Abstract
Osteoporosis affects nearly 10 million individuals in the United States. Conventional treatments include anti-resorptive drug therapies, but recently, it has been demonstrated that delivering a low magnitude, dynamic stimulus via whole body vibration can have an osteogenic effect without the need for large magnitude strain stimulus. Vibration of the vertebral body induces a range of stimuli that may account for the anabolic response including low magnitude strains, interfacial shear stress due to marrow movement, and blood transport. In order to evaluate the relative importance of these stimuli, we integrated a microstructural model of vertebral cancellous bone with a mixture theory model of the vertebral body. The predicted shear stresses on the surfaces of the trabeculae during vibratory loading are in the range of values considered to be stimulatory and increase with increasing solid volume fraction. Peak volumetric blood flow rates also varied with strain amplitude and frequency, but exhibited little dependence on solid volume fraction. These results suggest that fluid shear stress governs the response of the vertebrae to whole body vibration and that the marrow viscosity is a critical parameter which modulates the shear stress.
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References
Abbott TA, Lawrence BJ, Wallach S (1996) Osteoporosis: the need for comprehensive treatment guidelines. Clin Ther 18(1):127–149; discussion 126
Atkin R, Craine R (1976a) Continuum Theory of Mixtures: Applications. J Institute Math Appl 17(2):153–207
Atkin R, Craine R (1976b) Continuum theory of mixtures: basic theory and historical development. Q J Mech Appl Math 29:209–244
Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–164
Bryant JD, David T, Gaskell PH, King S, Lond G (1989) Rheology of bovine bone marrow. Proc Inst Mech Eng [H] 203(2):71–75
Burger EH, Klein-Nulend J, van der Plas A, Nijweide PJ (1995) Function of osteocytes in bone–their role in mechanotransduction. J Nutr 125(7 Suppl):2020S–2023S
Cowin SC, Weinbaum S, Zeng Y (1995) A case for bone canaliculi as the anatomical site of strain generated potentials. J Biomech 28(11):1281–1297
Currey J (1984) The mechanical adaptations of bones. Princeton, Princeton University Press
Davidson MR (2003) Pharmacotherapeutics for osteoporosis prevention and treatment. J Midwifery Womens Health 48(1):39–52
Drummond J, Tahir M (1984) Laminar Viscous-Flow Through Regular Arrays of Parallel Solid Cylinders. Int J Multiphase Flow 10(5):515–540
Flieger J, Karachalios T, Khaldi L, Raptou P, Lyritis G (1998) Mechanical stimulation in the form of vibration prevents postmenopausal bone loss in ovariectomized rats. Calcif Tissue Int 63(6):510–514
Fourie JG, Du Plessis JP (2002) Pressure drop modeling in cellular metallic foams. Chem Eng Sci 57:2781–2789
Fritton JC, Rubin CT, Qin YX, McLeod KJ (1997) Whole-body vibration in the skeleton: development of a resonance-based testing device. Ann Biomed Eng 25(5):831–839
Fritton SP, McLeod KJ, Rubin CT (2000) Quantifying the strain history of bone: spatial uniformity and self-similarity of low-magnitude strains. J Biomech 33(3):317–325
Fritz M (2000) Simulating the response of a standing operator to vibration stress by means of a biomechanical model. J Biomech 33(7):795–802
Griffith JF, Yeung DK, Antonio GE, Lee FK, Hong AW, Wong SY, Lau EM, Leung PC (2005) Vertebral bone mineral density, marrow perfusion, and fat content in healthy men and men with osteoporosis: dynamic contrast-enhanced MR imaging and MR spectroscopy. Radiology 236(3):945–951
Guo LX, Teo EC (2005) Prediction of the modal characteristics of the human spine at resonant frequency using finite element models. Proc Inst Mech Eng [H] 219(4):277–284
Huang QY, Kung AW (2006) Genetics of osteoporosis. Mol Genet Metab 88(4):295–306
Huang RP, Rubin CT, McLeod KJ (1999) Changes in postural muscle dynamics as a function of age. J Gerontol A Biol Sci Med Sci 54(8):B352–B357
Iwamoto J, Takeda T, Sato Y, Uzawa M (2005) Effect of whole-body vibration exercise on lumbar bone mineral density, bone turnover, and chronic back pain in post-menopausal osteoporotic women treated with alendronate. Aging Clin Exp Res 17(2):157–163
Judex S, Donahue LR, Rubin C (2002) Genetic predisposition to low bone mass is paralleled by an enhanced sensitivity to signals anabolic to the skeleton. Faseb J 16(10):1280–1282
Judex S, Boyd S, Qin YX, Turner S, Ye K, Muller R, Rubin C (2003) Adaptations of trabecular bone to low magnitude vibrations result in more uniform stress and strain under load. Ann Biomed Eng 31(1):12–20
Judex S, Lei X, Han D, Rubin C (2007) Low-magnitude mechanical signals that stimulate bone formation in the ovariectomized rat are dependent on the applied frequency but not on the strain magnitude. J Biomech 40(6):1333–1339
Kapur S, Baylink DJ, Lau KH (2003) Fluid flow shear stress stimulates human osteoblast proliferation and differentiation through multiple interacting and competing signal transduction pathways. Bone 32(3):241–251
Keaveny TM, Morgan EF, Niebur GL, Yeh OC (2001) Biomechanics of trabecular bone. Annu Rev Biomed Eng 3:307–333
Klein-Nulend J, van der Plas A, Semeins CM, Ajubi NE, Frangos JA, Nijweide PJ, Burger EH (1995a) Sensitivity of osteocytes to biomechanical stress in vitro. Faseb J 9(5):441–445
Klein-Nulend J, van der Plas A, Semeins CM, Ajubi NE, Frangos JA, Nijweide PJ, Burger EH (1995b) Sensitivity of osteocytes to biomechanical stress in vitro. Faseb J 9(5):441–445
Knothe Tate ML (2003) Whither flows the fluid in bone? An osteocyte’s perspective. J Biomech 36(10):1409–1424
Knothe Tate ML, Steck R, Forwood MR, Niederer P (2000) In vivo demonstration of load-induced fluid flow in the rat tibia and its potential implications for processes associated with functional adaptation. J Exp Biol 203(Pt 18):2737–2745
Kopperdahl DL, Keaveny TM (1998) Yield strain behavior of trabecular bone. J Biomech 31(7):601–608
Liu YJ, Shen H, Xiao P, Xiong DH, Li LH, Recker RR, Deng HW (2006) Molecular genetic studies of gene identification for osteoporosis: a 2004 update. J Bone Miner Res 21(10):1511–1535
Makhsous M, Hendrix R, Crowther Z, Nam E, Lin F (2005) Reducing whole-body vibration and musculoskeletal injury with a new car seat design. Ergonomics 48(9):1183–1199
Martin RB, Chow BD, Lucas PA (1990) Bone marrow fat content in relation to bone remodeling and serum chemistry in intact and ovariectomized dogs. Calcif Tissue Int 46(3):189–194
Morgan EF, Keaveny TM (2001) Dependence of yield strain of human trabecular bone on anatomic site. J Biomech 34(5):569–577
Morgan EF, Yeh OC, Chang WC, Keaveny TM (2001) Nonlinear behavior of trabecular bone at small strains. J Biomech Eng 123(1): 1–9
Mosekilde L (1988) Age-related changes in vertebral trabecular bone architecture–assessed by a new method. Bone 9(4):247–250
Nauman EA, Satcher RL, Keaveny TM, Halloran BP, Bikle DD (2001) Osteoblasts respond to pulsatile fluid flow with short-term increases in PGE(2) but no change in mineralization. J Appl Physiol 90(5):1849–1854
Otter MW, Palmieri vR, Cochran GVB (1990) Transcortical Streaming Potentials are Generated by Circulatory Pressure Gradients in Living Canine Tibia. J Orthop Res 8:119–126
Owan I, Burr DB, Turner CH, Qiu J, Tu Y, Onyia JE, Duncan RL (1997) Mechanotransduction in bone: osteoblasts are more responsive to fluid forces than mechanical strain. Am J Physiol 273(3 Pt 1):C810–C815
Piekarski K, Munro M (1977) Transport mechanism operating between blood supply and osteocytes in long bones. Nature 269(5623):80–82
Rice JR, Cleary MP (1976) Some basic diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys Space Phys 14(2):227–241
Roelofsen J, Kleinnulend J, Burger EH (1995) Mechanical Stimulation By Intermittent Hydrostatic Compression Promotes Bone-Specific Gene Expression In Vitro. J Biomech 28(12):1493–1503
Routh RH, Rumancik S, Pathak RD, Burshell AL, Nauman EA (2005) The relationship between bone mineral density and biomechanics in patients with osteoporosis and scoliosis. Osteoporos Int 16(12):1857–1863
Rubin C, Turner AS, Bain S, Mallinckrodt C, McLeod K (2001) Anabolism. Low mechanical signals strengthen long bones. Nature 412(6847):603–604
Rubin C, Turner AS, Mallinckrodt C, Jerome C, McLeod K, Bain S (2002a) Mechanical strain, induced noninvasively in the high- frequency domain, is anabolic to cancellous bone, but not cortical bone. Bone 30(3):445–452
Rubin C, Turner AS, Muller R, Mittra E, McLeod K, Lin W, Qin YX (2002b) Quantity and quality of trabecular bone in the femur are enhanced by a strongly anabolic, noninvasive mechanical intervention. J Bone Miner Res 17(2):349–357
Rubin C, Recker R, Cullen D, Ryaby J, McCabe J, McLeod K (2004) Prevention of postmenopausal bone loss by a low-magnitude, high-frequency mechanical stimuli: a clinical trial assessing compliance, efficacy, and safety. J Bone Miner Res 19(3):343–351
Rumancik S, Routh RH, Pathak RD, Burshell AL, Nauman EA (2005) Assessment of bone quantity and distribution in adult lumbar scoliosis: new dual-energy x-ray absorptiometry methodology and analysis. Spine 30(4):434–439
Sander EA, Shimko DA, Dee KC, Nauman EA (2003) Examination of continuum and micro-structural properties of human vertebral cancellous bone using combined cellular solid models. Biomech Model Mechanobiol 2(2):97–107
Shirazi-Adl A, Ahmed AM, Shrivastava SC (1986) A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. J Biomech 19(4):331
Torvinen S, Kannus P, Sievanen H, Jarvinen TA, Pasanen M, Kontulainen S, Nenonen A, Jarvinen TL, Paakkala T, Jarvinen M, Vuori I (2003) Effect of 8-month vertical whole body vibration on bone, muscle performance, and body balance: a randomized controlled study. J Bone Miner Res 18(5):876–884
Turner CH, Pavalko FM (1998) Mechanotransduction and functional response of the skeleton to physical stress: the mechanisms and mechanics of bone adaptation. Journal of Orthopaedic Sci 3(6):346–355
Vande Berg BC, Malghem J, Lecouvet FE, Maldague B (1998) Magnetic resonance imaging of normal bone marrow. Eur Radiol 8(8): 1327–1334
Verschueren SM, Roelants M, Delecluse C, Swinnen S, Vanderschueren D, Boonen S (2004) Effect of 6-month whole body vibration training on hip density, muscle strength, and postural control in postmenopausal women: a randomized controlled pilot study. J Bone Miner Res 19(3):352–359
Ward K, Alsop C, Caulton J, Rubin C, Adams J, Mughal Z (2004) Low magnitude mechanical loading is osteogenic in children with disabling conditions. J Bone Miner Res 19(3):360–369
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(3):339–360
Xie L, Jacobson JM, Choi ES, Busa B, Donahue LR, Miller LM, Rubin CT, Judex S (2006) Low-level mechanical vibrations can influence bone resorption and bone formation in the growing skeleton. Bone 39(5):1059–1066
Yeung DK, Griffith JF, Antonio GE, Lee FK, Woo J, Leung PC (2005) Osteoporosis is associated with increased marrow fat content and decreased marrow fat unsaturation: a proton MR spectroscopy study. J Magn Reson Imaging 22(2):279–285
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Dickerson, D.A., Sander, E.A. & Nauman, E.A. Modeling the mechanical consequences of vibratory loading in the vertebral body: microscale effects. Biomech Model Mechanobiol 7, 191–202 (2008). https://doi.org/10.1007/s10237-007-0085-y
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DOI: https://doi.org/10.1007/s10237-007-0085-y