Characterization of bone tissue by analysis of the ultrasonic waves scattered around cancellous bone

Accurate diagnosis of osteoporosis requires the nondestructive measurement of the thickness and interval of trabecular bones. This paper demonstrates procedure of analyzing the ultrasonic waves scattered by cancellous bone tissue and the success of estimating the average thickness and the average interval of trabecular bones. To determine primary mechanism of the scattered ultrasonic wave in a simple manner, we make some simplifying assumptions, i.e., all the axes of trabecular bones are vertical to the detecting plane, all the cross sections of trabecular bones cut by the detecting plane are perfect circles, and the trabecular bones are distributed periodically. These assumptions enable the formulation of an ideal model of the cancellous bone tissue, periodic distribution of perfect cylinders, and the scattering function is derived using the model. The experimentally estimated values of the thickness and interval of trabecular bone in formalinized human heel (in-vitro), are approximately equal to the values measured with a mechanical scale. The proposed procedures are applied for a human heel (in-vivo) and the estimated values of the interval and thickness are close to the expected values for a human heel.