Fractals in Biology and Medicine

1. Front Matter

   Pages i-ix

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2. Fractal Structures in Biological Systems

   1. Mandelbrot’s Fractals and the Geometry of Life: A Tribute to Benoît Mandelbrot on his 80th Birthday

      • Ewald R. Weibel

      Pages 3-16

   2. Gas Diffusion through the Fractal Landscape of the Lung: How Deep Does Oxygen Enter the Alveolar System?

      • Chen Hou, Stefan Gheorghiu, Marc-Olivier Coppens, Virginia H. Huxley, Peter Pfeifer

      Pages 17-30

   3. Is the Lung an Optimal Gas Exchanger?

      • S. Gheorghiu, S. Kjelstrup, P. Pfeifer3, M.-O. Coppens

      Pages 31-42

   4. 3D Hydrodynamics in the Upper Human Bronchial Tree: Interplay between Geometry and Flow Distribution

      • B. Mauroy

      Pages 43-53

   5. Fractal Aspects of Three-Dimensional Vascular Constructive Optimization

      • Horst K. Hahn, Manfred Georg, Heinz-Otto Peitgen

      Pages 55-66

   6. Cognition Network Technology: Object Orientation and Fractal Topology in Biomedical Image Analysis. Method and Applications

      • Martin Baatz, Arno Schäpe, Günter Schmidt, Maria Athelogou, Gerd Binnig

      Pages 67-73

   7. The Use of Fractal Analysis for the Quantification of Oocyte Cytoplasm Morphology

      • G. A. Losa, V. Peretti, F. Ciotola, N. Cocchia, G. De Vico

      Pages 75-82

3. Fractal Structures in Neurosciences

   1. Fractal Analysis: Pitfalls and Revelations in Neuroscience

      • H.F. Jelinek, N. Elston, B. Zietsch

      Pages 85-94

   2. Ongoing Hippocampal Neuronal Activity in Human: Is it Noise or Correlated Fractal Process?

      • Joydeep Bhattacharya, Jessica Edwards, Adam Mamelak, Erin M. Schuamn

      Pages 95-106

   3. Do Mental and Social Processes have a Self-similar Structure? The Hypothesis of Fractal Affect-Logic

      • L. Ciompi, M. Baatz

      Pages 107-119

   4. Scaling Properties of Cerebral Hemodynamics

      • M. Latka, M. Turalska, D. Kolodziej, D. Latka, B. Goldstein, B.J. West

      Pages 121-129

   5. A Multifractal Dynamical Model of Human Gait

      • Bruce J. West, Nicola Scafetta

      Pages 131-140

   6. Dual Antagonistic Autonomic Control Necessary for 1/f Scaling in Heart Rate

      • Zbigniew R. Struzik, Junichiro Hayano, Seiichiro Sakata, Shin Kwak, Yoshiharu Yamamoto

      Pages 141-151

4. Fractal Structures in Tumours and Diseases

   1. Tissue Architecture and Cell Morphology of Squamous Cell Carcinomas Compared to Granular Cell Tumours’ Pseudo-epitheliomatous Hyperplasia and to Normal Oral Mucosae

      • R. Abu-Eid, G. Landini

      Pages 155-164

   2. Statistical Shape Analysis Applied to Automatic Recognition of Tumor Cells

      • A. Micheletti

      Pages 165-174

   3. Fractal Analysis of Monolayer Cell Nuclei from Two Different Prognostic Classes of Early Ovarian Cancer

      • B. Nielsen, F. Albregtsen, H.E. Danielsen

      Pages 175-186

   4. Fractal Analysis of Vascular Network Pattern in Human Diseases

      • G. Bianciardi, C. De Felice, R. Cattaneo, S. Parrini, A. Monaco, G. Latini

      Pages 187-192

   5. Quantification of Local Architecture Changes Associated with Neoplastic Progression in Oral Epithelium using Graph Theory

      • G. Landini, I.E. Othman

      Pages 193-201

   6. Fractal Analysis of Canine Trichoblastoma

      • G. De Vico, M. Cataldi, P. Maiolino, S. Beltraminelli, G.A. Losa

      Pages 203-207

This book is a compilation of the presentations given at the Fourth International Symposium on Fractals in Biology and Medicine held in Ascona, Switzerland on - th 13 March 2004 and was dedicated to Professor Benoît Mandelbrot in honour of his 80 birthday. The Symposium was the fourth of a series that originated back in 1993, always in Ascona. The fourth volume consists of 29 contributions organized under four sections: Fractal structures in biological systems Fractal structures in neurosciences Fractal structures in tumours and diseases The fractal paradigm Mandelbrot’s concepts such as scale invariance, self-similarity, irregularity and iterative processes as tackled by fractal geometry have prompted innovative ways to promote a real progress in biomedical sciences, namely by understanding and analytically describing complex hierarchical scaling processes, chaotic disordered systems, non-linear dynamic phenomena, standard and anomalous transport diffusion events through membrane surfaces, morphological structures and biological shapes either in physiological or in diseased states. While most of biologic processes could be described by models based on power law behaviour and quantified by a single characteristic parameter [the fractal dimension D], other models were devised for describing fractional time dynamics and fractional space behaviour or both (- fractional mechanisms), that allow to combine the interaction between spatial and functional effects by introducing two fractional parameters. Diverse aspects that were addressed by all bio-medical subjects discussed during the symposium.

• 3D graphics
• Dynamics
• Fractals
• biology
• image analysis
• life sciences
• medical image analysis
• model
• modeling
• nonlinear dynamics
• topology

• Institute for Scientific Interdisciplinary Studies (ISSI), Locarno

  Gabriele A. Losa

• Faculty of Biology and Medicine, University of Lausanne, Lausanne

  Gabriele A. Losa

• Research Center for Physics and Mathematics, Locarno

  Danilo Merlini

• Department of Mathematical Physics, University of Ulm, Ulm

  Theo F. Nonnenmacher

• Institute of Anatomy, University of Berne, Bern 9

  Ewald R. Weibel

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