Fractals in physiology and medicine.

Nonlinear dynamics, a branch of the basic sciences that studies complex physical systems, offers novel approaches to long-standing problems of physiological form and function. The nonlinear concept of fractals, introduced and developed over the last decade, provides insights into the organization of complex structures such as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes. ImagesFIG. 2FIG. 4

[1]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[2]  W. Schottky.  Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern , 1918 .

[3]  C D Murray,et al.  The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[4]  E. Weibel,et al.  Architecture of the Human Lung , 1962, Science.

[5]  W. Rheinboldt,et al.  A COMPUTER MODEL OF ATRIAL FIBRILLATION. , 1964, American heart journal.

[6]  A. Tanenbaum.  Computer recreations , 1973 .

[7]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[8]  B Neubauer,et al.  Analysis of heart rate variations in patients with multiple sclerosis. A simple measure of autonomic nervous disturbances using an ordinary ECG. , 1978, Journal of neurology, neurosurgery, and psychiatry.

[9]  Frol'kis Vv,et al.  Aging of the Central Nervous System , 1979 .

[10]  R. M. Heethaar,et al.  Signal analysis of ventricular fibrillation , 1979 .

[11]  N. MacDonald.  Nonlinear dynamics , 1980, Nature.

[12]  Yukio Kosugi,et al.  Modulation of the Time Relation of Action Potential Impulses Propagating Along an Axon , 1981, IEEE Transactions on Biomedical Engineering.

[13]  V Kariniemi,et al.  Short-term variability of fetal heart rate during pregnancies with normal and insufficient placental function. , 1981, American journal of obstetrics and gynecology.

[14]  R. Ideker,et al.  The Transition to Ventricular Fibrillation Induced by Reperfusion After Acute Ischemia in the Dog: A Period of Organized Epicardial Activation , 1981, Circulation.

[15]  T. Musha,et al.  1/f Fluctuation of Heartbeat Period , 1982, IEEE Transactions on Biomedical Engineering.

[16]  E. Montroll,et al.  On 1/f noise and other distributions with long tails. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[17]  J Lefèvre,et al.  Teleonomical optimization of a fractal model of the pulmonary arterial bed. , 1983, Journal of theoretical biology.

[18]  A L Goldberger,et al.  Nonlinear dynamics, electrical alternans, and pericardial tamponade. , 1984, American heart journal.

[19]  Hearing impairment in elderly persons. , 1984, Journal of the American Geriatrics Society.

[20]  A L Goldberger,et al.  Nonlinear dynamics in heart failure: implications of long-wavelength cardiopulmonary oscillations. , 1984, American heart journal.

[21]  R. Cohen,et al.  Simple finite-element model accounts for wide range of cardiac dysrhythmias. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[22]  A L Goldberger,et al.  On a mechanism of cardiac electrical stability. The fractal hypothesis. , 1985, Biophysical journal.

[23]  M. Sernetz,et al.  The organism as bioreactor. Interpretation of the reduction law of metabolism in terms of heterogeneous catalysis and fractal structure. , 1985, Journal of theoretical biology.

[24]  D. Adam,et al.  Assessment of autonomic function in humans by heart rate spectral analysis. , 1985, The American journal of physiology.

[25]  M. Lewis,et al.  Fractal surfaces of proteins. , 1985, Science.

[26]  Nonlinear mechanisms in physiology and pathophysiology Toward a dynamical theory of health and disease , 1985 .

[27]  W. M. Smith,et al.  Development of an endocardial-epicardial gradient of activation rate during electrically induced, sustained ventricular fibrillation in dogs. , 1985, The American journal of cardiology.

[28]  Falls, motor dysfunction, and correlative neurohistologic changes in the elderly. , 1985, Clinics in geriatric medicine.

[29]  J. T. Colvin,et al.  Fractal models of protein structure, dynamics and magnetic relaxation , 1985 .

[30]  B. West.  An Essay on the Importance of Being Nonlinear , 1985 .

[31]  A. Goldberger,et al.  Beyond the principle of similitude: renormalization in the bronchial tree. , 1986, Journal of applied physiology.

[32]  D H Singer,et al.  Power spectral analysis of heart rate variability in sudden cardiac death: comparison to other methods. , 1986, IEEE transactions on bio-medical engineering.

[33]  Bruce J. West,et al.  Applications of Nonlinear Dynamics to Clinical Cardiology a , 1987, Annals of the New York Academy of Sciences.

[34]  M F Schlesinger.  Fractal time and 1/f noise in complex systems. , 1987, Annals of the New York Academy of Sciences.

[35]  E R Weibel,et al.  Morphometry of the human pulmonary acinus , 1988, The Anatomical record.

[36]  L. Mosekilde.  Age-related changes in vertebral trabecular bone architecture--assessed by a new method. , 1988, Bone.