Discovering a Biomechanical Prediction Model for Adolescent Idiopathic Scoliosis by Combining PINN with State Space Models

Biomechanics are crucial for diagnosing and analyzing Adolescent Idiopathic Scoliosis (AIS) in CT images. Recent research suggests that spine biomechanics follow equilibrium equations, but the exact mathematical model and parameters are not fully understood. In this study, we use equilibrium equations and state space models to develop a computational biomechanics framework. Specifically, we create a model combining biomechanical analysis based on equilibrium equations with state-space image segmentation. First, we propose PM-UNet, a segmentation method using a state-space model to capture bone structure in CT images. Then, Physical Information Neural Networks (PINN) with equilibrium equations, using control matrices α and β, calculate biomechanical properties. We validate the model by comparing results with FEM calculations. The experimental results show that the PM-UNet and PINN framework effectively extracts mechanical features and calculates biomechanical properties, providing a foundation for advanced analysis and improving surgical planning and brace design for AIS.