The fractal lung: Universal and species-related scaling patterns

Nelson, Thomas R.; West, Bruce J.; Goldberger, Ary L.

doi:10.1007/bf01951755

Cited by 110 publications

(74 citation statements)

References 9 publications

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“…Accordingly, even among mammals, structural variability remains high. For example, [27] describe the differences in the geometrical scaling properties of human lungs on one side, and of rats, dogs and hamsters lungs on the other side. Moreover, [25] show that the criteria of energetic optimality and of robustness for the gas exchanges, with respect to geometric variations, are incompatible.…”

Section: Theoretical Consequences Of This Interpretationmentioning

confidence: 99%

Randomness Increases Order in Biological Evolution

Longo

Montévil

2012

Computation, Physics and Beyond

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In this text3 , we revisit part of the analysis of anti-entropy in [4] and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness.

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Section: Theoretical Consequences Of This Interpretationmentioning

confidence: 99%

Randomness Increases Order in Biological Evolution

Longo

Montévil

2012

Computation, Physics and Beyond

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“…Thus, information in fractal phenomena is coupled across multiple scales, as for example, observed in the architecture of the mammalian lung [35,53,55], manifest in the long-range correlations in human gait [18,56] and measured in the human cardiovascular network [40], all of which are discussed in West [57]. The geometric interpretation of fractals is also given in the fractal nutrient model of allometry developed in WBE [64].…”

Section: Fractional Probability Calculusmentioning

confidence: 99%

Fractional dynamics of allometry

West

2011

fcaa

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Allometry relations (ARs) in physiology are nearly two hundred years old. In general if X ij is a measure of the size of the i th member of a complex host network from species j and Y ij is a property of a complex subnetwork embedded within the host network an intraspecies AR exists between the two when Y ij = aX b ij . We emphasize that the reductionist models of AR interpret X ij and Y ij as dynamic variables, albeit the ARs themselves are explicitly time independent. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret X i and Y i as averages over an ensemble of individuals to yields the interspecies AR Y i = a X i b . Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of intraspecies ARs is a little over a decade old and although well received it has not been universally accepted. An alternate perspective is given by the interspecies AR based on linear regression analysis of fluctuating data sets. We emphasize that the intraspecies and interspecies ARs are not the same and show that the interspecies AR can only be derived from the intraspecies one for a narrow distribution of fluctuations. This condition is not satisfied by metabolic data as is shown separately for aviary and mammal data sets. The empirical distribution of metabolic allometry coefficients is shown herein to be Pareto in form. A number of reductionist arguments conclude that the allometry exponent is universal, however herein we derive a deterministic relation between the allometry exponent and the allometry coefficient using the fractional calculus. The co-variation relation violates the universality assumption. We conclude that the interspecies physiologic AR is entailed by the scaling behavior of the probability density, which is derived using the fractional probability calculus.MSC 2010 : 91Exx, 28A80, 35R11, 37N25, 82C31, 82C41, 62J05

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“…Consequently, such functions are not the solutions to traditional equations of motion with integer-order derivatives, and therefore, the phenomena they describe are not simple mechanical processes. Thus, information in fractal phenomena is coupled across multiple scales, as, for example, observed in the architecture of the mammalian lung [114][115][116] and in cities [107]; manifest in the long-range correlations in human gait [117,118] and the extinction of biological species [103]; measured in the human cardiovascular network [119] and in a number of other contexts [13]. The geometric interpretation of fractals is also given in the fractal nutrient model of AR [11].…”

Section: Fractional Calculusmentioning

confidence: 99%

A Fractional Probability Calculus View of Allometry

West¹

2014

Systems

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The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social and life sciences. Herein, we present a theory of allometry that provides a foundation for the allometry relation between a network function and the size that is entailed by the hypothesis that the fluctuations in the two measures are described by a scaling of the joint probability density. The dynamics of such networks are described by the fractional calculus, whose scaling solutions entail the empirically observed allometry relations.

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The fractal lung: Universal and species-related scaling patterns

Cited by 110 publications

References 9 publications

Randomness Increases Order in Biological Evolution

Randomness Increases Order in Biological Evolution

Fractional dynamics of allometry

A Fractional Probability Calculus View of Allometry

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