FINITE ELEMENT MODELING OF IN VIVO HUMAN KNEE BONES USING HR-PQCT: EFFECTS OF BOUNDARY CONDITIONS AND MODEL CONFIGURATION ON PREDICTED STRAIN ENERGY DENSITY

Abstract

INTRODUCTION

Bone strength assessment is essential in musculoskeletal research for understanding bone mechanics under loading. High-resolution peripheral quantitative computed tomography (HR-pQCT) and micro-finite element (μFE) analysis provide insights into bone strength. While widely used for the distal radius and tibia, knee joint modeling is more complex due to interactions of bone, cartilage, and soft tissue, and the significantly larger size of the joint. This study aims to develop a knee bone μFE model using HR-pQCT data, focusing on boundary conditions and material properties affecting strain energy density (SED) in the femur and tibia.

OBJECTIVE

1) Investigate the influence of boundary conditions on stress distribution in knee joint finite element models. 2) Evaluate how the elastic modulus of load transfer material influences bone mechanics.

METHODS

HR-pQCT scans of a 35-year-old female with a recent ACL injury were performed on the knee joint in full extension. A boundary material was applied to simulate a transitional layer between the bone and surrounding tissues. The material was generated using a voxel-based approach that mapped to the bone shape by extruding filled slices along the Z-axis (Figure 1). Finite element models with uniaxial compression boundary conditions were generated with two configurations of boundary materials: bone-shaped boundary material, which adapts to the shape of the largest epiphysis of the bone, or rectangular boundary materials, which create a square-shaped material around the minimum/maximum bounds of the epiphysis bone regions. Both types of models were solved with a range of boundary material elastic moduli (2000, 2500, 3000, 3500 MPa) and lengths extending from the bone surface of 1, 3, 5, and 7 mm. The primary output was model SED in subchondral regions of interest (ROI) to test the boundary material’s impact on mechanical predictions.

RESULTS

Tibial models contained 500 million degrees of freedom, and femur models included 900 million. As load transfer material length increased beyond 1 mm, the mean SED within ROIs initially decreased, then increased beyond 3 mm—suggesting an optimal load transfer material length between 3 mm and 7 mm. SED skewness and kurtosis increased with material length, indicating more heterogeneous stress distributions. Longer segments (e.g., 5-7 mm) substantially increased computational cost, highlighting a trade-off between the extent of material used for load transfer and simulation efficiency. The bone-shaped boundary material method was more computationally efficient and produced less variability as material length increased. As the elastic modulus of the load transfer material increased, average SED values also increased, particularly with longer PMMA segments.

CONCLUSION

We found that load transfer material length and elastic modulus significantly influence tibial stress distribution, with an optimal material length between 3 mm and 5 mm balancing mechanical performance and computational efficiency.