DOI: 10.1051/jp2:1991168
J. Phys. II France 1 (1991) 273-278

Inspection of multidimensional phase spaces with an application to the dynamics of hormonal systems

U. Brosa¹, H.-M. Harms², K. Prank² and R.-D. Hesch<sup>2

1</sup>  FB Physik, Philipps-Universität Marburg and Brosa GmbH, Am Brücker Tor 4, D-3572 Amöneburg, Germany
²  Abteilung Klinische Endokrinologie im Zentrum Innere Medizin, Medizinische Hochschule Hannover, Konstanty-Gutschow-Straße 8, D-3000 Hannover 61, Germany

(Received 2 January 1991, accepted in final form 15 January 1991)

Abstract
We look directly into multidimensional phase spaces. This is useful if little is known about suitable observables and underlying laws. The dynamical system we examine is the human body, in particular the secretion of the parathyroid hormone (PTH). Time series of PTH concentrations are transformed to multidimensional data sets. From their representations in phase space we derive a suitable observable: the average lifetime of a PTH fluctuation. It provides a clear-cut discrimination between health and two metabolic bone diseases, viz. osteoporosis and hyperparathyroidism. The derivation is done step by step: First we consider multidimensional displays and observe that it is certain correlation function which plays an important role. Then a single number is taken from that correlation function, and a threshold value is suggested.

© Les Editions de Physique 1991