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 NormalAtrial Fibrillation Heart Rate Dynamics in Health and Disease Which 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 of Signal Transduction Picture? Answer: No feedback; No nonlinearity Complicated! but …Complex dynamics missing!

*** Danger *** Linear Fallacy: Widely-held assumption that biological systems 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 Suppl. 1:

Six Examples of Spiral Waves in Excitable Media From: J. Walleczek, ed. Self-Organized Biological Dynamics and Nonlinear Control Cambridge University Press, 2000.

Fractal: A tree-like object or process, composed of sub-units (and sub-sub- units, etc) that resemble the larger scale structure. This internal look-alike property is known as self-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 of sub-units (and sub-sub- units, etc) that resemble the larger scale structure. This internal look-alike property is known as self-similarity or scale-invariance. Multiscale Complexity and Fractals

Loss of Multiscale Fractal Complexity with Aging & Disease Single Scale Periodicity Uncorrelated Randomness Two Patterns of Pathologic Breakdown Healthy Dynamics: Multiscale Fractal Variability Lancet 1996; 347:1312 Nature 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 of DE-COMPLEXIFICATION OF DISEASE

Loss of Fractal Complexity Resolves Clinical Paradox Patients with wide range of disorders often display strikingly predictable (ordered) dynamics Reorder vs. Disorder Examples:Parkinsonism / Tremors Obsessive-compulsive behavior Nystagmus Cheyne-Stokes breathing Obstructive sleep apnea Ventricular Tachycardia Hyperkalemia  “Sine-wave” ECG Cyclic neutropenia etc., etc.

Warning! Excessive Regularity is Bad For Your Health Example: 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 in complex 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 ”

Start date: September 1, ,000+ visits to date 1 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 imminent cardiac arrhythmia (atrial fibrillation) during normal cardiac rhythm? Challenge 2002: Can you simulate/model complex healthy heart 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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