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Dynamical Disease: Identification, Temporal Aspects and Treatment Strategies for Human Illness Jacques Bélair University of Montreal

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Dynamical Disease: Identification, Temporal Aspects and Treatment Strategies for Human Illness Jacques Bélair University of Montreal Claremont Colleges Scholarship @ Claremont WM Keck Science Faculty Papers W.M. Keck Science Department 3-1-1995 Dynamical Disease: Identification, Temporal Aspects and Treatment Strategies for Human Illness Jacques Bélair University of Montreal Leon Glass McGill University Uwe an der Heiden Witten/Herdecke University John Milton Claremont McKenna College; Pitzer College; Scripps College Recommended Citation Bélair, Jacques, Leon Glass, Uwe an der Heiden, and John Milton. "Dynamical Disease: Identification, Temporal Aspects and Treatment Strategies of Human Illness." Chaos 5.1 (1995): 1-7. DOI: 10.1063/1.166069 This Article is brought to you for free and open access by the W.M. Keck Science Department at Scholarship @ Claremont. It has been accepted for inclusion in WM Keck Science Faculty Papers by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Dynamical disease: Identification, temporal aspects and treatment strategies of human illness Jacques Belair Centrefor Nonlinear Dynamics in Physiology and Medicine, McGill University; J6,55 Drummond Street, Montreal, Quebec H3G lY6, Canada; and Departement de Moshematiques et de Statistique, Centre de Recherches Mathematique, Universiie de Montreal, Montreal, Quebec H3C 3J7, Canada Leon Glass Centre for Nonlinear Dynamics in Physiology and Medici~e, McGill University, 3655 Drummond Street, Montreal, Quebec H$G 1Y6, Canada; and Department of Physiology, McGill University, 3655 DrummondStreet, Montreal, Quebec H3G 1Y6, Canada Uwe an der Heiden Departm~nt ofMathematics, University of Witten/Herdecke, StockumerStrasse 10, D 5810 WZ'tten, Germany John Milton Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, 3655 DrummondStreet, Montreal, Quebec H3G lY6, Canada: -and Department of Neurology and Committee. on Neurobiology, The University of Chicago Hospitals, 5841 South Maryland Avenue, Room B 206, Chicago, Illinois 60637 (Received 14 December 1994; accepted for publication 14 December 1994) 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. Linearandnonlinear 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. © 1995 American Institute ofPhysics. 4 I. INTRODUCTION Mackey and Glass.3• Dynamical diseases arise because of abnormalities in the underlying physiological control mecha­ Physicians have long recognized the importance of con­ nisms. The hallmark of a dynamical disease is a sudden, sidering the temporal dimension of illness for arriving at a qualitative change in the temporal pattern of physiological diagnosis and deriving treatment strategies. Diseases can be distinguished by their onset (acute versus sub-acute) and by variables. Such changes are often associated with changes in their subsequent clinical course (self-limiting, relapsing­ physiological parameters or anatomical structures. The sig­ remitting, cyclic, chronic progressive). Recognition of the nificance of identifying a dynamical disease is that it should temporal rhythms, combined with the knowledge that certain be possible to develop therapeutic strategies based on our temporal rhythms respond best to certain treatment strate­ understanding of dynamics combined with manipulation of gies, often provides a basis for therapy. the physiological parameters back. into normal ranges. The recentanddramatic advancesin molecular medicine Progress in this direction requires the careful documentation have shifted the attention of the medical community away of the temporal aspects of disease combined with suitable from considerations of temporal phenomena. At the current theoretical analyses. Several books, conferences and reviews S 1O time, a strong impetus for studying disease dynamics is com­ have focused on nonlinear dynamics and human disease - ing from the mathematics and physics communities. Ad­ A workshop held in Mont Tremblant, Quebec, Canada, vances in our· understanding about the nature of oscillatory February 1994 provided an opportunity to review recent ad­ phenomena in the discipline of nonlinear dynamics offer the vances in the study of dynamical disease. The meeting at­ possibility of applying this new knowledge to gain insights tracted a multidisciplinary audience of physicians, physiolo­ into the etiology and treatment of diseases. The mathematical gists, mathematicians, and physicists. Topics included the methods for understanding the origin, stability, and bifurca­ identification of dynamical diseases, methods for analyzing tions of dynamical behavior in nonlinear equations appear to the temporal aspects of diseases, onset and offset of rhythms, be ideally suited for the analysis of complex rhythms con­ mechanisms of oscillatory phenomena, and the design of fronted by the physician on a daily basis. treatment strategies. In this article we provide an overview of Although the origins for the application of nonlinear dy­ our current understanding of dynamical disease. Although namics to the study of human disease can be traced back to we emphasize material covered at the workshop, we also the analyses of certain cardiac arrhythmias in the 1920s,I.2 mention other work in order to provide a more balanced the concept of a dynamical disease was first proposed by overview of the field. CHAOS 5 (1),1995 1054-1500/95/5(1)/1/7/$6.00 © 1995 American Institute of Physics 1 Downloaded 30 Oct 2008 to 134.173.131 .214. Redistribution subject to AI P license or copyright; see http://chaos.aip.org/chaos/copyright.jsp 2 Belair et st: Dynamical disease II. DYNAMICAL DISEASES mortality andlor morbidity for which there is an adequate therapy. Collection of long time series often involves incon­ . In a typical medic al clinic, a significant proportion of venience and extra cost, and may be of little immediate ben­ patients present abnormalities in the dynamics of a physi­ efit to the patient based on current knowledge. Studies of ological process. Easily identified arrhythm ias are well dynamical disease are notable for the variety of lime series known in cardiology, respirology, and neurology. Arrhyth­ assembled, for the ingenuity of methodology used 10 collect mias may be significant causes of patient mortality, as in them, and the wide range of different methods that are being cardiac arrest. Symptoms which recur frequ enlly, such ob­ as developed to analyze them. structive sleep apnea or epileptic seizures, are important The techniques used to collect data include a variety of causes of patient morbidity. noninvas ive and inva sive techniques. Information about dy­ One obstacle confronted by non-physicians studying dy­ namical disease is deri ved from the following sources: n ~mi c a i disease is that they have litlle idea of the extraordi­ (1) Noninvasive methods . nary range of dynamics that can be found in the hunian body. patient diaries ;II The papers in this volume prov ide a glimpse into what is • mechanical displacements of respiratory going on. In an attem pt to docume nt dynamical disease in the structures; 12 nervous syste m, Milton and Black " carried out a literature • air flow velocities and concentrations of oxygen and survey that identified at least 32 diseases with interesting carbon dioxide in expired gases:" time courses in Which . symptoms andlor signs recur. Al­ motion of extremities using lasers and though many of these disorders are relatively commo n, for accelerometers; 13.14.22.23 example. see the discussions in this volume of hiccupS.1 2 • electromyographic (EMG) activity associated with Parkiasonism.P tardive dyskinesia.l" respiratory arrest,IS muscle;12.15,23 there are also many obscure disorders. For example, Milton • sound waves generated by the voice;24 and Black" identify 8 different disorders associated with changes in pressure on a pressure plate associated control of eye position and pupillary size. Even though the with changes in posture;2S. abnormal dynamics in these disorders are easy to observe magnetic fields from the brain;26 and can be recorded noninvasively, there has been little • blood pressure and electrical activity associated analysis to date of the rhythms from the perspective of basic with the heart beat.~7-3 o science and mathematics. (2) Invasive measurements One area in which dynamical aspects are significant, but • concentration of hormones in the blood; 17-19 still are not well understood is endocrinology. The mamma­ core body tempe rarurer" lian ovulation cycle is perhaps the most carefully studied, but • concentration of blood cells in the blood;>f there is still scant theoretical analy sis." Moreover, it is be­ intracardiac electrical activity, blood pressure and coming clear that, in general. hormone secretion displays wall motion?' complex pulsatile secretion pattern s. Since hormones are ac­ tive in such small quantities. and assays are expensive, sys­ The lime scales of measurements
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