Fractional calculus models of complex dynamics in biological tissues. (English) Zbl 1189.92007

Magin, Richard L.

Comput. Math. Appl. 59, No. 5, 1586-1593 (2010).

Summary: Fractional (non-integer order) calculus can provide a concise model for the description of the dynamic events that occur in biological tissues. Such a description is important for gaining an understanding of the underlying multiscale processes that occur when, for example, tissues are electrically stimulated or mechanically stressed. The mathematics of fractional calculus has been applied successfully in physics, chemistry, and material sciences to describe dielectrics, electrodes and viscoelastic materials over extended ranges of time and frequency. In heat and mass transfer, for example, the half-order fractional integral is the natural mathematical connection between thermal or material gradients and the diffusion of heat or ions. Since the material properties of tissues arise from the nanoscale and microscale architecture of subcellular, cellular, and extracellular networks, the challenge for bioengineers is to develop new dynamic models that predict macroscale behavior from microscale observations and measurements. We describe three areas of bioengineering research (bioelectrodes, biomechanics, bioimaging) where fractional calculus is being applied to build these new mathematical models.

MSC:

92C05	Biophysics
92C37	Cell biology
92C30	Physiology (general)
26A33	Fractional derivatives and integrals
28A80	Fractals

Keywords:

impedance; viscosity; stress

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