Don't You (Project Around Discs)? Neural Network Surrogate and Projected Gradient Descent for Calibrating an Intervertebral Disc Finite Element Model

Accurate calibration of finite element (FE) models of human intervertebral discs (IVDs) is essential for their reliability and application in diagnosing and planning treatments for spinal conditions. Traditional calibration methods are computationally intensive, requiring iterative, derivative-free optimization algorithms that often take hours or days to converge. This study addresses these challenges by introducing a novel, efficient, and effective calibration method for an L4-L5 IVD FE model using a neural network (NN) surrogate. The NN surrogate predicts simulation outcomes with high accuracy, outperforming other machine learning models, and significantly reduces the computational cost associated with traditional FE simulations. Next, a Projected Gradient Descent (PGD) approach guided by gradients of the NN surrogate is proposed to efficiently calibrate FE models. Our method explicitly enforces feasibility with a projection step, thus maintaining material bounds throughout the optimization process. The proposed method is evaluated against state-of-the-art Genetic Algorithm (GA) and inverse model baselines on synthetic and in vitro experimental datasets. Our approach demonstrates superior performance on synthetic data, achieving a Mean Absolute Error (MAE) of 0.06 compared to the baselines' MAE of 0.18 and 0.54, respectively. On experimental specimens, our method outperforms the baseline in 5 out of 6 cases. Most importantly, our approach reduces calibration time to under three seconds, compared to up to 8 days per sample required by traditional calibration. Such efficiency paves the way for applying more complex FE models, enabling accurate patient-specific simulations and advancing spinal treatment planning.