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“Dynamical” Vs. “Genetic” Disease:
What Do Complex Rhythms Reveal
About Pathophysiology?
Leon Glass
Isadore Rosenfeld Chair in Cardiology
McGill University, Montreal
Quebec, Canada
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
Genetic Disease:
Implications for Research
• Identify abnormalities
• Map abnormalities
• Determine genome (human genome
project)
• Develop therapies
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)
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)
Dynamical Disease (166 hits)
• Reimann (1963) – Periodic diseases
• Mackey and Glass (1977) – Dynamical
diseases associated with qualitative
changes in dynamics in physiological
systems
Reimann (1963)
Mackey and Glass (1977)
rate of change = production – destruction
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
Complex rhythms are ubiquitous in
physiological systems
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
Pure Parasystole
Rules of Pure Parasystole
Count 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)
Modulated Parasystole
Sinus beats reset the ectopic focus (Jalife and Moe, 1976)
Courtemanche, Glass, Rosengarten, Goldberger (1989)
Modulated Parasystole with Noise
Schulte-Frohlinde et al. (2001)
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
Cardiac arrhythmias suddenly start and stop
Mechanisms of Tachycardia
1. Reentry in a ring
2. Reentry in two dimensions
G. R. Mines (1913)
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
Macroscope for Studying Dynamics in Tissue Culture
Pacemakers and Reentry in Tissue Culture
Calcium Target
Calcium Spiral
Voltage Spiral
(Calcium Green)
(Calcium Green)
(di-4-ANEPPS)
Bursting Rhythms in Tissue Culture
Bub, Glass, Publicover, Shrier, PNAS (1998)
Anatomy of a burst
Cellular Automata Model of a Burst
Dynamics in a Ring of Cardiac Cells
Pacemaker
Nagai, Gonzalez, Shrier, Glass, PRL (2000)
Reentry
Cardiac ballet
FitzHugh-Nagumo Model of Propagation
Heptanol slows propagation and leads to
spiral breakup (may be similar to transition from
ventricular tachycardia to ventricular fibrillation)
Heptanol:
Bub, Shrier, Glass, PRL (2002)
Simulation of heptanol addition
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
T-wave alternans
Rosenbaum et al. (1994)
T-wave Alternans Predicts Arrhythmia
Point D2 Dimension
Skinner, Pratt, Vybiral (1993)
Can you detect atrial fibrillation based on the RR
intervals?
Normal
S.A. node
Atrial fibrillation
Atrium
A.V. node
Ventricle
R
P
T
R
http://www.aboutatrialfibrillation.com
National Resource for Complex Physiologic Signals
A. Goldberger, Director
http://www.physionet.org
Identification of Atrial Fibrillation
Tateno and Glass (2001)
Histogram of ΔRR Intervals during AF
Kolmogorov-Smirnov Test
KS Test Can Be Used to Identify AF
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
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
Control of Cardiac Chaos
In
Garfinkel, Spano, Ditto, Weiss (1992)
Identify the Unstable Fixed Point
Stimulate to Control Rhythm
Controlling Cardiac Alternans
Hall, Christini, et al. (1997)
Target Unstable Fixed Point
Stimulate to Control Alternans
Deep Brain Stimulation Controls
Parkinsonian Tremor
Benabid (1991)
Deep Brain Stimulation Induces
Bifurcations in Dynamics
Titcombe, Glass, Guehl, Beuter (2001)
Boundaries for Stimulation
Effectiveness
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
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
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.