Probabilistic biomechanical finite element simulations: whole-model classical hypothesis testing based on upcrossing geometry

TY - JOUR

T1 - Probabilistic biomechanical finite element simulations

T2 - whole-model classical hypothesis testing based on upcrossing geometry

AU - Pataky, Todd

AU - Koskei, Michihiko

AU - Cox, Philip Graham

N1 - © 2016, Pataky et al.

PY - 2016/11/7

Y1 - 2016/11/7

N2 - 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 fundamen- tals 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.

AB - 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 fundamen- tals 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.

KW - Biomechanics

KW - Computational statistics

KW - Finite element analysis

KW - Probabilistic simulation

KW - Random field theory

UR - http://www.scopus.com/inward/record.url?scp=85029247673&partnerID=8YFLogxK

U2 - 10.7717/peerj-cs.96

DO - 10.7717/peerj-cs.96

M3 - Article

SN - 2167-8359

VL - 2

JO - PeerJ

JF - PeerJ

IS - 11

M1 - e96

ER -