A new method for estimating in vivo bone mineral density (BMD) and characterizing the shape of cancellous bone has been proposed using the results of ultrasonic inspection for the diagnosis of osteoporosis. The method is based on two-dimensional bone area fraction S (percent bone area between bone and bone marrow) calculated from the difference in the speed of ultrasonic wave propagation through cancellous bone. It was shown that the two-dimensional area fraction of a heel bone gives a good relationship to the BMD by DXA (dual energy x-ray absorptiometry) testing of human heel bone (calcaneus) and spine (vertebrae lumbar), as expressed by the relation, BMD (g/cm2) = 0.0167S for heel bone (r = 0.83), and BMD (g/cm2) = 0.0254S + 0.123 for the spine (r = 0.77). Shape characterization is based on the image simulation procedure employing eight random variables from a computer and the statistical results of fractal analysis for numerous cancellous bone patterns. We also demonstrate the validity of the shape characterization technique using autopsy specimens as a diagnostic tool for osteoporosis.

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