Fractal Physiology, Complexity, and the Fractional Calculus

West, Bruce J.

doi:10.1002/0470037148.ch6

Cited by 9 publications

(5 citation statements)

References 74 publications

(154 reference statements)

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“…Note the similarity of these last three figures. So, as in the cases of HRV and BRV time series, we again find an erratic physiological time series to represent a random fractal process (West, 2006b ). In the SRV context, the implied clustering indicated by a slope greater than the random dashed line means that the intervals between strides change in clusters and not in a uniform manner over time.…”

Section: Manifestations Of Variabilitymentioning

confidence: 53%

“…The generalization of control theory to include fractional operators enables the designer to take into account memory and hereditary properties that are traditionally neglected in integer-order control theory (Podlubny, 1999 ), such as in traditional homeostasis. A fractional time integral is defined (West et al, 2003a ; West, 2006b )…”

Section: Control Of Variabilitymentioning

confidence: 99%

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Fractal physiology and the fractional calculus: a perspective

West¹

2010

Front. Physio.

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172

137

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This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.

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Section: Manifestations Of Variabilitymentioning

confidence: 53%

Section: Control Of Variabilitymentioning

confidence: 99%

Fractal physiology and the fractional calculus: a perspective

West¹

2010

Front. Physio.

Self Cite

172

137

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“…Later, control would return. We measured their hand movements to determine whether they showed 1/f scaling, a property of physiological systems that would indicate the mouse was being treated as part of a single system along with the rest of their body (Riley & Holden, 2012;West, 2006). As predicted, the hand-mouse movements of the participants exhibited 1/f scaling while the video game was working correctly.…”

Section: Radical Embodied Cognitive Sciencementioning

confidence: 83%

Radical Embodied Cognitive Science

Chemero

2013

Review of General Psychology

350

353

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This paper briefly introduces radical embodied cognitive science (RECS) and places it in historical perspective. Radical embodied cognitive science is an interdisciplinary approach to psychology that combines ideas from the phenomenological tradition with ecological psychology and dynamical systems modeling. It is argued that radical embodied cognitive science has a long history; it is as a direct descendent of the Jamesian functionalist approach to psychology. This approach to psychology is contrasted with the current trend of supplementing standard cognitive psychology with occasional references to the body. In contrast with these trends, radical embodied cognitive science is skeptical of the explanatory usefulness of mental representations. The future prospects of radical embodied cognitive science and the broader functionalist framework are discussed.

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“…While the coefficient in , the slope in the logarithmically transformed frequency power spectrum, estimates power-law scaling of activity amplitude in the frequency domain, the exponent from DFA estimates power-law scaling of variability in the time domain, and both and quantify temporal correlations in the time series [37] . We chose to use here instead of because, first, these two coefficients are related as [19] , [39] , and second, DFA has some advantages over other methods with respect to its robustness to non-stationarities in the data [40] . In the context of behavioral measurements, DFA has been applied to a wide range of studies, including heartbeat [41] , walking [42] , postural sway [43] , tapping to a repetitive signal [22] , and EEG recordings [44] .…”

Section: Methodsmentioning

confidence: 99%

A Demonstration of the Transition from Ready-to-Hand to Unready-to-Hand

2010

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The ideas of continental philosopher Martin Heidegger have been influential in cognitive science and artificial intelligence, despite the fact that there has been no effort to analyze these ideas empirically. The experiments reported here are designed to lend empirical support to Heidegger's phenomenology and more specifically his description of the transition between ready-to-hand and unready-to-hand modes in interactions with tools. In experiment 1, we found that a smoothly coping cognitive system exhibits type positively correlated noise and that its correlated character is reduced when the system is perturbed. This indicates that the participant and tool constitute a self-assembled, extended device during smooth coping and this device is disrupted by the perturbation. In experiment 2, we examine the re-organization of awareness that occurs when a smoothly coping, self-assembled, extended cognitive system is perturbed. We found that the disruption is accompanied by a change in attention which interferes with participants' performance on a simultaneous cognitive task. Together these experiments show that a smoothly coping participant-tool system can be temporarily disrupted and that this disruption causes a change in the participant's awareness. Since these two events follow as predictions from Heidegger's work, our study offers evidence for the hypothesized transition from readiness-to-hand to unreadiness-to-hand.

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Fractal Physiology, Complexity, and the Fractional Calculus

Cited by 9 publications

References 74 publications

Fractal physiology and the fractional calculus: a perspective

Fractal physiology and the fractional calculus: a perspective

Radical Embodied Cognitive Science

A Demonstration of the Transition from Ready-to-Hand to Unready-to-Hand

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