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R CA Sil L G and E UE T. F. Nonnenmacher G. A. Losa E. R. Weibel Editors Springer Basel AG Editors T. F. Nonnenmacher G. A. Losa Mathematische Physik Laboratorio di Patologia Cellulare UniversitätUlm Istituto Cantonale di Patologia Albert-Einstein-Allee 11 Via in Selva 24 D-89069 Ulm CH-6604 Locarno Germany Switzerland E. R. Weibel Anatomisches Institut der Universität Bern Bühlstrasse 26 CH-3012Bern Switzerland A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Fractals in biology and medicine / edited by T. F. Nonnenmacher, G. A. Losa, E. R. Weibel Includes bibliographical references and index. ISBN 978-3-0348-9652-8 ISBN 978-3-0348-8501-0 (eBook) DOI 10.1007/978-3-0348-8501-0 1. Medicine-Mathematics-Congress. 2. Biology-Mathematics-Congress. 3. Fractals-Congress. I. Nonnenmacher, T. F. (Theo F.), 1933-. II. Losa, G. A. (Gabriele A.), 1941-. III. Weibel, Ewald R. R853.M3F68 1993 574' .01'51474-dc20 Deutsche Bibliothek Cataloging-in-Publication Data Fractals in biology and medicine / ed. by T. F. Nonnenmacher ... - Basel; Boston; Berlin : Birkhäuser, 1993 ISBN 978-3-0348-9652-8 NE: Nonnenmacher, Theo F. [Hrsg.] The publisher and the editors can give no guarantee for the information on drug dosage and administration contained in this publication. The respective user must check its accuracy by consulting other sources of reference in each individual case. The use of registered names, trademarks etc. in this publication, even if not identified as such, does not imply that they are exempt from the relevant protective laws and regulations or free for general use. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. ©1994 Springe r Basel AG Originally published by Birkhäuser Verlag, PO Box 133, CH-4010 Basel, Switzerland in 1994 Softcover reprint of the hardcover 1st edition 1994 Camera-ready copy prepared by the editors Revision and layout by mathScreen online, CH-4123 Allschwil Printed on acid-free paper produced from chlorine-free pulp ISBN 978-3-0348-9652-8 98765432 1 Contents Foreword ........................................................... ix Preface: Summary of the Symposium ................................ 1 The Significance of Fractals for Biology and Medicine. An Introduction and Summary Ewald R. Weibel ..................................................... 2 Fractal Geometry and Biomedical Sciences .......................... 7 A Fractal's Lacunarity, and how it can be Tuned and Measured Benoit B. Mandelbrot .. . .............................................. 8 Spatial and Temporal Fractal Patterns in Cell and Molecular Biology Theo F. Nonnenmacher ............................................... 22 Chaos, Noise and Biological Data Bruce J. West, W. Zhang and H J. Mackey ............................. 38 Fractal Landscapes in Physiology & Medicine: Long-Range Correlations in DNA Sequences and Heart Rate Intervals C.-K. Peng, S.v. Buldyrev, J.M. Hausdorff, SHavlin, J.E.M.Mietus, M. Simons, H.E. Stanley, and AL Goldberger ..... . . . . . . . . . . . . . . . .5 5. . . . . Fractals in Biological Design and Morphogenesis ..................... 67 Design of Biological Organisms and Fractal Geometry Ewald R. Weibel ..................................................... 68 Fractal and Non-Fractal Growth of Biological Cell Systems Petre Tautu .......................................................... 86 Evolutionary Meaning, Functions and Morphogenesis of Branching Structures in Biology Giuseppe Damiani ................................................... 104 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 and Tohru Takahashi .................................. 116 Multivariate Characterization of Blood Vessel Morphogenesis in the Avian Chorioallantoic Membrane (CAM): Cell Proliferation, Length Density and Fractal Dimension Haymo Kurz, Jorg Wilting and Bodo Christ ............................ 132 Phyllotaxis or Self-Similarity in Plant Morphogenesis Franf;ois Rothen ................................ ..................... 141 vi Contents Fractals in Molecular and Cell Biology 159 Evolutionary Interplay Between Spontaneous Mutation and Selection: Aleatoric Contributions of Molecular Reaction Mechanisms Werner Arber ........................................................ 160 Error Propagation Theory of Chemically Solid Phase Synthesized Oligonucleotides and DNA Sequences for Biomedical Application Zeno Foldes-Papp, Armin Herold, Hartmut Seliger and Albrecht K. Kleinschmidt ............................................. 165 Fractional Relaxation Equations for Protein Dynamics Walter G. GlOckle and Theo F. Nonnenmacher ... ........ ............... 174 Measuring Fractal Dimensions of Cell Contours: Practical Approaches and their Limitations Gerd Baumann, Andreas Barth and Theo F. Nonnenmacher .............. 182 Fractal Properties of Pericellular Membrane from Lymphocytes and Leukemic Cells Gabriele A. Losa ..................................................... 190 Cellular Sociology: Parametrization of Spatial Relationships Based on Voronoi Diagram and Ulam Trees Raphael Marcelpoil, Franck Davoine and Michel Robert-Nicoud 201 A Fractal Analysis of Morphological Differentiation of Spinal Cord Neurons in Cell Culture Tom G. Smith, Jr. and E.A. Neale ...................................... 210 Fractal Dimensions and Dendritic Branching of Neurons in the Somatosensory Thalamus Klaus-D. Knijfki, Matthias Pawlak and Christiane Vahle-Hinz 221 Fractal Structure and Metabolic Functions 231 Organisms as Open Systems Manfred Sernetz ..................................................... 232 Transfer to and across Irregular Membranes Modelled by Fractal Geometry Bernard Sapoval ..................................................... 241 Scaling and Active Surface of Fractal Membranes Ricardo Gutfraind and Bernard Sapoval ............................... 251 Structure Formation in Excitable Media Martin Luneburg ..................................................... 266 Colony Morphology of the Fungus Aspergillus Oryzae Shu Matsuura and Sasuke Miyazima ................................... 274 Contents Vll Estimation of the Correlation Dimension of All-Night Sleep EEG Data with a Personal Super Computer Peter Achermann, Rolf Hartmann, Anton Gunzinger, Walter Guggenbiihl, and Alexander A. Borbely ......................... 283 Fractals in Pathology ................................................ 291 Changes in Fractal Dimension of Trabecular Bone in Osteoporosis: A Preliminary Study C.L. Benhamou, R. Harba, E. Lespessailles G. Jacquet, D. Tourliere and R. Jennane ...................................................... 292 Use of the Fractal Dimension to Characterize the Structure of . Cancellous Bone in Radiographs of the Proximal Femur Curtis B. Caldwell, John Rosson, James Surowiak and Trevor Hearn 300 Distribution of Local-Connected Fractal Dimension and the Degree of Liver Fattiness from Ultrasound Carl J.G. Evertsz, C. Zahlten, H.-O. Peitgen, I. Zuna, and G. van Kaick ............................................ 307 Fractal Dimension as a Characterisation Parameter of Premalignant and Malignant Epithelial Lesions of the Floor of the Mouth Gabriel Landini and John W. Rippin ................................... 315 Modelling ........................................................... 323 Modelling HlV/ AIDS Dynamics Philippe Blanchard... ........................... ..................... 324 Morphological Diagnosis Turns from Gestalt to Geometry Vittorio Pesce Delfino, Teresa Lettini, Michele Troia, and Eligio Vacca 331 Fluorescence Recovery after Photo bleaching Studied by Total Internal Reflection Microscopy: An Experimental System for Studies on Living Cells in Culture Torsten Mattfeldt, Theo F. Nonnenmacher, Armin Lambacher, Walter G. GlOckle and Otto Haferkamp ................................ 351 Anomalous Diffusion and Angle-Dependency in the Theory of Fluorescence Recovery after Photobleaching Walter G. GlOckle, Torsten Mattfeldt, and Theo F. Nonnenmacher 363 List of Speakers ..................................................... 373 List of Participants ............. . . . . . . . . . . . . . . . . . . . . . . . ... . 3. 7.6 . . . . . . . . Index............................................................... 382 Foreword This volume contains the scientific presentations given at the International Sym posium on fractals in biology and medicine held in Ascona, Switzerland, from February 1--4, 1993. Scientists from the United States, Austria, Canada, Japan, France, Germany, Great Britain, Italy and Switzerland came together to present and discuss their research papers as well as to exchange information on their experimental findings and theoretical interpretations. When we started to prepare for this conference, we had the feeling that the time had come to gather prominent scientists from around the world to discuss this topical subject. To our knowledge, this symposium has been the first com prehensive meeting of scientists on fractals in biology and medicine. Since the publication of Benoit Mandelbrot's book The Fractal Geometry of Nature, the fractal concept has been rapidly pushed forward essentially by mathematicians and physicists alike. However, apart from a few exceptions, it needed still more time to enter the fields of biology and medicine. One of the reasons for this de lay might have been the language barrier between the different fields: fractals, and mainly their graphical representations, are appealing and even accessible to intuitive understanding, but to translate the theoretical concepts at their basis into terms that can be interpreted in a biological context requires a level of mathemat ical understanding that is not typical for the group of biologists, for example. In order to bridge this language barrier, we invited an interdisciplinary group of sci entists to Monte Verita in Ascona. The members of this group have been working in different areas of science but most have focussed some or all of their activities on biomedical research problems. Almost all 90 participants could be accommodated in the conference building at Monte Verita and thus it was easy to make personal contacts. The exchange of information between different groups of researchers took place in small circles and within an exciting atmosphere, bringing the family of fractal researchers closer together. We are particularly grateful to all the renowned institutions who accepted to confer their scientific patronage and also to the sponsors who made the achievment of this symposium possible. Our thanks are also due to Mrs. Antonella Camponovo and Graziana Pelloni, Dr. Danilo Merlini, member of the scientific and organizing Committee, the col laborators Riccardo Graber, Lorenzo Leoni, and Cristo foro DUrig and to Mr. Luca Albertini, managing director of the Centro Seminariale Monte Verita, who made the conference run smoothly, and to Dr. Gerd Baumann for his editorial assistance while preparing this proceedings volume. In presenting the different contributions in this volume, we did not follow the chronological sequence of sessions. Rather, we arranged the proceedings as to grouping similar topics together. Ascona 1993 The editors x Foreword The symposium took place at the Centro Seminariale Monte Verita, Ascona, Switzerland, from February 1-4, 1993. Under the Auspices of - INTERNATIONAL SOCIETY FOR STEREOLOGY - SWISS ACADEMY OF SCIENCES - SWISS NATIONAL SCIENCE FOUNDATION - SWISS SOCIETY FOR CELL AND MOLECULAR BIOLOGY - COMMITTEE FOR DIAGNOSTIC QUANTITATIVE PATHOLOGY - WORKING GROUP OF THE EUROPEAN SOCIETY OF QUANTITATIVE PATHOLOGY - DIPARTIMENTO DELL'ISTRUZIONE E DELLA CULTURA AND DIPARTIMENTO DELLE OPERE SOCIALI, REPUBBLICA DEL CANTONE TICINO Financial Support was Received from - DIPARTIMENTO DELL'ISTRUZIONE E DELLA CULTURA DEL CANTONE TICINO - SWISS NATIONAL SCIENCE FOUNDATION - SWISS ACADEMY OF SCIENCES - FRATELLI MONZEGLIO, CARROZZERIA SA, LOCARNO - CITIA DI LOCARNO - BANCA DEL GOTTARDO, LOCARNO - SOCIETA ELETIRICA SOPRACENERINA, LOCARNO - RADIO DELLA SVIZZERA ITALIANA, RETE 2, LUGANO - PHILIPS AG, ZORICH - LEICA AG, ZURICH Preface Summary of the Symposium The Significance of Fractals for Biology and Medicine An Introduction and Summary Ewald R. Weibel Department of Anatomy University of Bern Biihlstrasse 26 CH-3000 Bern 9, Switzerland In his seminal book The Fractal Geometry of Nature Benoit Mandelbrot made the point that the mathematical construct of a geometry which allows for fractional dimensions will prove most useful in the characterization of natural phenomena, structures and processes alike. This should be particularly true in biology for a number of reasons. First, the complex structure of living creatures, from the whole organism down to the cells, is notoriously difficult to reduce to simple geomet ric descriptions, and functional processes have very often non-linear properties. Organisms develop and grow from small and simple units to gradually achieve their size and complexity. In living systems, design and performance commonly combine strict rules with some random variation which gives each individual its species characteristics and its individual traits. Furthermore, the wonderful variety observed in the plant and animal kingdoms is the result of stepwise «variation over a common theme» - they are similar but not alike with basic features preserved between related species but expressed in different size and proportions. All this has some resemblance to the construction principles of fractal geom etry where small changes in the algorithms yield a great variety of form so that one can expect considerable new insights from subjecting biological structures and processes to fractal analysis. And, finally, diseases appear often as modulations of basic design patterns so that fractal geometry may even have an impact on the study of disease in medical sciences. However, to introduce the concepts and tools of fractal geometry into biological and medical research is not easy. It requires skills that even a well-educated biologist cannot necessarily master. * The goal of the Symposium on Fractals in Biology and Medicine was first to explore the potential that fractal geometry offers for elucidating and explaining the complex make-up of biological organisms and then to develop the concepts, questions and methods required in research on fractal biology. In order to approach this task the conference brought together mathematicians, engineers, natural sci entists, biologists and medical scientists, because to discuss fractal geometry in

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