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MATHEMATICAL MODELING OF WOUND HEALING
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MATHEMATICAL MODELING OF WOUND HEALING

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  1. MATHEMATICAL MODELING OF WOUND HEALING Sujan Sunderan & Mahesh Visvanathan

  2. Systems biology is a well developed field in biology which aims at a system-level understanding of biological systems (H.Kitano, ICSB 2000). • Basic mechanisms cannot be understood by drawing diagrams and listing components. • Systems biology is a biology-based inter-disciplinary study. • Goal of systems biology is the construction and experimental validation of models thatexplain and predict behaviour of biological systems.

  3. What are wounds ?? • A wound is a type of injury • Caused by cuts or scrapes • Healing is a response to the injury

  4. PHASES OF WOUND HEALING  Inflammatory Phase  Proliferative Phase  Remodeling phase  Epithelialization [ David Keast, et al (1998) ]

  5. Aim  To investigate the effects of TNFα on acute wound healing.  To investigate the effects of EGF on acute wound healing. To investigate the effects of TGF-β on acute wound healing. To investigate the effects of MMP2 on acute wound healing.  To make a combined model.

  6. INTERACTION OVERVIEW

  7. TUMOR NECROSIS FACTOR – ALPHA (TNFα) TNFα is a pro-inflammatory cytokine Stimulates proliferation of fibroblasts Induces expression of PDGF, IL -1 and Collagenases TNFα accelerates killing of pathogens [ Cynthia H.T. Edwards Tarynn , et al (2005)]

  8. INTERACTION OVERVIEW – TNF-α

  9. EPIDERMAL GROWTH FACTOR (EGF)  EGF was discovered by Stanley Cohen.  Plays an important role in cell growth, proliferation and differentiation.  NO is a highly diffusible intercellular signaling molecule implicated in a wide range of biological effects.  NO influences on angiogenesis, inflammation, cell proliferation, matrix deposition, and remodeling. [ Mark R. Frey., et al 2004 ] [ Jian-dong LUO., et al 2005 ]

  10. INTERACTION OVERVIEW – EGF

  11. Differential Equations For the model -EGF Fibroblast equation [ Andrea S. Gobin., et al 2003, Jian-dong LUO., et al 2005 ] EGF equation [ Gianluca Tettamanti., et al 2004 ] Epithelial equation [ Mark R. Frey., et al 2004, Teruo Nishida., et al 1992, Jonathan A Sharratt., et al 1994 ]

  12. INOS equation [ Frank S., et al 2002 ] ENOS equation [ Jian-dong LUO., et al 2005 ] Collagen equation [ Lari Hakkinen., et al 2001, Akiko Okada et al 1997, Schaffer MR., et al 1997, Frank S., et al 1998 ]

  13. BASELINE PARAMETERS, VALUES & DESCRIPTION

  14. Pathogen response to varying O2 Levels

  15. TRANSFORMING GROWTH FACTOR BETA (TGF-β) TGF-β is a protein that controls proliferation, cellular differentiation, and other functions in most cells TGF-β trigger apoptosis Mitogenic and chemotactic for keratinocytes and fibroblasts Triggers migration of monocytes and inhibits degradation, promotes chemo attraction of inflammatory cells [ Jennings MT., et al 1998, Bottner M., et al 2000 ]

  16. INTERACTION OVERVIEW - TGF-β

  17. Differential Equations For the model -TGFβ Inflammation equation [ Miyasaki, K., et al 2002, Helen V. Waugh., et al 2006, Bellingan, G.J., et al 1996 ] Fibroblast equation [ Singer, A.J., et al 1999, Robson, M.C., 2001 ] TGF-β equation [ Bellingan, G.J., et al 1996 ]

  18. BASELINE PARAMETERS, VALUES & DESCRIPTION

  19. MATRIX METALLOPROTEINASE 2 (MMP-2)  72 kDa type IV collagenases is an enzyme that in humans is encoded by the MMP2 gene.  Involved in the breakdown of extracellular matrix.  Active role in in-vivo re-epithelialization. TIMP2 inhibits MMP2.  Endothelial cells αβ, degrades MMP2 in cells. [ Zielke, H. R., et al 1996, Naidoo C., et al 2009 ]

  20. INTERACTION OVERVIEW – MMP2

  21. Differential Equations For the model-MMP2 Inflammation equation [ Naidoo C., et al 2009 ] Damage equation [ Naidoo C., et al 2009 ] Collagen equation [ Grinnell F., et al 1992, Wysocki AB., et al 1993, Zhang, G 2006 ]

  22. Epithelial equation [ Ning - Sun Yang., et al 1981, David J., et al 2003 ] MMP-2 equation [ L.M., Young., et al 1998, Itoh, T., et al 2002, Takashi kobayashi., et al 2003 ] MMP2 - EGCG equation [ XianWu Cheng., et al 2003 ]

  23. BASELINE PARAMETERS, VALUES & DESCRIPTION

  24. Pathogen density increased to five times the baseline value

  25. Pathogen growth rate increased to five times the baseline value

  26. What is needed ? • A combined model to predict the growth of infection • A super set to various interactions to reduce the time of wound healing • A more precise and predict the behavior of wound.

  27. COMBINED MODEL INTERACTIONS

  28. Differential Equations For the overall model Inflammation equation Fibroblast equation Epithelial equation

  29. COMBINED WOUND HEALING MODEL

  30. DISCUSSION  Throughout our study we investigated, (1) the effect of TNFα on wound healing model. (2) the effect of EGF on wound healing model. (3) the response of pathogens to tissue O2 level. (4) the effect of fibroblast at wound site. (5) the effect of MMP2 on wound healing model. (6) the effect of TGF-β on wound healing model. (7) to identify the role of TGF-β, in diabetic patients. (8) the combined effect of all factors wound healing model.

  31. APPLICATIONS  It shows the use of system biology approach towards understanding wound healing.  It provides opportunity to test new mechanisms and novel therapeutics of wound healing Insilco.  We can use this model for in vivo validations.  Our model can increase the success rate of clinical studies.  It will aid in designing more appropriate animal studies.

  32. FUTURE PLANS  We will incorporate time delays in our model  We will study the impact of individual parameters on long term healing behavior  Factors like depth, shape, wound contraction and angiogenesis will be included in our study  We will create a cellular automaton model  We will include systemic effects on wound healing

  33. By Sujan Surendran S