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185651 
Journal Article 
Review 
Fractional calculus in biomechanics: a 3D viscoelastic model using regularized fractional derivative kernels with application to the human calcaneal fat pad 
Freed, AD; Diethelm, K 
2006 
Yes 
Biomechanics and Modeling in Mechanobiology
ISSN: 1617-7959
EISSN: 1617-7940 
5 
4 
203-215 
English 
16575573 
WOS:000242735900001 
A viscoelastic model of the K-BKZ (Kaye, Technical Report 134, College of Aeronautics, Cranfield 1962; Bernstein et al., Trans Soc Rheol 7: 391-410, 1963) type is developed for isotropic biological tissues and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. This elastic potential - via the K-BKZ hypothesis - also produces the tensorial structure of the viscoelastic model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including two functions whose origins lie in the fractional calculus. The Akaike information criterion is used to perform multi-model inference, enabling an objective selection to be made as to the best material function from within a candidate set. [References: 64] 
*Adipose Tissue/ph [Physiology]; Biomechanics; *Calcaneus/ph [Physiology]; Elasticity; Humans; Mathematics; *Models, Biological; Nonlinear Dynamics; Time Factors; Viscosity