Avalanches in the lung: A statistical mechanical model.
TLDR
It is found that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.Abstract:
We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.read more
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Self-organized criticality
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Complexity of chronic asthma and chronic obstructive pulmonary disease: implications for risk assessment, and disease progression and control
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Improved arterial oxygenation with biologically variable or fractal ventilation using low tidal volumes in a porcine model of acute respiratory distress syndrome.
Abdulaziz Boker,M. Ruth Graham,Keith R. Walley,Bruce M. McManus,Linda G. Girling,Elizabeth K.-Y. Walker,Gerald R. Lefevre,W. Alan C. Mutch +7 more
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References
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Book
The Theory of Branching Processes
TL;DR: A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations is given in this article, followed by a systematic development of branching processes, and a brief description of some of the important applications.
Book
Fractals and Disordered Systems
Armin Bunde,Shlomo Havlin +1 more
TL;DR: In this article, the authors present a model of 2D DLA growth in a 3D setting, which is based on the Laplace Equation (LE) and its variants.
Book
Fractal Physiology
William D. Deering,Bruce J. West +1 more
TL;DR: The nature of fractals and the use of fractal instead of classical scaling concepts to describe the irregular surfaces, structures, and processes exhibited by physiological systems are described in this paper.
Journal ArticleDOI
Fractals and Disordered Systems
TL;DR: The substantial progress in the field of phase transitions and surface restructuring mainly based on new techniques and successfully accompanied by theoretical approaches is comprehensively documented in the 14 chapters of this volume with numerous references as discussed by the authors.