Bianchi2015 -Model for lymphangiogenesis in normal and diabetic wounds

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Short description
Related Publication
  • A mathematical model for lymphangiogenesis in normal and diabetic wounds.
  • Bianchi A, Painter KJ, Sherratt JA
  • Journal of theoretical biology , 10/ 2015 , Volume 383 , pages: 61-86 , PubMed ID: 26254217
  • Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK. Electronic address:
  • Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-β and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-β and increasing the basal lymphatic endothelial cell growth rate, inter alia, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies.
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan

Metadata information

is (2 statements)
BioModels Database BIOMD0000000722
BioModels Database MODEL1811210001

isDescribedBy (1 statement)
PubMed 26254217

hasTaxon (2 statements)
Taxonomy Mus musculus
Taxonomy Rattus norvegicus

occursIn (1 statement)
Gene Ontology lymphangiogenesis

hasProperty (3 statements)
Mathematical Modelling Ontology Ordinary differential equation model
OMIT 0015769
Gene Ontology wound healing

Curation status


Connected external resources

SBGN view in Newt Editor

Name Description Size Actions

Model files

Wound Healing with Normal health condition.xml SBML file for the model. 54.45 KB Preview | Download

Additional files

Wound Healing with Diabetic health condition.cps Copasi file for Diabetic wound simulations. 99.76 KB Preview | Download
Wound Healing with Normal health condition.cps Copasi file for Normal health conditions. 97.69 KB Preview | Download

  • Model originally submitted by : Sarubini Kananathan
  • Submitted: Nov 21, 2018 11:35:17 AM
  • Last Modified: Nov 21, 2018 11:35:17 AM
  • Version: 4 public model Download this version
    • Submitted on: Nov 21, 2018 11:35:17 AM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000722
: Variable used inside SBML models

Species Initial Concentration/Amount

lymphatic endothelial cell
0.0 mmol

0.0 mmol
Active TGF beta

TGF-beta 1
30.0 mmol

inflammatory macrophage
1875.0 mmol

Vascular endothelial growth factor C
0.5 mmol
Reactions Rate Parameters
=> LECs; VEGF, Active_TGF_beta Body*(c1+VEGF/(c2+c3*VEGF))*1/(1+c4*Active_TGF_beta)*LECs c2 = 42.0; c1 = 0.42; c3 = 4.1; c4 = 0.24
LECs => ; Macrophages, Capillaries Body*(Macrophages+LECs+Capillaries)/k2*LECs k2 = 471000.0
LECs => Capillaries; VEGF Body*sigma*(delta1+delta2*VEGF)*LECs sigma = 0.0; delta2 = 0.001; delta1 = 0.05
=> Active_TGF_beta; Macrophages Body*(a_p*p_0*exp((-a_p)*T_L*time)+a_M*Macrophages)*(T_L+r1*Macrophages) p_0 = 250000.0; r1 = 3.0E-5; a_p = 0.029; T_L = 18.0; a_M = 0.45
Active_TGF_beta => Body*d1*Active_TGF_beta d1 = 500.0
=> Macrophages Body*s_M s_M = 542.0
Macrophages => ; Capillaries Body*rho*Capillaries*Macrophages rho = 1.0E-5
=> VEGF Body*S_V S_V = 1.9
VEGF => ; LECs Body*gamma*VEGF*LECs gamma = 0.0014
Curator's comment:
(added: 21 Nov 2018, 11:34:50, updated: 21 Nov 2018, 11:34:50)
Figure 10 of the reference publication has been reproduced. Initial conditions and values were taken from the publication. The main xml file attached is for wound healing in normal health conditions. To reproduce the figure, run the simulation with time step size of 0.1 and plot against data from both normal and diabetic wound healing simulations. The model was simulated using Copasi 4.24 and the figure was generated using Python 3.7.