Abstract
Several nonlinear and anisotropic constitutive models have been proposed to describe the biomechanical properties of soft tissues, and reliably estimating the unknown parameters in these models using experimental data is an important step towards developing predictive capabilities. However, the effect of parameter estimation technique on the resulting biomechanical parameters remains under-analyzed. Standard off-the-shelf techniques can produce unreliable results where the parameters are not uniquely identified and can vary with the initial guess. In this study, a thorough analysis of parameter estimation techniques on the resulting properties for four multi-parameter invariant-based constitutive models is presented. It was found that linear transformations have no effect on parameter estimation for the presented cases, and nonlinear transforms are necessary for any improvement. A distinct focus is put on the issue of non-convergence, and we propose simple modifications that not only improve the speed of convergence but also avoid convergence to a wrong solution. The proposed modifications are straightforward to implement and can avoid severe problems in the biomechanical analysis. The results also show that including the fiber angle as an unknown in the parameter estimation makes it extremely challenging, where almost all of the formulations and models fail to converge to the true solution. Therefore, until this issue is resolved, a non-mechanical—such as optical—technique for determining the fiber angle is required in conjunction with the planar biaxial test for a robust biomechanical analysis.
Highlights
Characterizing the biomechanical properties of soft tissues remains a crucial starting point for describing and predicting their behavior [1]
The Hessian matrix can be inverted accurately, and linear preconditioners have no advantage for the presented problem. This is an important characteristic of biomechanical problems: the challenges are different from other engineering fields, which necessitates different solutions
The improvements found in this study will motivate further work along these lines to improve the biomechanical parameter estimation and, analysis
Summary
Characterizing the biomechanical properties of soft tissues remains a crucial starting point for describing and predicting their behavior [1]. In order to describe the wealth of experimental data, different constitutive models have been developed, and nonlinearity and anisotropy remain a hallmark of these models [6]. With the increasing complexity of the constitutive models for soft tissues, the number of associated fitting parameters has increased. The process of fitting these models to the experimental data, knowns as parameter estimation, is an important step [7]. Due to the high nonlinearity and anisotropy, the parameters can become correlated, and the experimental data may not be sufficient to uniquely identify them [9,10]. Determining an optimum set of experiments required to uniquely and accurately estimate the model parameters is an active area of research [11]
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