Dynamical disease: Identification, temporal aspects and treatment strategies of human illness

Abstract

Dynamical diseases are characterized .by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Quebec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspectiveof nonlinear dynamics. Linearand nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques.

Nonlinear Analysis of Surface Electromyography

“…The timedependent entropy from the surface EMG signal and the entropy of the signal is lower for subjects with LBP than for healthy subjects. Furthermore, the entropy increases rapidly for short times [t < 10 ms], reaches a plateau value for intermediate times [10ms < t < 500 ms], and then increases diffusely for long times [approximately 500 ms] (Belair et al, 1995a). This behavior suggests that the plateau value is relevant for the physiology of skeletal muscles (Chialvo, 2002;Goldberger et al, 2002a).…”

Grand Challenges in Computational Physiology and Medicine

“…This is the only way in which integrative (often referred to as multi-scale) models that provide deep insights into physiological function will ever be developed. Finally, models of disease, which will likely take the form of normal physiological systems models operating in a different parameter regime (Belair et al, 1995; Huang et al, 2009), must not only be reconstructive and predictive, they must guide the way to improved therapies.…”

Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems

“…Consider a periodic solution of (3) e(t) and its 2qth-order approximation e(t) ê + < 2q k=0 E k exp (ik!t) (6) where <f1g denotes the real part of a complex function (or number), i = p 01;! is the fundamental frequency of the periodic solution, and E k is a complex number in the kth harmonic of the expansion, which satisfies…”

“…In order to carry out qualitative analysis, it is preferable to have simple models that possess such complicated, but typical features. For instance, it has been suggested [1], [2] to use simple electronic circuits as basic prototypes for biological systems suffering the socalled dynamical disease [3]- [6] or to use simple mechanical systems [7] to characterize some biological and engineering processes. A notable distinctive characteristic of such systems is the existence of time delays in the system models, typically in a feedback form.…”