Verification, validation and sensitivity studies in computational biomechanics

Abstract

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.

Figure 1

Overview of the verification and validation process. Verification deals with assessing the ability of the model to solve the mathematical representation of the conceptual model correctly and can be separated into code verification and calculation verification. Validation assures that the model represents the true mechanical behavior of the physical system with sufficient accuracy. Model accuracy is assessed using quantitative comparisons between computational predictions and experimental results. The computational model and/or experiment are revised if the model is determined to be inaccurate for the intended use. Adapted from [4] with permission.

Figure 2

Flowchart illustrating the path from conceptual to computational model. The conceptual model is the simplified representation of the reality of interest. Mathematical equations are used to describe the mechanical behavior of the conceptual model. Numerical algorithms are chosen to solve these mathematical equations and are coded appropriately. Physical parameters and discretization parameters are incorporated into the model. Adapted from [4] with permission.

Figure 3

Flow chart of the verification procedure. During model verification computational predictions are quantitatively compared to analytical solutions, semi-analytical solutions, or numerical solutions. Adapted from [5] with permission.

Figure 4

Theoretical and material point method (MPM) predictions for fiber stress vs. strain during uniaxial extension for a transversely isotropic hyperelastic material representation. Separate simulations were carried out with the fiber orientation aligned with (along) the direction of extension and transverse (cross) to the direction of extension. There was less than a 3% difference between analytical and computational results using both explicit and implicit integration. Reprinted from [43] with permission.

Figure 5

Top panel - fringe plot of 1st principal Green-Lagrange strains for a course mesh of the inferior glenohumeral ligament complex (1650 shell elements). Model deformation is correct, but mesh induced ‘hot-spots’ are prevalent. Bottom panel - refined mesh of the inferior glenohumeral ligament complex (6600 shell elements) showing considerable differences in strains when compared to the coarse mesh, especially in areas of ligament buckling. Average strains from this final mesh were less than one percent different than a mesh with twice as many elements. Reprinted from [28] with permission.

Figure 6

Flow chart of the validation procedure. During model validation computational predictions are quantitatively compared to experimental data that is organized in order of increasing complexity. Adapted from [5] with permission.

Figure 7

FE predicted vs. experimental cortical bone principal strains. Top panel - subject-specific, middle panel - constant trabecular modulus, bottom panel - constant cortical thickness. For the subject-specific model there was strong correlation between predicted and experimentally measured strains, with a best-fit line that did not differ significantly from the line y=x (Experimental strains=FE predicted strains). Predicted cortical bone strains were more sensitive to cortical bone thickness than trabecular modulus. Reprinted from [34] with permission.