Nonlinear elastic material property estimation of lower extremity residual limb tissues

Abstract

The interface stresses between the residual limb and prosthetic socket have been studied to investigate prosthetic fit. Finite-element models of the residual limb-prosthetic socket interface facilitate investigation of the mechanical interface and may serve as a potential tool for future prosthetic socket design. However, the success of such residual limb models to date has been limited, in large part due to inadequate material formulations used to approximate the mechanical behavior of residual limb soft tissues. Nonlinear finite-element analysis was used to simulate force-displacement data obtained during in vivo rate-controlled (1, 5, and 10 mm/s) cyclic indentation of the residual limb soft tissues of seven individuals with transtibial amputation. The finite-element models facilitated determination of an appropriate set of nonlinear elastic material coefficients for bulk soft tissue at discrete clinically relevant test locations. Axisymmetric finite-element models of the residual limb bulk soft tissue in the vicinity of the test location, the socket wall and the indentor tip were developed incorporating contact analysis, large displacement, and large strain, and the James-Green-Simpson nonlinear elastic material formulation. Model dimensions were based on medical imaging studies of the residual limbs. The material coefficients were selected such that the normalized sum of square error (NSSE) between the experimental and finite-element model indentor tip reaction force was minimized. A total of 95% of the experimental data were simulated using the James-Green-Simpson material formulation with an NSSE NOT THE PUBLISHED VERSION; this is the author's final, peer-reviewed manuscript. The published version may be accessed by following the link in the citation at the bottom of the page. Engineering, Vol 11, No. 1 (March 2003): 43-53. DOI. This article is © Institute of Electrical and Electronics Engineers (IEEE) and permission has been granted for this version to appear in e-Publications@Marquette. Institute of Electrical and Electronics Engineers (IEEE) does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Institute of Electrical and Electronics Engineers (IEEE). IEEE Transactions on Neural Systems and Rehabilitation2 less than 5%. The respective James-Green-Simpson material coefficients varied with subject, test location, and indentation rate. Therefore, these coefficients cannot be readily extrapolated to other sites or individuals, or to the same site and individual some time after testing. NomenclatureNonlinear elastic material coefficients; subscript indicates the order in strain invariant.Nonlinear elastic material coefficients in James-Green-Simpson material model; = order in first strain invariant 1 ; = order in second strain invariant 2 .Components of Green-Lagrange finite strain tensor.

Real-Time Patient-Specific Finite Element Analysis of Internal Stresses in the Soft Tissues of a Residual Limb: A New Tool for Prosthetic Fitting

“…The first attempt to use a nonlinear material model for the soft tissues of the residual limb, by Simpson et al 38 , employed a Mooney-Rivlin model with parameters obtained from indentation measurements 36 to understand the effects of liner design on limb surface stresses. Later, Tonuk and SilverThorn 41,42 were the only authors to study the utility of non-linear material models for representing the soft tissues of the residual limb in patient-specific models. Specifically, they studied the validity of linear-elastic material model for the soft tissues of the residual limb, with respect to a non-linear James-Green-Simpson strain energy function-based material model.…”

“…In the present study, we used indentations of up to 5 mm, which correspond to maximal forces of 500 g. Considering that our method is clinically oriented, and that in amputees with vascular disorders of the residual limb it is not desired to apply high focal pressures on tissues during indentation testing, we obtained the parameters of a linear elastic material model. A second consideration is that non-linear material models require prior computer analyses for fitting the material model parameters to the experimental (force-displacement) data from the individual 41,42 , which may be time-consuming in the clinic. Moreover, FE analyses involving non-linear material models are solved by iterative methods, which hamper the real-time solution process.…”

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

“…For example, Tönük and Silver-Thorn (2003) fit their experimental results using a James–Green–Simpson nonlinear elastic material model. The use of high-order constitutive equations however, typically requires additional assumptions about the material (isotropy and homogeneity in the case of Tönük and Silver-Thorn) lest a prohibitive number of independent material coefficients arise.…”

Physically Based Modelling and Simulation to Innovate Socket Design

“…During the last years, to get a better approximation of soft tissue behavior, nonlinear elastic and also nonlinear viscoelastic approximations have been adopted [27,28]. This increases the complexity of the FE model and requires additional computational time.…”