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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
1Challenge the future
Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical ModelW.M. Boon
Dr. ir. J. F. Vermolen Prof. dr. ir. C. Vuik Dr. ir. J. H. Dubbeldam D. Koppenol, MSc
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
2Challenge the future
Opzet
• Onderzoeksdoel• Biologisch proces• Wiskundig model
• Componenten• Contractie
• Resultaten• Conclusies & aanbevelingen
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
3Challenge the future
Onderzoeksdoel
• Wondgenezing• Vorming van nieuw weefsel
• Sterkte afhankelijk van de mate van isotropie• Samentrekking van het weefsel (contractie)
• Contractuur vorming• Modelleren van het volledige proces
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Gebied
• Doorsnede huid• Wondgebied• 3 weken
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Biologisch proces
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
6Challenge the future
Biologisch Proces
• Fibrine klont gevormd• Afbraak door tPA
• PDGF verspreidt via diffusie• Leukocyten arriveren• TGF-β wordt uitgescheden
• Chemoattractant• Fibroblasten arriveren
• Myofibroblasten• Celdeling
• Collageen productie• Contractie
Contractie
Fibroblasten en Myofibroblasten
PDGF
Leukocyten
tPA
Fibrine
TGF-β
Collageen
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Wiskundig model
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Componenten: Cellen
• Discrete schijven• Receptoren
• Leukocyten• Bloedsomloop
• Fibroblasten en myofibroblasten• Omliggend gebied• Celdeling
• Beweging• Celdood
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
9Challenge the future
Componenten: Cytokines
• Diffusievergelijkingen
• tPA: Afbraak fibrine• PDGF: Aantrekking leukocyten• TGF-β: Aantrekking (myo)fibroblasten
• Grid
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Componenten: Vezels
• Fibrine
• Collageen• Dichtheid en oriëntatie• Tensor
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Contractie
• Samentrekking van het weefsel• Tijdelijke krachten
• Fibroblasten en myofibroblasten• Permanente krachten
• Myofibroblasten• Vorming van contractuur
• Invloed op alle componenten• Discreet• Continu
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Tijdelijke krachten
• Puntkracht• Kromme rond cel
• Opsplitsen in lijnstukken• Meerdere puntkrachten
• Formulering
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Permanente krachten
• Contractuur vorming• Elementsgewijs• Timer per element
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Celpopulaties
0 100 200 300 400 5000
50
100
150
Tijd (uren)
Aan
tal c
elle
n
Leukocyten
Fibroblasten
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten cellen
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten cytokines
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
Tijd (uren)
Gem
idde
lde
conc
entr
atie
PDGF
TGF-
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten cytokines
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten vezels
0 100 200 300 400 5000
0.2
0.4
0.6
0.8
1
Tijd (uren)
Gem
idde
lde
dich
thei
d
Collageen
Fibrine
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten vezels
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Resultaten: Vezels
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
Time (hours)
Col
lage
en a
niso
trop
ie
95e percentielGemiddelde
5e percentiel
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Contractie
0 100 200 300 400 5000.85
0.9
0.95
1
1.05
Tijd (uren)
Rel
atie
ve o
pper
vlak
te
95e percentiel
Gemiddelde
5e percentiel
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Toename in tijdelijke krachten
0 100 200 300 400 5000.85
0.9
0.95
1
1.05
Tijd (uren)
Rel
atie
ve o
pper
vlak
te
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Conclusies en aanbevelingen
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Conclusies
• Hybride model: Discrete cellen en continue concentraties
• Verschillende stappen van wondgenezing• Toevoeging van contractie
• Bewegend grid• Invloed op alle componenten
• Vorming contractuur
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
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Aanbevelingen
• Groter oppervlak• Tensor representatie verder benutten• Differentiatie tot myofibroblast
• Model als basis
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Incorporation of Contracture Formation during Dermal Wound Healing: a Mathematical Model
27Challenge the future
Vragen