Research Papers

Site-Specific Quantification of Bone Quality Using Highly Nonlinear Solitary Waves

[+] Author and Article Information
Jinkyu Yang

Graduate Aerospace Laboratories (GALCIT), California Institute of Technology, Pasadena, CA 91125; Mechanical Engineering Department, University of South Carolina, Columbia, SC 29208

Sophia N. Sangiorgio1

Department of Orthopedic Surgery,University of California, Los Angeles,J. Vernon Luck, MDOrthopedic Research CenterLos Angeles Orthopedic Hospital,Los Angels, CA 90007Sophia.biomechanics@gmail.com

Sean L. Borkowski

J. Vernon Luck, MD Orthopaedic Research Center, Los Angeles Orthopedic Hospital, Los Angeles, CA 90007

Claudio Silvestro, Luigi De Nardo

Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta,” Politecnico di Milano, Milano 20133, Italy

Chiara Daraio

Graduate Aerospace Laboratories (GALCIT), California Institute of Technology, Pasadena, CA 91125

Edward Ebramzadeh

Department of Orthopedic Surgery,University of California, Los Angeles,J. Vernon Luck, MD Orthopedic Research Center, Los Angeles Orthopaedic Hospital, Los Angeles, CA 90007


Corresponding author.

J Biomech Eng 134(10), 101001 (Oct 01, 2012) (8 pages) doi:10.1115/1.4007364 History: Received September 07, 2011; Revised April 26, 2012; Posted August 17, 2012; Published October 01, 2012; Online October 01, 2012

Osteoporosis is a well recognized problem affecting millions of individuals worldwide. The ability to diagnose problems in an effective, efficient, and affordable manner and identify individuals at risk is essential. Site-specific assessment of bone mechanical properties is necessary, not only in the process of fracture risk assessment, but may also be desirable for other applications, such as making intraoperative decisions during spine and joint replacement surgeries. The present study evaluates the use of a one-dimensional granular crystal sensor to measure the elastic properties of bone at selected locations via direct mechanical contact. The granular crystal is composed of a tightly packed chain of particles that interact according to the Hertzian contact law. Such chains represent one of the simplest systems to generate and propagate highly nonlinear acoustic signals in the form of compact solitary waves. First, we investigated the sensitivity of the sensor to known variations in bone density using a synthetic cancellous bone substitute, representing clinical bone quality ranging from healthy to osteoporotic. Once the relationship between the signal response and known bone properties was established, the sensor was used to assess the bone quality of ten human cadaveric specimens. The efficacy and accuracy of the sensor was then investigated by comparing the sensor measurements with the bone mineral density (BMD) obtained using dual-energy x-ray absorptiometry (DEXA). The results indicate that the proposed technique is capable of detecting differences in bone quality. The ability to measure site-specific properties without exposure to radiation has the potential to be further developed for clinical applications.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of a granular crystal-based sensor. The vertical chain is composed of 20 spherical particles constrained by guides. The incident (dashed) and reflected HNSWs (solid), triggered by the striker impact, are recorded by the instrumented bead.

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Figure 2

(a) Schematic diagram showing the simplified model for the granular chain and bone contact. (b) The interaction of granular particles with the bounding bone can be modeled using a discrete particle model composed of point masses and nonlinear springs.

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Figure 6

Correlations for the ESP versus BMD. (a) Non site-specific, femoral neck ESP versus proximal femur BMD. (b) Non site-specific, greater trochanter ESP versus proximal femur BMD. (c) Non site-specific, inter trochanteric ESP versus proximal femur BMD. (d) Site-specific, femoral neck ESP versus femoral neck BMD. (e) Site-specific, greater trochanter ESP versus greater trochanter BMD. (f) Site-specific, inter trochanteric ESP versus inter trochanteric BMD.

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Figure 5

Time of flight (TOF) values as a function of the ESP stiffness parameters. The blue line denotes the numerical results based on the discrete particle model, while the circles represent the experimental results. The error bars are standard deviation values obtained from five experimental measurements using artificial bone specimens. The “high risk of fracture” or “osteoporotic” samples generate larger TOF values in comparison to the “healthy” specimens.

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Figure 4

Solitary wave interaction with artificial bone samples. The blue (solid) lines denote numerical force profiles, while the green (dotted) lines represent experimental measurements. To ease visualization, the signals are shifted by 100 N in the vertical axis. A group of rigid polyurethane foam simulates clinical bone quality ranging from healthy to osteoporotic status. The time of flight (TOF) values are extracted from the raw signals by measuring the time elapsed between the incident and the first reflected waves, measured by the instrumented particle.

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Figure 3

Schematic diagram of a human femur with 12 measurement locations for the HNSW-based evaluation in (a) anterior and (b) posterior views




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