Fractals in Biology and Medicine, Volume 4

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Gabriele A. Losa, Theo F. Nonnenmacher, Ewald R. Weibel
Springer Science & Business Media, Aug 18, 2005 - Computers - 314 pages
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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.
  

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Contents

Fractal Structures in Biological Systems
1
A Tribute to Benoit Mandelbrot on his 80th Birthday
3
How Deep Does Oxygen Enter the Alveolar System?
17
Is the Lung an Optimal Gas Exchanger?
31
Interplay between Geometry and Flow Distribution
43
Fractal Aspects of ThreeDimensional Vascular Constructive Optimization
55
Object Orientation and Fractal Topology in Biomedical Image Analysis Method and Applications
67
The Use of Fractal Analysis for the Quantification of Oocyte Cytoplasm Morphology
75
Fractal Analysis of Monolayer Cell Nuclei from Two Different Prognostic Classes of Early Ovarian Cancer
175
Fractal Analysis of Vascular Network Pattern in Human Diseases
187
Quantification of Local Architecture Changes Associated with Neoplastic Progression in Oral Epithelium using Graph Theory
193
Fractal Analysis of Canine Trichoblastoma
203
Fractal Dimension as a Novel Clinical Parameter in Evaluation of the Urodynamic Curves
209
Nonlinear Dynamics in Uterine Contractions Analysis
215
Computeraided Estimate and Modelling of the Geometrical Complexity of the Corneal Stroma
223
The Fractal Paradigm
231

Fractal Structures in Neurosciences
83
Pitfalls and Revelations in Neuroscience
85
Is it Noise or Correlated Fractal Process?
95
Do Mental and Social Processes have a Selfsimilar Structure? The Hypothesis of Fractal AffectLogic
107
Scaling Properties of Cerebral Hemodynamics
121
A Multifractal Dynamical Model of Human Gait
131
Dual Antagonistic Autonomic Control Necessary for 1f Scaling in Heart Rate
141
Fractal Structures in Tumours and Diseases
153
Tissue Architecture and Cell Morphology of Squamous Cell Carcinomas Compared to Granular Cell Tumours Pseudoepitheliomatous Hyperplasia an...
155
Statistical Shape Analysis Applied to Automatic Recognition of Tumor Cells
165
ComplexDynamical Extension of the Fractal Paradigm and its Applications in Life Sciences
233
Fractallike Features of Dinosaur Eggshells
245
Evolution and Regulation of Metabolic Networks
257
Some Biological Remarks
269
A Mystery of the Gompertz Function
277
Fractional Calculus and Symbolic Solution of Fractional Differential Equations
287
FoxFunction Representation of a Generalized Arrhenius Law and Applications
299
Index
309
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About the author (2005)

Ewald R. Weibel is Professor of Anatomy, University of Bern, Switzerland.