Dynamical Diseases

Abstract

Many phenomena in physiology and clinical medicine recur at regular, or almost regular, intervals. In 1963, Reimann' drew attention to a diverse group of diseases in which symptoms recurred at seven-day intervals, or integer multiples thereof, which he collectively referred to as periodic diseases. In all of these diseases, oscillations appeared in physiological systems not normally characterized by oscillations. Although in most of his patients these were regular oscillations, he noted that in some patients symptoms recurred in a more irregular manner. It is more common to observe oscillations in physiological control systems that occur on a more rapid time scale, that is, milliseconds to hours. Moreover, abnormalities in many of these physiological rhythms are of major clinical importance. For example, an abnormality in the cardiac rhythm, ventricular fibrillation, is a common life-threatening medical emergency. In addition to their clinical importance, observations of these oscillations demonstrate that there is a rich variety of dynamics that many physiological control systems can exhibit, ranging from rhythms with differing periodicities to irregular "noise-like" phenomena. As an extension of the concept of periodic diseases, the concept of a dynamical disease has been introduced." A dynamical disease is defined as a disease that occurs in an intact physiological control system operating in a range of control parameters that leads to abnormal dynamics. The signature of a dynamical disease is a change in the qualitative dynamics of some observable nature as one or more parameters are changed. These changes in dynamics would correspond mathematically to bifurcations in the relevant nonlinear equations describing the physiological system. This paper reviews the applicability of the concept of dynamical disease as it has developed over the past few years.