Mechanobiological modeling of vertebral growth and wedge angle formation in a functional spinal unit

Date

2026-1-22

Author

Çakmak, Serhat Onur

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Spinal growth is governed by complex mechanobiological interactions, and disturbances in these processes can lead to progressive deformities such as adolescent idiopathic scoliosis (AIS). Accurate computational modeling of growth regulation is therefore essential for improving our understanding of spinal development and supporting patient-specific treatment strategies. This study introduces a novel finite element framework to model growth processes controlled by the Hueter-Volkmann law, which links compressive stress to localized growth suppression. The proposed formulation adopts a decomposition based approach, in which the growth part of the deformation gradient is embedded directly into the constitutive equations through a multiplicative decomposition of the total deformation gradient. The model simultaneously solves for mechanical deformation and growth in a fully Lagrangian configuration, eliminating iterative growth direction updates. This design enhances numerical stability, maintains robustness under large deformations, and reduces computational effort. A comparison study is conducted using a Functional Spinal Unit (FSU) model. The wedge angles of the vertebral bodies in FSU are compared with those from a widely used method in the literature, where growth is simulated through a staggered scheme, with stress and thermal expansion solved sequentially. The results of the two approaches are found to be consistent. The proposed method demonstrated accurate wedge angle prediction, smoother deformation fields, reduced mesh distortion, and, in addition, offered nearly an order of magnitude higher computational efficiency, thus providing a novel, robust and efficient framework for long-term spinal growth simulations with significant potential for clinical decision-making and mechanobiological research.

Subject Keywords

Functional spinal unit (FSU), Finite element method (FEM), Mechanobiological growth, Hueter–Volkmann law, Vertebral wedging

URI

https://hdl.handle.net/11511/118476

Collections

Graduate School of Natural and Applied Sciences, Thesis