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A mathematical model for chronic wounds
1. | Mathematical Biosciences Institute and Department of Mathematics, Ohio State University, Columbus, OH 43210, United States |
2. | Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States |
References:
[1] |
C. K. Sen, G. M. Gordillo, S. Roy, R. Kirsner, L. Lambert, T. K Hunt, F. Gottrup, G. C. Gurtner and M. T. Longaker, Human skin wounds: A major and snowballing threat to public health and the economy, Wound Repair Regen., 17 (2009), 763-771.
doi: 10.1111/j.1524-475X.2009.00543.x. |
[2] |
R. F. Diegelmann and M. C. Evans, Wound healing: An overview of acute, fibrotic and delayed healing, Front Biosci., 9 (2004), 283-289.
doi: 10.2741/1184. |
[3] |
N. B. Menke, K. R. Ward, T. M. Witten, D. G. Bonchev and R. F. Diegelmann, Impaired wound healing, Clinics in Dermatology, 25 (2007), 19-25.
doi: 10.1016/j.clindermatol.2006.12.005. |
[4] |
A. J. Singer and R. A. Clark, Cutaneous wound healing, N. Engl. J. Med., 341 (1999), 738-746.
doi: 10.1056/NEJM199909023411006. |
[5] |
F. Werdin, M. Tennenhaus, H. Schaller and H. Rennekampff, Evidence-based management strategies for treatment of chronic wounds, Eplasty, 9:e19, (2009). |
[6] |
P. D. Dale, J. A. Sherratt and P. K. Maini, A mathematical model for collagen fibre formation during foetal and adult dermal wound healing, Proc. Biol. Sci., 263 (1996), 653-660.
doi: 10.1098/rspb.1996.0098. |
[7] |
G. J. Pettet, H. M. Byrne, D. L. S. Mcelwain and J. Norbury, A model of wound-healing angiogenesis in soft tissue, Math. Biosci., 136 (1996), 35-63.
doi: 10.1016/0025-5564(96)00044-2. |
[8] |
G. Pettet, M. A. J. Chaplain, D. L. S. Mcelwain and H. M. Byrne, On the role of angiogenesis in wound healing, Proc. R. Soc. Lond. B, 263 (1996), 1487-1493.
doi: 10.1098/rspb.1996.0217. |
[9] |
H. M. Byrne, M. A. J. Chaplain, D. L. Evans and I. Hopkinson, Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment, J. Theor. Med., 2 (2000), 175-197.
doi: 10.1080/10273660008833045. |
[10] |
R. C. Schugart, A. Friedman, R. Zhao and C. K. Sen, Wound angiogenesis as a function of tissue oxygen tension: A mathematical model, Proc. Nat. Acad. Sci. U.S.A., 105 (2008), 2628-2633.
doi: 10.1073/pnas.0711642105. |
[11] |
Y. Dor, V. Djonov and E. Keshet, Induction of vascular networks in adult organs: Implications to proangiogenic therapy, Ann. N.Y. Acad. Sci., 995 (2003), 208-216.
doi: 10.1111/j.1749-6632.2003.tb03224.x. |
[12] |
Y. Dor, V. Djonov and E. Keshet, Making vascular networks in the adult: Branching morphogenesis without a roadmap, Trends in Cell Biology, 13 (2003), 131-136.
doi: 10.1016/S0962-8924(03)00022-9. |
[13] |
S. R. McDougall, A. R. A. Anderson, M. A. J. Chaplain and J. A. Sherratt, Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies, Bull. Math. Biol., 64 (2002), 673-702.
doi: 10.1006/bulm.2002.0293. |
[14] |
A. Stephanou, S. R. McDougall, A. R. A. Anderson and M. A. J. Chaplain, Mathematical modelling of flow in 2d and 3d vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies, Mathematical and Computer Modelling, 41 (2005), 1137-1156.
doi: 10.1016/j.mcm.2005.05.008. |
[15] |
A. R. A. Anderson and M. A. J. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol., 60 (1998), 857-899.
doi: 10.1006/bulm.1998.0042. |
[16] |
C. Xue, A. Friedman and C. K. Sen, A mathematical model of ischemic cutaneous wounds, Proc. Nat. Acad. Sci. USA, 106 (2009), 16782-16787.
doi: 10.1073/pnas.0909115106. |
[17] |
A. Friedman, C. Huang and J. Yong, Effective permeability of the boundary of a domain, Comm. Partial Differential Equations, 20 (1995), 59-102. |
[18] |
S. Roy, S. Biswas, S. Khanna, G. Gordillo, V. Bergdall, J. Green, C. B. Marsh, L. J. Gould and C. K. Sen, Characterization of a pre-clinical model of chronic ischemic wound, Physiol. Genomics, 37 (2009), 211-224.
doi: 10.1152/physiolgenomics.90362.2008. |
[19] |
A. Friedman, B. Hu and C. Xue, Analysis of a mathematical model of ischemic cutaneous wounds, SIAM J. Math. Anal., 42 (2010), 2013-2040.
doi: 10.1137/090772630. |
show all references
References:
[1] |
C. K. Sen, G. M. Gordillo, S. Roy, R. Kirsner, L. Lambert, T. K Hunt, F. Gottrup, G. C. Gurtner and M. T. Longaker, Human skin wounds: A major and snowballing threat to public health and the economy, Wound Repair Regen., 17 (2009), 763-771.
doi: 10.1111/j.1524-475X.2009.00543.x. |
[2] |
R. F. Diegelmann and M. C. Evans, Wound healing: An overview of acute, fibrotic and delayed healing, Front Biosci., 9 (2004), 283-289.
doi: 10.2741/1184. |
[3] |
N. B. Menke, K. R. Ward, T. M. Witten, D. G. Bonchev and R. F. Diegelmann, Impaired wound healing, Clinics in Dermatology, 25 (2007), 19-25.
doi: 10.1016/j.clindermatol.2006.12.005. |
[4] |
A. J. Singer and R. A. Clark, Cutaneous wound healing, N. Engl. J. Med., 341 (1999), 738-746.
doi: 10.1056/NEJM199909023411006. |
[5] |
F. Werdin, M. Tennenhaus, H. Schaller and H. Rennekampff, Evidence-based management strategies for treatment of chronic wounds, Eplasty, 9:e19, (2009). |
[6] |
P. D. Dale, J. A. Sherratt and P. K. Maini, A mathematical model for collagen fibre formation during foetal and adult dermal wound healing, Proc. Biol. Sci., 263 (1996), 653-660.
doi: 10.1098/rspb.1996.0098. |
[7] |
G. J. Pettet, H. M. Byrne, D. L. S. Mcelwain and J. Norbury, A model of wound-healing angiogenesis in soft tissue, Math. Biosci., 136 (1996), 35-63.
doi: 10.1016/0025-5564(96)00044-2. |
[8] |
G. Pettet, M. A. J. Chaplain, D. L. S. Mcelwain and H. M. Byrne, On the role of angiogenesis in wound healing, Proc. R. Soc. Lond. B, 263 (1996), 1487-1493.
doi: 10.1098/rspb.1996.0217. |
[9] |
H. M. Byrne, M. A. J. Chaplain, D. L. Evans and I. Hopkinson, Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment, J. Theor. Med., 2 (2000), 175-197.
doi: 10.1080/10273660008833045. |
[10] |
R. C. Schugart, A. Friedman, R. Zhao and C. K. Sen, Wound angiogenesis as a function of tissue oxygen tension: A mathematical model, Proc. Nat. Acad. Sci. U.S.A., 105 (2008), 2628-2633.
doi: 10.1073/pnas.0711642105. |
[11] |
Y. Dor, V. Djonov and E. Keshet, Induction of vascular networks in adult organs: Implications to proangiogenic therapy, Ann. N.Y. Acad. Sci., 995 (2003), 208-216.
doi: 10.1111/j.1749-6632.2003.tb03224.x. |
[12] |
Y. Dor, V. Djonov and E. Keshet, Making vascular networks in the adult: Branching morphogenesis without a roadmap, Trends in Cell Biology, 13 (2003), 131-136.
doi: 10.1016/S0962-8924(03)00022-9. |
[13] |
S. R. McDougall, A. R. A. Anderson, M. A. J. Chaplain and J. A. Sherratt, Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies, Bull. Math. Biol., 64 (2002), 673-702.
doi: 10.1006/bulm.2002.0293. |
[14] |
A. Stephanou, S. R. McDougall, A. R. A. Anderson and M. A. J. Chaplain, Mathematical modelling of flow in 2d and 3d vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies, Mathematical and Computer Modelling, 41 (2005), 1137-1156.
doi: 10.1016/j.mcm.2005.05.008. |
[15] |
A. R. A. Anderson and M. A. J. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol., 60 (1998), 857-899.
doi: 10.1006/bulm.1998.0042. |
[16] |
C. Xue, A. Friedman and C. K. Sen, A mathematical model of ischemic cutaneous wounds, Proc. Nat. Acad. Sci. USA, 106 (2009), 16782-16787.
doi: 10.1073/pnas.0909115106. |
[17] |
A. Friedman, C. Huang and J. Yong, Effective permeability of the boundary of a domain, Comm. Partial Differential Equations, 20 (1995), 59-102. |
[18] |
S. Roy, S. Biswas, S. Khanna, G. Gordillo, V. Bergdall, J. Green, C. B. Marsh, L. J. Gould and C. K. Sen, Characterization of a pre-clinical model of chronic ischemic wound, Physiol. Genomics, 37 (2009), 211-224.
doi: 10.1152/physiolgenomics.90362.2008. |
[19] |
A. Friedman, B. Hu and C. Xue, Analysis of a mathematical model of ischemic cutaneous wounds, SIAM J. Math. Anal., 42 (2010), 2013-2040.
doi: 10.1137/090772630. |
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