Computer Models of Physiological Processes

Recommended Prerequisites

Basic knowledge and competences of Physiology, Linear Algebra, Analytical Geometry, Mathematics and Computers and Matlab Programming.

Teaching Methods

The course syllabus is taught in 24 h of theoretical lecturers, 36 h of laboratory practice and 10h of seminars. At lectures, the subjects are taught in an expository manner. At laboratory classes, students will perform computer simulations of lectures’ subjects and develop physiological models of the case studies (per group). At seminars, each group will present, and discuss, their work on the physiological process addressed. Every group must arrive at the equations and execute the computational simulations.
The teaching team is always available to answer questions.

Learning Outcomes

The Biomedical Sciences are increasingly using mathematical models able to assist the interpretation of physiological data.
The Biomedical Engineer of the future must understand a biological function from the point of view of engineering and interprets it in physiological terms. Along the learning process, each student will acquire knowledge and use appropriate tools for each of the proposed tasks.
The objectives of this course in terms of attitudes, abilities and skills are developing the attitude of autonomous methodical research, analysis and synthesis, acquire computer skills, autonomously manage information and solve problems, acquire the ability to work in an interdisciplinary team, communicate and apply knowledge to the profession.
As objectives of knowledge: know and manipulate computer programs, know the mathematical concepts relating to systems theory as well as to know the physiological processes that underlie the function under study.

Work Placement(s)

No

Syllabus

1. Systems theory and physiological models
The interest of the models in the study of flows of matter, energy and information in biological systems.  General systems theory. Analogue systems, transfer functions and state space. Nonlinear and chaotic systems. Computational implementations and simulations.

2. Mass transport across membranes
Functional models of the membrane. The diffusion of solutes and water transport. Nernst-Plank and Goldman equations. Donnan membrane model.

3. Electric potential to the surface
Electric dipoles. Potential created by an electric dipole at an outside point. Electrically charged membranes.
Double electric layer and the potential created at an outside point P. Potential created by fibers during the depolarization. Fictitious dipole. Surface potentials. Electrocardiogram.

Head Lecturer(s)

Maria Filomena Rabaça Roque Botelho

Assessment Methods

Assessment
Continuous assessment: 100.0%

Bibliography

Modeling and Simulation in Medicine and the Life Sciences. Hoppensteadt, Peskin, Springer, 2000
Physiological Control Systems: Analysis, Simulation, and Estimation. Khoo, Wiley&Sons, 2000
Biomedical Signal Processing and Signal Modelling. Bruce, Wiley&Sons, 2001
Systems and Signals, Chen, 3rd Ed, Oxford University Press, 2004
System Theory and Practical Applications of Biomedical Signals. Baura, Wiley&Sons, 2002
Dynamical Systems. Franklin, Powell & Niemi, Addison-Wesley, 1980
Biofísica Médica. Pedroso de Lima. Universidade de Coimbra, 3rd Ed, 2014
Intermediate Physics for Medicine and Biology (Biolog & Med Physics, Biomed Eng). Hobbie, Roth, Springer, 2007
Mathematical Techniques for Biology and Medicine, Simon, Dover Publications 1977
Mathematical Physiology, Keener, Sneyd, Springer 1998
Mathematical Biology, Murray, Springer, 2001
Mathematical Modelling in Medicine, Ottesen, Danielson (Eds), IOS Press, 2000
Medical Applications of Computer Modelling, Martonen (Ed), WIT Press, 2001.