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Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions

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 viro...

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Detalles Bibliográficos
Autores principales: Unni, Pranav, Seshaiyer, Padmanabhan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800962/
https://www.ncbi.nlm.nih.gov/pubmed/31687042
http://dx.doi.org/10.1155/2019/4079298
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author Unni, Pranav
Seshaiyer, Padmanabhan
author_facet Unni, Pranav
Seshaiyer, Padmanabhan
author_sort Unni, Pranav
collection PubMed
description 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.
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spelling pubmed-68009622019-11-04 Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions Unni, Pranav Seshaiyer, Padmanabhan Comput Math Methods Med Research Article 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. Hindawi 2019-10-08 /pmc/articles/PMC6800962/ /pubmed/31687042 http://dx.doi.org/10.1155/2019/4079298 Text en Copyright © 2019 Pranav Unni and Padmanabhan Seshaiyer. http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Unni, Pranav
Seshaiyer, Padmanabhan
Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title_full Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title_fullStr Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title_full_unstemmed Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title_short Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions
title_sort mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800962/
https://www.ncbi.nlm.nih.gov/pubmed/31687042
http://dx.doi.org/10.1155/2019/4079298
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