EPINN-GF: An enhanced physics-informed neural network integrating geometric features for stress prediction in complex...

Understanding spinal biomechanics is essential for exploring the functions of the spine and the pathogenesis of related diseases. Traditional numerical methods for biomechanical analysis are computationally expensive, while Physics-Informed Neural Network (PINN) struggles with complex solid geometries. This study develops an Enhanced Physics-Informed Neural Network that integrates Geometric Features (EPINN-GF) to address these limitations in predicting stress distribution for the complex spinal geometries.

The primary objective of this study is to improve both the accuracy and efficiency of predicting stress distributions in the complex spinal geometries using the proposed EPINN‑GF framework. The secondary objective is to facilitate the clinical translation to support the diagnosis, surgical planning, and personalized treatment for the spinal disorders, particularly Adolescent Idiopathic Scoliosis (AIS).

This study proposes EPINN-GF, which innovatively integrates geometric features and dual loss constraints. Specifically, the eigenvectors of the Laplacian operator, derived from spinal geometry coordinates, are utilized to capture both global and local structural characteristics of the spine. These eigenvectors, along with their corresponding normalized coordinates, serve as inputs to EPINN-GF. Furthermore, the equilibrium equations, which describe the balance between internal and external forces acting on the material, are embedded in the network's loss function.

Experimental results demonstrate the superiority of EPINN-GF in spinal stress prediction, with a mean squared error (MSE) of 227.59 MPa compared to 398.41 MPa, 271.43 MPa, and 343.61 MPa for Collocation-based PINN (C-PINN), Graph Neural Network (GNN), and Deep Energy Method (DEM), respectively. Despite the training time of 1917.71 s for the EPINN-GF, which is slightly longer than those of 1713.03 s and 1883.68 s for C-PINN and GNN, respectively, it achieves higher stress prediction accuracy, making it a promising tool for spinal disease diagnosis and modeling complex physical systems.

EPINN-GF accurately predicts stress in the geometrically complex spinal regions and multi-physical environments, offering the potential clinical value for the spinal disorders by enabling personalized treatment planning, optimizing surgical strategies, and supporting early AIS progression prediction.