Cite this article as: Sara Behforootan, Panagiotis E. Chatzistergos, Nachiappan Chockalingam and Roozbeh Naemi, A clinically applicable non-invasive method to quantitatively assess the visco-hyperelastic properties of human heel pad with implications for assessing the risk of mechanical trauma, Journal of the Mechanical Behavior of Biomedical Materials, http://dx.doi.org/10.1016Materials, http://dx.doi.org/10. /j.jmbbm.2017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Purpose: To develop a clinically viable non-invasive method of assessing the mechanical properties of the heel pad. Furthermore the effect of non-linear mechanical behaviour of the heel pad on its ability to uniformly distribute foot-ground contact loads in light of the effect of overloading is also investigated. Methods:An automated custom device for ultrasound indentation was developed along with custom algorithms for the automated subject specific modeling of heel pad. Non-time-dependent and time-dependent material properties were inverse engineered from results from quasistatic indentation and stress relaxation test respectively. The validity of the calculated coefficients was assessed for five healthy participants. The implications of altered mechanical properties on the heel pad's ability to uniformly distribute plantar loading were also investigated in a parametric analysis. Results:The subject specific heel pad models with coefficients calculated based on quasi-static indentation and stress relaxation were able to accurately simulate dynamic indentation.Average error in the predicted forces for maximum deformation was only 6.6 ± 4.0%. When the inverse engineered coefficients were used to simulate the first instance of heel strike the error in terms of peak plantar pressure was 27%. The parametric analysis indicated that the heel pad's ability to uniformly distribute plantar loads is influenced both by its overall deformability and by its stress/ strain behaviour. When overall deformability stays constant, changes in stress/strain behaviour leading to a more "linear" mechanical behaviour appear to improve the heel pad's ability to uniformly distribute plantar loading. Conclusions:The developed technique can accurately assess the visco-hyperelastic behaviour of heel pad. It was observed that specific change in stress-strain behaviour can enhance/weaken the heel pad's ability to uniformly distribute plantar loading that will increase/decrease the risk for overloading and trauma.

This study combines non-invasive mechanical testing with finite element (FE) modelling to assess for the first time the reliability of shear wave (SW) elastography for the quantitative assessment of the in-vivo nonlinear mechanical behavior of heel-pad. The heel-pads of five volunteers were compressed using a custom-made ultrasound indentation device. Tissue deformation was assessed from B-mode ultrasound and force was measured using a load cell to calculate the force - deformation graph of the indentation test. These results were used to design subject specific FE models and to inverse engineer the tissue's hyperelastic material coefficients and its stress - strain behavior. SW speed was measured for different levels of compression (from 0% to 50% compression). SW speed for 0% compression was used to assess the initial stiffness of heel-pad (i.e. initial shear modulus, initial Young's modulus). Changes in SW speed with increasing compressive loading were used to quantify the tissue's nonlinear mechanical behavior based on the theory of acoustoelasticity. Statistical analysis of results showed significant correlation between SW-based and FE-based estimations of initial stiffness, but SW underestimated initial shear modulus by 64%(±16). A linear relationship was found between the SW-based and FE-based estimations of nonlinear behavior. The results of this study indicate that SW elastography is capable of reliably assessing differences in stiffness, but the absolute values of stiffness should be used with caution. Measuring changes in SW speed for different magnitudes of compression enables the quantification of the tissue's nonlinear behavior which can significantly enhance the diagnostic value of SW elastography.

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Internal strain is known to be one of the contributors to plantar soft tissue damage. However, due to challenges related to measurement techniques, there is a paucity of research investigating the strain within the plantar soft tissue during daily weight-bearing activities. Therefore, the main aim of this study was to develop a non-invasive method for predicting heel pad strain during loading. An ultrasound indentation technique along with a mathematical model was employed to calculate visco-hyperelastic structural coefficients from the results of cyclic-dynamic indentation and stress-relaxation tests. Subject-specific structural coefficients of heel pads were calculated from twenty participants along with the assessment of plantar pressure. The average difference between the predicted and the measured force during the cyclic-dynamic indentation test was only 5.8%. Moreover, the average difference between the predicted and the in vivo strain during walking was 14%. No statistically significant correlation was observed between maximum strain and peak plantar pressure during walking; indicating that the measurement of strain along with plantar pressure can improve our understanding of the mechanical behaviour of the plantar soft tissue.

Mechanical properties of the plantar soft tissue, which acts as the interface between the skeleton and the ground, play an important role in distributing the force underneath the foot and in influencing the load transfer to the entire body during weight-bearing activities. Hence, understanding the mechanical behaviour of the plantar soft tissue and the mathematical equations that govern such behaviour can have important applications in investigating the effect of disease and injuries on soft tissue function. The plantar soft tissue of the foot shows a viscoelastic behaviour, where the reaction force is not only dependent on the amount of deformation but also influenced by the deformation rate. This chapter provides an insight into the mechanical behaviour of plantar soft tissue during loading with specific emphasis on heel pad, which is the first point of contact during normal gait. Furthermore, the methods of assessing the mechanical behaviour including the in vitro/in situ and in vivo are discussed, and examples of creep, stress relaxation, rate dependency and hysteresis behaviour of the heel pad are shown. In addition, the viscoelastic models that represent the mechanical behaviour of the plantar soft tissue under load along with the equations that govern this behaviour are elaborated and discussed.