Fractional Calculus Model of Electrical Impedance Applied to Human Skin

Autor: Goran Lazovic, Jovana Simic-Krstic, Gradimir N. Misevic, Zoran B. Vosika
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Medical Physics
Complex system
Biophysics
lcsh:Medicine
02 engineering and technology
Dermatology
Dermatologic Pathology
01 natural sciences
Biophysics Simulations
law.invention
symbols.namesake
Operator (computer programming)
Electricity
law
Diagnostic Medicine
0103 physical sciences
0202 electrical engineering
electronic engineering
information engineering
Taylor series
Electric Impedance
Applied mathematics
Humans
lcsh:Science
Representation (mathematics)
010301 acoustics
Biology
Skin
Physics
Multidisciplinary
Calculus
Mathematical model
lcsh:R
Electric Conductivity
Computational Biology
Models
Theoretical
Fractional calculus
Nonlinear system
Nonlinear Dynamics
Electrical network
symbols
Medicine
lcsh:Q
020201 artificial intelligence & image processing
Biophysic Al Simulations
Fractional Calculus
Mathematics
Research Article
Zdroj: PLoS ONE
PLoS ONE, Vol 8, Iss 4, p e59483 (2013)
ISSN: 1932-6203
Popis: Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Databáze: OpenAIRE
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