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RESEARCH PAPERS

Noninvasive Determination of Ulnar Stiffness From Mechanical Response—In Vivo Comparison of Stiffness and Bone Mineral Content in Humans

[+] Author and Article Information
C. R. Steele, L.-J. Zhou

Division of Applied Mechanics, Department of Mechanical Engineering, Stanford University, Stanford, Calif. 94305

D. Guido, C. Cheema

Aging Study Unit, Veterans Administration Center, Palo Alto, Calif.

R. Marcus

Aging Study Unit, Veterans Administration Center, and Department of Medicine, Stanford University

W. L. Heinrichs

Department of Gynecology and Obstetrics, Stanford University

J Biomech Eng 110(2), 87-96 (May 01, 1988) (10 pages) doi:10.1115/1.3108423 History: Received August 03, 1987; Revised March 03, 1988; Online June 12, 2009

Abstract

An approach referred to as Mechanical Response Tissue Analysis (MRTA) has been developed for the noninvasive determination of mechanical properties of the constituents of the intact limb. Of specific interest in the present study is the bending stiffness of the ulna. The point mechanical impedance properties in the low frequency regime, between 60 and 1,600 Hz are used. The procedure requires a proper design of the probe for good contact of the skin at midshaft and proper support of the proximal and distal ends of the forearm to obtain an approximation to “simple support” of the ulna. A seven-parameter model for the mechanical response is then valid, which includes the first mode of anterior-posterior beam bending of the ulna, the damping and spring effect of the soft tissue between probe and bone, and the damping of musculature. A dynamic analyzer (HP3562A) provides in seconds the impedance curve and the pole-zero curve fit. The physical parameters are obtained from a closed-form solution in terms of the curve-fit parameters. The procedure is automated and is robust and analytically reliable at about the five percent level. Some 80 human subjects have been evaluated by this mechanical response system and by the Norland single photon absorptiometer, providing for the first time in vivo , a comparison of elastic bending stiffness (ulna) and bone mineral content (radius). Three functional parameters of potential clinical value are the cross-sectional bending stiffness EI , the axial load capability P cr (Euler buckling load) and the bone “sufficiency” S , defined as the ratio of P cr to body weight. The correlation between EI and bone mineral (r = 0.81) is only slightly less than previous in vitro results with both measurements on the same bone (r = 0.89). When sufficiency is taken into consideration, the correlation of P cr and bone mineral content is improved (r = 0.89). An implication is that “quality” of bone is a factor which is not indicated by bone mineral content but which is indicated by stiffness. Bone mineral is necessary for proper stiffness but not sufficient. Therefore mechanical measurement should provide a new dimension to be used toward a better understanding of the factors related to bone health and disease.

Copyright © 1988 by ASME
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