“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.