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Computer modelling of bone’s adaptation: the role of normal strain, shear strain and fluid flow

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Abstract

Bone loss is a serious health problem. In vivo studies have found that mechanical stimulation may inhibit bone loss as elevated strain in bone induces osteogenesis, i.e. new bone formation. However, the exact relationship between mechanical environment and osteogenesis is less clear. Normal strain is considered as a prime stimulus of osteogenic activity; however, there are some instances in the literature where osteogenesis is observed in the vicinity of minimal normal strain, specifically near the neutral axis of bending in long bones. It suggests that osteogenesis may also be induced by other or secondary components of mechanical environment such as shear strain or canalicular fluid flow. As it is evident from the literature, shear strain and fluid flow can be potent stimuli of osteogenesis. This study presents a computational model to investigate the roles of these stimuli in bone adaptation. The model assumes that bone formation rate is roughly proportional to the normal, shear and fluid shear strain energy density above their osteogenic thresholds. In vivo osteogenesis due to cyclic cantilever bending of a murine tibia has been simulated. The model predicts results close to experimental findings when normal strain, and shear strain or fluid shear were combined. This study also gives a new perspective on the relation between osteogenic potential of micro-level fluid shear and that of macro-level bending shear. Attempts to establish such relations among the components of mechanical environment and corresponding osteogenesis may ultimately aid in the development of effective approaches to mitigating bone loss.

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Abbreviations

\(\varepsilon _{i}\) :

normal strain at surface coordinate ‘i’

M :

bending moment

\(y_{i}\) :

distance from the neutral axis to surface coordinate ‘i’

E :

Young’s modulus of the bone

I :

area moment of inertia

\(\gamma _{i}\) :

shear strain at surface coordinate ‘i’

V :

vertical shear force

\(Q_{i}\) :

first moment of area

\(t_{i}\) :

width of the section at point ‘i’

\(P_{steady}\) :

steady-state response of the pore pressure

B :

relative compressibility constant or Skempton coefficient

\(\upsilon _{u}\) :

Poisson’s ratio of the solid bone matrix under undrained conditions

a :

thickness of the cortex

\(y^{*}\) :

dimensionless length parameter

\(t^{*}\) :

dimensionless time parameter

\(\varOmega \) :

dimensionless frequency parameter

t :

time

c :

diffusion coefficient

\(\omega \) :

angular frequency (\(=\)2 \(\pi {f}\))

\(\upsilon \) :

Poisson’s ratio of the bone

H :

dimensionless stress coefficient

\(S_{i}\) :

fluid shear stress at surface coordinate ‘i’

\(b_{o}\) :

radius of the canaliculus

\(a_{o}\) :

radius of the cell process

\(\lambda \) :

dimensionless length ratio (\({=}b_o /\sqrt{k_p}\))

\(k_{p}\) :

Darcy’s law permeability constant

\(I_{o}\) :

modified Bessel function of the first kind

\(K_{o}\) :

modified Bessel function of the third kind

q :

the ratio of the radius of the canaliculus, \(b_{o}\), to the radius of the cell process, \(a_{o,}\)(\({=}{b}_{{o}} /{a}_{{o}})\)

\(U_{i}^{\varepsilon }, U_{i}^{\gamma }, U_i^s\) :

strain energy density (SED) due to the normal strain, the shear strain and the fluid shear, respectively, at surface coordinate ‘i’

\(U_{ref}^\varepsilon , U_{ref}^\gamma , U_{ref}^s\) :

reference SED for normal strain, shear strain and fluid shear, respectively.

C :

bone’s surface remodelling rate coefficient

G :

shear modulus of the bone

\(G_{osc}\) :

shear modulus of the osteocyte

\(\Delta _i\) :

natural bone growth rate at surface coordinate ‘i’

References

  • Akhter MP, Raab DM, Turner CH, Kimmel DB, Recker RR (1992) Characterization of in vivo strain in the rat tibia during external application of a four-point bending load. J Biomech 25:1241–1246. doi:10.1016/0021-9290(92)90082-C

    Article  Google Scholar 

  • Ausk BJ, Gross TS, Srinivasan S (2006) An agent based model for real-time signaling induced in osteocytic networks by mechanical stimuli. J Biomech 39:2638–2646. doi:10.1016/j.jbiomech.2005.08.023

    Article  Google Scholar 

  • Beamer WG, Donahue LR, Rosen CJ, Baylink DJ (1996) Genetic variability in adult bone density among inbred strains of mice. Bone 18:397–403. doi:10.1016/8756-3282(96)00047-6

    Article  Google Scholar 

  • Bertram JE, Biewener AA (1988) Bone curvature: sacrificing strength for load predictability? J Theor Biol 131:75–92

    Article  Google Scholar 

  • Birkhold AI, Razi H, Duda GN, Weinkamer R, Checa S, Willie BM (2014) Mineralizing surface is the main target of mechanical stimulation independent of age: 3D dynamic in vivo morphometry. Bone 66:15–25. doi:10.1016/j.bone.2014.05.013

    Article  Google Scholar 

  • Birkhold AI, Razi H, Duda GN, Weinkamer R, Checa S, Willie BM (2016) The Periosteal Bone Surface is Less Mechano-Responsive than the Endocortical. Sci Rep 6:1–11

    Article  Google Scholar 

  • Brown TD, Pedersen DR, Gray ML et al (1990) Toward an identification of mechanical parameters initiating periosteal remodeling: A combined experimental and analytic approach. J Biomech 23:893–905. doi:10.1016/0021-9290(90)90354-6

    Article  Google Scholar 

  • Burr DB, Robling AG, Turner CH (2002) Effects of biomechanical stress on bones in animals. Bone 30:781–786. doi:10.1016/S8756-3282(02)00707-X

    Article  Google Scholar 

  • Carpenter RD (2006) Mechanobiology of bone cross-sectional development, adaptation, and strength. Dissertation, Stanford University

  • Carpenter RD, Carter DR (2008) The mechanobiological effects of periosteal surface loads. Biomech Model Mechanobiol 7:227–242. doi:10.1007/s10237-007-0087-9

    Article  Google Scholar 

  • Carter RD, Beaupré GS, Giori NJ, Helms JA (1998) Mechanobiology of skeletal regeneration. Clin Orthop 355:S41–S55

    Article  Google Scholar 

  • Chennimalai Kumar N, Dantzig JA, Jasiuk IM et al (2009) Numerical modeling of long bone adaptation due to mechanical loading: Correlation with experiments. Ann Biomed Eng 38:594–604. doi:10.1007/s10439-009-9861-4

    Article  Google Scholar 

  • Cowin SC (1993) Bone stress adaptation models. J Biomech Eng 115:528–533. doi:10.1115/1.2895535

    Article  Google Scholar 

  • Cowin SC, Hart RT, Balser JR, Kohn DH (1985) Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients. J Biomech 18:665–684

    Article  Google Scholar 

  • De Souza RL, Matsuura M, Eckstein F et al (2005) Non-invasive axial loading of mouse tibiae increases cortical bone formation and modifies trabecular organization: A new model to study cortical and cancellous compartments in a single loaded element. Bone 37:810–818. doi:10.1016/j.bone.2005.07.022

    Article  Google Scholar 

  • De Margerie E, Sanchez S, Cubo J, Castanet J (2005) Torsional resistance as a principal component of the structural design of long bones: comparative multivariate evidence in birds. Anat. Rec A Discov Mol Cell Evol Biol 282:49–66

    Google Scholar 

  • Dirschl DR, Henderson RC, Oakley WC (1997) Accelerated bone mineral loss following a hip fracture: a prospective longitudinal study. Bone 21:79–82. doi:10.1016/S8756-3282(97)00082-3

    Article  Google Scholar 

  • Feldman D, Marcus R, Nelson D, Rosen CJ (2007) Chapter 21—Skeletal development: mechanical consequences of growth, aging, and disease. In: Marcus R, Feldman D, Nelson DA, Rosen CJ (eds) Osteoporosis. Elsevier Science, New York, pp 563–600

    Google Scholar 

  • Ferguson VL, Ayers RA, Bateman TA, Simske SJ (2003) Bone development and age-related bone loss in male C57BL/6J mice. Bone 33:387–398. doi:10.1016/S8756-3282(03)00199-6

    Article  Google Scholar 

  • Florio CS, Narh KA (2012) Effect of modeling method on prediction of cortical bone strength adaptation under various loading conditions. Meccanica 48:393–413. doi:10.1007/s11012-012-9609-3

    Article  MATH  Google Scholar 

  • Flurkey K, Currer J, Harrison D (2007) Chapter 20—Mouse models in aging research. In: James GF, Barthold S, Davisson M, Newcomer CE, Quimby FW, Smith A (eds) The mouse in biomedical research, Second edn. Academic Press, Burlington, pp 637–672

    Chapter  Google Scholar 

  • Fridez P, Rakotomanana L, Terrier A, Leyvraz P (1998) Three dimensional model of bone external adaptation. In: Middleton J, Jones M, Pande G (eds) Computer Methods In Biomechanics & Biomedical Engineering 2: 189–196

  • Fritton J, Myers E, Wright T, Vandermeulen M (2005) Loading induces site-specific increases in mineral content assessed by microcomputed tomography of the mouse tibia. Bone 36:1030–1038. doi:10.1016/j.bone.2005.02.013

    Article  Google Scholar 

  • Gross TS, Edwards JL, Mcleod KJ, Rubin CT (1997) Strain gradients correlate with sites of periosteal bone formation. J Bone Miner Res 12:982–988. doi:10.1359/jbmr.1997.12.6.982

    Article  Google Scholar 

  • Hamilton N, Coombe D, Tran D, Zernicke RF (2004) Simulating load induced fluid flow and nutrient transport in bone. 5th Comb. Meet. Orthop. Res. Soc. Can. USA Jpn. Eur

  • Hillam RA, Skerry TM (1995) Inhibition of bone resorption and stimulation of formation by mechanical loading of the modeling rat ulna in vivo. J Bone Miner Res 10:683–689. doi:10.1002/jbmr.5650100503

    Article  Google Scholar 

  • Huiskes R, Weinans H, Grootenboer HJ et al (1987) Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20:1135–1150. doi:10.1016/0021-9290(87)90030-3

    Article  Google Scholar 

  • Huo B, Lu XL, Hung CT et al (2008) Fluid flow induced calcium response in bone cell network. Cell Mol Bioeng 1:58–66. doi:10.1007/s12195-008-0011-0

    Article  Google Scholar 

  • Inman CL, Warren GL, Hogan HA, Bloomfield SA (1999) Mechanical loading attenuates bone loss due to immobilization and calcium deficiency. J Appl Physiol 87:189–195

    Google Scholar 

  • Jing D, Baik AD, Lu XL et al (2014) In situ intracellular calcium oscillations in osteocytes in intact mouse long bones under dynamic mechanical loading. FASEB J 28:1582–1592. doi:10.1096/fj.13-237578

    Article  Google Scholar 

  • Judex S, Gross TS, Zernicke RF (1997) Strain gradients correlate with sites of exercise-induced bone-forming surfaces in the adult skeleton. J Bone Miner Res 12:1737–1745. doi:10.1359/jbmr.1997.12.10.1737

    Article  Google Scholar 

  • Kameo Y, Adachi T, Hojo M (2009) Fluid pressure response in poroelastic materials subjected to cyclic loading. J Mech Phys Solids 57:1815–1827. doi:10.1016/j.jmps.2009.08.002

    Article  MathSciNet  MATH  Google Scholar 

  • Kotha SP, Hsieh Y-F, Strigel RM et al (2004) Experimental and finite element analysis of the rat ulnar loading model—correlations between strain and bone formation following fatigue loading. J Biomech 37:541–548. doi:10.1016/j.jbiomech.2003.08.009

    Article  Google Scholar 

  • Klein-Nulend J, Bacabac R, Bakker A et al (2012) Mechanical loading and how it affects bone cells: the role of the osteocyte cytoskeleton in maintaining our skeleton. Eur Cell Mater 24:278–291

    Article  Google Scholar 

  • Kuruvilla SJ, Fox SD, Cullen DM, Akhter MP (2008) Site specific bone adaptation response to mechanical loading. J Musculoskelet Neuronal Interact 8:71–78

    Google Scholar 

  • LaMothe JM (2004) Rest insertion combined with high-frequency loading enhances osteogenesis. J Appl Physiol 96:1788–1793. doi:10.1152/japplphysiol.01145.2003

    Article  Google Scholar 

  • Lau RY, Guo X (2011) A review on current osteoporosis research: with special focus on disuse bone loss. J Osteoporos 2011:1–6. doi:10.4061/2011/293808

    Article  Google Scholar 

  • Lee KCL, Maxwell A, Lanyon LE (2002) Validation of a technique for studying functional adaptation of the mouse ulna in response to mechanical loading. Bone 31:407–412. doi:10.1016/S8756-3282(02)00842-6

    Article  Google Scholar 

  • Lemaire T, Lemonnier S, Naili S (2012) On the paradoxical determinations of the lacuno-canalicular permeability of bone. Biomech Model Mechanobiol 11:933–946. doi:10.1007/s10237-011-0363-6

    Article  Google Scholar 

  • Levenston ME, Beaupré GS, Carter DR (1998) Loading mode interactions in simulations of long bone cross-sectional adaptation. Comput Methods Biomech Biomed Engin 1:303–319. doi:10.1080/01495739808936709

    Article  Google Scholar 

  • Lu XL, Huo B, Park M, Guo XE (2012) Calcium response in osteocytic networks under steady and oscillatory fluid flow. Bone 51:466–473. doi:10.1016/j.bone.2012.05.021

    Article  Google Scholar 

  • Lynch ME, Main RP, Xu Q et al (2011) Tibial compression is anabolic in the adult mouse skeleton despite reduced responsiveness with aging. Bone 49:439–446. doi:10.1016/j.bone.2011.05.017

    Article  Google Scholar 

  • Maimoun L, Fattal C, Micallef JP et al (2006) Bone loss in spinal cord-injured patients: from physiopathology to therapy. Spinal Cord 44:203–210. doi:10.1038/sj.sc.3101832

    Article  Google Scholar 

  • Main RP, Lynch ME, van der Meulen MCH (2010) In vivo tibial stiffness is maintained by whole bone morphology and cross-sectional geometry in growing female mice. J Biomech 43:2689–2694. doi:10.1016/j.jbiomech.2010.06.019

    Article  Google Scholar 

  • Main RP (2007) Ontogenetic relationships between in vivo strain environment, bone histomorphometry and growth in the goat radius. J Anat 210:272–293

    Article  Google Scholar 

  • Malachanne E, Dureisseix D, Jourdan F (2011) Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements. J Mech Behav Biomed Mater 4:849–857

    Article  Google Scholar 

  • Marie PJ (2013) Targeting integrins to promote bone formation and repair. Nat Rev Endocrinol 9:288–295

    Article  Google Scholar 

  • Martínez G, Cerrolaza M (2006) A bone adaptation integrated approach using BEM. Eng Anal Bound Elem 30:107–115. doi:10.1016/j.enganabound.2005.08.010

    Article  MATH  Google Scholar 

  • Matsumoto HN, Koyama Y, Takakuda K (2008) Effect of mechanical loading timeline on periosteal bone formation. J Biomech Sci Eng 3:176–187. doi:10.1299/jbse.3.176

    Article  Google Scholar 

  • Mosley JR, March BM, Lynch J, Lanyon LE (1997) Strain magnitude related changes in whole bone architecture in growing rats. Bone 20:191–198

    Article  Google Scholar 

  • Moustafa A, Sugiyama T, Prasad J et al (2012) Mechanical loading-related changes in osteocyte sclerostin expression in mice are more closely associated with the subsequent osteogenic response than the peak strains engendered. Osteoporos Int 23:1225–1234. doi:10.1007/s00198-011-1656-4

    Article  Google Scholar 

  • Patel TK, Brodt MD, Silva MJ (2014) Experimental and finite element analysis of strains induced by axial tibial compression in young-adult and old female C57Bl/6 mice. J Biomech 47:451–457. doi:10.1016/j.jbiomech.2013.10.052

    Article  Google Scholar 

  • Pereira AF, Shefelbine SJ (2014) The influence of load repetition in bone mechanotransduction using poroelastic finite-element models: the impact of permeability. Biomech Model Mechanobiol 13:215–225. doi:10.1007/s10237-013-0498-8

    Article  Google Scholar 

  • Pereira AF, Javaheri B, Pitsillides A, Shefelbine S (2015) Predicting cortical bone adaptation to axial loading in the mouse tibia. PeerJ Prepr 3:e1390

    Article  Google Scholar 

  • Popov EP, Balan TA (1998) Engineering mechanics of solids, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Prasad J, Wiater BP, Nork SE et al (2010) Characterizing gait induced normal strains in a murine tibia cortical bone defect model. J Biomech 43:2765–2770. doi:10.1016/j.jbiomech.2010.06.030

    Article  Google Scholar 

  • Price C, Zhou X, Li W, Wang L (2011) Real-time measurement of solute transport within the lacunar-canalicular system of mechanically loaded bone: Direct evidence for load-induced fluid flow. J Bone Miner Res 26:277–285. doi:10.1002/jbmr.211

    Article  Google Scholar 

  • Razi H, Birkhold AI, Zaslansky P et al (2015) Skeletal maturity leads to a reduction in the strain magnitudes induced within the bone: a murine tibia study. Acta Biomater 13:301–310. doi:10.1016/j.actbio.2014.11.021

    Article  Google Scholar 

  • Roberts MD, Santner TJ, Hart RT (2009) Local bone formation due to combined mechanical loading and intermittent hPTH-(1–34) treatment and its correlation to mechanical signal distributions. J Biomech 42:2431–2438. doi:10.1016/j.jbiomech.2009.08.030

    Article  Google Scholar 

  • Robling AG, Castillo AB, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8:455–498

    Article  Google Scholar 

  • Rubin CT, Recker R, Cullen D et al (2003) 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 19:343–351. doi:10.1359/JBMR.0301251

    Article  Google Scholar 

  • Rubin CT, Lanyon LE (1985) Regulation of bone mass by mechanical strain magnitude. Calcif Tissue Int 37:411–417. doi:10.1007/BF02553711

    Article  Google Scholar 

  • Sakai D, Kii I, Nakagawa K et al (2011) Remodeling of actin cytoskeleton in mouse periosteal cells under mechanical loading induces periosteal cell proliferation during bone formation. PLoS ONE 6:e24847. doi:10.1371/journal.pone.0024847

    Article  Google Scholar 

  • Sample SJ, Collins RJ, Wilson AP et al (2010) Systemic effects of ulna loading in male rats during functional adaptation. J Bone Miner Res 25:2016–2028. doi:10.1002/jbmr.101

    Article  Google Scholar 

  • Shackelford LC (2004) Resistance exercise as a countermeasure to disuse-induced bone loss. J Appl Physiol 97:119–129. doi:10.1152/japplphysiol.00741.2003

    Article  Google Scholar 

  • Sheng M-C, Baylink DJ, Beamer WG et al (1999) Histomorphometric studies show that bone formation and bone mineral apposition rates are greater in C3H/HeJ (high-density) than C57Bl/6J (low-density) mice during growth. Bone 25:421–429

    Article  Google Scholar 

  • Skedros JG, Hunt KJ, Hughes PE, Winet H (2003) Ontogenetic and regional morphologic variations in the turkey ulna diaphysis: Implications for functional adaptation of cortical bone. Anat Rec A Discov Mol Cell Evol Biol 273:609–629

    Article  Google Scholar 

  • Somerville JM, Aspden RM, Armour KE et al (2004) Growth of C57bl/6 mice and the material and mechanical properties of cortical bone from the tibia. Calcif Tissue Int 74:469–475. doi:10.1007/s00223-003-0101-x

    Article  Google Scholar 

  • Srinivasan S (2003) Enabling bone formation in the aged skeleton via rest-inserted mechanical loading. Bone 33:946–955. doi:10.1016/S8756-3282(03)00274-6

    Article  Google Scholar 

  • Srinivasan S, Ausk BJ, Poliachik SL et al (2007) Rest-inserted loading rapidly amplifies the response of bone to small increases in strain and load cycles. J Appl Physiol 102:1945–1952. doi:10.1152/japplphysiol.00507.2006

    Article  Google Scholar 

  • Srinivasan S, Ausk BJ, Prasad J et al (2010) Rescuing loading induced bone formation at senescence. PLoS Comput Biol 6:e1000924. doi:10.1371/journal.pcbi.1000924

    Article  Google Scholar 

  • Srinivasan S, Gross TS (1999) Canalicular fluid flow in bone: A basis for bone formation at sites of minimal strain. 45th Ann Meet, Orthop. Res. Soc. ORS Poster

  • Srinivasan S, Gross TS (2000) Canalicular fluid flow induced by bending of a long bone. Med Eng Phys 22:127–133. doi:10.1016/S1350-4533(00)00021-7

    Article  Google Scholar 

  • Srinivasan S, Prasad J, Ausk BJ, Kwon R, Worton L, Gross TS, BainSD, Gardiner EM (2013) Concurrent optimization of Cyclosporin A and mechanical loading identifies multiple optima to rescue senescentbone adaptation. Orthop Res Soc ORS Poster

  • Srinivasan S, Weimer DA, Agans SC et al (2002) Low-magnitude mechanical loading becomes osteogenic when rest is inserted between each load cycle. J Bone Miner Res 17:1613–1620. doi:10.1359/jbmr.2002.17.9.1613

    Article  Google Scholar 

  • Steck R, Niederer P, Tate MK (2000) A finite difference model of load-induced fluid displacements within bone under mechanical loading. Med Eng Phys 22:117–125. doi:10.1016/S1350-4533(00)00017-5

    Article  Google Scholar 

  • Sugiyama T, Price JS, Lanyon LE (2010) Functional adaptation to mechanical loading in both cortical and cancellous bone is controlled locally and is confined to the loaded bones. Bone 46:314–321

    Article  Google Scholar 

  • Tate MK, 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 203:2737–2745

    Google Scholar 

  • Taylor WR, Warner MD, Clift SE (2003) Finite element prediction of endosteal and periosteal bone remodelling in the turkey ulna: effect of remodelling signal and dead-zone definition. Proc Inst Mech Eng 217:349–356. doi:10.1243/095441103770802513

    Article  Google Scholar 

  • Taylor R, Zheng C, Jackson R, Doll J, Chen J, Holzbaur K, Besier T, Kuhl E (2009) The phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players. Comput Methods Biomech Biomed Engin 12:83–93

    Article  Google Scholar 

  • Thompson DW (1942) On growth and form. In: Bonner JT (ed) Cambridge University, pp. 241

  • Turner CH, Forwood M, Rho JY, Yoshikawa T (1994) Mechanical strain threshold for lamellar bone formation. J Bone Miner Res 9:87–97

    Article  Google Scholar 

  • Turner CH, Pavalko FM (1998) Mechanotransduction and functional response of the skeleton to physical stress: the mechanisms and mechanics of bone adaptation. J Orthop Sci 3:346–355. doi:10.1007/s007760050064

    Article  Google Scholar 

  • Turner CH, Owan I, Alvey T, Hulman J, Hock J (1998) Recruitment and proliferative responses of osteoblasts after mechanical loading in vivo determined using sustained-release bromodeoxyuridine. Bone 22:463–469

    Article  Google Scholar 

  • Verbruggen SW, Vaughan TJ, McNamara LM (2012) Strain amplification in bone mechanobiology: a computational investigation of the in vivo mechanics of osteocytes. J R Soc Interface 9:2735–2744. doi:10.1098/rsif.2012.0286

    Article  Google Scholar 

  • Vico L, Collet P, Guignandon A et al (2000) Effects of long-term microgravity exposure on cancellous and cortical weight-bearing bones of cosmonauts. The Lancet 355:1607–1611. doi:10.1016/S0140-6736(00)02217-0

    Article  Google Scholar 

  • Wagner DW, Chan S, Castillo AB, Beaupre GS (2013) Geometric mouse variation: Implications to the axial ulnar loading protocol and animal specific calibration. J Biomech 46:2271–2276. doi:10.1016/j.jbiomech.2013.06.027

    Article  Google Scholar 

  • Wallace IJ, Demes B, Mongle C et al (2014) Exercise-induced bone formation is poorly linked to local strain magnitude in the sheep tibia. PLoS ONE 9:e99108. doi:10.1371/journal.pone.0099108

    Article  Google Scholar 

  • Wang B, Zhou X, Price C et al (2013) Quantifying load-induced solute transport and solute-matrix interaction within the osteocyte lacunar-canalicular system. J Bone Miner Res 28:1075–1086. doi:10.1002/jbmr.1804

    Article  Google Scholar 

  • Weatherholt AM, Fuchs RK, Warden SJ (2013) Cortical and trabecular bone adaptation to incremental load magnitudes using the mouse tibial axial compression loading model. Bone 52:372–379. doi:10.1016/j.bone.2012.10.026

    Article  Google Scholar 

  • 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. doi:10.1016/0021-9290(94)90010-8

    Article  Google Scholar 

  • Wergedal JE, Sheng MH-C, Ackert-Bicknell CL et al (2005) Genetic variation in femur extrinsic strength in 29 different inbred strains of mice is dependent on variations in femur cross-sectional geometry and bone density. Bone 36:111–122. doi:10.1016/j.bone.2004.09.012

    Article  Google Scholar 

  • Willie BM, Birkhold AI, Razi H et al (2013) Diminished response to in vivo mechanical loading in trabecular and not cortical bone in adulthood of female C57Bl/6 mice coincides with a reduction in deformation to load. Bone 55:335–346. doi:10.1016/j.bone.2013.04.023

    Article  Google Scholar 

  • Yang H, Butz KD, Duffy D et al (2014) Characterization of cancellous and cortical bone strain in the in vivo mouse tibial loading model using microCT-based finite element analysis. Bone 66:131–139. doi:10.1016/j.bone.2014.05.019

    Article  Google Scholar 

  • You L, Cowin SC, Schaffler MB, Weinbaum S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J Biomech 34:1375–1386

    Article  Google Scholar 

  • Zeng Y, Cowin SC, Weinbaum S (1994) A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon. Ann Biomed Eng 22:280–292. doi:10.1007/BF02368235

    Article  Google Scholar 

  • Zhang P (2006) Diaphyseal bone formation in murine tibiae in response to knee loading. J Appl Physiol 100:1452–1459. doi:10.1152/japplphysiol.00997.2005

    Article  Google Scholar 

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Acknowledgments

The authors acknowledge the institute fellowship and the computational facilities provided by IIT, Ropar, for this study.

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  1. School of Mechanical Materials and Energy Engineering, Indian Institute of Technology Ropar, Room No. 303, Nangal Road, Rupnagar, Punjab, 140001, India

    Abhishek Kumar Tiwari & Jitendra Prasad

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Tiwari, A.K., Prasad, J. Computer modelling of bone’s adaptation: the role of normal strain, shear strain and fluid flow. Biomech Model Mechanobiol 16, 395–410 (2017). https://doi.org/10.1007/s10237-016-0824-z

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