Instantaneous Generation of Subject-Specific Finite Element Models of the Hip Capsule

Abstract

Subject-specific hip capsule models could offer insights into impingement and dislocation risk when coupled with computer-aided surgery, but model calibration is time-consuming using traditional techniques. This study developed a framework for instantaneously generating subject-specific finite element (FE) capsule representations from regression models trained with a probabilistic approach. A validated FE model of the implanted hip capsule was evaluated probabilistically to generate a training dataset relating capsule geometry and material properties to hip laxity. Multivariate regression models were trained using 90% of trials to predict capsule properties based on hip laxity and attachment site information. The regression models were validated using the remaining 10% of the training set by comparing differences in hip laxity between the original trials and the regression-derived capsules. Root mean square errors (RMSEs) in laxity predictions ranged from 1.8° to 2.3°, depending on the type of laxity used in the training set. The RMSE, when predicting the laxity measured from five cadaveric specimens with total hip arthroplasty, was 4.5°. Model generation time was reduced from days to milliseconds. The results demonstrated the potential of regression-based training to instantaneously generate subject-specific FE models and have implications for integrating subject-specific capsule models into surgical planning software.

Keywords: hip capsule; statistical shape model; subject-specific models; surrogate modeling; total hip arthroplasty.

Figure 1

Anterior (a) and posterior (b) views of the implanted hip capsule were divided into six sectors, numbered circumferentially from the most superior attachment of the capsule.

Figure 2

Workflow to develop the multilinear regression model. A training set of hip capsule models was generated from a validated FE model, including capsule properties, geometric variability, and the resulting hip laxity (top left). The training set was used to formulate a multilinear regression model that predicts capsule properties from hip laxity (bottom left). The regression model was tested through comparisons with FE models from the validation set (top right) and by predicting capsule properties for cadaveric hip specimen (bottom right).

Figure 3

Automated workflow to identify origin and insertion sites of the hip capsule in a database of hip bony geometry.

Figure 4

Convergence of the multivariate regression model where the cumulative RMSE decreased as the number of trials in the training set increased.

Figure 5

Origin and insertion of the capsule were approximated as ellipses to aid in parametrization and automation of the capsule creation. The black, red, and green lines represent mean, +2 standard deviations, and −2 standard deviations of PCs 1–4, respectively.

Figure 6

Probabilistic response of all 40 laxity parameters from the 500 trials during I-E rotation (a) and Ad-AB (b) rotations. Error bars show ±1 standard deviation.

Figure 7

Box plot of RMSE when using different hip laxities in the training sets. Horizontal bars indicate statistical differences between sets (p < 0.05), circles indicate the mean RMSE, and + indicate outliers.

Figure 8

RMSE between FE models created using multilinear regression and test models from the initial probabilistic analysis for each combination of input laxity data. Horizontal red lines represent the mean RMSE across all 40 laxity measures.

Figure 9

Correlation between experimental laxity and FE model predictions calibrated using multilinear regression, using Training Sets 2 (a) and 8 (b).