InterPore2025

Towards a Predictive Model for Vertebral Failure: Coupled Tumor Growth and Bone Remodeling Framework

20 May 2025, 11:50

15m

Oral Presentation (MS20) Biophysics of living porous media MS20

Speaker

Dr Hani Cheikh Sleiman (Department of Mechanical Engineering, University College London, London, UK)

Description

Bone metastases, particularly in the spine, present a significant clinical challenge as they weaken the structural integrity of vertebrae, increasing the risk of fractures and spinal cord injuries. Tumours disrupt the normal balance of bone remodelling through a complex interplay of molecular signalling, biochemical changes, and mechanical forces, resulting in lesions characterized by excessive bone resorption or formation. Therefore, to accurately predict bone failure, it is essential to first model tumour growth and its effect on bone formation and resorption.

This work aims to develop a mathematical model to predict vertebral failure by first constructing a coupled tumour growth and bone remodelling framework. The tumour environment is treated as a porous medium where the different cell populations are assumed to behave as viscous fluids. The deformable bone matrix constitutes the solid scaffold, while the pore space is saturated by the tumour cells, host cells and the interstitial fluid. The tumour cell phase is further split between two species: living tumour cells and necrotic ones. We also account for cells metabolism and oxygenation by adding an oxygen specie in the interstitial fluid phase.

However, to investigate the impact of the tumour on bone formation and resorption, additional species need to be incorporated into the multiphase system. Specifically, two cell populations—osteoblasts and osteoclasts—must be included within the host cells phase. Additionally, two signalling molecules, RANKL and OPG, which regulate the differentiation and activation of these cells, must be introduced as species within the interstitial fluid phase.
The coupling of the tumour growth and bone remodelling models enables the prediction of microstructural evolution over time. By linking this evolution to the bone's mechanical properties, it becomes possible to run damage mechanics models to predict crack initiation and propagation in the vertebrae, thereby facilitating the characterization of fracture risk.
Starting from the general conservation equations of mass and momentum derived using the Thermodynamically Constrained Averaging Theory (TCAT), we formulate the mathematical model for the coupled tumour-bone system, resulting in a system of Partial Differential Equations (PDEs). This system is numerically solved using the Finite Element Method (FEM) Firedrake software.
The model is applied to patient-specific geometries obtained from labelled CT scans, and the resulting fields of mechanical properties are used as inputs for a damage mechanics model to simulate fracture initiation and propagation under various loading scenarios. Finally, the parameterisation of the model to adapt it to patient-specific settings will be discussed, along with its potential application in supporting medical decision-making.