Abstract
Statistical analyses of biomechanical finite element (FE) simulations are frequently conducted on scalar metrics extracted from anatomically homologous regions, like maximum von Mises stresses from demarcated bone areas. The advantages of this approach are numerical tabulability and statistical simplicity, but disadvantages include region demarcation subjectivity, spatial resolution reduction, and results interpretation complexity when attempting to mentally map tabulated results to original anatomy. This study proposes a method which abandons the two aforementioned advantages to overcome these three limitations. The method is inspired by parametric random field theory (RFT), but instead uses a non-parametric analogue to RFT which permits flexible model-wide statistical analyses through non-parametrically constructed probability densities regarding volumetric upcrossing geometry. We illustrate method fundamentals using basic 1D and 2D models, then use a public model of hip cartilage compression to highlight how the concepts can extend to practical biomechanical modeling. The ultimate whole-volume results are easy to interpret, and for constant model geometry the method is simple to implement. Moreover, our analyses demonstrate that the method can yield biomechanical insights which are difficult to infer from single simulations or tabulated multi-simulation results. Generalizability to non-constant geometry including subject-specific anatomy is discussed.
Highlights
In numerical finite element (FE) simulations of biomechanical continua model inputs like material properties and load magnitude are often imprecisely known
How to cite this article Pataky et al (2016), Probabilistic biomechanical finite element simulations: whole-model classical hypothesis testing based on upcrossing geometry
Maximum absolute t values differed amongst the field variables (Figs. 7D–7F), with stress exhibiting the largest maximum absolute t values
Summary
In numerical finite element (FE) simulations of biomechanical continua model inputs like material properties and load magnitude are often imprecisely known This uncertainty arises from a variety of sources including: measurement inaccuracy, in vivo measurement inaccessibility, and natural between-subject material, anatomical and loading variability (Cheung et al, 2005; Ross et al, 2005; Cox et al, 2011; Cox, Rinderknecht & Blanco, 2015; Fitton et al, 2012b). Despite this uncertainty, an investigator must choose specific parameter. Parameters are typically derived from published data, empirical estimation, or mechanical intuition (Kupczik et al, 2007; Cox et al, 2012; Cox, Kirkham & Herrel, 2013; Rayfield, 2011; Cuff, Bright & Rayfield, 2015)
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