Numerical modelling of the angiogenesis process in wound contraction

Biomechanics and Modeling in Mechanobiology

Volumn 12, Issue 2, 2013, Pages 349-360

  Valero, C ^a   Javierre, E ^a   Garcia Aznar J M ^a   Gomez Benito M J ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Angiogenesis; Contraction; Finite element method; Mechanochemical analysis; Wound healing

Indexed keywords

BLOOD VESSELS; CAPILLARITY; CELL CULTURE; DEFORMATION; LAGRANGE MULTIPLIERS; MICROCIRCULATION; NUMERICAL METHODS; TISSUE; TISSUE REGENERATION;

ANGIOGENESIS; ANGIOGENESIS PROCESS; BIOLOGICAL PROCESS; DEVELOPED MODEL; ELLIPTICALS; MECHANOCHEMICAL ANALYSE; MECHANOCHEMICALS; VASCULATURE; WOUND CONTRACTION; WOUND HEALING;

FINITE ELEMENT METHOD;

OXYGEN; VASCULOTROPIN; MESENCHYME DERIVED GROWTH FACTOR; MESENCHYME-DERIVED GROWTH FACTOR; SIGNAL PEPTIDE;

ANGIOGENESIS; ARTICLE; CAPILLARY DENSITY; CELL DENSITY; CELL PROLIFERATION; CONTRACTION STRESS; EXTRACELLULAR MATRIX; FIBROBLAST; GEOMETRY; HALF LIFE TIME; MACROPHAGE; MATHEMATICAL MODEL; MORPHOLOGY; OXYGEN CONCENTRATION; WOUND CONTRACTION; WOUND HEALING; BIOLOGICAL MODEL; BIOMECHANICS; CAPILLARY; CELL COUNT; COMPUTER SIMULATION; ELASTICITY; HUMAN; MECHANICAL STRESS; METABOLISM; PATHOLOGY; SKIN; VASCULARIZATION;

BIOMECHANICS; CAPILLARIES; CELL COUNT; COMPUTER SIMULATION; ELASTICITY; FIBROBLASTS; HUMANS; INTERCELLULAR SIGNALING PEPTIDES AND PROTEINS; MODELS, BIOLOGICAL; NEOVASCULARIZATION, PHYSIOLOGIC; OXYGEN; SKIN; STRESS, MECHANICAL; WOUND HEALING;

EID: 84880701493     PISSN: 16177959     EISSN: 16177940     Source Type: Journal    
DOI: 10.1007/s10237-012-0403-x     Document Type: Article

References (40)

1. Anderson A, Chaplain M (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis RID A-5355-2010. Bull Math Biol 60: 857-899. doi: 10.1006/bulm.1998.0042
2. Carmeliet P, Jain R (2000) Angiogenesis in cancer and other diseases. Nature 407: 249-257. doi: 10.1038/35025220
3. Chaplain M (2000) Mathematical modelling of angiogenesis RID A-5355-2010. J Neurooncol 50: 37-51. doi: 10.1023/A:1006446020377
4. Cheung J, Zhang M, Leung A, Fan Y (2005) Three-dimensional finite element analysis of the foot during standing - a material sensitivity study RID F-8331-2011. J Biomech 38: 1045-1054. doi: 10.1016/j.jbiomech.2004.05.035
5. Delalleau A, Josse G, Lagarde J-, Zahouani H, Bergheau J- (2008) A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo. Skin Res Technol 14: 152-164. doi: 10.1111/j.1600-0846.2007.00269.x
6. Flegg JA, McElwain DLS, Byrne HM, Turner IW (2009) A three species model to simulate application of hyperbaric oxygen therapy to chronic wounds. PLoS Comput Biol 5: e1000451. doi: 10.1371/journal.pcbi.1000451
7. Flegg JA, Byrne HM, McElwain LS (2010) Mathematical model of hyperbaric oxygen therapy applied to chronic diabetic wounds. Bull Math Biol 72: 1867-1891. doi: 10.1007/s11538-010-9514-7
8. Flynn C, Taberner A, Nielsen P (2011) Modeling the mechanical response of in vivo human skin under a rich set of deformations. Ann Biomed Eng 39: 1935-1946. doi: 10.1007/s10439-011-0292-7
9. Geris L, Schugart R, Van Oosterwyck H (2010) In silico design of treatment strategies in wound healing and bone fracture healing. Philos Trans R Soc A Math Phys Eng Sci 368: 2683-2706. doi: 10.1098/rsta.2010.0056
10. Glazier J, Graner F (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E 47: 2128-2154. doi: 10.1103/PhysRevE.47.2128
11. Gros J, Farinelli W, Sadow P, Anderson R, Bruns R (1995) On the mechanism of skin wound contraction - a granulation-tissue knockout with a normal phenotype. Proc Natl Acad Sci USA 92: 5982-5986. doi: 10.1073/pnas.92.13.5982
12. Gurtner GC, Werner S, Barrandon Y, Longaker MT (2008) Wound repair and regeneration. Nature 453: 314-321. doi: 10.1038/nature07039
13. Hendriks F, Brokken D, van Eemeren J, Oomens C, Baaijens F, Horsten J (2003) A numerical-experimental method to characterize the non-linear mechanical behaviour of human skin. Skin Res Technol 9: 274-283. doi: 10.1034/j.1600-0846. 2003.00019.x
14. Hibbit D, Karlson B, Sorensen P (2011) Theory manual, version 6.9. HKS inc. Pawtucket
15. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester, pp 295-304
16. Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall International, Englewood Cliffs
17. Javierre E, Vermolen FJ, Vuik C, van der Zwaag S (2008) Numerical modelling of epidermal wound healing. Springer, Berlin; Heidelberger Platz 3, D-14197 Berlin, Germany
18. Javierre E, Moreo P, Doblaré M, García-Aznar JM (2009) Numerical modeling of a mechano-chemical theory for wound contraction analysis RID F-8256-2010. Int J Solids Struct 46: 3597-3606. doi: 10.1016/j.ijsolstr. 2009.06.010
19. Lapeer RJ, Gasson PD, Karri V (2011) A hyperelastic finite-element model of human skin for interactive real-time surgical simulation. IEEE Trans Biomed Eng 58: 1013-1022. doi: 10.1109/TBME.2009.2038364
20. Linder-Ganz E, Shabshin N, Itzchak Y, Yizhar Z, Siev-Ner I, Gefen A (2008) Strains and stresses in sub-dermal tissues of the buttocks are greater in paraplegics than in healthy during sitting. J Biomech 41: 567-580. doi: 10.1016/j.jbiomech.2007.10.011
21. Maggelakis S (2003) A mathematical model of tissue replacement during epidermal wound healing. Appl Math Model 27: 189-196. doi: 10.1016/S0307- 904X(02)00100-2
22. Manoussaki D (2003) A mechanochemical model of angiogenesis and vasculogenesis. ESAIM-Math Model Numer Anal Model Math Anal Numer 37: 581-599. doi: 10.1051/m2an:2003046
23. Mantzaris N, Webb S, Othmer H (2004) Mathematical modeling of tumor-induced angiogenesis. J Math Biol 49: 111-187. doi: 10.1007/s00285-003- 0262-2
24. McGrath M, Simon R (1983) Wound geometry and the kinetics of wound contraction. Plast Reconstr Surg 72: 66-72
25. Moreo P, Garcia-Aznar JM, Doblare M (2008) Modeling mechanosensing and its effect on the migration and proliferation of adherent cells RID F-8256-2010. Acta Biomater 4: 613-621. doi: 10.1016/j.actbio.2007.10.014
26. Murphy K, Hall C, Maini P, McCue S, McElwain D (2012) A fibrocontractive mechanochemical model of dermal wound closure incorporating realistic growth factor kinetics. Bull Math Biol 74(5): 1-28. doi: 10.1007/s11538-011-9712-y
27. Murray J, Cook J, Tyson R, Lubkin S (1998) Spatial pattern formation in biology: I. Dermal wound healing. II. Bacterial patterns RID F-8802-2011. J Frankl Inst Eng Appl Math 335: 303-332. doi: 10.1016/S0016
28. Olsen L, Sherratt J, Maini P (1995) A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. J Theor Biol 177: 113-128. doi: 10.1006/jtbi.1995.0230
29. Olsen L, Sherratt J, Maini P (1996) A mathematical model for fibro-proliferative wound healing disorders. Bull Math Biol 58: 787-808. doi: 10.1007/BF02459482
30. Pettet G, Byrne H, Mcelwain D, Norbury J (1996a) A model of wound-healing angiogenesis in soft tissue. Math Biosci 136: 35-63. doi: 10.1016/0025-5564(96) 00044-2
31. Pettet G, Chaplain M, McElwain D, Byrne H (1996b) On the role of angiogenesis in wound healing RID A-5355-2010. Proc R Soc Lond Ser B Biol Sci 263: 1487-1493. doi: 10.1098/rspb.1996.0217
32. Risau W (1997) Mechanisms of angiogenesis. Nature 386: 671-674
33. Roy S, Biswas S, Khanna S, Gordillo G, Bergdall V, Green J, Marsh CB, Gould LJ, Sen CK (2009) Characterization of a preclinical model of chronic ischemic wound. Physiol Genomics 37: 211-224. doi: 10.1152/physiolgenomics. 90362.2008
34. Schreml S, Szeimies RM, Prantl L, Karrer S, Landthaler M, Babilas P (2010) Oxygen in acute and chronic wound healing. Br J Dermatol 163: 257-268. doi: 10.1111/j.1365-2133.2010.09804.x
35. Schugart RC, Friedman A, Zhao R, Sen CK (2008) Wound angiogenesis as a function of tissue oxygen tension: a mathematical model. Proc Natl Acad Sci USA 105: 2628-2633. doi: 10.1073/pnas.0711642105
36. Singer A, Clark R (1999) Mechanisms of disease - cutaneous wound healing. N Engl J Med 341: 738-746
37. Tranquillo R, Murray J (1992) Continuum model of fibroblast-driven wound contraction - inflammation-mediation. J Theor Biol 158: 135-172. doi: 10.1016/S0022-5193(05)80715-5
38. Williams PL, Warwick R (1980) Gray's anatomy. Churchill Livingstone, Edinburgh
39. Xue C, Friedman A, Sen CK (2009) A mathematical model of ischemic cutaneous wounds. Proc Natl Acad Sci USA 106: 16782-16787. doi: 10.1073/pnas.0909115106
40. Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth Heinemann, Oxford