A mathematical method for quantifying in vivo mechanical behaviour of heel pad under dynamic load

• Published in: Medical & biological engineering & computing 2016-03, Vol.54 (2-3), p.341-350
• Main Authors: Naemi, Roozbeh, Chatzistergos, Panagiotis E., Chockalingam, Nachiappan
• Format: Article
• Language: English
• Subjects: Analysis; Biomechanical Phenomena; Biomechanics; Biomedical and Life Sciences; Biomedical Engineering and Bioengineering; Biomedicine; Computer Applications; Computer based modeling; Deformation; Density; Elasticity; Energy dissipation; Feet; Foot diseases; Hardness tests; Heel - physiology; Heels; Human Physiology; Humans; Imaging; Load; Male; Mathematical analysis; Mathematical models; Mechanical properties; Models, Biological; Musculoskeletal system; Nonlinear Dynamics; Original Article; Radiology; Stress measurement; Stress, Mechanical; Stress-strain relationships; Studies; Tissues; Ultrasonic imaging; Ultrasonics; Viscoelasticity; Viscosity; Walking; Weight-Bearing - physiology
• ISSN: 0140-0118; 1741-0444
• DOI: 10.1007/s11517-015-1316-5

Mechanical behaviour of the heel pad, as a shock attenuating interface during a foot strike, determines the loading on the musculoskeletal system during walking. The mathematical models that describe the force deformation relationship of the heel pad structure can determine the mechanical behaviour of heel pad under load. Hence, the purpose of this study was to propose a method of quantifying the heel pad stress–strain relationship using force–deformation data from an indentation test. The energy input and energy returned densities were calculated by numerically integrating the area below the stress–strain curve during loading and unloading, respectively. Elastic energy and energy absorbed densities were calculated as the sum of and the difference between energy input and energy returned densities, respectively. By fitting the energy function, derived from a nonlinear viscoelastic model, to the energy density–strain data, the elastic and viscous model parameters were quantified. The viscous and elastic exponent model parameters were significantly correlated with maximum strain, indicating the need to perform indentation tests at realistic maximum strains relevant to walking. The proposed method showed to be able to differentiate between the elastic and viscous components of the heel pad response to loading and to allow quantifying the corresponding stress–strain model parameters.