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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abràmoff MD, Magalhães PJ, Ram SJ (2004) Image processing with imageJ. Biophotonics Int 11(7):36–41. https://doi.org/10.1201/9781420005615.ax4
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
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
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
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
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
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
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
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
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
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
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
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
Frost HM (1994) Wolff’s Law and bone’s structural adaptations to mechanical usage: an overview for clinicians. Angle Orthod 64:175–188
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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 20, 957–968 (2021). https://doi.org/10.1007/s10237-021-01423-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-021-01423-x