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A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading

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Abstract

The importance of fluid-flow-induced shear stress and matrix-induced cell deformation in transmitting the global tendon load into a cellular mechanotransduction response is yet to be determined. A multiscale computational tendon model composed of both matrix and fluid phases was created to examine how global tendon loading may affect fluid-flow-induced shear stresses and membrane strains at the cellular level. The model was then used to develop a quantitative experiment to help understand the roles of membrane strains and fluid-induced shear stresses on the biological response of individual cells. The model was able to predict the global response of tendon to applied strain (stress, fluid exudation), as well as the associated cellular response of increased fluid-flow-induced shear stress with strain rate and matrix-induced cell deformation with strain amplitude. The model analysis, combined with the experimental results, demonstrated that both strain rate and strain amplitude are able to independently alter rat interstitial collagenase gene expression through increases in fluid-flow-induced shear stress and matrix-induced cell deformation, respectively.

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References

  1. Adeeb S, Ali A, Shrive N, Frank C and Smith D (2004). Modelling the behaviour of ligaments: a technical note. Comput Methods Biomech Biomed Eng 7: 33–42

    Article  Google Scholar 

  2. Archambault JM, Elfervig-Wall MK, Tsuzaki M, Herzog W and Banes AJ (2002). Rabbit tendon cells produce MMP-3 in response to fluid flow without significant calcium transients. J Biomech 35: 303–309

    Article  Google Scholar 

  3. Arnoczky SP, Lavagnino M, Whallon JH and Hoonjan A (2002a). In situ cell nucleus deformation in tendons under tensile load; a morphological analysis using confocal laser microscopy. J Orthop Res 20: 29–35

    Article  Google Scholar 

  4. Arnoczky SP, Tian T, Lavagnino M, Gardner K, Schuler P and Morse P (2002b). Activation of stress-activated protein kinases (SAPK) in tendon cells following cyclic strain: the effects of strain frequency, strain magnitude, and cytosolic calcium. J Orthop Res 20: 947–952

    Article  Google Scholar 

  5. Arnoczky SP, Tian T, Lavagnino M and Gardner K (2004). Ex vivo static tensile loading inhibits MMP-1 expression in rat tail tendon cells through a cytoskeletally based mechanotransduction mechanism. J Orthop Res 22: 328–333

    Article  Google Scholar 

  6. Arnoczky SP, Lavagnino M and Egerbacher M (2007). The response of tendon cells to changing loads: implications in the etiopathogenesis of tendinopathy. In: Woo, SL, Renstrom, P, and Arnoczky, SP (eds) Tendinopathy in athletes, pp 46–59. Blackwell, Oxford

    Chapter  Google Scholar 

  7. Ateshian GA, Likhitpanichkul M and Hung CT (2006). A mixture theory analysis for passive transport in osmotic loading of cells. J Biomech 39: 464–475

    Google Scholar 

  8. Ateshian GA, Costa KD and Hung CT (2007). A theoretical analysis of water transport through chondrocytes. Biomech Model Mechanobiol 6: 91–101

    Article  Google Scholar 

  9. Atkinson TS, Haut RC and Altiero NJ (1997). A poroelastic model that predicts some phenomenological responses of ligaments and tendons. J Biomech Eng 119: 400–405

    Article  Google Scholar 

  10. Banes AJ, Tsuzaki M, Yamamoto J, Fischer T, Brigman B, Brown T and Miller L (1995). Mechanoreception at the cellular level: the detection, interpretation, and diversity of responses to mechanical signals. Biochem Cell Biol 73: 349–365

    Article  Google Scholar 

  11. Belkoff SM and Haut RC (1992). Microstructurally based model analysis of gamma-irradiated tendon allografts. J Orthop Res 10: 461–464

    Article  Google Scholar 

  12. Brown RA, Prajapati R, McGrouther DA, Yannas IV and Eastwood M (1998). Tensional homeostasis in dermal fibroblasts: mechanical responses to mechanical loading in three-dimensional substrates. J Cell Physiol 175: 323–332

    Article  Google Scholar 

  13. Butler SL, Kohles SS, Thielke RJ, Chen C and Vanderby R (1997). Interstitial fluid flow in tendons or ligaments: a porous medium finite element simulation. Med Biol Eng Comput 35: 742–746

    Article  Google Scholar 

  14. Chen CT, Malkus DS and Vanderby R (1998). A fiber matrix model for interstitial fluid flow and permeability in ligaments and tendons. Biorheology 35: 103–118

    Article  Google Scholar 

  15. Diamant J, Keller A, Baer E, Litt M and Arridge RG (1972). Collagen; ultrastructure and its relation to mechanical properties as a function of ageing. Proc R Soc Lond B Biol Sci 180: 293–315

    Google Scholar 

  16. Frank EH and Grodzinsky AJ (1987). Cartilage electromechanics—II. A continuum model of cartilage electrokinetics and correlation with experiments. J Biomech 20: 629–639

    Article  Google Scholar 

  17. Giori NJ, Beaupre GS and Carter DR (1993). Cellular shape and pressure may mediate mechanical control of tissue composition in tendons. J Orthop Res 11: 581–591

    Article  Google Scholar 

  18. Guilak F and Mow VC (2000). The mechanical environment of the chondrocyte: a biphasic finite element model of cell–matrix interactions in articular cartilage. J Biomech 33: 1663–1673

    Article  Google Scholar 

  19. Gupta T and Haut Donahue TL (2006). Role of cell location and morphology in the mechanical environment around meniscal cells. Acta Biomater 2: 483–492

    Article  Google Scholar 

  20. Han S, Gemmell SJ, Helmer KG, Grigg P, Wellen JW, Hoffman AH and Sotak CH (2000). Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport. J Magn Reson 144: 217–227

    Article  Google Scholar 

  21. Han Y, Cowin SC, Schaffler MB and Weinbaum S (2004). Mechanotransduction and strain amplification in osteocyte cell processes. Proc Natl Acad Sci USA 101: 16689–16694

    Article  Google Scholar 

  22. Hannafin JA and Arnoczky SP (1994). Effect of cyclic and static tensile loading on water content and solute diffusion in canine flexor tendons: an in vitro study. J Orthop Res 12: 350–356

    Article  Google Scholar 

  23. Hannafin JA, Arnoczky SP, Hoonjan A and Torzilli PA (1995). Effect of stress deprivation and cyclic tensile loading on the material and morphologic properties of canine flexor digitorum profundus tendon: an in vitro study. J Orthop Res 13: 907–914

    Article  Google Scholar 

  24. Hansen KA, Weiss JA and Barton JK (2002a). Recruitment of tendon crimp with applied tensile strain. J Biomech Eng 124: 72–77

    Article  Google Scholar 

  25. Haridas B, Butler DL, Malaviya P, Boivin G, Awad H, Smith F (1999) Transversely isotropic poroelastic finite element simulations of the intact and surgically translocated rabbit flexor tendon. Proceedings of the 1999 ASME Summer Bioengineering Conference

  26. Haut RC (1985). The effect of a lathyritic diet on the sensitivity of tendon to strain rate. J Biomech Eng 107: 166–174

    Google Scholar 

  27. Haut TL and Haut RC (1997). The state of tissue hydration determines the strain-rate-sensitive stiffness of human patellar tendon. J Biomech 30: 79–81

    Article  Google Scholar 

  28. Helmer KG, Nair G, Cannella M and Grigg P (2006). Water movement in tendon in response to a repeated static tensile load using one-dimensional magnetic resonance imaging. J Biomech Eng 128: 733–741

    Article  Google Scholar 

  29. Hewitt J, Guilak F, Glisson R and Vail TP (2001). Regional material properties of the human hip joint capsule ligaments. J Orthop Res 19: 359–364

    Article  Google Scholar 

  30. Hurschler C, Loitz-Ramage B and Vanderby R (1997). A structurally based stress-stretch relationship for tendon and ligament. J Biomech Eng 119: 392–399

    Article  Google Scholar 

  31. Ingber DE (1997). Tensegrity: the architectural basis of cellular mechanotransduction. Annu Rev Physiol 59: 575–599

    Article  Google Scholar 

  32. Iwasaki H, Eguchi S, Ueno H, Marumo F and Hirata Y (2000). Mechanical stretch stimulates growth of vascular smooth muscle cells via epidermal growth factor receptor. Am J Physiol Heart Circ Physiol 278: H521–529

    Google Scholar 

  33. Jin G, Sah RL, Li YS, Lotz M, Shyy JY and Chien S (2000). Biomechanical regulation of matrix metalloproteinase-9 in cultured chondrocytes. J Orthop Res 18: 899–908

    Article  Google Scholar 

  34. Johnson GA, Livesay GA, Woo SL and Rajagopal KR (1996). A single integral finite strain viscoelastic model of ligaments and tendons. J Biomech Eng 118: 221–226

    Article  Google Scholar 

  35. Kastelic J, Palley I and Baer E (1980). A structural mechanical model for tendon crimping. J Biomech 13: 887–893

    Article  Google Scholar 

  36. Kwan MK and Woo SL (1989). A structural model to describe the nonlinear stress-strain behavior for parallel-fibered collagenous tissues. J Biomech Eng 111: 361–363

    Google Scholar 

  37. Lai WM, Mow VC and Roth V (1981). Effects of nonlinear strain-dependent permeability and rate of compression on the stress behavior of articular cartilage. J Biomech Eng 103: 61–66

    Google Scholar 

  38. Lambert CA, Soudant EP, Nusgens BV and Lapiere CM (1992). Pretranslational regulation of extracellular matrix macromolecules and collagenase expression in fibroblasts by mechanical forces. Lab Invest 66: 444–451

    Google Scholar 

  39. Lanir Y, Salant EL and Foux A (1988). Physico-chemical and microstructural changes in collagen fiber bundles following stretch in-vitro. Biorheology 25: 591–603

    Google Scholar 

  40. Lavagnino M and Arnoczky SP (2005). In vitro alterations in cytoskeletal tensional homeostasis control gene expression in tendon cells. J Orthop Res 23: 1211–1218

    Article  Google Scholar 

  41. Lavagnino M, Arnoczky SP, Tian T and Vaupel Z (2003). Effect of amplitude and frequency of cyclic tensile strain on the inhibition of MMP-1 mRNA expression in tendon cells: an in vitro study. Connect Tissue Res 44: 181–187

    Article  Google Scholar 

  42. Lavagnino M, Arnoczky SP, Frank K and Tian T (2005). Collagen fibril diameter distribution does not reflect changes in the mechanical properties of in vitro stress-deprived tendons. J Biomech 38: 69–75

    Google Scholar 

  43. Lujan TJ, Underwood CJ, Henninger HB, Thompson BM and Weiss JA (2007). Effect of dermatan sulfate glycosaminoglycans on the quasi-static material properties of the human medial collateral ligament. J Orthop Res 25: 894–903

    Article  Google Scholar 

  44. Mochitate K, Pawelek P and Grinnell F (1991). Stress relaxation of contracted collagen gels: disruption of actin filament bundles, release of cell surface fibronectin, and down-regulation of DNA and protein synthesis. Exp Cell Res 193: 198–207

    Article  Google Scholar 

  45. Mullender M, El Haj AJ, Yang Y, Burger EH, Klein-Nulend J and Duin MA (2004). Mechanotransduction of bone cells in vitro: mechanobiology of bone tissue. Med Biol Eng Comput 42: 14–21

    Article  Google Scholar 

  46. Ng CP, Hinz B and Swartz MA (2005). Interstitial fluid flow induces myofibroblast differentiation and collagen alignment in vitro. J Cell Sci 118: 4731–4739

    Article  Google Scholar 

  47. Puxkandl R, Zizak I, Paris O, Keckes J, Tesch W, Bernstorff S, Purslow P and Fratzl P (2002). Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Philos Trans R Soc Lond B Biol Sci 357: 191–197

    Article  Google Scholar 

  48. Redaelli A, Vesentini S, Soncini M, Vena P, Mantero S and Montevecchi FM (2003). Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons—a computational study from molecular to microstructural level. J Biomech 36: 1555–1569

    Article  Google Scholar 

  49. Ritty TM, Roth R and Heuser JE (2003). Tendon cell array isolation reveals a previously unknown fibrillin-2-containing macromolecular assembly. Structure (Camb) 11: 1179–1188

    Article  Google Scholar 

  50. Robinson PS, Lin TW, Jawad AF, Iozzo RV and Soslowsky LJ (2004). Investigating tendon fascicle structure-function relationships in a transgenic-age mouse model using multiple regression models. Ann Biomed Eng 32: 924–931

    Article  Google Scholar 

  51. Scott JE (2003). Elasticity in extracellular matrix ‘shape modules’ of tendon, cartilage, etc. A sliding proteoglycan-filament model. J Physiol 553: 335–343

    Article  Google Scholar 

  52. Stouffer DC, Butler DL and Hosny D (1985). The relationship between crimp pattern and mechanical response of human patellar tendon–bone units. J Biomech Eng 107: 158–165

    Article  Google Scholar 

  53. Voet A (1997). A comparison of finite element codes for the solution of biphasic poroelastic problems. Proc Inst Mech Eng 211: 209–211

    Article  Google Scholar 

  54. Wang JH (2006). Mechanobiology of tendon. J Biomech 39: 1563–1582

    Article  Google Scholar 

  55. Wang JL, Parnianpour M, Shirazi-Adl A and Engin AE (1997). Failure criterion of collagen fiber: viscoelastic behavior simulated by using load control data. Theory Appl Fracture Mechs 27: 1–12

    Article  Google Scholar 

  56. Weiss JA and Maakestad BJ (2006). Permeability of human medial collateral ligament in compression transverse to the collagen fiber direction. J Biomech 39: 276–283

    Article  Google Scholar 

  57. Wellen J, Helmer KG, Grigg P and Sotak CH (2005). Spatial characterization of T1 and T2 relaxation times and the water apparent diffusion coefficient in rabbit Achilles tendon subjected to tensile loading. Magn Reson Med 53: 535–544

    Article  Google Scholar 

  58. Wilson A, Shelton F, Chaput C, Frank C, Butler D and Shrive N (1997). The shear behaviour of the rabbit medial collateral ligament. Med Eng Phys 19: 652–657

    Article  Google Scholar 

  59. Wilson W, van Donkelaar CC, van Rietbergen B, Ito K and Huiskes R (2004). Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech 37: 357–366

    Article  Google Scholar 

  60. Woo SL, Gomez MA, Woo YK and Akeson WH (1982). Mechanical properties of tendons and ligaments. II. The relationships of immobilization and exercise on tissue remodeling. Biorheology 19: 397–408

    Google Scholar 

  61. Woo SL, Livesay GA, Runco TJ and Young EP (1997). Structure and function of tendons and ligaments. In: Mow, VC and Hayes, WC (eds) Basic orthopaedic biomechanics, pp 209–251. Lippincott-raven, Philadelphia

    Google Scholar 

  62. Yasuda K and Hayashi K (1999). Changes in biomechanical properties of tendons and ligaments from joint disuse. Osteoarthritis Cartilage 7: 122–129

    Article  Google Scholar 

  63. Yin L and Elliott DM (2004). A biphasic and transversely isotropic mechanical model for tendon: application to mouse tail fascicles in uniaxial tension. J Biomech 37: 907–916

    Article  Google Scholar 

  64. You J, Yellowley CE, Donahue HJ, Zhang Y, Chen Q and Jacobs CR (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: 387–393

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratory for Comparative Orthopaedic Research, College of Veterinary Medicine, Michigan State University, East Lansing, MI, 48824, USA

    Michael Lavagnino, Steven P. Arnoczky & Oscar Caballero

  2. Orthopaedic Biomechanics Laboratories, College of Osteopathic Medicine, Michigan State University, East Lansing, MI, 48824, USA

    Eugene Kepich & Roger C. Haut

Authors
  1. Michael Lavagnino
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  2. Steven P. Arnoczky
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  3. Eugene Kepich
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  4. Oscar Caballero
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  5. Roger C. Haut
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Correspondence to Michael Lavagnino.

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Lavagnino, M., Arnoczky, S.P., Kepich, E. et al. A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading. Biomech Model Mechanobiol 7, 405–416 (2008). https://doi.org/10.1007/s10237-007-0104-z

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  • DOI: https://doi.org/10.1007/s10237-007-0104-z

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