Mathematical modeling of fracture healing in mice: Comparison between experimental data and numerical simulation results

Medical and Biological Engineering and Computing

Volumn 44, Issue 4, 2006, Pages 280-289

  Geris, Liesbet ^a   Gerisch, Alf ^b   Maes, Christa ^a   Carmeliet, Geert ^a   Weiner, Rüdiger ^b   Vander Sloten, Jos ^a   Van Oosterwyck, Hans ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

Animal model; Fracture healing; Numerical simulation; Tissue differentiation

Indexed keywords

BONE; COMPUTER SIMULATION; FINITE VOLUME METHOD; FRACTURE; MATHEMATICAL MODELS; PATHOLOGY;

ANIMAL MODEL; FRACTURE HEALING; TISSUE DIFFERENTIATION;

CARTILAGE;

GROWTH FACTOR;

ANIMAL EXPERIMENT; ANIMAL MODEL; ANIMAL TISSUE; ARTICLE; CARTILAGE; CONTROLLED STUDY; EXPERIMENTAL MODEL; FRACTURE HEALING; INTERMETHOD COMPARISON; INTRAMEDULLARY NAILING; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MORPHOMETRICS; MOUSE; NONHUMAN; OUTCOMES RESEARCH; PARAMETRIC TEST; PATHOLOGIC FRACTURE; QUALITATIVE ANALYSIS; QUANTITATIVE STUDY; SIMULATION; TIBIA FRACTURE; TISSUE DIFFERENTIATION;

ANIMALS; CARTILAGE; COMPUTER SIMULATION; FRACTURE HEALING; MICE; MODELS, ANIMAL; TIBIAL FRACTURES;

EID: 33745475995     PISSN: 01400118     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11517-006-0040-6     Document Type: Article

References (39)

1. Adam JA (1999) A simplified model of wound healing (with particular reference to the critical size defect). Math Comput Model 30:23-32
2. Anderson ARA, Chaplain MAJ (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis. B Math Biol 60:857-900
3. Arnold JS, Adam JA (1999) A simplified model of wound healing II: The critical size defect in two dimensions. Math Comput Model 30:47-60
4. Bailón-Plaza A, van der Meulen MCH (2001) A mathematical framework to study the effects of growth factor influences on fracture healing. J Theor Biol 212:191-209
5. Bailó-Plaza A, van der Meulen MCH (2003) Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. J Biomech 36:1069-1077
6. Barnes GL, Kostenuik PJ, Gerstenfeld LC, Einhorn TA (1999) Growth factor regulation of fracture repair. J Bone Miner Res 14(11):1805-1815
7. Carter DR, Beaupré GS, Giori NJ, Helms JA (1998) Mechanobiology of skeletal regeneration. Clin Orthop Relat R 355S:S41-S55
8. Cho T-J, Gerstenfeld LC, Einhorn TA (2002) Differential temporal expression of members of the transforming growth factor β superfamily during murine fracture healing. J Bone Miner Res 17(3):513-520
9. Coffey RJ, Russell WE, Barnard JA (1990) Pharmacokinetics of TGF beta with emphasis on effects in liver and gut. Ann NY Acad Sci 593:285-291
10. Colnot C, Thompson Z, Miclau T, Werb Z, Helms JA (2003) Altered fracture repair in the absence of MMP9. Development 130:4123-4133
11. Cruess RL, Dumont JR (1985) Healing of Bone. In: Newton CD, Nunamaker DM (eds) Textbook of small animal orthopaedics. International Veterinary Information Service, Ithaca, New York, USA
12. Dallon JC, Sherratt JA, Maini PK (1999) Mathematical modelling of extracellular matrix dynamics using discrete cells: Fiber orientation and tissue regeneration. J Theor Biol 199:449-471
13. Dasch JR, Pace DR, Waegell W, Inenaga D, Ellingsworth L (1989) Monoclonal antibodies recognizing transforming growth factor-beta. Bioactivity neutralization and transforming growth factor beta 2 affinity purification. J Immunol 142:1536-1541
14. Dimitriou R, Tsiridis E, Giannoudis PV (2005) Current concepts of molecular aspects of bone healing. Injury 36 (available online)
15. Edelman ER, Nugent MA, Karnovsky MJ (1993) Perivascular and intravenous administration of basic fibroblast growth factor: Vascular and solid organ deposition. Proc Natl Acad Sci USA 90:1513-1517
16. Einhorn TA (1998) The cell and molecular biology of fracture healing. Clin Orthop Relat R 355S:S7-S21
17. Fedarko NS, D'Avis P, Frazier CR, Burrill MJ, Fergusson V, Tayback M, Sponseller PD, Shapiro JR (1995) Cell proliferation of human fibroblasts and osteoblasts in osteogenesis imperfecta: Influence of age. J Bone Miner Res 10:1705-1712
18. Gaffney EA, Maini PK, Sherratt JA, Ruft S (1999) The mathematical modelling of cell kinetics in corneal epithelial wound healing. J Theor Biol 197:15-40
19. Gerisch A (2001) Numerical methods for the simulation of taxis-diffusion-reaction systems. PhD Thesis, Martin-Luther-Universität Halle-Wittenberg
20. Gerisch A, Chaplain MAJ (2006) Robust numerical methods for taxis-diffusion-reaction systems: Applications to biomedical problems. Math Comput Model 43:49-75
21. Gerstenfeld LC, Cullinane DM, Barnes GL, Graves DT, Einhorn TA (2003) Fracture healing as a post-natal developmental process: Molecular, spatial, and temporal aspects of its regulation. J Cell Biochem 88:873-884
22. Gerstenfeld LC, Cho T-J, Kon T, Aizawa T, Tsay A, Fitch J, Barnes GL, Graves DT, Einhorn TA (2003b) Impaired fracture healing in the absence of TNF-α signaling: The role of TNF-α in endochondral cartilage resorption. J Bone Miner Res 18(9):1584-1592
23. Gruler H, Bültmann BD (1984) Analysis of cell movement. Blood Cells 10:61-77
24. Hadjiargyrou M, Lombardo F, Zhao S, Ahrens W, Joo J, Ahn H, Jurman M, White DW, Rubin CT (2002) Transcriptional profiling of bone regeneration. J Biol Chem 277(33):30177-30182
25. Hundsdorfer W, Verwer JG (2003) Numerical solution of time-dependent advection-diffusion-reaction equations. Springer Series in Computational Mathematics 33, Springer, Berlin Heidelberg New York
26. Joyce ME, Roberts AB, Sporn MB, Bolander ME (1990) Transforming growth factor-β and the initiation of chondrogenesis and osteogenesis in the rat femur. J Cell Biol 110:2195-2207
27. Levine HA, Pamuk S, Sleeman BD, Nilsen-Hamilton M (2001) Mathematical modelling of capillary formation and development in tumor angiogenesis: penetration into the stroma. B Math Biol 63:801-863
28. McDougall SR, Anderson ARA, Chaplain MAJ, Sherratt JA (2002) Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies. B Math Biol 64:673-702
29. Olsen L, Sherratt JA, Maini PK, Arnold F (1997) A mathematical model for the capillary endothelial cell-extracellular matrix interactions in woundhealing angiogenesis. IMA J Math Appl Med Biol 14:261-281
30. Pettet GJ, Byrne HM, McElwain DLS, Norburry J (1996) A model of wound-healing angiogenesis in soft tissue. Math Biosci 136:35-63
31. Plank MJ, Sleeman BD, Jones PF (2004) A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins. J Theor Biol 229:435-454
32. Seeherman H, Li R, Wozney J (2003) A review of preclinical program development for evaluating injectable carriers for osteogenic factors. J Bone Joint Surg Am 85:96-108
33. Sherratt JA, Murray JD (1990) Models of epidermal wound healing. Proc R Soc Lond B Biol 241:29-36
34. Southwood LL, Frisbie DD, Kawcak CE, McIlwraith CW (2004) Delivery of growth factors using gene therapy to enhance bone healing. Vet Surg 33:565-578
35. Street J, Bao M, deGuzman L, Bunting S, Peale FV Jr., Ferrara N, Steinmetz H, Hoeffel J, Cleland JL, Daugherty A, van Bruggen N, Redmond HP, Carano RAD, Filvaroff EH (2002) Vascular endothelial growth factor stimulates bone repair by promoting angiogenesis and bone turnover. Proc Natl Acad Sci USA 99(15):9656-9661
36. Tranquillo RT, Murray JD (1992) Continuum model of fibroblast-driven wound contraction-inflammation mediation. J Theor Biol 158:135-172
37. Turner ND, Knapp JR, Byers FM, Kopchick JJ (2001) Physical and mechanical characteristics of tibias from transgenic mice expressing mutant bovine growth hormone genes. Exp Biol Med 226:133-139
38. Vander A, Sherman J, Luciano D (1998) Human physiology: The mechanisms of body function. WCB McGraw-Hill, Boston
39. Weiner R, Schmitt BA, Podhaisky H (1997) ROWMAP - a ROW-code with Krylov techniques for large stiff ODEs. Appl Numer Math 25:303-319