A novel phase field method for modeling the fracture of long bones

A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power-law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

Predicting the stiffness and strength of human femurs with real metastatic tumors

BACKGROUND

Predicting patient specific risk of fracture in femurs with metastatic tumors and the need for surgical intervention are of major clinical importance. Recent patient-specific high-order finite element methods (p-FEMs) based on CT-scans demonstrated accurate results for healthy femurs, so that their application to metastatic affected femurs is considered herein.

METHODS

Radiographs of fresh frozen proximal femur specimens from donors that died of cancer were examined, and seven pairs with metastatic tumor were identified. These were CT-scanned, instrumented by strain-gauges and loaded in stance position at three inclination angles. Finally the femurs were loaded until fracture that usually occurred at the neck. Histopathology was performed to determine whether metastatic tumors are present at fractured surfaces. Following each experiment p-FE models were created based on the CT-scans mimicking the mechanical experiments. The predicted displacements, strains and yield loads were compared to experimental observations.

RESULTS

The predicted strains and displacements showed an excellent agreement with the experimental observations with a linear regression slope of 0.95 and a coefficient of regression R(2)=0.967. A good correlation was obtained between the predicted yield load and the experimental observed yield, with a linear regression slope of 0.80 and a coefficient of regression R(2)=0.78.

DISCUSSION

CT-based patient-specific p-FE models of femurs with real metastatic tumors were demonstrated to predict the mechanical response very well. A simplified yield criterion based on the computation of principal strains was also demonstrated to predict the yield force in most of the cases, especially for femurs that failed at small loads. In view of the limited capabilities to predict risk of fracture in femurs with metastatic tumors used nowadays, the p-FE methodology validated herein may be very valuable in making clinical decisions.