Fractals in Biology and Medicine. Volume 1

400 Pages·9.7 MB·english

by  Nonnenmacher T.F.

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
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The use of registered names, trademarks etc. in this publication, even if not identified as such, does not imply that
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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