Fluid–structure interaction (FSI) modeling of bone marrow through trabecular bone structure under compression

Abstract

The present study has sought to investigate the fluid characteristic and mechanical properties of trabecular bone using fluid–structure interaction (FSI) approach under different trabecular bone orientations. This method imposed on trabecular bone structure at both longitudinal and transverse orientations to identify effects on shear stress, permeability, stiffness and stress regarded to the trabeculae. Sixteen FSI models were performed on different range trabecular cubes of 27 mm3 with eight models developed for each longitudinal and transverse direction. Results show that there was a moderate correlation between permeability and porosity, and surface area in the longitudinal and transverse orientations. For the longitudinal orientation, the permeability values varied between 3.66 × 10–8 and 1.9 × 10–7 and the sheer stress values varied between 0.05 and 1.8 Pa, whilst for the transverse orientation, the permeability values varied between 5.95 × 10–10 and 1.78 × 10–8 and the shear stress values varied between 0.04 and 3.1 Pa. Here, transverse orientation limits the fluid flow from passing through the trabeculae due to high shear stress disturbance generated within the trabecular bone region. Compared to physiological loading direction (longitudinal orientation), permeability is higher within the range known to trigger a response in bone cells. Additionally, shear stresses also increase with bone surface area. This study suggests the shear stress within bone marrow in real trabecular architecture could provide the mechanical signal to marrow cells that leads to bone anabolism and can depend on trabecular orientation.

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References

  1. Abràmoff MD, Magalhães PJ, Ram SJ (2004) Image processing with imageJ. Biophotonics Int 11(7):36–41. https://doi.org/10.1201/9781420005615.ax4

    Article  Google Scholar 

  2. Bacabac RG, Smit TH, Mullender MG et al (2004) Nitric oxide production by bone cells is fluid shear stress rate dependent. Biochem Biophys Res Commun 315:823–829. https://doi.org/10.1016/j.bbrc.2004.01.138

    Article  Google Scholar 

  3. Bakker AD, Soejima K, Klein-Nulend J, Burger EH (2001) The production of nitric oxide and prostaglandin E(2) by primary bone cells is shear stress dependent. J Biomech 34:671–677. https://doi.org/10.1016/S0021-9290(00)00231-1

    Article  Google Scholar 

  4. Bayraktar HH, Morgan EF, Niebur GL et al (2004) Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech 37:27–35. https://doi.org/10.1016/S0021-9290(03)00257-4

    Article  Google Scholar 

  5. Birmingham E, Grogan JA, Niebur GL et al (2013) Computational modelling of the mechanics of trabecular bone and marrow using fluid structure interaction techniques. Ann Biomed Eng 41:814–826. https://doi.org/10.1007/s10439-012-0714-1

    Article  Google Scholar 

  6. Birmingham E, Niebur GL, McNamara LM, McHugh PE (2016) An experimental and computational investigation of bone formation in mechanically loaded trabecular bone explants. Ann Biomed Eng 44:1191–1203. https://doi.org/10.1007/s10439-015-1378-4

    Article  Google Scholar 

  7. Bryant JD, David T, Gaskell PH et al (1989) Rheology of bovine bone marrow. Proc. Inst Mech Eng Part H J Eng Med 203:71–75

    Article  Google Scholar 

  8. Burgers TA, Mason J, Niebur G, Ploeg HL (2008) Compressive properties of trabecular bone in the distal femur. J Biomech 41:1077–1085. https://doi.org/10.1016/j.jbiomech.2007.11.018

    Article  Google Scholar 

  9. Chevalier Y, Pahr D, Allmer H et al (2007) Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation. J Biomech 40:3333–3340. https://doi.org/10.1016/j.jbiomech.2007.05.004

    Article  Google Scholar 

  10. Cowin SC (2002) Mechanosensation and fluid transport in living bone. J Musculoskelet Neuronal Interact 2:256–260. https://doi.org/10.1016/S0142-9612(03)00267-9

    Article  Google Scholar 

  11. de Gusmão CVB, Belangero WD (2009) How do bone cells sense mechanical loading? Rev Bras Ortop. https://doi.org/10.1016/S2255-4971(15)30157-9

    Article  Google Scholar 

  12. Eswaran SK, Gupta A, Adams MF, Keaveny TM (2006) Cortical and trabecular load sharing in the human vertebral body. J Bone Miner Res 21:307–314. https://doi.org/10.1359/jbmr.2006.21.2.307

    Article  Google Scholar 

  13. Fields AJ, Lee GL, Liu XS et al (2011) Influence of vertical trabeculae on the compressive strength of the human vertebra. J Bone Miner Res 26:263–269. https://doi.org/10.1002/jbmr.207

    Article  Google Scholar 

  14. Frost HM (1994) Wolff’s Law and bone’s structural adaptations to mechanical usage: an overview for clinicians. Angle Orthod 64:175–188

    Google Scholar 

  15. Grimm MJ, Williams JL (1997) Measurements of permeability in human calcaneal trabecular bone. J Biomech 30:743–745. https://doi.org/10.1016/S0021-9290(97)00016-X

    Article  Google Scholar 

  16. Gurkan UA, Akkus O (2008) The mechanical environment of bone marrow: A review. Ann Biomed Eng 36:1978–1991. https://doi.org/10.1007/s10439-008-9577-x

    Article  Google Scholar 

  17. Haider IT, Speirs AD, Frei H (2013) Effect of boundary conditions, impact loading and hydraulic stiffening on femoral fracture strength. J Biomech 46:2115–2121. https://doi.org/10.1016/j.jbiomech.2013.07.004

    Article  Google Scholar 

  18. Harrigan TP, Jasty M, Mann RW, Harris WH (1988) Limitations of the continuum assumption in cancellous bone. J Biomech 21:269–275. https://doi.org/10.1016/0021-9290(88)90257-6

    Article  Google Scholar 

  19. Hwa HJ (2004) Could the intraosseous fluid in cancellous bone bear external load significantly within the elastic range? Proc Inst Mech Eng Part H J Eng Med 218:375–379. https://doi.org/10.1243/0954411042632153

    Article  Google Scholar 

  20. Klein-Nulend J, van der Plas A, Semeins CM et al (1995) Sensitivity of osteocytes to biomechanical stress in vitro. FASEB J 9:441–445. https://doi.org/10.1096/fasebj.9.5.7896017

    Article  Google Scholar 

  21. Klein-Nulend J, Bacabac RG, Bakker AD (2012) Mechanical loading and how it affects bone cells: the role of the osteocyte cytoskeleton in maintaining our skeleton. Eur Cells Mater 24:278–291

    Article  Google Scholar 

  22. Knothe Tate ML, Knothe U (2000) An ex vivo model to study transport processes and fluid flow in loaded bone. J Biomech 33:247–254. https://doi.org/10.1016/S0021-9290(99)00143-8

    Article  Google Scholar 

  23. Kohles SS, Roberts JB, Upton ML et al (2001) Direct perfusion measurements of cancellous bone anisotropic permeability. J Biomech 34:1197–1202. https://doi.org/10.1016/S0021-9290(01)00082-3

    Article  Google Scholar 

  24. Laouira A, Rahmoun J, Naceur H et al (2015) On the influence of marrow on the mechanical behavior of porcine trabecular bone under dynamic loading: A numerical investigation. Comput Methods Biomech Biomed Engin 18:1974–1975. https://doi.org/10.1080/10255842.2015.1069584

    Article  Google Scholar 

  25. Li YJ, Batra NN, You L et al (2004) Oscillatory fluid flow affects human marrow stromal cell proliferation and differentiation. J Orthop Res 22:1283–1289. https://doi.org/10.1016/j.orthres.2004.04.002

    Article  Google Scholar 

  26. Liebschner MAK, Keller TS (2005) Hydraulic strengthening affects the stiffness and strength of cortical bone. Ann Biomed Eng 33:26–38. https://doi.org/10.1007/s10439-005-8960-0

    Article  Google Scholar 

  27. Liu XS, Zhang XH, Guo XE (2009) Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone. Bone 45:158–163. https://doi.org/10.1016/j.bone.2009.04.201

    Article  Google Scholar 

  28. Md Saad AP, Syahrom A (2018) Study of dynamic degradation behaviour of porous magnesium under physiological environment of human cancellous bone. Corros Sci 131:45–56. https://doi.org/10.1016/j.corsci.2017.10.026

    Article  Google Scholar 

  29. Metzger TA, Kreipke TC, Vaughan TJ et al (2015) The in situ mechanics of trabecular bone marrow: the potential for mechanobiological response. J Biomech Eng 137:011006. https://doi.org/10.1115/1.4028985

    Article  Google Scholar 

  30. Nagaraja S, Couse TL, Guldberg RE (2005) Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech 38:707–716. https://doi.org/10.1016/j.jbiomech.2004.05.013

    Article  Google Scholar 

  31. Niebur GL, Yuen JC, Hsia AC, Keaveny TM (1999) Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng 121:629. https://doi.org/10.1115/1.2800865

    Article  Google Scholar 

  32. Niebur GL, Feldstein MJ, Keaveny TM (2002) Biaxial failure behavior of bovine tibial trabecular bone. J Biomech Eng 124:699. https://doi.org/10.1115/1.1517566

    Article  Google Scholar 

  33. Ochoa JA, Sanders AP, Kiesler TW et al (1997) In vivo observations of hydraulic stiffening in the canine femoral head. J Biomech Eng 119:103. https://doi.org/10.1115/1.2796051

    Article  Google Scholar 

  34. Odgaard A, Linde F (1991) The underestimation of Young’s modulus in compressive testing of cancellous bone specimens. J Biomech 24:691–698. https://doi.org/10.1016/0021-9290(91)90333-I

    Article  Google Scholar 

  35. Sandino C, Kroliczek P, McErlain DD, Boyd SK (2014) Predicting the permeability of trabecular bone by micro-computed tomography and finite element modeling. J Biomech 47:3129–3134. https://doi.org/10.1016/j.jbiomech.2014.06.024

    Article  Google Scholar 

  36. Shi X, Wang X, Niebur GL (2009) Effects of loading orientation on the morphology of the predicted yielded regions in trabecular bone. Ann Biomed Eng 37:354–362. https://doi.org/10.1007/s10439-008-9619-4

    Article  Google Scholar 

  37. Shi X, Liu XS, Wang X et al (2010a) Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone. Bone 46:1260–1266. https://doi.org/10.1016/j.bone.2010.02.005

    Article  Google Scholar 

  38. Shi X, Sherry Liu X, Wang X et al (2010b) Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directions. J Biomech 43:2460–2466. https://doi.org/10.1016/j.jbiomech.2010.05.032

    Article  Google Scholar 

  39. Shim VPW, Yang LM, Liu JF, Lee VS (2006) Characterisation of the dynamic compressive mechanical properties of cancellous bone from the human cervical spine. Int J Impact Eng 32:525–540. https://doi.org/10.1016/j.ijimpeng.2005.03.006

    Article  Google Scholar 

  40. Stauber M, Rapillard L, Van Lenthe GH et al (2006) Importance of individual rods and plates in the assessment of bone quality and their contribution to bone stiffness. J Bone Miner Res 21:586–595. https://doi.org/10.1359/jbmr.060102

    Article  Google Scholar 

  41. Syahrom A, Abdul Kadir MR, Abdullah J, Öchsner A (2013) Permeability studies of artificial and natural cancellous bone structures. Med Eng Phys 35:792–799. https://doi.org/10.1016/j.medengphy.2012.08.011

    Article  Google Scholar 

  42. Teichtahl AJ, Wluka AE, Wijethilake P et al (2015) Wolff’s law in action: a mechanism for early knee osteoarthritis. Arthritis Res Ther 17:1–9. https://doi.org/10.1186/s13075-015-0738-7

    Article  Google Scholar 

  43. Teo JCM, Si-Hoe KM, Keh JEL, Teoh SH (2007) Correlation of cancellous bone microarchitectural parameters from microCT to CT number and bone mechanical properties. Mater Sci Eng C 27:333–339. https://doi.org/10.1016/j.msec.2006.05.003

    Article  Google Scholar 

  44. Ulrich D, Van Rietbergen B, Laib A, Ruegsegger P (1999) The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone. https://doi.org/10.1016/S8756-3282(99)00098-8

    Article  Google Scholar 

  45. van Lenthe GH, Stauber M, Müller R (2006) Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone 39:1182–1189. https://doi.org/10.1016/j.bone.2006.06.033

    Article  Google Scholar 

  46. Vaughan TJ, Voisin M, Niebur GL, Mcnamara LM (2014) Multiscale modelling of trabecular bone marrow: understanding the micromechanical environment of mesenchymal stem cells during osteoporosis. J Biomech Eng 137:011003. https://doi.org/10.1115/1.4028986

    Article  Google Scholar 

  47. Verbruggen SW, Vaughan TJ, McNamara LM (2012) Loading-induced interstitial fluid flow in bone mechanobiology: an FSI approach to the osteocyte environment. In: ASME 2012 Summer Bioengineering Conference, SBC 2012. pp 517–518

  48. Verbruggen SW, Vaughan TJ, McNamara LM (2014) Fluid flow in the osteocyte mechanical environment: a fluid-structure interaction approach. Biomech Model Mechanobiol 13:85–97. https://doi.org/10.1007/s10237-013-0487-y

    Article  Google Scholar 

  49. Wang L, Cowin SC, Weinbaum S, Fritton SP (2000) Modeling tracer transport in an osteon under cyclic loading. Ann Biomed Eng 28:1200–1209. https://doi.org/10.1114/1.1317531

    Article  Google Scholar 

  50. Weinbaum S, Cowin SC, Zeng Y (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J Biomech 27:339–360. https://doi.org/10.1016/0021-9290(94)90010-8

    Article  Google Scholar 

  51. Whitehouse WJ (1974) The quantitative morphology of anisotropic trabecular bone. J Microsc 101:153–168. https://doi.org/10.1111/j.1365-2818.1974.tb03878.x

    Article  Google Scholar 

  52. Widmer RP, Ferguson SJ (2013) A comparison and verification of computational methods to determine the permeability of vertebral trabecular bone. Proc Inst Mech Eng Part H J Eng Med 227:617–628. https://doi.org/10.1177/0954411912462814

    Article  Google Scholar 

  53. Wittkowske C, Reilly GC, Lacroix D, Perrault CM (2016) In vitro bone cell models: impact of fluid shear stress on bone formation. Front Bioeng Biotechnol. https://doi.org/10.3389/fbioe.2016.00087

    Article  Google Scholar 

  54. You J, Yellowley CE, Donahue HJ et al (2000) Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loading-induced oscillatory fluid flow. J Biomech Eng 122:387. https://doi.org/10.1115/1.1287161

    Article  Google Scholar 

  55. Yourek G, Mccormick SM, Mao JJ, Reilly GC (2010) Shear stress induces osteogenic differentiation of human mesenchymal stem cells. Regen Med 5:713–724. https://doi.org/10.2217/rme.10.60

    Article  Google Scholar 

  56. Yu Y, Zhang Y, Martin JA, Ozbolat IT (2013) Evaluation of cell viability and functionality in vessel-like bioprintable cell-laden tubular channels. J Biomech Eng 135:091011. https://doi.org/10.1115/1.4024575

    Article  Google Scholar 

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Acknowledgements

This project was sponsored by the Kementerian Pendidikan Malaysia (KPM) through Grant scheme (TRGS/1/2016/UM/01/4/2). The authors would also like to thank the Research Management Centre, Universiti Teknologi Malaysia, for managing the project.

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Correspondence to Ardiyansyah Syahrom.

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Rabiatul, A.A.R., Fatihhi, S.J., Md Saad, A.P. et al. Fluid–structure interaction (FSI) modeling of bone marrow through trabecular bone structure under compression. Biomech Model Mechanobiol (2021). https://doi.org/10.1007/s10237-021-01423-x

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Keywords

  • FSI
  • Trabecular bone
  • Compressive loading
  • Numerical analysis
  • Bone marrow