A Novel Decomposition-Based Growth Model for Simulating Stress-Modulated Spinal Growth.

Understanding the mechanobiological mechanisms of spinal growth is essential for modeling progressive deformities, particularly adolescent idiopathic scoliosis (AIS). In this study, we present a novel finite element methodology for simulating mechanobiological growth governed by the Hueter-Volkmann law. The approach is developed in the large deformation framework and uses the Hueter-Volkmann law for the first time in a decomposition-based framework in which the growth is incorporated into the constitutive model via multiplicative decomposition of the deformation gradient. For comparison purposes, we also implement the sequential method widely used in the literature. Although both approaches are based on the Hueter-Volkmann law, which relates the normal compressive stress on the growth plate to local growth inhibition, they differ significantly in how this principle is integrated into the finite element framework. Unlike the sequential method, which requires successive growth computation and mechanical solution steps, along with repeated updates of the growth direction, the proposed decomposition-based approach solves stress-induced deformations and growth simultaneously. It is formulated in the Lagrangian configuration, eliminating the need to update the growth direction throughout the simulation. The proposed formulation not only offers superior numerical stability but also exhibits lower computational complexity compared to the sequential method, particularly under large deformations. The method is evaluated using a finite element model of a simplified Functional Spinal Unit (FSU) under symmetric and asymmetric compressive loading over a two-year growth period. While both approaches produce comparable wedge angle progression, the decomposition-based formulation, which more realistically resembles the actual growth process, results in smoother deformations, less element distortion, and substantially reduced computational cost. Additionally, a robust wedge angle calculation technique is introduced using least plane fitting to full endplate nodes of the vertebral bodies, improving geometric accuracy and reducing mesh sensitivity. Together, these features establish a reliable and efficient framework for long-term spinal growth simulations and offer a promising foundation for future patient-specific modeling and clinical applications.