Methodology for the analysis of rhythms in non-linear systems (Extract)

Translation by Isobel Hié, Les Rythmes Lectures et théories, sous la direction de J.J. Wunenburger Centre culturel international de Cerisy, "Conversciences", p 31-56, L'Harmattan, ISBN 2-7384-1355-2 Copyright(c) L'Harmattan

I. INTRODUCTION TO THE STUDY OF RHYTHMS

Rhythmic or cyclical rhythm is one of the fundamental properties of rhythms which is why the study of biological rhythms has been arousing increasing interest over the last fifteen years. (1) (2)

These studies show a much narrower relationship between living systems and their surroundings than was formerly thought. Some observations lead to the belief that the exact time a therapeutic act is carried out on a living organism can have a bearing on its effectiveness. In fact, some studies have made the hypothesis that a surgical operation is more effective at certain times of the day and that it could be the same when administering medicines.(3)(4)

There is also an epistemological interest in knowing whether factors causing these cycles are endogenous or exogenous or yet again due to an interaction between the two. It is certain that if most biological systems have cycles, this is largely due to the succession of light and darkness. However, in the absence of light stimulation the question is when these rhythms continue, if it is a matter of endogenous rhythms learnt during evolution, for instance. Twenty-four hour rhythms are not the only biological rhythms detectable in living systems, there are also rhythms over a longer period (monthly, annual rhythms and those lasting a number of years) as well as shorter rhythms (rhythms lasting several hours, minutes or a second, etc.)

As a result, the study of the data from biological fluctuations can be the means of underlining the existence of an underlying rhythm. It might be of interest, for example, to take into account the periodic variability in the measures, like blood concentration in hormones, blood pressure in certain pathologies, the sensitivity of pharmacodynamic receptors to an active principal, the yield of a biological compartment for established enzymatic reactions.

Before tackling the necessary statistical processing for the detection of cycles in a system, it is essential to represent the system to be studied by means of a model: one that is explicative or one that is representative and predictive. As living systems are particularly complex and their responses to demands from their surroundings equally so, we will limit ourselves to structuring a representative model. In this representation we must consider two principal classes: linear and non-linear systems.

1. HALBERG F. (1963) Circadian (about 24 hours), Rhythms in experimental medicine. Proc. Royal Med. 253256

2. REINBERG A. (1966) L'homme et les rythmes circadiens, Cahiers Sandoz, 8, 1.50.

3. REINBERG A. and Sidi E. (1966) Circadian changes in the inhibitory effects of an antihistaminic drug-in man. I. Invest, Dermat. 46.115.

4. REINBERG A., HALBERG F., GHATA J. GERVAIS P., ALBULKEER C., DUPONT J., GAUDEAU C. (1970) Rythmes circadiens de diverses fonctions physiologique de l'homme, Association des physiologistes de Grenoble 1-3.