Physiological Modeling
This is an undergraduate-level course. Students from engineering, physics, mathematics, statistics, and biology are all welcome to attend, provided that the prerequisites are satisfied.
Description:
The course aims to show how physiological problems can be formulated mathematically, and how such models can be used for analysis, prediction, and therapy design. A wide selection of mathematical models in physiology will be presented from the cellular level up to the systems level, including respiration/perfusion, muscle contraction, inner ear, and retina. Differential equations, Laplace transform, and computer-aided tools will be introduced and used during the course for modeling, simulation, and analysis purposes.
Course Objectives and Outcomes:
The objective of this course is to learn the basic concepts and tools for modeling physiological systems using engineering analogies. In particular, it will be learned how physiological problems can be formulated and studied mathematically, and how such models can pose challenging mathematical questions, whose solution will help gaining insights into the modeled physiological processes.
Topics Covered:
Biochemical Reactions; Cellular Homeostasis; Membrane Ion Channels; Electrical Flow in Neurons; Heart and Blood Circulation; Respiration; Muscle Contraction; Retina and Vision; Differential Equations; Elements of Statistical Modeling; Numerical simulations in MATLAB
Prerequisite: MATH 1132Q; BIOL 1107
Required, Elective, or Selected Elective: Elective.
Lectures: 1 lecture per week (3 hours)
Grading: Homework: 30%; Midterm: 30%; Project: 40%
A syllabus can be found here.
Textbook:
[TB] James Keener & James Sneyd (2009) Mathematical Physiology. Second edition, vol. 1-2. ISBN: 978-0-387-09419-9
Other Recommended References:
[R1] Claudio Cobelli & Ewart Carson (2008) Introduction to Modeling in Physiology and Medicine. ISBN: 978-0-12-160240-6
[R2] John D. Enderle & Joseph D. Bronzino (2012) Introduction to Biomedical Engineering. ISBN: 978-012-374-979-6
[R3] Eugene M. Izhikevich (2011) Dynamical Systems in Neuroscience. ISBN: 978-026-251-420-0
Plan of Lectures and Assignments
| Lecture | Topic | References/Reading | Assignment |
| 1 | Introduction; Numerical Methods for ODE Integration; MATLAB ode solvers | Lecture Notes. R1: Ch. 2-3 | Homework 1 |
| 2 | Biochemical and Enzyme Reactions | Lecture Notes. TB: Ch. 1. R2: Ch. 8 | Homework 2 |
| 3 | Modified Enzyme Reactions; Hemoglobin | Lecture Notes. TB: Ch. 1, 13 | Homework 3 |
| 4 | Passive Transport in Cells | Lecture Notes. TB: Ch. 1 | Homework 4 |
| 5 | Nernst Potential and Ion Channels | Lecture Notes. TB: Ch. 1-3 | Homework 5 |
| 6 | Neural Excitability and Synapses | Lecture Notes. TB: Ch. 5, 8. R3: Ch. 2 | Homework 6 |
| 7 | MIDTERM EXAM | – | – |
| 8 | Microcirculation and Filtration | Lecture Notes. TB: Ch. 2, 11 | Homework 7 |
| 9 | Systemic Circulatory System | Lecture Notes. TB: Ch. 11 | Homework 8 |
| 10 | Alveolar Gas Exchange | Lecture Notes. TB: Ch. 14 | Homework 9 |
| 11 | Gastrointestinal Fluid Absorption | Lecture Notes. TB: Ch. 18 | Homework 10 |
| 12 | Force-Velocity Models of Muscles | Lecture Notes. TB: Ch. 15 | Homework 11 |
| 13 | Photoreceptors and Receptive Fields | Lecture Notes. TB: Ch. 19 | – |
| 14 | FINAL PROJECT DISCUSSION | – | – |