Unni2019 - Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
Model Identifier
BIOMD0000000888
Short description
Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions Pranav Unni 1 and Padmanabhan Seshaiyer Abstract Over the last few decades, there have been significant developments in theoretical, experimental, and clinical approaches to understand the dynamics of cancer cells and their interactions with the immune system. These have led to the development of important methods for cancer therapy including virotherapy, immunotherapy, chemotherapy, targeted drug therapy, and many others. Along with this, there have also been some developments on analytical and computational models to help provide insights into clinical observations. This work develops a new mathematical model that combines important interactions between tumor cells and cells in the immune systems including natural killer cells, dendritic cells, and cytotoxic CD8+ T cells combined with drug delivery to these cell sites. These interactions are described via a system of ordinary differential equations that are solved numerically. A stability analysis of this model is also performed to determine conditions for tumor-free equilibrium to be stable. We also study the influence of proliferation rates and drug interventions in the dynamics of all the cells involved. Another contribution is the development of a novel parameter estimation methodology to determine optimal parameters in the model that can reproduce a given dataset. Our results seem to suggest that the model employed is a robust candidate for studying the dynamics of tumor cells and it helps to provide the dynamic interactions between the tumor cells, immune system, and drug-response systems.
Format
SBML
(L2V4)
Related Publication
- Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions.
- Unni P, Seshaiyer P
- Computational and mathematical methods in medicine , 1/ 2019 , Volume 2019 , pages: 4079298 , PubMed ID: 31687042
- American International School Chennai, Chennai, Tamilnadu, India.
- Over the last few decades, there have been significant developments in theoretical, experimental, and clinical approaches to understand the dynamics of cancer cells and their interactions with the immune system. These have led to the development of important methods for cancer therapy including virotherapy, immunotherapy, chemotherapy, targeted drug therapy, and many others. Along with this, there have also been some developments on analytical and computational models to help provide insights into clinical observations. This work develops a new mathematical model that combines important interactions between tumor cells and cells in the immune systems including natural killer cells, dendritic cells, and cytotoxic CD8+ T cells combined with drug delivery to these cell sites. These interactions are described via a system of ordinary differential equations that are solved numerically. A stability analysis of this model is also performed to determine conditions for tumor-free equilibrium to be stable. We also study the influence of proliferation rates and drug interventions in the dynamics of all the cells involved. Another contribution is the development of a novel parameter estimation methodology to determine optimal parameters in the model that can reproduce a given dataset. Our results seem to suggest that the model employed is a robust candidate for studying the dynamics of tumor cells and it helps to provide the dynamic interactions between the tumor cells, immune system, and drug-response systems.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Metadata information
hasInstance (2 statements)
hasProperty (1 statement)
isDescribedBy (1 statement)
hasProperty (1 statement)
isDescribedBy (1 statement)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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unni2019.xml | SBML L2V4 Representation of Unni2019 - Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions | 57.32 KB | Preview | Download |
Additional files |
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unni2019.cps | COPASI 4.24 (Build 197) representation of Unni2019 - Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions | 86.84 KB | Preview | Download |
unni2019.sedml | SEDML L1V2 Representation of Unni2019 - Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions | 3.13 KB | Preview | Download |
- Model originally submitted by : Mohammad Umer Sharif Shohan
- Submitted: Dec 10, 2019 10:27:59 PM
- Last Modified: Dec 10, 2019 10:27:59 PM
Revisions
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species | Initial Concentration/Amount |
---|---|
T Tumor Mass |
100.0 mmol |
N natural killer cell |
1.0 mmol |
L T-lymphocyte |
1.0 mmol |
D dendritic cell |
1.0 mmol |
Reactions
Reactions | Rate | Parameters |
---|---|---|
=> T | compartment*a*T*(1-b*T) | a = 0.431; b = 2.17E-8 |
=> N; T | compartment*(s_1+g_1*N*T*T/(h_1+T*T)) | s_1 = 13000.0; g_1 = 0.0; h_1 = 0.0 |
=> L; D, T, N | compartment*(f_2*D*T+r_1*N*T) | f_2 = 0.01; r_1 = 0.0 |
D => ; L, N, T | compartment*(((f_1*L+d_2*N)-d_3*T)*D-g*D) | f_1 = 1.0E-8; d_2 = 4.0E-6; g = 0.024; d_3 = 1.0E-4 |
T => ; N, D, L | compartment*(c_1*N+j*D+k*L)*T | c_1 = 3.5E-6; j = 1.0E-7; k = 1.0E-7 |
N => ; T, D | compartment*((c_2*T+d_1*D)*N+e*N) | d_1 = 1.0E-6; c_2 = 1.0E-7; e = 0.0412 |
=> D | compartment*s_2 | s_2 = 480.0 |
L => ; T, N | compartment*(h*L*T+u*N*L*L+i*L) | i = 0.02; h = 3.42E-10; u = 1.8E-8 |
Curator's comment:
(added: 10 Dec 2019, 22:27:46, updated: 10 Dec 2019, 22:27:46)
(added: 10 Dec 2019, 22:27:46, updated: 10 Dec 2019, 22:27:46)
The model has been encoded in COPASI 4.24 (Build 197) and figure 2 (a,b) has been reproduced from the publication.
The model has been produced to generate the model where no treatment was given. So some of the parameters for the case of addition of drug needs to be added in case anyone one to produce after treatment condition simulation