Using singular value distribution (SVD) of backscattered impulse response matrix to differentiate between low and high porosity in cortical bone

The goal of this study is to investigate whether singular value distribution (SVD) of the impulse response matrix can be used to differentiate between healthy and osteoporotic bone using backscattered signals from cortical bone samples ex-vivo. Two human cortical bone samples from the tibia were used, with a low (11% porosity, 64 μm average pore diameter, 17 pore/mm2) and high porosity (30% porosity, 105 μm average pore diameter, 14.73 pore/mm2). In order to take the effect of randomness into account, for each sample, three measurements at different locations of tibia were performed. The propagation matrix consisting of backscattered signals was collected by measuring the impulse response between each pair of elements of a linear array transducer (7.8 MHz central frequency). The singular value distribution of the propagation matrix in the frequency domain was evaluated for overlapping 0.5 μs time windows in the 6–9 MHz range. After normalizing, the probability density function of the SVD was evaluated and the strongest singular value was compared for low and high porosities. The results show a 20% difference on average for the largest singular value between high and low porosity, showing a potential of this method to differentiate between healthy and osteoporotic bone.