Mathematical modelling of wound healing processes to help the treatment of chronic wounds Etelvina Javierre In collaboration with: Fred Vermolen, Sergey.

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Mathematical modelling of wound healing processes to help the treatment of chronic wounds Etelvina Javierre In collaboration with: Fred Vermolen, Sergey Zemskov (TU Delft) Pedro Moreo, José Manuel García-Aznar (UZ)

IV Modelling Week UCM June 14-22, MEDICAL MOTIVATION Open wounds compromise organ integrity by: decreasing the mechanical strength of surrounding tissue putting the immunology system at risk impairing organ function Cancer as a wound that does not heal

IV Modelling Week UCM June 14-22, MEDICAL MOTIVATION Type of pathologyNumber of patients per yearTotal cost per year Trauma35.2 million [USA data] Thermal injury1 million [USA data] Venous ulcers [USA data] $ 5.8 Billion Pressure ulcers1.4 million [USA data] $ 2.2 Billion Diabetic leg ulceration [EU data] 600 Million€ Prevalence of diabetic ulcers6-7 million [EU data] > 5000 Million€ LEA in diabetic patients65800 [EU data] 2.6 Billion€ References: Clark et al., J. Investigative Dermatology, 2007, vol. 127, pp Rasanen et al., Acta Orthop. 2007, vol. 78, pp

3 INDUSTRIAL RELEVANCE IV Modelling Week UCM June 14-22, 2010 Podiatry services for profesional athletes, but also general clinical practice Multidisciplinary team of podiatrists, physiotherapist, physicians and engineers

4 INDUSTRIAL RELEVANCE IV Modelling Week UCM June 14-22, 2010

5 NORMAL WOUND HEALING IV Modelling Week UCM June 14-22, 2010

6 EVENTS THAT WE ARE GOING TO TARGET IV Modelling Week UCM June 14-22, Re-epithelialization -repair of the connectivity of the basal membrane -cell migration and mitosis triggered by released factors 2.Angiogenesis -repair of the vascular network -growth of vascular tips towards regions of low oxygen tension 3.ECM synthesis and wound contraction -cellular synthesis of ECM components -cell deformation and remodelling of ECM

7 EVENTS THAT WE ARE GOING TO TARGET IV Modelling Week UCM June 14-22, Re-epithelialization -repair of the connectivity of the basal membrane -cell migration and mitosis triggered by released factors 2.Angiogenesis -repair of the vascular network -growth of vascular tips towards regions of low oxygen tension 3.ECM synthesis and wound contraction -cellular synthesis of ECM components -cell deformation and remodelling of ECM

8 EVENTS THAT WE ARE GOING TO TARGET IV Modelling Week UCM June 14-22, Re-epithelialization -repair of the connectivity of the basal membrane -cell migration and mitosis triggered by released factors 2.Angiogenesis -repair of the vascular network -growth of vascular tips towards regions of low oxygen tension 3.ECM synthesis and wound contraction -cellular synthesis of ECM components -cell deformation and remodelling of ECM

9 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix IV Modelling Week UCM June 14-22, 2010

10 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - IV Modelling Week UCM June 14-22, 2010

11 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - random dispersal IV Modelling Week UCM June 14-22, 2010

12 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - chemotaxis IV Modelling Week UCM June 14-22, 2010

13 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - passive convection IV Modelling Week UCM June 14-22, 2010

14 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - chemical and mechanical enhancement of proliferation IV Modelling Week UCM June 14-22, 2010

15 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - differentiation from other species IV Modelling Week UCM June 14-22, 2010

16 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - differentiation to other species IV Modelling Week UCM June 14-22, 2010

17 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of cell density = cell migration cell proliferation cell disappearance + - cell death IV Modelling Week UCM June 14-22, 2010

18 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix IV Modelling Week UCM June 14-22, 2010

19 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - IV Modelling Week UCM June 14-22, 2010

20 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - diffusion IV Modelling Week UCM June 14-22, 2010

21 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - passive convection IV Modelling Week UCM June 14-22, 2010

22 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - cell production of chemical species IV Modelling Week UCM June 14-22, 2010

23 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - chemical uptake by cells IV Modelling Week UCM June 14-22, 2010

24 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix rate of change of chemical species = chemical transport chemical production chemical depletion + - chemical decay IV Modelling Week UCM June 14-22, 2010

25 HOW ARE WE GOING TO MODEL THEM? Coupled systems of convection-diffusion-reactions Cellular species Chemical biofactors Extracellular matrix IV Modelling Week UCM June 14-22, 2010 rate of change of ECM density = movement due to deformation synthesis degradation+ - body forces = ECM resistive forces cell traction forces +

26 NUMERICAL SOLUTION Self developed FE code in Matlab® -mesh generation -spatial discretization: -element matrices construction and assembly -temporal discretization: IMEM methods -moving boundaries Analysis to be conducted -healing of planar and circular wounds in 1D -sensitivity analyses to identify crucial parameters -healing of general wounds in 2D -evaluation of the results against experimental data IV Modelling Week UCM June 14-22, 2010

27 NUMERICAL SOLUTION Self developed FE code in Matlab® -mesh generation -spatial discretization: -element matrices construction and assembly -temporal discretization: IMEM methods -moving boundaries Analysis to be conducted -healing of planar and circular wounds in 1D -sensitivity analyses to identify crucial parameters -healing of general wounds in 2D -evaluation of the results against experimental data IV Modelling Week UCM June 14-22, 2010