Item Details

Fractal Physiology

James B. Bassingthwaighte, Larry S. Liebovitch, Bruce J. West
Format
Book
Published
New York : Published for the American Physiological Society by Oxford University Press, 1994.
Language
English
Series
The American Physiological Society Methods in Physiology Series
Methods in Physiology Series
ISBN
0195080130 (acid-free paper)
Contents
  • Introduction: fractals really are everywhere
  • Fractals are everywhere
  • Structures in space
  • Processes in time
  • Meaning of fractals
  • Properties of fractals and chaos
  • Properties of fractal phenomena in space and time
  • Self-similarity: parts that look like the whole
  • Scaling: the measure depends on the resolution
  • Fractal dimension: a quantitative measure of self-similarity and scaling
  • Surprising statistical properties of fractals
  • Fractal dimension: self-similar and self-accline scaling
  • Branching in the lung: power law scaling
  • More complex scaling relationship: weierstrass scaling
  • Branching in the lung: weierstrass scaling
  • Fractal measures of heterogeneity and correlation
  • Dispersional analysis
  • Rescaled range analysis: the hurst exponent, H
  • Correlation versus distance
  • History of fractal correlation analysis
  • Generating fractals
  • Mandelbrot set
  • Line replacement rules
  • Area and volume replacement rules
  • Logistic equation
  • Iterated function systems
  • Collage theorem
  • Lindenmayer systems
  • Cellular automata
  • Cellular growth processes.
  • (cont) Generating one-dimensional fractal time series
  • Properties of chaotic phenomena
  • Fractals and chaos share ideas and methods but they are not the same thing
  • Defining properties of chaos
  • Additional features of chaos
  • Change in perspective
  • From time to topology: is a process driven by chance or necessity
  • Distinguishing chaos from randomness
  • Methods suggestive of underlying chaos
  • Phase space and pseudo-phase space
  • Additional types of deterministic relationships
  • Capacity, correlation and information dimensions
  • Good news and bad news about this analysis
  • Physiological applications
  • Ion channel kinetics: a fractal time sequence of conformational states
  • Patch clamp
  • Models of ion channel kinetics
  • Comparison of Markov and fractal models
  • Uncovering mechanisms giving fractal channel kinetics
  • Fractals in nerve and muscle
  • Spread of excitation
  • Fractal heart
  • Fractal neurons
  • Spatiotemporal organization
  • Intraorgan flow heterogeneities
  • Methods of measuring regional flows
  • Estimating the fractal D for flow heterogeneity.
  • (cont) Fractal vascular anatomy
  • Dichotomous branching fractal network models for flow heterogeneity
  • Scaling relationships within an organ
  • Scaling relationships from animal to animal
  • Do fractal rules extend to microvascular units
  • Fractal flow and fractal washout
  • Fractal growth
  • Primitive growth patterns
  • Influences of matrix structure on the form
  • More general types of aggregation processes
  • Neuronal growth patterns
  • Algorithms for vascular growth
  • Patterns of vascular branching
  • Phylogeny versus ontogeny
  • Mechanisms that produce fractals
  • Fractals describe phenomena and give hints about their causes
  • Single process or many processes
  • Single causes that spread across many scales
  • Different causes that become linked across many scales
  • Chaos in physiological systems
  • Cardiovascular chaos
  • Metabolism
  • Chaotic brain
  • Physiological advantages of chaos
  • Special situations.
Description
xi, 364 p. : ill. ; 24 cm.
Notes
Includes bibliographical references (p. 328-354) and index.
Publisher no.
77229
Technical Details
  • Access in Virgo Classic

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    a| Introduction: fractals really are everywhere -- Fractals are everywhere -- Structures in space -- Processes in time -- Meaning of fractals -- Properties of fractals and chaos -- Properties of fractal phenomena in space and time -- Self-similarity: parts that look like the whole -- Scaling: the measure depends on the resolution -- Fractal dimension: a quantitative measure of self-similarity and scaling -- Surprising statistical properties of fractals -- Fractal dimension: self-similar and self-accline scaling -- Branching in the lung: power law scaling -- More complex scaling relationship: weierstrass scaling -- Branching in the lung: weierstrass scaling -- Fractal measures of heterogeneity and correlation -- Dispersional analysis -- Rescaled range analysis: the hurst exponent, H -- Correlation versus distance -- History of fractal correlation analysis -- Generating fractals -- Mandelbrot set -- Line replacement rules -- Area and volume replacement rules -- Logistic equation -- Iterated function systems -- Collage theorem -- Lindenmayer systems -- Cellular automata -- Cellular growth processes.
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    0
      
    a| (cont) Generating one-dimensional fractal time series -- Properties of chaotic phenomena -- Fractals and chaos share ideas and methods but they are not the same thing -- Defining properties of chaos -- Additional features of chaos -- Change in perspective -- From time to topology: is a process driven by chance or necessity -- Distinguishing chaos from randomness -- Methods suggestive of underlying chaos -- Phase space and pseudo-phase space -- Additional types of deterministic relationships -- Capacity, correlation and information dimensions -- Good news and bad news about this analysis -- Physiological applications -- Ion channel kinetics: a fractal time sequence of conformational states -- Patch clamp -- Models of ion channel kinetics -- Comparison of Markov and fractal models -- Uncovering mechanisms giving fractal channel kinetics -- Fractals in nerve and muscle -- Spread of excitation -- Fractal heart -- Fractal neurons -- Spatiotemporal organization -- Intraorgan flow heterogeneities -- Methods of measuring regional flows -- Estimating the fractal D for flow heterogeneity.
    505
    0
      
    a| (cont) Fractal vascular anatomy -- Dichotomous branching fractal network models for flow heterogeneity -- Scaling relationships within an organ -- Scaling relationships from animal to animal -- Do fractal rules extend to microvascular units -- Fractal flow and fractal washout -- Fractal growth -- Primitive growth patterns -- Influences of matrix structure on the form -- More general types of aggregation processes -- Neuronal growth patterns -- Algorithms for vascular growth -- Patterns of vascular branching -- Phylogeny versus ontogeny -- Mechanisms that produce fractals -- Fractals describe phenomena and give hints about their causes -- Single process or many processes -- Single causes that spread across many scales -- Different causes that become linked across many scales -- Chaos in physiological systems -- Cardiovascular chaos -- Metabolism -- Chaotic brain -- Physiological advantages of chaos -- Special situations.
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