The fundamentals of low-frequency ultrasound for diagnosis of bone tissue

The subject of the paper is presentation of theoretical and methodological fundamentals for a novel low-frequency ultrasonic method of identification of macroscopic mechanical properties and parameters of macroscopic inhomogeneity of bone tissue. The issue is directly associated with non-invasive assessment of bone fracture risk, being result of the diseases such as osteoporosis, osteomalacia, osteopenia etc. In the present paper the heel bone is modeled as a set of three-layers characterized by continuously inhomogeneous distribution of acoustical properties. The border between the cortical and cancellous bone in calcaneus is not sharp, thus at the distance about 1 cm there is observed the transition region with gradual changes of the properties from the low porosity cortical bones to the high porosity cancellous bone. As the length of transition region is on the order of a few centimeters the low frequency ultrasound (50-200 kHz) is required to be sensitive to this size of inhomogeneity. Identification of the lamination parameters of calcaneal bone (e.g. length of transition regions) and the mechanical (acoustical) properties of each inhomogeneous layer is the crucial element of the proposed novel diagnostic method.