Orthogonal relationships between ultrasonic velocity and material properties of bovine cancellous bone

Osteoporotic fractures follow a period of asymptomatic bone loss and hence bone strength, predominantly in cancellous bone. An effective management of osteoporosis requires an understanding of the mechanical behaviour of cancellous bone including the anisotropic dependence. Ultrasound velocity (V) and elasticity (Young's modulus, E) were measured in the three orthogonal directions in 20 mm cubes of bovine cancellous bone. Student paired t-test analysis showed significant variations in velocity and elasticity for the three orthogonal directions, the highest significance being between proximal-distal (PD) and antero-posterior (AP) directions with t = 5.63 and 4.09 for velocity and elasticity respectively, the lowest significance between medio-lateral (ML) and antero-posterior directions. Elasticity followed a power law relationship with apparent density (p) as reported in the literature, the exponent (b) being direction dependent (b = 1.98 +/- 0.21 for PD, 2.42 +/- 0.24 for AP and 2.03 +/- 0.17 for ML). The adjusted R2 values between elasticity and apparent density were highly significant (79.9% for PD, 81.9% for AP and 85.7% for ML). The relationship between velocity and apparent density is less significant in terms of the amount of variance explained (48.5% for PD, 63.3% for AP and 64.4% for ML). R2 values relating elasticity and velocity were again highly significant (79.4% for PD, 82.9% for AP and 80.5% for ML) and the coefficients, determined by regression analysis, independent of direction. Analysis of velocity, elasticity and density data for a range of reference materials demonstrated that experimentally measured longitudinal wave velocity could be reliably substituted into the bar wave equation (v = square root E/p). This implies that a combination of velocity and apparent density may be an improved indicator of bone fragility than density alone.