Ebook: Fractals in Biology and Medicine

This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Benoît Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision. The book should be of interest to researchers and students from molecular and cell biology, biomedicine, biomathematics, analytical morphology, immunology and neurology who are interested in the combination of mathematics and life sciences.

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This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Beno?t Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision. The book should be of interest to researchers and students from molecular and cell biology, biomedicine, biomathematics, analytical morphology, immunology and neurology who are interested in the combination of mathematics and life sciences.

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This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Beno?t Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision. The book should be of interest to researchers and students from molecular and cell biology, biomedicine, biomathematics, analytical morphology, immunology and neurology who are interested in the combination of mathematics and life sciences.

Content:
Front Matter....Pages i-ix
Mandelbrot’s Fractals and the Geometry of Life: A Tribute to Beno?t Mandelbrot on his 80th Birthday....Pages 3-16
Gas Diffusion through the Fractal Landscape of the Lung: How Deep Does Oxygen Enter the Alveolar System?....Pages 17-30
Is the Lung an Optimal Gas Exchanger?....Pages 31-42
3D Hydrodynamics in the Upper Human Bronchial Tree: Interplay between Geometry and Flow Distribution....Pages 43-53
Fractal Aspects of Three-Dimensional Vascular Constructive Optimization....Pages 55-66
Cognition Network Technology: Object Orientation and Fractal Topology in Biomedical Image Analysis. Method and Applications....Pages 67-73
The Use of Fractal Analysis for the Quantification of Oocyte Cytoplasm Morphology....Pages 75-82
Fractal Analysis: Pitfalls and Revelations in Neuroscience....Pages 85-94
Ongoing Hippocampal Neuronal Activity in Human: Is it Noise or Correlated Fractal Process?....Pages 95-106
Do Mental and Social Processes have a Self-similar Structure? The Hypothesis of Fractal Affect-Logic....Pages 107-119
Scaling Properties of Cerebral Hemodynamics....Pages 121-129
A Multifractal Dynamical Model of Human Gait....Pages 131-140
Dual Antagonistic Autonomic Control Necessary for 1/f Scaling in Heart Rate....Pages 141-151
Tissue Architecture and Cell Morphology of Squamous Cell Carcinomas Compared to Granular Cell Tumours’ Pseudo-epitheliomatous Hyperplasia and to Normal Oral Mucosae....Pages 155-164
Statistical Shape Analysis Applied to Automatic Recognition of Tumor Cells....Pages 165-174
Fractal Analysis of Monolayer Cell Nuclei from Two Different Prognostic Classes of Early Ovarian Cancer....Pages 175-186
Fractal Analysis of Vascular Network Pattern in Human Diseases....Pages 187-192
Quantification of Local Architecture Changes Associated with Neoplastic Progression in Oral Epithelium using Graph Theory....Pages 193-201
Fractal Analysis of Canine Trichoblastoma....Pages 203-207
Fractal Dimension as a Novel Clinical Parameter in Evaluation of the Urodynamic Curves....Pages 209-214
Nonlinear Dynamics in Uterine Contractions Analysis....Pages 215-222
Computer-Aided Estimate and Modelling of the Geometrical Complexity of the Corneal Stroma....Pages 223-230
Complex-Dynamical Extension of the Fractal Paradigm and its Applications in Life Sciences....Pages 233-244
Fractal-like Features of Dinosaur Eggshells....Pages 245-256
Evolution and Regulation of Metabolic Networks....Pages 257-268
Cytoskeleton as a Fractal Percolation Cluster: Some Biological Remarks....Pages 269-275
A Mystery of the Gompertz Function....Pages 277-286
Fractional Calculus and Symbolic Solution of Fractional Differential Equations....Pages 287-298
Fox-Function Representation of a Generalized Arrhenius Law and Applications....Pages 299-308
Back Matter....Pages 309-314

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This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Beno?t Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision. The book should be of interest to researchers and students from molecular and cell biology, biomedicine, biomathematics, analytical morphology, immunology and neurology who are interested in the combination of mathematics and life sciences.

Content:
Front Matter....Pages i-ix
Mandelbrot’s Fractals and the Geometry of Life: A Tribute to Beno?t Mandelbrot on his 80th Birthday....Pages 3-16
Gas Diffusion through the Fractal Landscape of the Lung: How Deep Does Oxygen Enter the Alveolar System?....Pages 17-30
Is the Lung an Optimal Gas Exchanger?....Pages 31-42
3D Hydrodynamics in the Upper Human Bronchial Tree: Interplay between Geometry and Flow Distribution....Pages 43-53
Fractal Aspects of Three-Dimensional Vascular Constructive Optimization....Pages 55-66
Cognition Network Technology: Object Orientation and Fractal Topology in Biomedical Image Analysis. Method and Applications....Pages 67-73
The Use of Fractal Analysis for the Quantification of Oocyte Cytoplasm Morphology....Pages 75-82
Fractal Analysis: Pitfalls and Revelations in Neuroscience....Pages 85-94
Ongoing Hippocampal Neuronal Activity in Human: Is it Noise or Correlated Fractal Process?....Pages 95-106
Do Mental and Social Processes have a Self-similar Structure? The Hypothesis of Fractal Affect-Logic....Pages 107-119
Scaling Properties of Cerebral Hemodynamics....Pages 121-129
A Multifractal Dynamical Model of Human Gait....Pages 131-140
Dual Antagonistic Autonomic Control Necessary for 1/f Scaling in Heart Rate....Pages 141-151
Tissue Architecture and Cell Morphology of Squamous Cell Carcinomas Compared to Granular Cell Tumours’ Pseudo-epitheliomatous Hyperplasia and to Normal Oral Mucosae....Pages 155-164
Statistical Shape Analysis Applied to Automatic Recognition of Tumor Cells....Pages 165-174
Fractal Analysis of Monolayer Cell Nuclei from Two Different Prognostic Classes of Early Ovarian Cancer....Pages 175-186
Fractal Analysis of Vascular Network Pattern in Human Diseases....Pages 187-192
Quantification of Local Architecture Changes Associated with Neoplastic Progression in Oral Epithelium using Graph Theory....Pages 193-201
Fractal Analysis of Canine Trichoblastoma....Pages 203-207
Fractal Dimension as a Novel Clinical Parameter in Evaluation of the Urodynamic Curves....Pages 209-214
Nonlinear Dynamics in Uterine Contractions Analysis....Pages 215-222
Computer-Aided Estimate and Modelling of the Geometrical Complexity of the Corneal Stroma....Pages 223-230
Complex-Dynamical Extension of the Fractal Paradigm and its Applications in Life Sciences....Pages 233-244
Fractal-like Features of Dinosaur Eggshells....Pages 245-256
Evolution and Regulation of Metabolic Networks....Pages 257-268
Cytoskeleton as a Fractal Percolation Cluster: Some Biological Remarks....Pages 269-275
A Mystery of the Gompertz Function....Pages 277-286
Fractional Calculus and Symbolic Solution of Fractional Differential Equations....Pages 287-298
Fox-Function Representation of a Generalized Arrhenius Law and Applications....Pages 299-308
Back Matter....Pages 309-314
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