Advertisement

Annals of Biomedical Engineering

, Volume 41, Issue 4, pp 814–826 | Cite as

Computational Modelling of the Mechanics of Trabecular Bone and Marrow Using Fluid Structure Interaction Techniques

  • E. Birmingham
  • J. A. Grogan
  • G. L. Niebur
  • L. M. McNamara
  • P. E. McHugh
Article

Abstract

Bone marrow found within the porous structure of trabecular bone provides a specialized environment for numerous cell types, including mesenchymal stem cells (MSCs). Studies have sought to characterize the mechanical environment imposed on MSCs, however, a particular challenge is that marrow displays the characteristics of a fluid, while surrounded by bone that is subject to deformation, and previous experimental and computational studies have been unable to fully capture the resulting complex mechanical environment. The objective of this study was to develop a fluid structure interaction (FSI) model of trabecular bone and marrow to predict the mechanical environment of MSCs in vivo and to examine how this environment changes during osteoporosis. An idealized repeating unit was used to compare FSI techniques to a computational fluid dynamics only approach. These techniques were used to determine the effect of lower bone mass and different marrow viscosities, representative of osteoporosis, on the shear stress generated within bone marrow. Results report that shear stresses generated within bone marrow under physiological loading conditions are within the range known to stimulate a mechanobiological response in MSCs in vitro. Additionally, lower bone mass leads to an increase in the shear stress generated within the marrow, while a decrease in bone marrow viscosity reduces this generated shear stress.

Keywords

Bone Bone marrow Fluid structure interaction Computational fluid dynamics Shear stress Mesenchymal stem cells Osteoporosis Mechanobiology 

Notes

Acknowledgments

The authors have no conflicts of interest to declare. The authors acknowledge Dr. Nathan Quinlan for very useful discussions. The authors would like to acknowledge funding from the Irish Research Council, under the EMBARK program (E. Birmingham) and the Science Foundation Ireland E.T.S. Walton program 07/W.I./B1806 (G.L. Niebur).

References

  1. 1.
    Arnsdorf, E. J., P. Tummala, R. Y. Kwon, and C. R. Jacobs. Mechanically induced osteogenic differentiation—the role of RhoA, ROCKII and cytoskeletal dynamics. J. Cell Sci. 122:546–553, 2009.PubMedCrossRefGoogle Scholar
  2. 2.
    Bakker, A. D., M. Joldersma, J. Klein-Nulend, and E. H. Burger. Interactive effects of PTH and mechanical stress on nitric oxide and PGE2 production by primary mouse osteoblastic cells. Am. J. Physiol. Endocrinol. Metab. 285:E608–E613, 2003.PubMedGoogle Scholar
  3. 3.
    Birmingham, E., G. L. Niebur, P. E. McHugh, G. Shaw, F. P. Barry, and L. M. McNamara. Osteogenic differentiation of mesenchymal stem cells is regulated by osteocyte and osteoblast cells in a simplified bone niche. Eur. Cell Mater. 23:13–27, 2012.PubMedGoogle Scholar
  4. 4.
    Böhm, H. J. A short introduction to continuum micromechanics. In: Mechanics of Microstructured Materials, edited by H. J. Böhm, editor. Springer-Verlag, 2004, pp. 1–40.Google Scholar
  5. 5.
    Bryant, J. D., T. David, P. H. Gaskell, S. King, and G. Lond. Rheology of bovine bone marrow. Proc. Inst. Mech. Eng. H 203:71–75, 1989.PubMedGoogle Scholar
  6. 6.
    Burr, D. B., C. Milgrom, D. Fyhrie, M. Forwood, M. Nyska, A. Finestone, S. Hoshaw, E. Saiag, and A. Simkin. In vivo measurement of human tibial strains during vigorous activity. Bone 18:405–410, 1996.PubMedCrossRefGoogle Scholar
  7. 7.
    Carter, D. R., and W. C. Hayes. The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. Am. 59:954–962, 1977.PubMedGoogle Scholar
  8. 8.
    Cartmell, S. H., B. D. Porter, A. J. García, and R. E. Guldberg. Effects of medium perfusion rate on cell-seeded three-dimensional bone constructs in vitro. Tissue Eng. 9:1197–1203, 2003.PubMedCrossRefGoogle Scholar
  9. 9.
    Case, N., B. Sen, J. A. Thomas, M. Styner, Z. Xie, C. R. Jacobs, and J. Rubin. Steady and oscillatory fluid flows produce a similar osteogenic phenotype. Calcif. Tissue Int. 88:189–197, 2011.PubMedCrossRefGoogle Scholar
  10. 10.
    Castillo, A. B., and C. R. Jacobs. Mesenchymal stem cell mechanobiology. Curr. Osteoporos. Rep. 8:98–104, 2010.PubMedCrossRefGoogle Scholar
  11. 11.
    Cohen, A., D. W. Dempster, E. M. Stein, T. L. Nickolas, H. Zhou, D. J. McMahon, R. Müller, T. Kohler, A. Zwahlen, J. M. Lappe, P. Young, R. R. Recker, and E. Shane. Increased marrow adiposity in premenopausal women with idiopathic osteoporosis. J. Clin. Endocrinol. Metab. 2012. doi: 10.1210/jc.2012-1477.Google Scholar
  12. 12.
    Coughlin, T. R., and G. L. Niebur. Fluid shear stress in trabecular bone marrow due to low-magnitude high-frequency vibration. J. Biomech. doi: 10.1016/j.jbiomech.2012.06.020.
  13. 13.
    Di Iorgi, N., M. Rosol, S. D. Mittelman, and V. Gilsanz. Reciprocal relation between marrow adiposity and the amount of bone in the axial and appendicular skeleton of young adults. J. Clin. Endocrinol. Metab. 93:2281–2286, 2008.PubMedCrossRefGoogle Scholar
  14. 14.
    Dickerson, D. A., E. A. Sander, and E. A. Nauman. Modeling the mechanical consequences of vibratory loading in the vertebral body: microscale effects. Biomech. Model. Mechanobiol. 7:191–202, 2008.PubMedCrossRefGoogle Scholar
  15. 15.
    Downey, D. J., P. A. Simkin, and R. Taggart. The effect of compressive loading on intraosseous pressure in the femoral head in vitro. J. Bone Joint Surg. Am. 70:871–877, 1988.PubMedGoogle Scholar
  16. 16.
    DS SIMULIA. Abaqus 6.11 theory manual. Providence, RI, USA: DS SIMULIA Corp., 2011.Google Scholar
  17. 17.
    Estes, B. T., J. M. Gimble, and F. Guilak. Mechanical signals as regulators of stem cell fate. Curr. Top. Dev. Biol. 60:91–126, 2004.PubMedCrossRefGoogle Scholar
  18. 18.
    Fuchs, E., T. Tumbar, and G. Guasch. Socializing with the neighbors: stem cells and their niche. Cell 116:769–778, 2004.PubMedCrossRefGoogle Scholar
  19. 19.
    Gibson, L. J. The mechanical behaviour of cancellous bone. J. Biomech. 18:317–328, 1985.PubMedCrossRefGoogle Scholar
  20. 20.
    Goldenstein, J., G. Kazakia, and S. Majumdar. In vivo evaluation of the presence of bone marrow in cortical porosity in postmenopausal osteopenic women. Ann. Biomed. Eng. 38:235–246, 2010.PubMedCrossRefGoogle Scholar
  21. 21.
    Grimm, M. J., and J. L. Williams. Measurements of permeability in human calcaneal trabecular bone. J. Biomech. 30:743–745, 1997.PubMedCrossRefGoogle Scholar
  22. 22.
    Guilak, F., D. M. Cohen, B. T. Estes, J. M. Gimble, W. Liedtke, and C. S. Chen. Control of stem cell fate by physical interactions with the extracellular matrix. Cell Stem Cell 5:17–26, 2009.PubMedCrossRefGoogle Scholar
  23. 23.
    Gurkan, U. A., and O. Akkus. The mechanical environment of bone marrow: a review. Ann. Biomed. Eng. 36:1978–1991, 2008.PubMedCrossRefGoogle Scholar
  24. 24.
    Hasegawa, K., C. H. Turner, R. R. Recker, E. Wu, and D. B. Burr. Elastic properties of osteoporotic bone measured by scanning acoustic microscopy. Bone 16:85–90, 1995.PubMedGoogle Scholar
  25. 25.
    Hu, M., J. Cheng, and Y.-X. Qin. Dynamic hydraulic flow stimulation on mitigation of trabecular bone loss in a rat functional disuse model. Bone 51:819–825, 2012.PubMedCrossRefGoogle Scholar
  26. 26.
    Keaveny, T. M., E. F. Morgan, G. L. Niebur, and O. C. Yeh. Biomechanics of trabecular bone. Annu. Rev. Biomed. Eng. 3:307–333, 2001.PubMedCrossRefGoogle Scholar
  27. 27.
    Kuhn, N. Z., and R. S. Tuan. Regulation of stemness and stem cell niche of mesenchymal stem cells: implications in tumorigenesis and metastasis. J. Cell. Physiol. 222:268–277, 2010.PubMedCrossRefGoogle Scholar
  28. 28.
    Lam, H., and Y.-X. Qin. The effects of frequency-dependent dynamic muscle stimulation on inhibition of trabecular bone loss in a disuse model. Bone 43:1093–1100, 2008.PubMedCrossRefGoogle Scholar
  29. 29.
    Liedert, A., D. Kaspar, R. Blakytny, L. Claes, and A. Ignatius. Signal transduction pathways involved in mechanotransduction in bone cells. Biochem. Biophys. Res. Commun. 349:1–5, 2006.PubMedCrossRefGoogle Scholar
  30. 30.
    Liney, G. P., C. P. Bernard, D. J. Manton, L. W. Turnbull, and C. M. Langton. Age, gender, and skeletal variation in bone marrow composition: a preliminary study at 3.0 Tesla. J. Magn. Reson. Imaging 26:787–793, 2007.PubMedCrossRefGoogle Scholar
  31. 31.
    Mazzag, B., and A. I. Barakat. The effect of noisy flow on endothelial cell mechanotransduction: a computational study. Ann. Biomed. Eng. 39:911–921, 2011.PubMedCrossRefGoogle Scholar
  32. 32.
    Mullins, L. P., J. P. McGarry, M. S. Bruzzi, and P. E. McHugh. Micromechanical modelling of cortical bone. Comput. Methods Biomech. Biomed. Eng. 10:159–169, 2007.CrossRefGoogle Scholar
  33. 33.
    Nauman, E. A., K. E. Fong, and T. M. Keaveny. Dependence of intertrabecular permeability on flow direction and anatomic site. Ann. Biomed. Eng. 27:517–524, 1999.PubMedCrossRefGoogle Scholar
  34. 34.
    Nauman, E. A., R. L. Satcher, T. M. Keaveny, B. P. Halloran, and D. D. Bikle. Osteoblasts respond to pulsatile fluid flow with short-term increases in PGE2 but no change in mineralization. J. Appl. Physiol. 90:1849–1854, 2001.PubMedGoogle Scholar
  35. 35.
    Ochoa, J. A., A. P. Sanders, D. A. Heck, and B. M. Hillberry. Stiffening of the femoral head due to inter-trabecular fluid and intraosseous pressure. J. Biomech. Eng. 113:259–262, 1991.PubMedCrossRefGoogle Scholar
  36. 36.
    Ochoa, J. A., A. P. Sanders, T. W. Kiesler, D. A. Heck, J. P. Toombs, K. D. Brandt, and B. M. Hillberry. In vivo observations of hydraulic stiffening in the canine femoral head. J. Biomech. Eng. 119:103–108, 1997.PubMedCrossRefGoogle Scholar
  37. 37.
    Porter, B., R. Zauel, H. Stockman, R. Guldberg, and D. Fyhrie. 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. J. Biomech. 38:543–549, 2005.PubMedCrossRefGoogle Scholar
  38. 38.
    Potier, E., J. Noailly, and K. Ito. Directing bone marrow-derived stromal cell function with mechanics. J. Biomech. 43:807–817, 2010.PubMedCrossRefGoogle Scholar
  39. 39.
    Qin, Y. X., T. Kaplan, A. Saldanha, and C. Rubin. Fluid pressure gradients, arising from oscillations in intramedullary pressure, is correlated with the formation of bone and inhibition of intracortical porosity. J. Biomech. 36:1427–1437, 2003.PubMedCrossRefGoogle Scholar
  40. 40.
    Qin, Y.-X., and H. Lam. Intramedullary pressure and matrix strain induced by oscillatory skeletal muscle stimulation and its potential in adaptation. J. Biomech. 42:140–145, 2009.PubMedCrossRefGoogle Scholar
  41. 41.
    Qin, Y.-X., W. Lin, and C. Rubin. The pathway of bone fluid flow as defined by in vivo intramedullary pressure and streaming potential measurements. Ann. Biomed. Eng. 30:693–702, 2002.PubMedCrossRefGoogle Scholar
  42. 42.
    Riddle, R. C., and H. J. Donahue. From streaming-potentials to shear stress: 25 years of bone cell mechanotransduction. J. Orthop. Res. 27:143–149, 2009.PubMedCrossRefGoogle Scholar
  43. 43.
    Rosen, C. J., and M. L. Bouxsein. Mechanisms of disease: is osteoporosis the obesity of bone? Nat. Clin. Pract. Rheumatol. 2:35–43, 2006.PubMedCrossRefGoogle Scholar
  44. 44.
    Sandino, C., J. A. Planell, and D. Lacroix. A finite element study of mechanical stimuli in scaffolds for bone tissue engineering. J. Biomech. 41:1005–1014, 2008.PubMedCrossRefGoogle Scholar
  45. 45.
    Schofield, R. The relationship between the spleen colony-forming cell and the haemopoietic stem cell. Blood Cells 4:7–25, 1978.PubMedGoogle Scholar
  46. 46.
    Sharp, L. A., Y. W. Lee, and A. S. Goldstein. Effect of low-frequency pulsatile flow on expression of osteoblastic genes by bone marrow stromal cells. Ann. Biomed. Eng. 37:445–453, 2009.PubMedCrossRefGoogle Scholar
  47. 47.
    Teo, J. C. M., and S. H. Teoh. Permeability study of vertebral cancellous bone using micro-computational fluid dynamics. Comput. Methods Biomech. Biomed. Eng. 15:417–423, 2012.CrossRefGoogle Scholar
  48. 48.
    Turner, C. H., and F. M. Pavalko. Mechanotransduction and functional response of the skeleton to physical stress: the mechanisms and mechanics of bone adaptation. J. Orthop. Sci. 3:346–355, 1998.PubMedCrossRefGoogle Scholar
  49. 49.
    Vande Berg, B. C., J. Malghem, F. E. Lecouvet, and B. Maldague. Magnetic resonance imaging of the normal bone marrow. Skeletal Radiol. 27:471–483, 1998.PubMedCrossRefGoogle Scholar
  50. 50.
    Watt, F. M., and B. L. Hogan. Out of Eden: stem cells and their niches. Science 287:1427–1430, 2000.PubMedCrossRefGoogle Scholar
  51. 51.
    Weisberg, S. P., D. McCann, M. Desai, M. Rosenbaum, R. L. Leibel, and A. W. Ferrante, Jr. Obesity is associated with macrophage accumulation in adipose tissue. J. Clin. Invest. 112:1796–1808, 2003.PubMedGoogle Scholar
  52. 52.
    White, F. M. Fluid Mechanics. New York: McGraw Hill, 1998.Google Scholar
  53. 53.
    White, D. R., H. Q. Woodard, and S. M. Hammond. Average soft-tissue and bone models for use in radiation dosimetry. Br. J. Radiol. 60:907–913, 1987.PubMedCrossRefGoogle Scholar
  54. 54.
    Yeung, D. K. W., J. F. Griffith, G. E. Antonio, F. K. H. Lee, J. Woo, and P. C. Leung. Osteoporosis is associated with increased marrow fat content and decreased marrow fat unsaturation: a proton MR spectroscopy study. J. Magn. Reson. Imaging 22:279–285, 2005.PubMedCrossRefGoogle Scholar
  55. 55.
    Yoo, A., and I. Jasiuk. Couple-stress moduli of a trabecular bone idealized as a 3D periodic cellular network. J. Biomech. 39:2241–2252, 2006.PubMedCrossRefGoogle Scholar
  56. 56.
    Zhong, Z., and O. Akkus. Effects of age and shear rate on the rheological properties of human yellow bone marrow. Biorheology 48:89–97, 2011.PubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • E. Birmingham
    • 1
  • J. A. Grogan
    • 1
  • G. L. Niebur
    • 2
  • L. M. McNamara
    • 1
  • P. E. McHugh
    • 1
  1. 1.Biomechanics Research Centre (BMEC), Mechanical and Biomedical Engineering, College of Engineering and InformaticsNational University of Ireland GalwayGalwayIreland
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA

Personalised recommendations