What Do Complex Rhythms Reveal

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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

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 from

ventricular 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

T

R

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.