dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy

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This is an updated version of a previous model that described the dynamics of cancer treatment, with descriptions of tumour cell numbers, specific and non-specific immune cells (NK, CD8+ T cells and other lymphocytes) with inclusion of chemo- and immunotherapy. This model incorporates new data to provide an improved and more comprehensive model, with specific emphasis on better descriptions of IL-2 dynamics.
Related Publication
  • Mathematical model creation for cancer chemo-immunotherapy
  • de Pillis, L., Fister, K.R., Gu, W., Collins, C., Daub, M., Gross, D., Moore, J., Preskill, B.
  • Computational and Mathematical Methods in Medicine , 9/ 2009 , Volume 10 , Issue 3 , pages: 165-184 , DOI: 10.1080/17486700802216301
  • Department of Mathematics, Harvey Mudd College, Claremont, CA, United States
  • One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841-862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8+T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8+T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8+T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8+T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters.
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database MODEL1908050002
BioModels Database BIOMD0000000779

hasProperty (3 statements)
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Interleukin Therapy
NCIt Chemotherapy

isDescribedBy (1 statement)

Curation status

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dePillis2009.cps COPASI file of dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy 151.71 KB Preview | Download
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  • Model originally submitted by : Johannes Meyer
  • Submitted: Aug 5, 2019 3:28:45 PM
  • Last Modified: Aug 5, 2019 3:28:45 PM
  • Version: 2 public model Download this version
    • Submitted on: Aug 5, 2019 3:28:45 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000779
: Variable used inside SBML models

Species Initial Concentration/Amount
T Tumour Cells

Neoplastic Cell
1.0E7 item
L CD8 T Cells

CD8-Positive T-Lymphocyte
526800.0 item
I IL 2

1073.0 item
N Natural Killer Cells

natural killer cell
2.5E8 item
Reactions Rate Parameters
T_Tumour_Cells => ; N_Natural_Killer_Cells compartment*c*N_Natural_Killer_Cells*T_Tumour_Cells c = 2.9077E-13
=> L_CD8_T_Cells; T_Tumour_Cells compartment*j*T_Tumour_Cells*L_CD8_T_Cells/(k+T_Tumour_Cells) j = 0.01245; k = 2.019E7
L_CD8_T_Cells => ; M_Chemotherapy_Drug compartment*K_L*(1-exp((-1)*delta_L*M_Chemotherapy_Drug))*L_CD8_T_Cells K_L = 0.0486; delta_L = 1.8328
=> I_IL_2 compartment*v_I v_I = 0.0
T_Tumour_Cells => ; M_Chemotherapy_Drug compartment*K_T*(1-exp((-1)*delta_T*M_Chemotherapy_Drug))*T_Tumour_Cells K_T = 0.9; delta_T = 1.8328
N_Natural_Killer_Cells => ; M_Chemotherapy_Drug compartment*K_N*(1-exp((-1)*delta_N*M_Chemotherapy_Drug))*N_Natural_Killer_Cells K_N = 0.0675; delta_N = 1.8328
=> L_CD8_T_Cells; N_Natural_Killer_Cells, T_Tumour_Cells compartment*r_1*N_Natural_Killer_Cells*T_Tumour_Cells r_1 = 2.9077E-11
I_IL_2 => compartment*mu_I*I_IL_2 mu_I = 11.7427
=> N_Natural_Killer_Cells; I_IL_2 compartment*p_N*N_Natural_Killer_Cells*I_IL_2/(g_N+I_IL_2) g_N = 250360.0; p_N = 0.068
=> L_CD8_T_Cells; I_IL_2 compartment*p_I*L_CD8_T_Cells*I_IL_2/(g_I+I_IL_2) p_I = 2.971; g_I = 2503.6
Curator's comment:
(added: 05 Aug 2019, 15:28:29, updated: 05 Aug 2019, 15:28:29)
Reproduced plot of Figure 1 in the original publication. Model simulated and plot produced using COPASI 4.24 (Build 197).