Fractals in biology and medicine

S. Havlin, S. V. Buldyrev, A. L. Goldberger, R. N. Mantegna, S. M. Ossadnik, C. K. Peng, M. Simons, H. E. Stanley

Research output: Contribution to journalArticlepeer-review

118 Scopus citations

Abstract

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent α quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

Original languageEnglish
Pages (from-to)171-201
Number of pages31
JournalChaos, Solitons and Fractals
Volume6
Issue numberC
DOIs
StatePublished - 1995

Bibliographical note

Funding Information:
We are grateful to R. Bansil, A.-L. Barabasi, K.R. Bhaskar, E Caserta, G. Daccord, W. Eldred,~. Garik, Z.D. Goldberger, Z. Hantos, J.M. Hausdorff, R.E. Hausman, P. Ivanov, T.J. LaMont, H. Larralde, M.E. Matsa, J. Mi-etus, A. Neer, J. Nittmann, E Pdtak, I. Rabin, F. Sciortino, A. Shehter, M.H.R. Stanley, B. Suki, P. Trunfio, M. Uideja, and G.H. Weiss for major contribution~i to those results reviewed here that represent collaborative research efforts. We also wish to thank C. Cantor, C. DeLisi, M. Frank-Kamenetskii, A.Yu. Grosberg, G. Huber, I. Labat, L. Liebovitch, G.S. Michaels, P. Munson, R. Nossal, R. Nussinov, R.D. Rosenberg, J.J. Schwartz, M. Schwartz, E.I. Shakhnovich, M.F. Shlesinger, N. Shworak, and E.N. Trifonov for valuable discussions. Partial support was provided to to SVB and HES by the National Science Foundation, to ALG by the G. Harold and Leila Y. Mathers Charitable Foundation, the National Heart, Lung and Blood Institute and the National Aeronautics and Space Administration, to SH by Israel-USA Binational Science foundation, and to C-KP by an NIH/NIMH Postdoctoral NRSA Fellowship.

Funding

We are grateful to R. Bansil, A.-L. Barabasi, K.R. Bhaskar, E Caserta, G. Daccord, W. Eldred,~. Garik, Z.D. Goldberger, Z. Hantos, J.M. Hausdorff, R.E. Hausman, P. Ivanov, T.J. LaMont, H. Larralde, M.E. Matsa, J. Mi-etus, A. Neer, J. Nittmann, E Pdtak, I. Rabin, F. Sciortino, A. Shehter, M.H.R. Stanley, B. Suki, P. Trunfio, M. Uideja, and G.H. Weiss for major contribution~i to those results reviewed here that represent collaborative research efforts. We also wish to thank C. Cantor, C. DeLisi, M. Frank-Kamenetskii, A.Yu. Grosberg, G. Huber, I. Labat, L. Liebovitch, G.S. Michaels, P. Munson, R. Nossal, R. Nussinov, R.D. Rosenberg, J.J. Schwartz, M. Schwartz, E.I. Shakhnovich, M.F. Shlesinger, N. Shworak, and E.N. Trifonov for valuable discussions. Partial support was provided to to SVB and HES by the National Science Foundation, to ALG by the G. Harold and Leila Y. Mathers Charitable Foundation, the National Heart, Lung and Blood Institute and the National Aeronautics and Space Administration, to SH by Israel-USA Binational Science foundation, and to C-KP by an NIH/NIMH Postdoctoral NRSA Fellowship.

FundersFunder number
Israel-USA Binational Science Foundation
NIH/NIMH
National Science Foundation
National Aeronautics and Space Administration
G. Harold and Leila Y. Mathers Charitable Foundation
Israel National Road Safety Authority

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