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Mathematical Models to Assess Foot–Ground Interaction: An Overview


Medicine & Science in Sports & Exercise: August 2013 - Volume 45 - Issue 8 - p 1524–1533
doi: 10.1249/MSS.0b013e31828be3a7
Applied Sciences

ABSTRACT The mechanical properties of the interface between the human body and the ground play an important role in attenuating the foot strike impact during locomotion. Understanding the properties of such an impact-attenuating system and the mathematical models governing its behavior has major implications in determining the load on the musculoskeletal system during locomotion. This interface consists of the plantar soft tissue and the sole complex of the shoe that together act like a sophisticated suspension system with generic viscoelastic properties. The interface has generally been modeled as a system of spring and damper, in which the reaction force deformation is expressed by a mathematical equation that represents the reaction force as a nonlinear function of the deformation and deformation rate of the interface. This overview intends to provide an insight into the different mathematical models that have been used to describe such relationship and into further understanding the role of the reaction model parameters in determining the behavior of the interface under compression. Various models included within this review ranged from the models representing the plantar soft tissue behavior during barefoot walking to those that consider the sole complex force–deformation behavior during shod foot running. The barefoot models are categorized under in vitro/in situ and in vivo, whereas the models representing the sole complex behavior are investigated before discussing the shod foot models. The mathematical models varied from those in which the reaction force was a nonlinear function of interface deformation to those that considered the deformation rate of the interface as a contributing factor to the interface reaction force. Ultimately, the implication of the reaction models in determining the load on the musculoskeletal system is discussed.

Faculty of Health Sciences, Staffordshire University, Stoke-on-Trent, UNITED KINGDOM

Address for correspondence: Roozbeh Naemi, Ph.D., Faculty of Health Sciences, Staffordshire University, Leek Road, Stoke-on-Trent ST4 2DF, United Kingdom; E-mail:

Submitted for publication September 2012.

Accepted for publication February 2013.

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© 2013 American College of Sports Medicine