0
Research Papers

Directional Tortuosity as a Predictor of Modulus Damage for Vertebral Cancellous Bone

[+] Author and Article Information
David P. Fyhrie

Department of Orthopaedic Surgery,
University of California-Davis Medical Center,
4635 2nd Avenue, Suite 2000,
Sacramento, CA 95817
Department of Biomedical Engineering,
University of California Davis,
4635 2nd Avenue, Suite 2000,
Sacramento, CA 95817
e-mail: dpfyhrie@ucdavis.edu

Roger Zauel

Bone and Joint Center,
Henry Ford Health System,
Detroit, MI 48202

1Corresponding author.

Manuscript received June 30, 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), 011007 (Jan 01, 2015) (6 pages) Paper No: BIO-14-1304; doi: 10.1115/1.4029177 History: Received June 30, 2014; Revised November 17, 2014; Accepted November 20, 2014; Online December 10, 2014

There are many methods used to estimate the undamaged effective (apparent) moduli of cancellous bone as a function of bone volume fraction (BV/TV), mean intercept length (MIL), and other image based average microstructural measures. The MIL and BV/TV are both only functions of the cancellous microstructure and, therefore, cannot directly account for damage induced changes in the intrinsic trabecular hard tissue mechanical properties. Using a nonlinear finite element (FE) approximation for the degradation of effective modulus as a function of applied effective compressive strain, we demonstrate that a measurement of the directional tortuosity of undamaged trabecular hard tissue strongly predicts directional effective modulus (r2> 0.90) and directional effective modulus degradation (r2> 0.65). This novel measure of cancellous bone directional tortuosity has the potential for development into an anisotropic approach for calculating effective mechanical properties as a function of trabecular level material damage applicable to understanding how tissue microstructure and intrinsic hard tissue moduli interact to determine cancellous bone quality.

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

References

Kannus, P., Palvanen, M., Niemi, S., Parkkari, J., Jarvinen, M., and Vuori, I., 1996, “Increasing Number and Incidence of Osteoporotic Fractures of the Proximal Humerus in Elderly People,” BMJ, 313(7064), pp. 1051–1052. [CrossRef] [PubMed]
Lips, P., 1997, “Epidemiology and Predictors of Fractures Associated With Osteoporosis,” Am. J. Med., 103(2A), pp. 3S–8S [Discussion, pp. 8S–11S]. [CrossRef] [PubMed]
Ciarelli, T. E., Fyhrie, D. P., Schaffler, M. B., and Goldstein, S. A., 2000, “Variations in Three-Dimensional Cancellous Bone Architecture of the Proximal Femur in Female Hip Fractures and in Controls,” J. Bone Miner. Res., 15(1), pp. 32–40. [CrossRef] [PubMed]
Hardisty, M. R., Zauel, R., Stover, S. M., and Fyhrie, D. P., 2013, “The Importance of Intrinsic Damage Properties to Bone Fragility: A Finite Element Study,” ASME J. Biomech. Eng., 135(1), p. 011004. [CrossRef]
Burr, D. B., 2004, “Bone Quality: Understanding What Matters,” J. Musculoskeletal Neuronal Interact., 4(2), pp. 184–186. Available at: http://www.ismni.org/jmni/pdf/16/17BURR.pdf?origin=publication_detail
Ettinger, B., Burr, D. B., and Ritchie, R. O., 2013, “Proposed Pathogenesis for Atypical Femoral Fractures: Lessons From Materials Research,” Bone, 55(2), pp. 495–500. [CrossRef] [PubMed]
Amin, S., Kopperdhal, D. L., Melton, L. J., 3rd, Achenbach, S. J., Therneau, T. M., Riggs, B. L., Keaveny, T. M., and Khosla, S., 2011, “Association of Hip Strength Estimates by Finite-Element Analysis With Fractures in Women and Men,” J. Bone Miner. Res., 26(7), pp. 1593–1600. [CrossRef] [PubMed]
Keaveny, T. M., McClung, M. R., Genant, H. K., Zanchetta, J. R., Kendler, D., Brown, J. P., Goemaere, S., Recknor, C., Brandi, M. L., Eastell, R., Kopperdahl, D. L., Engelke, K., Fuerst, T., Radcliffe, H. S., and Libanati, C., 2014, “Femoral and Vertebral Strength Improvements in Postmenopausal Women With Osteoporosis Treated With Denosumab,” J. Bone Miner. Res., 29(1), pp. 158–165. [CrossRef] [PubMed]
Bridges, D., Randall, C., and Hansma, P. K., 2012, “A New Device for Performing Reference Point Indentation Without a Reference Probe,” Rev. Sci. Instrum., 83(4), p. 044301. [CrossRef] [PubMed]
Guerri-Fernandez, R. C., Nogues, X., Quesada Gomez, J. M., Torres Del Pliego, E., Puig, L., Garcia-Giralt, N., Yoskovitz, G., Mellibovsky, L., Hansma, P. K., and Diez-Perez, A., 2013, “Microindentation for In Vivo Measurement of Bone Tissue Material Properties in Atypical Femoral Fracture Patients and Controls,” J. Bone Miner. Res., 28(1), pp. 162–168. [CrossRef] [PubMed]
Randall, C., Bridges, D., Guerri, R., Nogues, X., Puig, L., Torres, E., Mellibovsky, L., Hoffseth, K., Stalbaum, T., Srikanth, A., Weaver, J. C., Rosen, S., Barnard, H., Brimer, D., Proctor, A., Candy, J., Saldana, C., Chandrasekar, S., Lescun, T., Nielson, C. M., Orwoll, E., Herthel, D., Kopeikin, H., Yang, H. T., Farr, J. N., McCready, L., Khosla, S., Diez-Perez, A., and Hansma, P. K., 2013, “Applications of a New Handheld Reference Point Indentation Instrument Measuring Bone Material Strength,” ASME J. Med. Devices, 7(4), p. 410051. [CrossRef]
Liu, X., Wang, X., and Niebur, G. L., 2003, “Effects of Damage on the Orthotropic Material Symmetry of Bovine Tibial Trabecular Bone,” J. Biomech., 36(12), pp. 1753–1759. [CrossRef] [PubMed]
Diab, T., Condon, K. W., Burr, D. B., and Vashishth, D., 2006, “Age-Related Change in the Damage Morphology of Human Cortical Bone and Its Role in Bone Fragility,” Bone, 38(3), pp. 427–431. [CrossRef] [PubMed]
Diab, T., and Vashishth, D., 2005, “Effects of Damage Morphology on Cortical Bone Fragility,” Bone, 37(1), pp. 96–102. [CrossRef] [PubMed]
Vashishth, D., Koontz, J., Qiu, S. J., Lundin-Cannon, D., Yeni, Y. N., Schaffler, M. B., and Fyhrie, D. P., 2000, “In Vivo Diffuse Damage in Human Vertebral Trabecular Bone,” Bone, 26(2), pp. 147–152. [CrossRef] [PubMed]
Fyhrie, D. P., and Schaffler, M. B., 1994, “Failure Mechanisms in Human Vertebral Cancellous Bone,” Bone, 15(1), pp. 105–109. [CrossRef] [PubMed]
Arthur Moore, T. L., and Gibson, L. J., 2002, “Microdamage Accumulation in Bovine Trabecular Bone in Uniaxial Compression,” ASME J. Biomech. Eng., 124(1), pp. 63–71. [CrossRef]
Moore, T. L., and Gibson, L. J., 2001, “Modeling Modulus Reduction in Bovine Trabecular Bone Damaged in Compression,” ASME J. Biomech. Eng., 123(6), pp. 613–622. [CrossRef]
Vajjhala, S., Kraynik, A. M., and Gibson, L. J., 2000, “A Cellular Solid Model for Modulus Reduction Due to Resorption of Trabeculae in Bone,” ASME J. Biomech. Eng., 122(5), pp. 511–515. [CrossRef]
Follet, H., Bruyere-Garnier, K., Peyrin, F., Roux, J. P., Arlot, M. E., Burt-Pichat, B., Rumelhart, C., and Meunier, P. J., 2005, “Relationship Between Compressive Properties of Human OS Calcis Cancellous Bone and Microarchitecture Assessed From 2D and 3D Synchrotron Microtomography,” Bone, 36(2), pp. 340–351. [CrossRef] [PubMed]
Kabel, J., Odgaard, A., van Rietbergen, B., and Huiskes, R., 1999, “Connectivity and the Elastic Properties of Cancellous Bone,” Bone, 24(2), pp. 115–120. [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]
Doube, M., Klosowski, M. M., Arganda-Carreras, I., Cordelieres, F. P., Dougherty, R. P., Jackson, J. S., Schmid, B., Hutchinson, J. R., and Shefelbine, S. J., 2010, “BoneJ: Free and Extensible Bone Image Analysis in ImageJ,” Bone, 47(6), pp. 1076–1079. [CrossRef] [PubMed]
Larsen, L. G., Choi, J., Nungesser, M. K., and Harvey, J. W., 2012, “Directional Connectivity in Hydrology and Ecology,” Ecol. Appl, 22(8), pp. 2204–2220. [CrossRef] [PubMed]
Hou, F. J., Lang, S. M., Hoshaw, S. J., Reimann, D. A., and Fyhrie, D. P., 1998, “Human Vertebral Body Apparent and Hard Tissue Stiffness,” J. Biomech., 31(11), pp. 1009–1015. [CrossRef] [PubMed]
Fyhrie, D. P., Lang, S. M., Hoshaw, S. J., Schaffler, M. B., and Kuo, R. F., 1995, “Human Vertebral Cancellous Bone Surface Distribution,” Bone, 17(3), pp. 287–291. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

A 5 mm cubical FE model with 50 μm voxels to illustrate apparent and intrinsic properties

Grahic Jump Location
Fig. 2

Connections between points on two parallel lines (“loading platens”) illustrating how different connections are ideal (T = 1) or less than ideal (T > 1). Tortuosity (T) is defined as the line length between the points divided by the distance between the loading platens.

Grahic Jump Location
Fig. 3

An illustration using a 2D “trabecular bone specimen” of how to calculate average tortuosity. For all point pairs A–B on the loading planes (platens): average the ratio of the shortest distance between points to the distance between the planes.

Grahic Jump Location
Fig. 4

2D illustration for the distance matrix. For node “n3,” the distance matrix is the list of nodes and length of the connection. For example, “n3, n7, 21/2d” is the connection from the center to the upper right. The list of all connections for all 3 × 3 regions centered on a filled pixel is the distance matrix of a 2D binary image.

Grahic Jump Location
Fig. 5

Model stiffness (for all models) was strongly separated by load direction, but was closely related to tortuosity. The contour lines are the density of points for models of the XX (blue; lower right) and ZZ (red; upper left) directions. Lines are splines to show the general trend.

Grahic Jump Location
Fig. 6

Stiffness (damaged and undamaged) was a strong power function of tortuosity independent of direction. Dark markers are undamaged and light are damaged. Damage moved the damaged points roughly parallel to the regression line.

Grahic Jump Location
Fig. 7

The change in stiffness was strongly predicted by change in tortuosity for both directions. Solid markers are for the X direction and open circles are for the Z direction. The exponential fit suggests that the increase in tortuosity has a nonlinear effect on stiffness.

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