0
Research Papers

Changes of Elastic Constants and Anisotropy Patterns in Trabecular Bone During Disuse-Induced Bone Loss Assessed by Poroelastic Ultrasound

[+] Author and Article Information
Luis Cardoso, Mitchell B. Schaffler

Department of Biomedical Engineering,
The City College of New York,
New York, NY 10031

Manuscript received July 1, 2014; final manuscript received November 17, 2014; accepted manuscript posted November 20, 2014; published online December 10, 2014. Assoc. Editor: Ara Nazarian.

J Biomech Eng 137(1), 011008 (Jan 01, 2015) (9 pages) Paper No: BIO-14-1309; doi: 10.1115/1.4029179 History: Received July 01, 2014; Revised November 17, 2014; Accepted November 20, 2014; Online December 10, 2014

Currently, the approach most widely used to examine bone loss is the measurement of bone mineral density (BMD) using dual X-ray absorptiometry (DXA). However, bone loss due to immobilization creates changes in bone microarchitecture, which in turn are related to changes in bone mechanical function and competence to resist fracture. Unfortunately, the relationship between microarchitecture and mechanical function within the framework of immobilization and antiresorptive therapy has not being fully investigated. The goal of the present study was to investigate the structure–function relationship in trabecular bone in the real-world situations of a rapidly evolving osteoporosis (disuse), both with and without antiresorptive treatment. We evaluated the structure–function relationship in trabecular bone after bone loss (disuse-induced osteoporosis) and bisphosphonate treatment (antiresorptive therapy using risedronate) in canine trabecular bone using μCT and ultrasound wave propagation. Microstructure values determined from μCT images were used into the anisotropic poroelastic model of wave propagation in order to compute the apparent elastic constants (EC) and elastic anisotropy pattern of bone. Immobilization resulted in a significant reduction in trabecular thickness (Tb.Th) and bone volume fraction (BV/TV), while risedronate treatment combined with immobilization exhibited a lesser reduction in Tb.Th and BV/TV, suggesting that risedronate treatment decelerates bone loss, but it was unable to fully stop it. Risedronate treatment also increased the tissue mineral density (TMD), which when combined with the decrease in Tb.Th and BV/TV may explain the lack of significant differences in vBMD in both immobilization and risedronate treated groups. Interestingly, changes in apparent EC were much stronger in the superior–inferior (SI) direction than in the medial–lateral (ML) and anterior–posterior (AP) anatomical directions, producing changes in elastic anisotropy patterns. When data were pooled together, vBMD was able to explain 58% of ultrasound measurements variability, a poroelastic wave propagation analytical model (i.e., BMD modulated by fabric directionality) was able to predict 81% of experimental wave velocity variability, and also explained 91% of apparent EC and changes in elastic anisotropy patterns. Overall, measurements of vBMD were unable to distinguish changes in apparent EC due to immobilization or risedronate treatment. However, anisotropic poroelastic ultrasound (PEUS) wave propagation was able to distinguish functional changes in apparent EC and elastic anisotropy patterns due to immobilization and antiresorptive therapy, providing an enhanced discrimination of anisotropic bone loss and the structure–function relationship in immobilized and risedronate-treated bone, beyond vBMD.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Steiger, P., 1995, “Standardization of Measurements for Assessing BMD by DXA,” Calcif. Tissue Int., 57(6), p. 469. [CrossRef] [PubMed]
Steiger, P., 1995, “Standardization of Postero-Anterior (PA) Spine BMD Measurements by DXA. Committee for Standards in DXA,” Bone, 17(4), p. 435. [CrossRef] [PubMed]
Van Rietbergen, B., Odgaard, A., Kabel, J., and Huiskes, R., 1998, “Relationships Between Bone Morphology and Bone Elastic Properties Can Be Accurately Quantified Using High-Resolution Computer Reconstructions,” J. Orthop. Res., 16(1), pp. 23–28. [CrossRef] [PubMed]
Van Rietbergen, B., Odgaard, A., Kabel, J., and Huiskes, R., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657. [CrossRef] [PubMed]
Kanis, J. A., Melton, L. J., III, Christiansen, C., Johnston, C. C., and Khaltaev, N., 1994, “The Diagnosis of Osteoporosis,” J. Bone Miner. Res., 9(8), pp. 1137–1141. [CrossRef] [PubMed]
Formica, C. A., 1998, “Standardization of BMD Measurements,” Osteoporos Int., 8(1), pp. 1–3. [CrossRef] [PubMed]
Nielsen, S. P., 2000, “The Fallacy of BMD: A Critical Review of the Diagnostic Use of Dual X-Ray Absorptiometry,” Clin. Rheumatol., 19(3), pp. 174–183. [CrossRef] [PubMed]
Grigorian, M., Shepherd, J. A., Cheng, X. G., Njeh, C. F., Toschke, J. O., and Genant, H. K., 2002, “Does Osteoporosis Classification Using Heel BMD Agree Across Manufacturers?” Osteoporos. Int., 13(8), pp. 613–617. [CrossRef] [PubMed]
Bolotin, H. H., 2007, “DXA in vivo BMD Methodology: An Erroneous and Misleading Research and Clinical Gauge of Bone Mineral Status, Bone Fragility, and Bone Remodelling,” Bone, 41(1), pp. 138–154. [CrossRef] [PubMed]
Veenland, J. F., Link, T. M., Konermann, W., Meier, N., Grashuis, J. L., and Gelsema, E. S., 1997, “Unraveling the Role of Structure and Density in Determining Vertebral Bone Strength,” Calcif. Tissue Int., 61(6), pp. 474–479. [CrossRef] [PubMed]
Smit, T. H., Odgaard, A., and Schneider, E., 1997, “Structure and Function of Vertebral Trabecular Bone,” Spine, 22(24), pp. 2823–2833. [CrossRef] [PubMed]
Turner, C. H., 2002, “Determinants of Skeletal Fragility and Bone Quality,” J. Musculoskeletal Neuronal Interact., 2(6), pp. 527–528.
Turner, C. H., 2002, “Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality,” Osteoporos. Int., 13(2), pp. 97–104. [CrossRef] [PubMed]
van Lenthe, G. H., and Huiskes, R., 2002, “How Morphology Predicts Mechanical Properties of Trabecular Structures Depends on Intra-Specimen Trabecular Thickness Variations,” J. Biomech., 35(9), pp. 1191–1197. [CrossRef] [PubMed]
Currey, J. D., 2001, “Bone Strength: What Are We Trying to Measure?” Calcif. Tissue Int., 68(4), pp. 205–210. [CrossRef] [PubMed]
Currey, J. D., and Zioupos, P., 2001, “The Effect of Porous Microstructure on the Anisotropy of Bone-Like Tissue: A Counterexample,” J. Biomech., 34(5), pp. 707–710. [CrossRef] [PubMed]
Cowin, S. C., 1985, “The Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147. [CrossRef]
Turner, C. H., and Cowin, S. C., 1987, “Dependence of Elastic-Constants of an Anisotropic Porous Material Upon Porosity and Fabric,” J. Mater. Sci., 22(9), pp. 3178–3184. [CrossRef]
Turner, C. H., Cowin, S. C., Rho, J. Y., Ashman, R. B., and Rice, J. C., 1990, “The Fabric Dependence of the Orthotropic Elastic-Constants of Cancellous Bone,” J. Biomech., 23(6), pp. 549–561. [CrossRef] [PubMed]
Yang, G., Kabel, J., van Rietbergen, B., Odgaard, A., Huiskes, R., and Cowin, S. C., 1998, “The Anisotropic Hooke's Law for Cancellous Bone and Wood,” J. Elast., 53(2), pp. 125–146. [CrossRef] [PubMed]
Kabel, J., van Rietbergen, B., Odgaard, A., and Huiskes, R., 1999, “Constitutive Relationships of Fabric, Density, and Elastic Properties in Cancellous Bone Architecture,” Bone, 25(4), pp. 481–486. [CrossRef] [PubMed]
Gross, T., Pahr, D. H., Peyrin, F., and Zysset, P. K., 2012, “Mineral Heterogeneity Has a Minor Influence on the Apparent Elastic Properties of Human Cancellous Bone: A SRmuCT-Based Finite Element Study,” Comput. Methods Biomech. Biomed. Eng., 15(11), pp. 1137–1144. [CrossRef]
Cardoso, L., and Cowin, S. C., 2011, “Fabric Dependence of Quasi-Waves in Anisotropic Porous Media,” J. Acoust. Soc. Am., 129(5), pp. 3302–3316. [CrossRef] [PubMed]
Cardoso, L., and Cowin, S. C., 2012, “Role of Structural Anisotropy of Biological Tissues in Poroelastic Wave Propagation,” Mech. Mater., 44, pp. 174–188. [CrossRef] [PubMed]
Cowin, S. C., and Cardoso, L., 2010, “Fabric Dependence of Bone Ultrasound,” Acta Bioeng. Biomech., 12(2), pp. 3–23. [PubMed]
Cowin, S. C., and Cardoso, L., 2011, “Fabric Dependence of Wave Propagation in Anisotropic Porous Media,” Biomech. Model. Mechanobiol., 10(1), pp. 39–65. [CrossRef] [PubMed]
Moesen, M., Cardoso, L., and Cowin, S. C., 2012, “A Symmetry Invariant Formulation of the Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 54, pp. 70–83. [CrossRef] [PubMed]
Cardoso, L., Meunier, A., and Oddou, Ch., 2008, “In Vitro Acoustic Wave Propagation in Human and Bovine Cancellous Bone as Predicted by Biot's Theory,” J. Mech. Med. Biol., 8(2), pp. 1–19. [CrossRef]
Cardoso, L., Teboul, F., Sedel, L., Oddou, C., and Meunier, A., 2003, “In Vitro Acoustic Waves Propagation in Human and Bovine Cancellous Bone,” J. Bone Miner. Res., 18(10), pp. 1803–1812. [CrossRef] [PubMed]
Souzanchi, M. F., Palacio-Mancheno, P., Borisov, Y. A., Cardoso, L., and Cowin, S. C., 2012, “Microarchitecture and Bone Quality in the Human Calcaneus: Local Variations of Fabric Anisotropy,” J. Bone Miner. Res., 27(12), pp. 2562–2572. [CrossRef] [PubMed]
Li, C. Y., Majeska, R. J., Laudier, D. M., Mann, R., and Schaffler, M. B., 2005, “High-Dose Risedronate Treatment Partially Preserves Cancellous Bone Mass and Microarchitecture During Long-Term Disuse,” Bone, 37(3), pp. 287–295. [CrossRef] [PubMed]
Li, C. Y., Price, C., Delisser, K., Nasser, P., Laudier, D., Clement, M., Jepsen, K. J., and Schaffler, M. B., 2005, “Long-Term Disuse Osteoporosis Seems Less Sensitive to Bisphosphonate Treatment Than Other Osteoporosis,” J. Bone Miner. Res., 20(1), pp. 117–124. [CrossRef] [PubMed]
Palacio-Mancheno, P. E., Larriera, A. I., Doty, S. B., Cardoso, L., and Fritton, S. P., 2014, “3D Assessment of Cortical Bone Porosity and Tissue Mineral Density Using High-Resolution MicroCT: Effects of Resolution and Threshold Method,” J. Bone Miner. Res., 29(1), pp. 142–150. [CrossRef] [PubMed]
Bouxsein, M. L., Boyd, S. K., Christiansen, B. A., Guldberg, R. E., Jepsen, K. J., and Muller, R., 2010, “Guidelines for Assessment of Bone Microstructure in Rodents Using Micro-Computed Tomography,” J. Bone Miner. Res., 25(7), pp. 1468–1486. [CrossRef] [PubMed]
Cowin, S. C., and Turner, C. H., 1992, “On the Relationship Between the Orthotropic Young's Moduli and Fabric,” J. Biomech., 25(12), pp. 1493–1494. [CrossRef] [PubMed]
Cowin, S. C., 2004, “Anisotropic Poroelasticity: Fabric Tensor Formulation,” Mech. Mater., 36(8), pp. 665–677. [CrossRef]
Cowin, S. C., and Mehrabadi, M. M., 1989, “Identification of the Elastic Symmetry of Bone and Other Materials,” J. Biomech., 22(6–7), pp. 503–515. [CrossRef] [PubMed]
Odgaard, A., 1997, “Three-Dimensional Methods for Quantification of Cancellous Bone Architecture,” Bone, 20(4), pp. 315–328. [CrossRef] [PubMed]
Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M., and Huiskes, R., 1997, “Fabric and Elastic Principal Directions of Cancellous Bone Are Closely Related,” J. Biomech., 30(5), pp. 487–495. [CrossRef] [PubMed]
Odgaard, A., and Gundersen, H. J., 1993, “Quantification of Connectivity in Cancellous Bone, With Special Emphasis on 3-D Reconstructions,” Bone, 14(2), pp. 173–182. [CrossRef] [PubMed]
Harrigan, T. P., and Mann, R. W., 1984, “Characterization of Microstructural Anisotropy in Orthotropic Materials Using a 2nd Rank Tensor,” J. Mater. Sci., 19(3), pp. 761–767. [CrossRef]
Whitehouse, W. J., 1974, “The Quantitative Morphology of Anisotropic Trabecular Bone,” J. Microsc., 101(Pt 2), pp. 153–168. [CrossRef] [PubMed]
Hosokawa, A., and Otani, T., 1997, “Ultrasonic Wave Propagation in Bovine Cancellous Bone,” J. Acoust. Soc. Am., 101(1), pp. 558–562. [CrossRef] [PubMed]
Hosokawa, A., and Otani, T., 1998, “Acoustic Anisotropy in Bovine Cancellous Bone,” J. Acoust. Soc. Am., 103(5 Pt 1), pp. 2718–2722. [CrossRef] [PubMed]
Wear, K. A., 2010, “Decomposition of Two-Component Ultrasound Pulses in Cancellous Bone Using Modified Least Squares Prony Method—Phantom Experiment and Simulation,” Ultrasound Med. Biol., 36(2), pp. 276–287. [CrossRef] [PubMed]
Wear, K. A., Laib, A., Stuber, A. P., and Reynolds, J. C., 2005, “Comparison of Measurements of Phase Velocity in Human Calcaneus to Biot Theory,” J. Acoust. Soc. Am., 117(5), pp. 3319–3324. [CrossRef] [PubMed]
Mizuno, K., Somiya, H., Kubo, T., Matsukawa, M., Otani, T., and Tsujimoto, T., 2010, “Influence of Cancellous Bone Microstructure on Two Ultrasonic Wave Propagations in Bovine Femur: An In Vitro Study,” J. Acoust. Soc. Am., 128(5), pp. 3181–3189. [CrossRef] [PubMed]
Mizuno, K., Matsukawa, M., Otani, T., Laugier, P., and Padilla, F., 2009, “Propagation of Two Longitudinal Waves in Human Cancellous Bone: An In Vitro Study,” J. Acoust. Soc. Am., 125(5), pp. 3460–3466. [CrossRef] [PubMed]
Mizuno, K., Matsukawa, M., Otani, T., Takada, M., Mano, I., and Tsujimoto, T., 2008, “Effects of Structural Anisotropy of Cancellous Bone on Speed of Ultrasonic Fast Waves in the Bovine Femur,” IEEE Trans. Ultrason. Ferroelectr Freq. Control, 55(7), pp. 1480–1487. [CrossRef] [PubMed]
Biot, M. A., 1952, “Propagation of Elastic Waves in a Cylindrical Bore Containing a Fluid,” J. Appl. Phys., 23(9), pp. 977–1005. [CrossRef]
Biot, M. A., 1956, “Propagation of Elastic Waves in a Fluid Saturated Porous Solid. II. High Frequency Range,” J. Acoust. Soc. Am., 28(2), pp. 179–191. [CrossRef]
Biot, M. A., 1956, “Propagation of Elastic Waves in a Fluid Saturated Porous Solid. I. Low Frequency Range,” J. Acoust. Soc. Am., 28(2), pp. 168–178. [CrossRef]
Biot, M. A., and Willis, D. G., 1957, “Elastic Coefficients of the Theory of Consolidation,” ASME J. Appl. Mech., 24, pp. 594–601.
Biot, M. A., 1962, “Generalized Theory of Acoustic Propagation in Porous Dissipative Media,” J. Acoust. Soc. Am., 34(9A), pp. 1254–1264. [CrossRef]
Biot, M. A., 1962, “Mechanics of Deformation and Acoustic Propagation in Porous Media,” J. Appl. Phys., 33(4), pp. 1482–1498. [CrossRef]
Cowin, S. C., 1999, “Bone Poroelasticity,” J. Biomech., 32(3), pp. 217–238. [CrossRef] [PubMed]
Gourion-Arsiquaud, S., Allen, M. R., Burr, D. B., Vashishth, D., Tang, S. Y., and Boskey, A. L., 2010, “Bisphosphonate Treatment Modifies Canine Bone Mineral and Matrix Properties and Their Heterogeneity,” Bone, 46(3), pp. 666–672. [CrossRef] [PubMed]
Allen, M. R., and Burr, D. B., 2011, “Bisphosphonate Effects on Bone Turnover, Microdamage, and Mechanical Properties: What We Think We Know and What We Know That We Don't Know,” Bone, 49(1), pp. 56–65. [CrossRef] [PubMed]
Uhthoff, H. K., and Jaworski, Z. F., 1978, “Bone Loss in Response to Long-Term Immobilisation,” J. Bone Joint Surg. Br., 60-B(3), pp. 420–429. [PubMed]
Allen, M. R., and Burr, D. B., 2008, “Changes in Vertebral Strength–Density and Energy Absorption–Density Relationships Following Bisphosphonate Treatment in Beagle Dogs,” Osteoporos. Int., 19(1), pp. 95–99. [CrossRef] [PubMed]
Day, J. S., Ding, M., Bednarz, P., van der Linden, J. C., Mashiba, T., Hirano, T., Johnston, C. C., Burr, D. B., Hvid, I., Sumner, D. R., and Weinans, H., 2004, “Bisphosphonate Treatment Affects Trabecular Bone Apparent Modulus Through Micro-Architecture Rather Than Matrix Properties,” J. Orthop. Res., 22(3), pp. 465–471. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

3D images from μCT scanning. (a) shows the CN + VEH; (b) displays IM + VEH, in (c) an example from the CN + RIS group and a sample form IM + RIS is shown in (d). The different thickness in trabeculae can be observed in each group.

Grahic Jump Location
Fig. 2

Global changes in microarchitecture, TMD and vBMD as a consequence of immobilization and antiresorptive treatment. (a)–(c) show the Tb.Th, Tb.Sp, and Tb.N, respectively, and (d)–(f) correspond to BV/TV, TMD, and vBMD. There is a similar pattern for Tb.Th, Tb.N, BV/TV, TMD, and vBMD, and Tb.Sp exhibits the opposite trend. However, significant differences were only found in Tb.Th and BV/TV when comparing CN + VEH versus IM + VEH, indicating a significant effect of immobilization in Tb.Th and BV/TV, and when comparing CN + RIS versus IM + RIS, indicating that immobilization has an effect in Tb.Th and BV/TV, but not in Tb.N, Tb. Sp, TMD, or BMD. It was also found a difference in Tb.Th between IM + VEH and IM + RIS groups, but there is not a difference in Tb.Th or BV/TV when comparing CN + VEH versus IM + RIS, indicating that RIS treatment was effective in slowing the bone loss produced by immobilization.

Grahic Jump Location
Fig. 3

Magnitude of Fabric components F1, F2, and F3 (eigenvalues) from trabecular bone samples in the CN + VEH, IM + VEH, CN + RIS, and IM + RIS groups. No significant differences were observed due to immobilization or risedronate treatment; however, the comparison of F1, F2, and F3 within each treated group indicates that bone is orthotropic and remained orthotropic after immobilization and risedronate treatment.

Grahic Jump Location
Fig. 4

Fabric anisotropy in all three anatomical planes are shown as ellipsoidal plots for the CN + VEH, IM + VEH, CN + RIS, and IM + RIS groups. Each group shows mean-SD values (red solid inner ellipsoids), the intermediate ellipsoids (blue) represent the mean values and the open mesh ellipsoids show mean + SD. There is a clear fabric anisotropy (p < 0.05) given by directional dependent microarchitecture within each group. Such DA was found similar in all groups (p > 0.05), indicating that immobilization and risedronate treatment had no significant effect on anisotropy of microarchitecture.

Grahic Jump Location
Fig. 5

Ultrasonic wave velocities and apparent EC as a function of vBMD (a), theoretical PEUS wave velocities (b), and theoretical EC (c). Coefficient of correlation between wave velocities and vBMD was R2= 0.58. Theoretical poroelastic wave propagation theory was able to predict 81% of experimental wave velocity variability (R2= 0.81), and the theoretical poroelastic constants were higher correlated to experimental constants (R2= 0.91) that vBMD or wave velocity.

Grahic Jump Location
Fig. 6

The shift from an ellipsoid (CN + VEH) to a more spherical shape (IM + VEH) shows that bone loss is not uniform in all directions. The antiresorptive therapy during immobilization (IM + RIS) exhibit an ellipsoid smaller than CN + RIS, consistent with bone loss, but it maintains the same anisotropy ratio as the control group, indicating a conservation of mechanical function.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In