Phase field modeling for fracture prediction in goat tibia using an open-source quantitative computer tomography based finite element framework

Abstract

While predicting mechanical responses under various stress scenarios is of significant interest in the field of orthopedic research, finite element (FE) modeling studies specifically focusing on the tibia remain notably limited. Given that mechanical properties and structural form of goat tibiae closely mimic those of human tibiae, they can serve as excellent models for comparative orthopedic research. While existing literature on goat bone research offers rich in vivo models, it lacks a validated FE model of the tibia subjected to thorough spatial error assessment. The purpose of this study is to develop a novel FE modeling framework for goat tibia with prediction of failure load and crack location using a phase field fracture method. In particular, this study applies established model forms for the spatial density dependence of elastic moduli and fracture toughness from human long bones to the modeling of goat tibia for the first time and assesses the accuracy of simulated versus measured behavior. The framework involves constructing a mesh of the bone geometry from a 3D quantitative computed tomography (QCT) scan of the goat tibia. To make the process accessible and extensible, open-source software was utilized throughout the entire modeling process for the first time. To validate this FE model, we conducted a uniaxial compression test by applying the load along the shaft axis. A Digital Image Correlation (DIC) system provided high-resolution strain measurements across the surface of the tibia, with the results found to align well with FE simulation outcomes. Subsequently, a high-performance computing (HPC) environment was used to couple the elastic model with a phase field fracture model – resulting in fracture initiation and evolution predictions that closely mirror experimental observations. This QCT-based approach offers a framework for personalized modeling of goat tibia and, in the future, human tibiae, thereby enabling patient-specific analysis relating to fracture risk, implant effectiveness, and optimal treatment strategies.