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A Mechanobiological Model for Tissue Differentiation that Includes Angiogenesis: A Lattice-Based Modeling Approach

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Abstract

Mechanobiological models have previously been used to predict the time course of the tissue differentiation process, with the local mechanical environment as the regulator of cell activity. However, since the supply of oxygen and nutrients to cells is also a regulator of cell differentiation and oxygen diffusion is limited to few hundred micrometers from capillaries, the morphology of the new vascular network may also play a critical role in the process. In this paper, a computational model for tissue differentiation based on the local mechanical environment and the local vascularity is presented. A regular lattice is used to simulate cell activity (migration, proliferation, differentiation, apoptosis, and angiogenesis). The algorithm for capillary network formation includes mechanoregulation of vessel growth. A simulation of tissue differentiation in a bone/implant gap under shear was performed. The model predicts capillary networks similar to those found in experimental studies and heterogeneous patterns of tissue differentiation, which are influenced by the morphology of the capillary network. Higher mechanical loads caused slower vascular development and delayed bone tissue formations.

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References

  1. Anderson, C. B. Mechanics of fluids. In: Marks’s Standard Handbook of Mechanical Engineers, edited by Y. Baumesiter. New York: McGraw-Hill, 2006, pp. 3.48–3.76

  2. Andreykiv A., F. van Keulen, P. J. Prendergast (2008) Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells. Biomech. Model. Mechanobiol. 7:443–461

    Article  PubMed  CAS  Google Scholar 

  3. Armstrong C. G., V. C. Mow (1982) Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration and water content. J. Bone Joint Surg. Am., 64, 88–94

    PubMed  CAS  Google Scholar 

  4. Aspenberg P., S. Goodman, S. Toksvig-Larsen, L. Ryd, T. Albrektsson (1992) Intermittent micromotion inhibits bone ingrowth. Titanium implants in rabbits. Acta Orthop. Scand., 63, 141–145

    Article  PubMed  CAS  Google Scholar 

  5. Blenman P. R., D. R. Carter, G. S. Beaupre (1989) Role of mechanical loading in the progressive ossification of a fracture callus. J. Orthop. Res., 7, 398–407. doi:10.1002/jor.1100070312

    Article  PubMed  CAS  Google Scholar 

  6. Branemark P. I. (1983) Osseointegration and its experimental background. J. Prosthet. Dent. 50, 399–410. doi:10.1016/S0022-3913(83)80101-2

    Article  PubMed  CAS  Google Scholar 

  7. Brey E. M., T. W. King, C. Johnston, L. V. McIntire, G. P. Reece, C. W. Patrick (2002) A technique for quantitative three-dimensional analysis of microvascular structure. Microvasc. Res. 63 279–264. doi:10.1006/mvre.2002.2395

    Article  PubMed  Google Scholar 

  8. Brunski J. B. (1999) In vivo bone response to biomechanical loading at the bone/dental-implant interface. Adv. Dent. Res., 13, 99–119

    Article  PubMed  CAS  Google Scholar 

  9. Burke D. W., D. O. O’Connor, E. B. Zalenski, M. Jasty, W. H. Harris (1991) Micromotion of cemented and uncemented femoral components. J. Bone Joint Surg. 73B, 33–37

    Google Scholar 

  10. Byrne D. P., D. Lacroix, J. A. Planell, D. J. Kelly, P. J. Prendergast (2007) Simulation of tissue differentiation in a scaffold as a function of porosity, Young’s modulus and dissolution rate: application of mechanobiological models in tissue engineering. Biomaterials 28, 5544–5554. doi:10.1016/j.biomaterials.2007.09.003

    Article  PubMed  CAS  Google Scholar 

  11. Carmeliet P., M. K. Jain (2000) Angiogenesis in cancer and other diseases. Nature, 407, 249–257. doi:10.1038/35025220

    Article  PubMed  CAS  Google Scholar 

  12. Carter D. R., P. R. Blenman, G. S. Beaupre (1988) Correlations between mechanical stress history and tissue differentiation in initial fracture healing. J. Orthop. Res. 7, 398–407

    Google Scholar 

  13. Cenni E. (2005) Angiogenesis and bone regeneration. J. Bone Joint Surg., 87B, 58

    Google Scholar 

  14. Claes L., K. Eckert-Hubner, P. Augat (2002) The effect of mechanical stability on local vascularisation and tissue differentiation in callus healing. J. Orthop. Res. 20, 1099–1105. doi:10.1016/S0736-0266(02)00044-X

    Article  PubMed  Google Scholar 

  15. Claes L., K. Eckert-Hubner, P. Augat (2003) The fracture gap size influences the local vascularisation and tissue differentiation in callus healing. Langenbecks Arch. Surg. 388, 316–322. 10.1007/s00423-003-0396-0

    Article  PubMed  Google Scholar 

  16. Claes L. E., C. A. Heigele (1999) Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J. Biomech. 32, 255–266. doi:10.1016/S0021-9290(98)00153-5

    Article  PubMed  CAS  Google Scholar 

  17. Colnot C., Z. Thompson, T. Miclau, Z. Werb, J. A. Helms (2003) Altered fracture repair in the absence of MMP9. Development 130, 4123–4133. 10.1242/dev.00559

    Article  PubMed  CAS  Google Scholar 

  18. Colton C. K. (1995) Implantable biohybrid artificial organs. Cell Transplant. 4, 415. 10.1016/0963-6897(95)00025-S

    Article  PubMed  CAS  Google Scholar 

  19. Cowin S. C. (1999) Bone poroelasticity. J. Biomech. 32, 217–238. 10.1016/S0021-9290(98)00161-4

    Article  PubMed  CAS  Google Scholar 

  20. Eckardt H., M. Ding, M. Lind, E. S. Hansen, K. S. Cristensen, I. Hvid (2005) Recombinant human vascular endothelial growth factor enhances bone healing in an experimental non-union model. J. Bone Joint Surg. Br., 87, 1434–1438. 10.1302/0301-620X.87B10.16226

    Article  PubMed  CAS  Google Scholar 

  21. Gerber H. P., T. H. Vu, A. M. Ryan, J. Kowalski, Z. Werb, N. Ferrara (1999) VEGF couples hypertrophic cartilage remodelling, ossification and angiogenesis during endochondral bone formation. Nat. Med. 5, 623–628. 10.1038/9467

    Article  PubMed  CAS  Google Scholar 

  22. Geris L., A. Andreykiv, H. Van Oosterwyck, J. V. Sloten, F. van Keulen, J. Duyck, I. Naert (2004) Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber. J. Biomech. 37, 763–769. 10.1016/j.jbiomech.2003.09.026

    Article  PubMed  CAS  Google Scholar 

  23. Geris L., A. Gerisch, J. V. Stolen, R. Weiner, H. V. Oosterwyck (2007) Angiogenesis in bone fracture healing: a bioregulatory model. J. Theor. Biol. 251, 137–158. 10.1016/j.jtbi.2007.11.008

    Article  PubMed  CAS  Google Scholar 

  24. Götz H. E., M. Müller, A. Emmel, U. Holzwarth, R. G. Erben, R. Stangl (2004) Effect of surface finish on the osseointegration of laser-treated titanium alloy implants. Biomaterials 25, 4057–4064. 10.1016/j.biomaterials.2003.11.002

    Article  PubMed  CAS  Google Scholar 

  25. Haller, A. Experimentorum de ossiem formatione. In: Opera minora. Laussanne: Francisci Grasset, 1763, p. 400

  26. Hausman M. R., M. B. Schaffler, R. J. Majesta (2001) Prevention of fracture healing in rats by an inhibitor of angiogenesis. Bone 29, 560–564. 10.1016/S8756-3282(01)00608-1

    Article  PubMed  CAS  Google Scholar 

  27. Hirao M., N. Tamai, N. Tsumaki, H. Yoshikawa, A. Myoui (2006) Oxygen tension regulates chondrocyte differentiation and function during endochondral ossification. J. Biol. Chem. 281, 31079–31092. 10.1074/jbc.M602296200

    Article  PubMed  CAS  Google Scholar 

  28. Hori R. Y., J. L. Lewis (1982) Mechanical properties of the fibrous tissue found at the bone-cement interface following total joint replacement. J. Biomed. Mater. Res., 16, 911–927. 10.1002/jbm.820160615

    Article  PubMed  CAS  Google Scholar 

  29. Huiskes R., W. D. Van Driel, P. J. Prendergast, K. Søballe (1997) A biomechanical regulatory model for peri-prosthetic fibrous tissue differentiation. J. Mater. Sci.: Mater. Med. 8, 785–788. 10.1023/A:1018520914512

    Article  CAS  Google Scholar 

  30. Isaksson H., O. Comas, C. C. van Donkelaar, J. Mediavilla, W. Wilson, R. Huiskes, K. Ito (2006) Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity. J. Biomech. 40, 2002–2011. 10.1016/j.jbiomech.2006.09.028

    Article  PubMed  Google Scholar 

  31. Isaksson H., C. C. van Donkelaar, R. Huiskes, K. Ito (2008) A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. J. Theor. Biol. 21, 230–246. 10.1016/j.jtbi.2008.01.030

    Article  Google Scholar 

  32. Isaksson H., W. Wilson, C. C. van Donkellaar, R. Huiskes, K. Ito 2006 Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing. J. Biomech. 39, 1507–1516. 10.1016/j.jbiomech.2005.01.037

    Article  PubMed  Google Scholar 

  33. Kanichai M., D. Ferguson, P. J. Prendergast, V. A. Campbell (2008) Hypoxia promotes chondrogenesis in rat mesenchymal stem cells: a role for AKT and Hypoxia-Inducible Factor (HIF)-1α. J. Cell. Physiol. 216:708–715

    Article  PubMed  CAS  Google Scholar 

  34. Kearney E. M., P. J. Prendergast, V. A. Campbell (2008) Mechanisms of strain-mediated mesenchymal stem cell apoptosis. J. Biomech. Eng., 130, 061004

    Article  PubMed  CAS  Google Scholar 

  35. Kelly D. J., P. J. Prendergast (2005) Mechano-regulation of stem cell differentiation and tissue regeneration in osteochondral defects. J. Biomech. 38, 1413–1422. 10.1016/j.jbiomech.2004.06.026

    Article  PubMed  CAS  Google Scholar 

  36. Kelly D. J., P. J. Prendergast (2006) Prediction of optimal mechanical properties for a scaffold used in osteochondral defect repair. Tissue Eng. 12, 2509–2519. 10.1089/ten.2006.12.2509

    Article  PubMed  CAS  Google Scholar 

  37. Kenyon B. M., E. E. Voest, C. C. Chen, E. Flynn, J. Folkman, R. J. D’Amato (1996) A model of angiogenesis in the mouse cornea. Invest. Ophthalmol. Vis. Sci. 37, 1625–1632

    PubMed  CAS  Google Scholar 

  38. Lacroix D., P. J. Prendergast (2002) A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35, 1163–1171. 10.1016/S0021-9290(02)00086-6

    Article  PubMed  CAS  Google Scholar 

  39. Lanza R., E. D. Thomas, J. Thomson, R. Pedersen (2005) Essentials of Stem Cell Biology. Academic Press, New York

    Google Scholar 

  40. Liu X., G. L. Niebur (2008) Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm. Biomech. Model. Mechanobiol. 7:335–344

    Article  PubMed  Google Scholar 

  41. Lu C., R. Marcucio, T. Miclau (2006) Assessing angiogenesis during fracture healing. Iowa Orthop. J. 26, 17–26

    PubMed  Google Scholar 

  42. Montgomery D. C., G. C. Runger (2006) Applied Statistics and Probability for Engineers, 4th edition. New York: John Wiley & Sons

    Google Scholar 

  43. Moore D. C., C. W. Leblanc, R. Müller, J. J. Crisco III, M. G. Ehrlich (2003) Physiologic weight-bearing increases new vessel formation during distraction osteogenesis: a micro-tomographic imaging study. J. Orthop. Res. 21, 489–496. 10.1016/S0736-0266(02)00234-6

    Article  PubMed  Google Scholar 

  44. Morgan E. F., M. T. Longaker, D. R. Carter (2006) Relationships between tissue dilatation and differentiation in distraction osteogenesis. Matrix Biol. 25(2), 94–103. 10.1016/j.matbio.2005.10.006

    Article  PubMed  CAS  Google Scholar 

  45. Norrby K. (1998) Microvascular density in terms of number and length of microvessel segments per unit tissue volume in mammalian angiogenesis. Microvasc. Res. 55, 43–53. 10.1006/mvre.1997.2054

    Article  PubMed  CAS  Google Scholar 

  46. Prendergast P. J., R. Huiskes, K. Søballe (1997) Biophysical stimuli on cells during tissue differentiation at implants interfaces. J. Biomech. 30, 539–548. 10.1016/S0021-9290(96)00140-6

    Article  PubMed  CAS  Google Scholar 

  47. Prendergast P. J., M. C. H. van der Meulen (2001) Mechanics of bone regeneration. In: Cowin S. C. (Ed.), Bone Mechanics Handbook. CRC Press LCC, Boca Raton, FL, pp. 32.1–32.13

    Google Scholar 

  48. Pérez M., P. J. Prendergast (2007) Random-walk model of cell-dispersal included in mechanobiological simulation of tissue differentiation. J. Biomech. 40, 2244–2253. 10.1016/j.jbiomech.2006.10.020

    Article  PubMed  Google Scholar 

  49. Rai B., M. E. Oest, K. M. Dupont, K. H. Ho, S. H. Teoh, R. E. Guldberg (2007) Combination of platelet-rich plasma with plycaprolactone-tricalcium phosphate scaffolds for segmental bone repair. J. Biomed. Mater. Res. 81, 888. 10.1002/jbm.a.31142

    Article  CAS  Google Scholar 

  50. Rossi F., H. E. MacLean, W. Yuan, R. O. Francis, E. Semenova, C. S. Lin, H. M. Kronenberg, D. Cobrinik (2002) p107 and p130 co-ordinately regulate proliferation, Cbfa1 expression, and hypertrophic differentiation during endochondral bone development. Dev. Biol. 247, 271–285. 10.1006/dbio.2002.0691

    Article  PubMed  CAS  Google Scholar 

  51. Ruan J., P. Prasad (2006) The influence of human head tissue properties on intracranial pressure response during direct head impact. Int. J. Veh. Saf., 1, 282–291

    Google Scholar 

  52. Schenk R. K., D. Buser (1998) Osseointegration: a reality. Periodontology 2000 7:22–35. 10.1111/j.1600-0757.1998.tb00120.x

    Article  Google Scholar 

  53. Shefelbine S. J., P. Augat, L. Claes, U. Simon (2005) Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic. J. Biomech. 38, 2440–2450. 10.1016/j.jbiomech.2004.10.019

    Article  PubMed  Google Scholar 

  54. Sholley M. M., G. P. Ferguson, H. R. Seibel, J. L. Montour, J. D. Wilson (1984) Mechanisms of neovascularisation: vascular sprouting can occur without proliferation of endothelial cells. Lab. Invest. 51, 624–634

    PubMed  CAS  Google Scholar 

  55. Smit T. H., J. M. Huyghe, S. C. Cowin (2002) Estimation of the poroelastic parameters of cortical bone. J. Biomech., 35, 829–835. 10.1016/S0021-9290(02)00021-0

    Article  PubMed  Google Scholar 

  56. Smith-Adaline E. A., S. K. Volkman, M. A. Ignelzi Jr., J. Slade, S. Platte, S. A. Goldstein (2004) Mechanical environment alters tissue formation patterns during fracture healing. J. Orthop. Res. 22, 1079–1085. 10.1016/j.orthres.2004.02.007

    Article  PubMed  CAS  Google Scholar 

  57. Stokes C. L., D. A. Lauffenburger (1991) Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J. Cell Sci. 99, 419–430

    PubMed  Google Scholar 

  58. Szmukler-Moncler, S., H. Salama, Y. Reingewirtz, and J. H. Dubruille. Timing of loading and effect of micromotion on bone-dental implant interface: review of experimental literature. J. Biomed. Mater. Res. 43:192–203, 1998. doi:10.1002/(SICI)1097-4636(199822)43:2<192::AID-JBM14>3.0.CO;2-K

    Google Scholar 

  59. Tepic S., T. Macirowski, R. W. Mann (1983) Mechanical properties of articular cartilage elucidated by osmotic loading and ultrasound. Proc. Natl. Acad. Sci. USA 80: 3331–3333. 10.1073/pnas.80.11.3331

    Article  PubMed  CAS  Google Scholar 

  60. Terranova V. P., R. Diflorio, R. M. Lyall, S. Hic, R. Friesel, T. Maciag (1985) Human endothelial cells are chemotactic to endothelial cell growth factor and heparin. J. Cell Sci. 101, 2330–2334

    CAS  Google Scholar 

  61. Trueta J. (1963) The role of the vessels in osteogenesis. J. Bone Joint Surg., 45B, 402–418

    Google Scholar 

  62. Wallace A. L., E. R. Draper, R. K. Strachan, I. D. McCarthy, S. P. Hughes (1994) The vascular response to fracture micromovement. Clin. Orthop. 301, 281–290

    PubMed  Google Scholar 

  63. Young S., J. D. Kretlow, C. Nguyen, A. G. Bashoura, L. S. Baggett, J. A. Jansen, M. Wong, A. G. Mikos (2008) Microcomputed tomography characterization of neovascularisation in bone tissue engineering applications. Tissue Eng. 14, 295–306

    CAS  Google Scholar 

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Acknowledgments

This work was supported by the European Commission, Sixth Framework Programme Priority, SmartCap, and Science Foundation Ireland.

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Checa, S., Prendergast, P.J. A Mechanobiological Model for Tissue Differentiation that Includes Angiogenesis: A Lattice-Based Modeling Approach. Ann Biomed Eng 37, 129–145 (2009). https://doi.org/10.1007/s10439-008-9594-9

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