A comparison of DXA and CT based methods for estimating the strength of the femoral neck in post-menopausal women

Abstract

Summary

The study goal was to compare simple two-dimensional (2D) analyses of bone strength using dual energy x-ray absorptiometry (DXA) data to more sophisticated three-dimensional (3D) finite element analyses using quantitative computed tomography (QCT) data. DXA- and QCT-derived femoral neck geometry, simple strength indices, and strength estimates were well correlated.

Introduction

Simple 2D analyses of bone strength can be done with DXA data and applied to large data sets. We compared 2D analyses to 3D finite element analyses (FEA) based on QCT data.

Methods

Two hundred thirteen women participating in the Study of Women's Health Across the Nation (SWAN) received hip DXA and QCT scans. DXA BMD and femoral neck diameter and axis length were used to estimate geometry for composite bending (BSI) and compressive strength (CSI) indices. These and comparable indices computed by Hip Structure Analysis (HSA) on the same DXA data were compared to indices using QCT geometry. Simple 2D engineering simulations of a fall impacting on the greater trochanter were generated using HSA and QCT femoral neck geometry; these estimates were benchmarked to a 3D FEA of fall impact.

Results

DXA-derived CSI and BSI computed from BMD and by HSA correlated well with each other (R = 0.92 and 0.70) and with QCT-derived indices (R = 0.83–0.85 and 0.65–0.72). The 2D strength estimate using HSA geometry correlated well with that from QCT (R = 0.76) and with the 3D FEA estimate (R = 0.56).

Conclusions

Femoral neck geometry computed by HSA from DXA data corresponds well enough to that from QCT for an analysis of load stress in the larger SWAN data set. Geometry derived from BMD data performed nearly as well. Proximal femur breaking strength estimated from 2D DXA data is not as well correlated with that derived by a 3D FEA using QCT data.

Appendix

2D beam analysis used for strength estimates by HSA and QCA methods

The free-body diagram of the femur simulating a fall impact is depicted in Fig. 1a. F _I is the ground reaction force assumed to be equal to body weight (W), F _H is the force acting through the center of the femoral head force assumed to be approximately equal to 5/6 of the body weight, and F _S is femoral shaft force assumed to be equal to 1/6 of the body weight [26]. The shaft axis was assumed to be inclined 10° to the ground surface at impact (θ). Forces and moments were balanced to achieve static equilibrium, where l ₁ and l ₂ were derived as:

$$ {l_1} = NL \cdot \cos (\theta (180 - \alpha - \theta )) $$

$$ {l_2} = 5 \cdot NL \cdot \cos (\theta (180 - \alpha - \theta )) $$

Internal forces in the neck resulting from external forces F _I , F _H, and F _S are shown in Fig. 1b, where M _F, P _F, and V are bending moment, axial load, and shear force, respectively, on the cross section.

The small shear forces were neglected.

$$ {M_{\text{F}}} = {F_{{{\text{H}}2}}} = \frac{5}{6}W \cdot d \cdot \sin (\alpha + \theta - 90^\circ ) $$

$$ {P_{\text{F}}} = {F_{{{\text{H}}1}}} = \frac{5}{6}W\cos (\alpha + \theta - 90^\circ ) $$

Using engineering beam theory, axial stresses on the medial and lateral surface of the femoral neck are computed:

$$ \sigma = \pm \frac{{{M_{\text{F}}} \cdot y}}{{{I_{\text{x}}}}} + \frac{{{P_{\text{F}}}}}{A} $$

where M _F and P _F are the bending moment and axial load on the cortical cross section, and y is the perpendicular distance from the neutral axis of bending (from HSA). By convention stresses on the lateral surface in compression are positive while at the medial surface, the bending moment produces negative tensile stress. Strength estimates were then derived as:

$$ {F_{\text{s}}} = {F_i}\frac{{{\sigma_y}}}{\sigma } $$

where σ _y = ultimate yield stress in compression for cortical bone tissue [27]. Note that strength was also evaluated in tension on the medial surface in both HSA and QCA models, but without exception, values were smaller on the compressive surface, hence only the latter were used.