CURVED BEAM MODEL OF THE PROXIMAL FEMUR FOR ESTIMATING STRESS USING DUAL-ENERGY X-RAY ABSORPTIOMETRY DERIVED STRUCTURAL GEOMETRY

The investigation of individual differences in hip strength requires a method to measure structural geometry in vivo and a valid analytical approach to calculate mechanical stress. We developed a method fur der iving structural geometry of the femur from the proximal shaft through the femoral neck, using data from dual energy x-ray absorptiometry. T he geometric properties are employed in a two-dimensional curved beam model of the proximal femur to estimate stresses on the lateral and me dial bone surfaces. Stresses calculated by this method are compared wi th those from the conventional flexure formula and with results produc ed from a cadaver femur with use of three-dimensional finite element a nalysis of computed tomography data. Loading conditions simulating a o ne-legged stance and a fall on the greater trochanter are employed. St resses calculated by curved beam theory are in much better agreement w ith three-dimensional finite element analysis than are those for which the conventional straight beam formula was used. In simulation of a f all on the greater trochanter, all three methods show peaks of stress at the femoral neck but only the curved beam and finite element analys is methods show an additional peak at the medial intertrochanteric mar gin. Both neck and trochanter regions correspond to common failure sit es for hip fractures in the elderly. The curved beam treatment of hip structure derived from dual-energy x-ray absorptiometry provides an ap proach for the in vivo engineering analysis of hip structure that is n ot practical by other methods.