by Etter, Kuncicky and
Engineer's
Guide to MATLAB, by Edward B. Magrab
Class Description:
Applied mathematics and numerical methods
for biomedical applications.
Computer modeling using Matlab and
other software packages commonly used in academics and industry for
experimental design, analysis and mathematical modeling. The objective
of this course is to provide the mathematical and computational foundation for
model development and analysis. Students will learn to apply mathematical
methods in modeling systems at the cellular level.
Course Objectives:
By the end of
this course, students should:
1.
Learn
to apply principles of engineering and physics to solve physiological problems.
2.
Learn
to develop and solve mathematical models.
3.
Learn
to develop code and apply computational algorithms.
4.
Learn
to use software packages such as Matlab, Femlab, LSODE.
5.
Learn
to research pertinent scientific literature
6.
Learn
to write concise but complete reports.
POINTS
DISTRIBUTION: HW Assignments 25%
Project 25%
Mid
Term Exam 25%
Final
Exam 25%
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Week Topic Reference
1 Introduction to
Mathematical Modeling, Reaction Kinetics Ch.1
Keener
2 Setting up Mass Balances, Non-Dimensionilization
3 Matrix Algebra and
solution of systems of ODEs, Stability analysis
4-5 ODEs, PDEs (Similarity
transformation, separation of variables)
6-7 Numerical
Methods (Optimization, Finite difference)
8 Mid
Term Exam
9 Membrane potential, control
of cell volume Ch.2 Keener
10 Ion channels, Hodgkin-Huxley
model Ch.3-4
Keener
11 Calcium Dynamics Ch.5,12 Keener
12 Pancreatic b-cell and
bursting activity Ch. 6 Keener
13 cable equation Ch. 8 Keener
14 Receptor-ligand
binding Ch. 2 Lauffenburger
15 Signal Transduction Ch.
5 Lauffenburger
15 Final Exam
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Grading Scale
95-100 A
90-94.9 A-
86-89.9 B+
82-85.9 B
78-81.9 B-
74-77.9 C+
70-73.9 C
66-69.9 C-
60-65.9 D