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“Dynamical” Vs. “Genetic” Disease:
What Do Complex Rhythms Reveal About Pathophysiology?
Leon GlassIsadore Rosenfeld Chair in Cardiology
McGill University, MontrealQuebec, Canada
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Genetic Disease (40,000 hits)
• Garrod (1908) – Inborn errors of metabolism show Mendelian inheritance
• Pauling et al. (1949) – Sickle cell anemia: a molecular disease
• Ingram (1956) – Chemical difference between normal human and sickle cell anemia hemoglobin
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Genetic Disease: Implications for Research • Identify abnormalities• Map abnormalities • Determine genome (human
genome project)• Develop therapies
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Genetic Disease: Implications for therapy
• Prevention• Environmental modifications
(restrict toxic agents, replace deficient products or organs, remove toxic substances or organs)
• Gene therapy (increase or decrease expression of genes)
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Genetic Disease: Limitations of Concept
• Disease arises from interactions between genetics and environment
• Complex polygenic diseases are common and still not well understood
• Gene therapy is of limited utility so far• People still get sick and must be
treated• Disorders are often dynamic (even
genetic ones)
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Dynamical Disease (166 hits)
• Reimann (1963) – Periodic diseases
• Mackey and Glass (1977) – Dynamical diseases associated with qualitative changes in dynamics in physiological systems
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Reimann (1963)
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Mackey and Glass (1977)
rate of change = production – destruction
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Dynamical Disease: Implications for Research• Collect data from complex rhythms
over long times (http://www.physionet.org)
• Develop mathematical models and study effects of parameter changes
• Develop biological models that display complex rhythms
• Develop therapies
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Complex rhythms are ubiquitous in physiological systems
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Dynamical Disease: Implications for Research• Collect data from complex rhythms
over long times (http://www.physionet.org)
• Develop mathematical models and study effects of parameter changes
• Develop biological models that display complex rhythms
• Develop therapies
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Pure Parasystole
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Rules of Pure ParasystoleCount the number of sinus beats between ectopic beats. In this sequence: (1) there are 3 integers; (2) one is odd;(3) the sum of the two smaller is one less than the largest.
Glass, Goldberger, Belair (1986)
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Modulated ParasystoleSinus beats reset the ectopic focus (Jalife and Moe, 1976)
Courtemanche, Glass, Rosengarten, Goldberger (1989)
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Modulated Parasystole with Noise
Schulte-Frohlinde et al. (2001)
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Parasystole: Conclusions
• Interesting mathematics and physics (number theory, stochastic nonlinear
difference equations) explain arrhythmia
• Limited significance for medicine to date
• Potential significance – classification of complex arrhythmia
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Cardiac arrhythmias suddenly start and stop
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Mechanisms of Tachycardia
1. Reentry in a ring
2. Reentry in two dimensions
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G. R. Mines (1913)
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Dynamical Disease: Implications for Research• Collect data from complex rhythms
over long times (http://www.physionet.org)
• Develop mathematical models and study effects of parameter changes
• Develop biological models that display complex rhythms
• Develop therapies
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Macroscope for Studying Dynamics in Tissue Culture
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Calcium Spiral (Calcium Green)
Voltage Spiral(di-4-ANEPPS)
Calcium Target (Calcium Green)
Pacemakers and Reentry in Tissue Culture
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Bub, Glass, Publicover, Shrier, PNAS (1998)
Bursting Rhythms in Tissue Culture
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Anatomy of a burst
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Cellular Automata Model of a Burst
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Pacemaker
Nagai, Gonzalez, Shrier, Glass, PRL (2000)
Dynamics in a Ring of Cardiac Cells
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Reentry
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Cardiac ballet
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FitzHugh-Nagumo Model of Propagation
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Heptanol:
Heptanol slows propagation and leads to spiral breakup (may be similar to transition fromventricular tachycardia to ventricular fibrillation)
Bub, Shrier, Glass, PRL (2002)
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Simulation of heptanol addition
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Dynamical Disease: Implications for Therapy• Analyze complex rhythms for diagnosis
and prognosis• Develop novel methods for control
based on dynamics of physiological system
• Add noise to improve perception or to perturb dynamics
• Adjust parameters (e.g. by giving drugs) to normal range
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T-wave alternans
Rosenbaum et al. (1994)
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T-wave Alternans Predicts Arrhythmia
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Point D2 Dimension
Skinner, Pratt, Vybiral (1993)
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Normal Atrial fibrillation
http://www.aboutatrialfibrillation.com
S.A. node
Ventricle
A.V. node
Atrium
P
R
TR
Can you detect atrial fibrillation based on the RR intervals?
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National Resource for Complex Physiologic Signals A. Goldberger, Director
http://www.physionet.org
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Identification of Atrial Fibrillation
Tateno and Glass (2001)
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Histogram of ΔRR Intervals during AF
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Kolmogorov-Smirnov Test
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KS Test Can Be Used to Identify AF
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Applications of Dynamics for Diagnosis and
Prognosis • Many potential applications –
cardiac arrhythmias, epilepsy, tremor, blood diseases
• Need for independent tests of algorithms by those with no stake in utility
• Data sets of rare time series will be indispensable
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Dynamical Disease: Implications for Therapy• Analyze complex rhythms for diagnosis
and prognosis• Develop novel methods for control
based on dynamics of physiological system
• Add noise to improve perception or to perturb dynamics
• Adjust parameters (e.g. by giving drugs) to normal range
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Control of Cardiac Chaos
I n
Garfinkel, Spano, Ditto, Weiss (1992)
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Identify the Unstable Fixed Point
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Stimulate to Control Rhythm
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Controlling Cardiac Alternans
Hall, Christini, et al. (1997)
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Target Unstable Fixed Point
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Stimulate to Control Alternans
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Deep Brain Stimulation Controls Parkinsonian
Tremor
Benabid (1991)
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Deep Brain Stimulation Induces Bifurcations in Dynamics
Titcombe, Glass, Guehl, Beuter (2001)
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Boundaries for Stimulation Effectiveness
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Dynamical Disease: Implications for Therapy• Analyze complex rhythms for diagnosis
and prognosis• Develop novel methods for control
based on dynamics of physiological system
• Add noise to improve perception or to perturb dynamics
• Adjust parameters (e.g. by giving drugs) to normal range
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Add noise to improve perception or to perturb dynamics
• Collins et al. – Stimulate feet to improve balance, ventilate with variable volumes
• Paydarfar et al. – Vibrate mattress to suppress apnea in infants
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Overview
• Both in medicine and mathematics there is strong emphasis on qualitative features of dynamics
• Mathematical models often capture critical features of clinical dynamics
• Dynamics gives insight into mechanisms • New strategies for diagnosis, prognosis,
and therapy are being developed by scientists working together with physicians.