A mathematical model for cell differentiation, as an evolutionary and regulated process

REFERENCES

• AbrahamssonI, BerglundhT, LinderE, LangNP, LindheJ. 2004. Early bone formation adjacent to rough and turned endosseous implant surfaces. An experimental study in the dog. Clin Oral Implants Res. 15(4):381–392.
   PubMed Web of Science ®Google Scholar
• AmbardD, SwiderP. 2006. A predictive mechano-biological model of the bone-implant healing. Eur J Mech A Solids. 2:927–937.
   Web of Science ®Google Scholar
• AmorN, GerisL, Vander SlotenJ, Van OosterwyckH. 2011. Computational modelling of biomaterial surface interactions with blood platelets and osteoblastic cells for the prediction of contact osteogenesis. Acta Biomater. 7:779–790.
   PubMed Web of Science ®Google Scholar
• AndreykivA, vanKeulenF, PrendergastPJ. 2007. Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells. Biomech Model Mechanobiol. 7:443–461.
   PubMed Web of Science ®Google Scholar
• Bailon-PlazaA, van der MeulenMCH. 2001. A mathematical framework to study the effects of growth factor influences on fracture healing. J Theor Biol. 212:191–209.
   PubMed Web of Science ®Google Scholar
• Bailon-PlazaA, van der MeulenMCH. 2003. Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. J Biomech. 36:1069–1077.
   PubMed Web of Science ®Google Scholar
• BeckGR, ZerlerB, MoranE. 2001. Gene array analysis of osteoblast differentiation. Cell Growth Differ. 12:61–83.
   PubMedGoogle Scholar
• BerglundhT, AbrahamssonI, LangNP, LindheJ. 2003. De novo alveolar bone formation adjacent to endosseous implants. Clin Oral Implants Res. 14(3):251–262.
   PubMed Web of Science ®Google Scholar
• CarterDR, BeaupréGS, GioriNJ, HelmsJA. 1998. Mechanobiology of skeletal regeneration. Clin Orthop Relat Res. 355S:S41–S55.
   Google Scholar
• ClaesLE, HeigeleCA. 1999. Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech. 32(3):255–266.
   PubMed Web of Science ®Google Scholar
• DoblaréM, García-AznarJM. 2006. On numerical modelling of growth, differentiation and damage in structural living tissues. Arch Comput Meth Eng. 13:471–513.
   Web of Science ®Google Scholar
• DuyckJ, VandammeK, GerisL, Van OosterwyckH, De CoomanM, VanderslotenJ, PuersR, NaertI. 2006. The influence of micro-motion on the tissue differentiation around immediately loaded cylindrical turned titanium implants. Arch Oral Biol. 51:1–9.
   PubMed Web of Science ®Google Scholar
• DuyckJ, SlaetsE, SasaguriK, VandammeK, NaertI. 2007. Effect of intermittent loading and surface roughness on peri-implant bone formation in a bone chamber model. J Clin Periodontol. 34:998–1006.
   PubMed Web of Science ®Google Scholar
• García-AznarJM, KuiperJH, Gómez-BenitoMJ, DoblaréM, RichardsonJ. 2007. Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth. J Biomech. 40:1467–1476.
   PubMed Web of Science ®Google Scholar
• GerisL, VandammeK, NaertI, Vander SlotenJ, DuyckJ, Van OosterwyckH. 2008. Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber. J Biomech. 41:145–154.
   PubMed Web of Science ®Google Scholar
• GerisL, Vander SlotenJ, Van OosterwyckH. 2009. In silico biology of bone modelling and remodelling: regeneration. Philos Transact A Math Phys Eng Sci. 367:2031–2053.
   Web of Science ®Google Scholar
• GerisL, ReedAAC, Vander SlotenJ, SimpsonAHRW, Van OosterwyckH. 2010. Occurrence and treatment of bone atrophic non-unions investigated by an integrative approach. PLoS Comput Biol. 6(9):e1000915.
   PubMed Web of Science ®Google Scholar
• GerisL, SlotenJ, OosterwyckH. 2010. Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions. Biomech Model Mechanobiol. 9:713–724.
   PubMed Web of Science ®Google Scholar
• GerisL, VandammeK, NaertI, Van OosterwyckJ, Vander SlotenH, DuyckJ. 2010c. Mechanical loading affects angiogenesis and osteogenesis in an in vivo bone chamber: a modeling study. Tissue Eng Part A. 16(11):3353–3361.
   PubMed Web of Science ®Google Scholar
• Gómez-BenitoMJ, García-AznarJM, KuiperJH, DoblaréM. 2005. Influence of fracture gap size on the pattern of long bone healing: a computational study. J Theor Biol. 235:105–119.
   PubMed Web of Science ®Google Scholar
• HundsdorferW, VerwerJG. 2003. Numerical solution of time-dependent advection–diffusion–reaction equations. Heidelberg, New York: Springer-Verlag.
   Google Scholar
• IsakssonH, WilsonW, van DonkelaarCC, HuiskesR, KeitaI. 2006. Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing. J Biomech. 39:1507–1516.
   PubMed Web of Science ®Google Scholar
• IsakssonH, ComasO, vanDonkelaarCC, MediavillaJ, WilsonW, HuiskesR, KeitaI. 2007. Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity. J Biomech. 40:2002–2011.
   PubMed Web of Science ®Google Scholar
• IsakssonH, vanDonkelaarCC, HuiskesR, ItoK. 2008. A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. J Theor Biol. 252:230–246.
   PubMed Web of Science ®Google Scholar
• LeVequeRJ. 2002. Finite-volume methods for hyperbolic problems. Cambridge University Press.
   Google Scholar
• LianJB, SteinGS. 1995. Development of the osteoblast phenotype: molecular mechanisms mediating osteoblast growth and differentiation. Iowa Orthop J. 15:118–140.
   PubMedGoogle Scholar
• LiuX, NieburGL. 2008. Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm. Biomech Model Mechanobiol. 7:335–344.
   PubMed Web of Science ®Google Scholar
• MoreoP, García-AznarJM, DoblaréM. 2009. Bone ingrowth on the surface of endosseous implants. Part 1: mathematical model. J Theor Biol. 260(1):1–12.
   PubMed Web of Science ®Google Scholar
• PerezMA, PrendergastPJ. 2007. Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation. J Biomech. 40:2244–2253.
   PubMed Web of Science ®Google Scholar
• PrendergastPJ, HuiskesR, SøballeK. 1997. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech. 30:539–548.
   PubMed Web of Science ®Google Scholar
• ProkharauPA, VermolenFJ, Garcí-a-AznarJM. 2012. Model for direct bone apposition on pre-existing surfaces, during peri-implant osseointegration. J Theor Biol. 304:131–142.
   PubMed Web of Science ®Google Scholar
• Reina-RomoE, Gómez-BenitoMJ, García-AznarJM, DomínquezJ, DoblaréM. 2009. Modeling distraction osteogenesis: analysis of the distraction rate. Biomech Model Mechanobiol. 8:323–335.
   PubMed Web of Science ®Google Scholar
• RöderI. 2003. Dynamical modeling of hematopoietic stem cell organization. University of Leipzig.
   Google Scholar
• VandammeK, NaertI, GerisL, Vander SlotenJ, PuersR, DuyckJ. 2007a. Histodynamics of bone tissue formation around immediately loaded cylindrical implants in the rabbit. Clin Oral Implants Res. 18:471–480.
   PubMed Web of Science ®Google Scholar
• VandammeK, NaertI, GerisL, Vander SlotenJ, PuersR, DuyckJ. 2007b. Influence of controlled immediate loading and implant design on peri-implant bone formation. J Clin Periodontol. 34:172–181.
   PubMed Web of Science ®Google Scholar
• VandammeK, NaertI, GerisL, Vander SlotenJ, PuersR, DuyckJ. 2007c. The effect of micro-motion on the tissue response around immediately loaded roughened titanium implants in the rabbit. Eur J Oral Sci. 115:21–29.
   PubMed Web of Science ®Google Scholar
• YamaguchiA, KomoriT, SudaT. 2000. Regulation of osteoblast differentiation mediated by bone morphogenetic proteins, hedgehogs, and Cbfa1. Endocr Rev. 21(4):393–411.
   PubMed Web of Science ®Google Scholar