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Fractals in Biology and Medicine

  • Book
  • © 1994

Overview

Editors:
  1. T. F. Nonnenmacher

    1. Mathematische Physik, Universität Ulm, Ulm, Germany

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  2. G. A. Losa

    1. Laboratorio di Patologia Cellulare, Istituto Cantonale di Patologia, Locarno, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  3. E. R. Weibel

    1. Anatomisches Institut, Universität Bern, Bern, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Mathematics and Biosciences in Interaction (MBI)

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Table of contents (33 chapters)

  1. Front Matter

    Pages i-x
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  2. Preface Summary of the Symposium

    1. Front Matter

      Pages 1-1
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    2. The Significance of Fractals for Biology and Medicine An Introduction and Summary

      • Ewald R. Weibel
      Pages 2-6

  3. Fractal Geometry and Biomedical Sciences

    1. Front Matter

      Pages 7-7
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    2. A Fractal’s Lacunarity, and how it can be Tuned and Measured

      • Benoit B. Mandelbrot
      Pages 8-21

    3. Spatial and Temporal Fractal Patterns in Cell and Molecular Biology

      • Theo F. Nonnenmacher
      Pages 22-37

    4. Chaos, Noise and Biological Data

      • Bruce J. West, W. Zhang, H. J. Mackey
      Pages 38-54

    5. Fractal Landscapes in Physiology & Medicine: Long-Range Correlations in DNA Sequences and Heart Rate Intervals

      • C.-K. Peng, S. V. Buldyrev, J. M. Hausdorff, S. Havlin, J. E. Mietus, M. Simons et al.
      Pages 55-65

  4. Fractals in Biological Design and Morphogenesis

    1. Front Matter

      Pages 67-67
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    2. Design of Biological Organisms and Fractal Geometry

      • Ewald R. Weibel
      Pages 68-85

    3. Fractal and Non-Fractal Growth of Biological Cell Systems

      • Petre Tautu
      Pages 86-103

    4. Evolutionary Meaning, Functions and Morphogenesis of Branching Structures in Biology

      • Giuseppe Damiani
      Pages 104-115

    5. Relationship Between the Branching Pattern of Airways and the Spatial Arrangement of Pulmonary Acini — A Re-Examination from a Fractal Point of View

      • Hiroko Kitaoka, Tohru Takahashi
      Pages 116-131

    6. Multivariate Characterization of Blood Vessel Morphogenesis in the Avian Chorioallantoic Membrane (CAM): Cell Proliferation, Length Density and Fractal Dimension

      • Haymo Kurz, Jörg Wilting, Bodo Christ
      Pages 132-140

    7. Phyllotaxis or Self-Similarity in Plant Morphogenesis

      • François Rothen
      Pages 141-157

  5. Fractals in Molecular and Cell Biology

    1. Front Matter

      Pages 159-159
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    2. Evolutionary Interplay Between Spontaneous Mutation and Selection: Aleatoric Contributions of Molecular Reaction Mechanisms

      • Werner Arber
      Pages 160-164

    3. Error Propagation Theory of Chemically Solid Phase Synthesized Oligonucleotides and DNA Sequences for Biomedical Application

      • Zeno Földes-Papp, Armin Herold, Hartmut Seliger, Albrecht K. Kleinschmidt
      Pages 165-173

    4. Fractional Relaxation Equations for Protein Dynamics

      • Walter G. Glöckle, Theo F. Nonnenmacher
      Pages 174-181

    5. Measuring Fractal Dimensions of Cell Contours: Practical Approaches and their Limitations

      • Gerd Baumann, Andreas Barth, Theo F. Nonnenmacher
      Pages 182-189
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Keywords

About this book

"Fractals in Biology and Medicine" explores the potential of fractal geometry for describing and understanding biological organisms, their development and growth as well as their structural design and functional properties. It extends these notions to assess changes associated with disease in the hope to contribute to the understanding of pathogenetic processes in medicine. The book is the first comprehensive presentation of the importance of the new concept of fractal geometry for biological and medical sciences. It collates in a logical sequence extended papers based on invited lectures and free communications presented at a symposium in Ascona, Switzerland, attended by leading scientists in this field, among them the originator of fractal geometry, Benoit Mandelbrot. "Fractals in Biology and Medicine" begins by asking how the theoretical construct of fractal geometry can be applied to biomedical sciences and then addresses the role of fractals in the design and morphogenesis of biological organisms as well as in molecular and cell biology. The consideration of fractal structure in understanding metabolic functions and pathological changes is a particularly promising avenue for future research.

Editors and Affiliations

  • Mathematische Physik, Universität Ulm, Ulm, Germany

    T. F. Nonnenmacher

  • Laboratorio di Patologia Cellulare, Istituto Cantonale di Patologia, Locarno, Switzerland

    G. A. Losa

  • Anatomisches Institut, Universität Bern, Bern, Switzerland

    E. R. Weibel

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