DIMACS April, 2002

Nonlinear Dynamics, Chaos, and Complexity in Bedside Medicine

Ary L. Goldberger, M.D.

Harvard Medical School

NIH/NCRR Research Resource for

Complex Physiologic Signals (PhysioNet)

A Time Series Challenge:

Heart Failure Heart Failure

Normal Atrial Fibrillation

Heart Rate Dynamics in Health and DiseaseWhich time series is normal?

Cardiac Electrical System

How is Heart Rate Dynamics Regulated?Coupled Feedback Systems Operating Over Wide Range of Temporal/Spatial Scales

Three Themes

• Healthy systems show complex dynamics, with long-range (fractal) correlations and multiscale nonlinear interactions.

• Life-threatening pathologies and aging are associated with breakdown of fractal scaling and loss of nonlinear complexity.

• Open-source databases and software tools are needed to catalyze advances in complex signal analysis.

Hallmarks of Complexity

• Nonstationarity• Statistics change with time

• Nonlinearity• Components interact in unexpected ways ( “cross-talk” )

• Multiscale Variability• Fluctuations may have fractal properties

Healthy Heart Rate Dynamics

Is the Physiologic World Linear or Nonlinear?

• Linear World:• Things add up• Proportionality of input/output• High predictability, no surprises

• Nonlinear World:• Whole sum of parts (“emergent” properties)• Small changes may have huge effects• Low predictability, anomalous behaviors

What’s Wrong with this Type ofSignal Transduction Picture?

Answer: No feedback; No nonlinearityComplicated! but …Complex dynamics missing!

*** Danger ***

Linear Fallacy: Widely-held assumption that biologicalsystems can be largely understood by dissecting out micro-components and analyzing them in isolation.

“Rube Goldberg physiology”

Nonlinear/Fractal Mechanisms in Physiology

• Bad news: your data are complex!

• Good news: there are certain generic mechanisms that do not depend on details of system (universalities)

Wonderful World of Complexity:

• Abrupt changes• Bifurcations

• Bursting

• Bistability

• Hysteresis• Nonlinear oscillations• Multiscale (fractal) variability• Deterministic chaos

• Nonlinear waves: spirals; scrolls; solitons

• Stochastic resonance • Time irreversibility• Complex networks• Emergent properties

Sampler of Nonlinear Mechanisms in Physiology

Ref: Goldberger et al. PNAS 2002 99 Suppl. 1: 2466-2472.

Six Examples ofSpiral Waves in Excitable Media

From: J. Walleczek, ed. Self-Organized Biological Dynamics and Nonlinear ControlCambridge University Press, 2000.

Fractal: A tree-like object or process, composed ofsub-units (and sub-sub-units, etc) that resemble thelarger scale structure.

This internal look-alike property is known asself-similarity or scale-invariance.

Multiscale Complexity and Fractals

Fractal Self-Organization:Coronary Artery Tree

Fractal Self-Organization:His-Purkinje Conduction Network

Fractal Self-Organization:Purkinje Cells in Cerebellum

Fractal: A tree-like object or process, composed ofsub-units (and sub-sub-units, etc) that resemble thelarger scale structure.

This internal look-alike property is known asself-similarity or scale-invariance.

Multiscale Complexity and Fractals

Loss of Multiscale Fractal Complexitywith Aging & Disease

Single Scale Periodicity Uncorrelated Randomness

Two Patterns ofPathologic Breakdown

Healthy Dynamics: Multiscale Fractal Variability

Lancet 1996; 347:1312Nature 1999; 399:461

Fractal Analysis of Nonstationary Time Series

Fractal Scaling in Health and Disease

Why is it Healthy to be Fractal?

• Healthy function requires capability to cope with unpredictable environments

• Fractal systems generate broad repertoire of response adaptability

• Absence of characteristic time scale helps prevent mode-locking (pathologic resonances)

• The output of many systems becomes more regular and predictable with pathologic perturbations

• Clinical medicine not feasible without such stereotypic, predictable behaviors – clinicians look for characteristic patterns/scales

• Healthy function: multi-scale dynamics/scale-free behavior harder to characterize

Concept ofDE-COMPLEXIFICATION OF DISEASE

Loss of Fractal ComplexityResolves Clinical Paradox

Patients with wide range of disorders often display strikingly predictable (ordered) dynamics

Reorder vs. Disorder

Examples: Parkinsonism / TremorsObsessive-compulsive behaviorNystagmusCheyne-Stokes breathingObstructive sleep apneaVentricular TachycardiaHyperkalemia “Sine-wave” ECGCyclic neutropeniaetc., etc.

Warning!

Excessive Regularity is Bad For Your HealthExample: Photic (Stroboscopic) Stimulation and Seizures

What’s the Cure?

• Physiologic dynamics exhibit an extraordinary range of complexity that defies:

• Conventional statistics• Homeostatic models

• Important information hidden incomplex signal fluctuations relating to:

• Basic signaling mechanisms• Novel biomarkers

Finding and Using Hidden Information

The Bad News for Complex Signal Analysis

• Databases are largely unavailable

or incompletely documented

• Investigators use different, undocumented software tools on different databases

“ Babel-ography ”

www.physionet.orgStart date: September 1, 1999

100,000+ visits to date1 terabyte of data downloaded!

NCRR Research Resource for Complex Physiologic Signals - “PhysioNet”

PhysioNet• Dissemination portal• Tutorials• Discussion Groups

Design of the PhysioNet Resource

PhysioBank• Reference Datasets

•Multi-Parameter (e.g. sleep apnea; intensive care unit)

•ECG•Gait•Other Neurological•Images

• Data supporting publications• 30+ gigabytes currently online• 1+ terabytes online in 2003

Design of the PhysioNet Resource

PhysioToolkit• Open source software• Data analysis packages• Physiologic models• Software from publications

Design of the PhysioNet Resource

PhysioNet Signal Analysis Competitions

• Challenge 2001:Can you forecast an imminentcardiac arrhythmia (atrial fibrillation) during normal cardiac rhythm?

• Challenge 2002:Can you simulate/model complex healthyheart rate variability?

• Future:Seizure forecasting; Biomedical image processing, etc.

• Homeostasis revisited:

Physiologic control

Complex (fractal/nonlinear) dynamics

• Loss of fractal/nonlinear complexity:New markers of life-threatening pathology/aging

• Needed: Open-source data and software for basic mechanisms and bedside diagnostics

Conclusions

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