Frascoli2014 - A dynamical model of tumour immunotherapy

  public model
Model Identifier
BIOMD0000000787
Short description 
This is a coupled ordinary differential equation model of tumour-immune dynamics, accounting for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass.
Format
SBML (L2V4)
Related Publication
  • A dynamical model of tumour immunotherapy.
  • Frascoli F, Kim PS, Hughes BD, Landman KA
  • Mathematical biosciences , 7/ 2014 , Volume 253 , pages: 50-62 , PubMed ID: 24759513
  • Department of Mathematics, Swinburne University of Technology, VIC, Australia. Electronic address: ffrascoli@swin.edu.au.
  • A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear dependence on biologically relevant conditions.
Contributors
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database MODEL1908120001
BioModels Database BIOMD0000000787

isDescribedBy (1 statement)
PubMed 24759513

hasProperty (4 statements)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Name Description Size Actions

Model files
Frascoli2014.xml SBML L2V4 Representation of Frascoli2014 - A dynamical model of tumour immunotherapy 25.67 KB Preview | Download

Additional files
Frascoli2014.cps COPASI file of Frascoli2014 - A dynamical model of tumour immunotherapy 48.48 KB Preview | Download
Frascoli2014.sedml SED-ML file of Frascoli2014 - A dynamical model of tumour immunotherapy 2.54 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Aug 12, 2019 10:21:28 AM
  • Last Modified: Aug 12, 2019 10:21:28 AM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Aug 12, 2019 10:21:28 AM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000787
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
V Tumor Volume

Tumor Volume 		1.0 item
C Cytotoxic T Lymphocytes Coverage

cytotoxic T cell ; T cell mediated cytotoxicity directed against tumor cell target 		0.1 item
Reactions
Reactions Rate Parameters
V_Tumor_Volume => ; C_Cytotoxic_T_Lymphocytes_Coverage compartment*rho*k*V_Tumor_Volume^(2/3)*min_C rho = 4.83597586204941; min_C = 0.1; k = 0.2
=> V_Tumor_Volume compartment*rho*r_t*V_Tumor_Volume^(2/3) rho = 4.83597586204941; r_t = 0.1
C_Cytotoxic_T_Lymphocytes_Coverage => compartment*d_c*C_Cytotoxic_T_Lymphocytes_Coverage d_c = 0.2
=> C_Cytotoxic_T_Lymphocytes_Coverage; V_Tumor_Volume compartment*rho*r_c*V_Tumor_Volume^(2/3)*C_Cytotoxic_T_Lymphocytes_Coverage r_c = 0.001; rho = 4.83597586204941
Curator's comment:
(added: 12 Aug 2019, 10:20:18, updated: 12 Aug 2019, 10:20:18)
Reproduced plot of Figure 1B in the original publication. Model simulated and plot produced using COPASI 4.24 (Build 197).