Post on 31-Mar-2015
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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
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 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)
Modulated ParasystoleSinus 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
Calcium Spiral (Calcium Green)
Voltage Spiral(di-4-ANEPPS)
Calcium Target (Calcium Green)
Pacemakers and Reentry in Tissue Culture
Bub, Glass, Publicover, Shrier, PNAS (1998)
Bursting Rhythms in Tissue Culture
Anatomy of a burst
Cellular Automata Model of a Burst
Pacemaker
Nagai, Gonzalez, Shrier, Glass, PRL (2000)
Dynamics in a Ring of Cardiac Cells
Reentry
Cardiac ballet
FitzHugh-Nagumo Model of Propagation
Heptanol:
Heptanol slows propagation and leads to spiral breakup (may be similar to transition fromventricular tachycardia to ventricular fibrillation)
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)
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?
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
I n
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.