Advancing Sensitivity Analysis of an Intervertebral Disc Finite Element Model: A Comparative Approach Using Neural Networks

Abstract

Introduction: Sensitivity analysis (SA) is essential for identifying influential input parameters in finite element (FE) models, such as those of the intervertebral disc (IVD). However, in complex IVD models, efficient methods often lack accuracy, while precise methods are computationally prohibitive. Surrogate models, like neural networks (NNs), provide a solution by enabling both efficient and accurate SA of such models. Methods: This study leveraged an NN surrogate trained on an L4L5 IVD FE model to compare variance-based methods (Sobol analysis and Fourier Amplitude Sensitivity Test), the gradient-based Integrated Gradients (IG) approach, and linear model-based SA methods (CoD-ratio, CAR²-ratio, and Pearson’s correlation coefficients) for their applicability. Performance evaluation of each method involved mean absolute deviation and Normalized Discounted Cumulative Gain (NDCG) scores, with Sobol analysis results as the reference. A detailed SA of the model was conducted using Sobol analysis results to examine total-order and interaction effects of the model parameters. Results: All methods effectively identified influential parameters, as indicated by high NDCG scores. Only variance-based methods, though, consistently quantified parameter influence and captured interactions. Neglecting interaction effects resulted in unexplained variances up to 25%, highlighting the need to consider total-order effects. Key model parameters were those related to fiber orientation and annulus fibrosus stiffness. Conclusion: Variance-based global SA methods, enabled by the NN surrogate, were essential for fully understanding the FE model sensitivity, capturing total-order effects and parameter interactions. The IG method effectively identified key parameters, while the novel application of the NDCG scores demonstrated the strength of surrogate-assisted methods in assessing parameter influence.