Cancellous bone lamellae strongly affect microcrack propagation and apparent mechanical properties: separation of patients with osteoporotic fracture from normal controls using a 2D nonlinear finite element method (biomechanical stereology)

Abstract

Biomechanical stereology is proposed as a two-dimensional (2D) finite element (FE) method to estimate the ability of bone tissue to sustain damage and to separate patients with osteoporotic fracture from normal controls. Briefly, 2D nonlinear compact tension FE models were created from quantitative back scattered electron images taken of iliac crest bone specimens collected from the individuals with or without osteoporotic fracture history. The effects of bone mineral microstructure on predicted bone fracture toughness and microcrack propagation were examined. The 2D FE models were used as surrogates for the real bone tissues. The calculated microcrack propagation results and bone mechanical properties were examined as surrogates for measurements from mechanical testing of actual specimens. The results for the 2D FE simulation separated patients with osteoporotic fracture from normal controls even though only the variability in tissue mineral microstructure was used to build the models. The models were deliberately created to ignore all differences in mean mineralization. Hence, the current results support the following hypotheses: (1) that material heterogeneity is important to the separation of patients with osteoporotic fracture from normal controls; and (2) that 2D nonlinear finite element modeling can produce surrogate mechanical parameters that separate patients with fracture from normal controls.

Figure 1

(a) A 200×200 pixel region (white box) was cut from a qBSE image of human iliac cancellous bone. The distribution of bone mineral as grayscale values is plotted below. (b) A compact tension specimen finite element model was used in biomechanical stereology. Dimensions of the compact tension FE model were plotted. Cancellous bone qBSE image was used to replace the tip regions. The unit of the image is pixel, while each pixel is equals to 0.756 mm in the finite element model.

Figure 2

Linear regression between deflection, force, stiffness and compliance and the number of failed elements. The change rates of deflection, force, stiffness and compliance were obtained from the slopes of the linear regressions.

Figure 3

Representative microcrack propagation in the notch root regions in the specimens from the fracture group (A) and the normal group (B). The black pixels are the opened notch.

Figure 4

A receiver operating characteristic (ROC) curve is a graphical plot of the sensitivity (True Positive) vs. (1-specificity) (False Negative) for a binary classifier system as its discrimination threshold is varied. (a) Crack area was used to separate the specimens of patients with osteoporotic fracture from normal controls. The area under the ROC curve (AUC) was 0.83. (b) The first stiffness was used to separate the specimens of patients with osteoporotic fracture from normal controls. The AUC was 0.82.