Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip

Abstract

Clinical implementation of quantitative computed tomography-based finite element analysis (QCT/FEA) of proximal femur stiffness and strength to assess the likelihood of proximal femur (hip) fractures requires a unified modeling procedure, consistency in predicting bone mechanical properties, and validation with realistic test data that represent typical hip fractures, specifically, a sideways fall on the hip. We, therefore, used two sets (n = 9, each) of cadaveric femora with bone densities varying from normal to osteoporotic to build, refine, and validate a new class of QCT/FEA models for hip fracture under loading conditions that simulate a sideways fall on the hip. Convergence requirements of finite element models of the first set of femora led to the creation of a new meshing strategy and a robust process to model proximal femur geometry and material properties from QCT images. We used a second set of femora to cross-validate the model parameters derived from the first set. Refined models were validated experimentally by fracturing femora using specially designed fixtures, load cells, and high speed video capture. CT image reconstructions of fractured femora were created to classify the fractures. The predicted stiffness (cross-validation R (2) = 0.87), fracture load (cross-validation R (2) = 0.85), and fracture patterns (83% agreement) correlated well with experimental data.

FIGURE 1

Experimental setup. The distal end of the femur was embedded in a block of dental cement and clamped in a fixture. The fixture was placed at an angle of 10° with the y-axis and could rotate about the x-axis. The fixture contained a six-component load cell. The lateral aspect of the greater trochanter was embedded in a cup with dental cement which was placed on a load cell rigidly attached to the testing machine. The femur head was positioned underneath an aluminum cup. This cup was connected to a load cell that could move in the x and y directions using very low friction linear bearings attached to the machine actuator.

FIGURE 2

Overview of the QCT/FEA modeling. The QCT scan was segmented to obtain a 3D model. This model was meshed with finite elements. Material properties were assigned to the elements based on the HU values. Boundary conditions were then applied and the model was solved to simulate the fracture.

FIGURE 3

Meshes used in the convergence study. Uniform meshes with maximum element edge lengths of (a) 5.0, (b) 2.5, and (c) 1.5 mm were generated. (d) A smart mesh with non-uniform element edge lengths was developed to achieve results consistent with the 1.5 mm uniform mesh in a fraction of the computational time.

FIGURE 4

Typical load–displacement curve synchronized with fracture events from high speed video. At point a, loading initiates. At point b, ultimate load is reached. Failure occurs at point c. At point d, the bone is completely broken.

FIGURE 5

Load–displacement curves from experimental data and QCT/FEA models for one normal bone and one osteoporotic bone.

FIGURE 6

Linear regression models for training and validation sets. Experimental stiffness was predicted by (a) QCT/FEA-estimated stiffness and (b) femoral neck aBMD. Experimental ultimate load was predicted by (c) QCT/FEA-estimated ultimate load and (d) femoral neck aBMD. The models in the training set were cross-validated by the validation set.

FIGURE 7

Comparison of fracture pattern predictions to high speed video and CT reconstruction of experimental fractures for (a) the training set and (b) the validation set.

FIGURE 7

Comparison of fracture pattern predictions to high speed video and CT reconstruction of experimental fractures for (a) the training set and (b) the validation set.