F. Kappel¹, T. Kenner², D. Schneditz², M. Moser², J. Batzel¹,
R. Pilgram², D. Auerbach², M. Bachar¹, M. Fink¹

1Department of Mathematics

This course will examine some important concepts and systems in human physiology both from the perspective of the physiologist and the mathematician. As an end result of this seminar it is hoped that both the physiologist's and the mathematician's perspective will complement each other and advance joint knowledge.

A number of physiological systems in the human body act to stabilize critical quantities or state variables such as systemic blood pressure. In general, the mechanism involves a negative feedback loop which depends on a sensory system which provides information to a controller which acts to maintain a stable level of this quantity. Furthermore, many physiologists believe that physiological control systems often act to optimize the efficiency and to minimize variations in the system in an effort to conserve energy or to minimize deviations from steady state values of critical quantities. For these reasons optimal control theory can be used to study physiological systems.

The inspiration for the course stems from a joint Physiology and Mathematics working seminar within the Cardiovascular respiratory Control Group of the Special Research Center for Optimization and Control at the University of Graz (Spezialforschungsbereich F-003) sponsored by the Austrian Science Fund).

This working group is preparing an international workshop on "Cardiovascular and Respiratory Control Modeling" which will be held from June 14-16, 2001 in Graz. The web page for this workshop can be found from the KFUG Mathematics web page or at:

http://bedvgm.kfunigraz.ac.at:8001/jerry/conference.html

A major fraction of food is used to generate the energy to carry out our current activities utilizing enzymes to break down and to synthesize major fuel substrates such as carbohydrates and fats. The fate of glucose, one of the most important fuel substrates, is controlled by the hormone insulin. Failure of glucose and insulin control frequently occurs with western lifestyle leading to diabetes mellitus and subsequent multiple tissue damage. Analysis of actions and physiologic control mechanisms required to substitute for lost function will be provided in this lecture.

Energy-production and -storage

Information-storage and —transmission

The genome

Genotype and phenotype

An attempt to define "life"

The minimum size of a living system

Scaling

The meanings of the term "receptor"

Description of the term "enzyme"

Mathematical description of enzymatic reactions

Some specific properties of living systems

Spontaneous activity

noise

Reactions to input (stimuli)

Threshold

"all or none"

stimulus-response relation

adaptation

asymmetry

unidirectional rate sensitivity

Nonlinearity of living systems

The question of linearization

Simple and complex models (viewpoint of a physiologist)

Description of cells and cell-functions, cell systems - examples

Blood pressure is one of the most important driving forces to transport nutrients and metabolites across the body and to the cells which are bathed in the extracellular fluid. The control of blood pressure and extracellular fluid volume is related. This lecture will provide an introduction to short term, mid term, and long term control of blood pressure and volume homeostasis and discuss the classic Guyton/Coleman model.

Matter, heat, energy and momentum are constantly transported through the body, each in their own peculiar way. Their motion serves the most varied purposes: thought, emotion, tonus and mobility, heating, growth, metabolism, transparency, reproduction, to mention but a few. So many variable quantities are involved, and investigating how various quantities scale (vary by being multiplied with a factor) with one another - based on a simple analysis of the dimensions involved - helps in both understanding and modeling these processes.

Exercise requires a large flow of oxygen from the atmosphere to the mitochondria in the working muscle by a multi-step process. The transfer via the lung and the cardiovascular system has distinct physical barriers each of them posing a limitation to optimum oxygen transfer under certain circumstances. The basics of oxygen transport and metabolism and the control of oxygen uptake and its limitations at exercise will be analyzed.