Persistent Link:
http://hdl.handle.net/10150/194473
Title:
Mathematical Models of Tumor Growth and Therapy
Author:
Robertson-Tessi, Mark
Issue Date:
2010
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A number of mathematical models of cancer growth and treatment are presented. The most significant model presented is of the interactions between a growing tumor and the immune system. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector-T-cell-mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for.The model is applied to tumors of different growth rates and antigenicities to gauge the relative importance of the various immunosuppressive mechanisms in a tumor. The results suggest that there is an optimum antigenicity for maximal immune system effect. The immunosuppressive effects of further increases in antigenicity outweigh the increase in tumor cell control due to larger populations of tumor-killing effector T cells. The model is applied to situations involving cytoreductive treatment, specifically chemotherapy and a number of immunotherapies. The results how that for some types of tumors, the immune system is able to remove any tumor cells remaining after the therapy is finished. In other cases, the immune system acts to prolong remission periods. A number of immunotherapies are found to be ineffective at removing a tumor burden alone, but offer significant improvement on therapeutic outcome when used in combination with chemotherapy.Two simplified classes of cancer models are also presented. A model of cellular metabolism is formulated. The goal of the model is to understand the differences between normal cell and tumor cell metabolism. Several theories explaining the Crabtree Effect, hereby tumor cells reduce their aerobic respiration in the presence of glucose, have been put forth in the literature; the models test some of these theories, and examine their plausibility.A model of elastic tissue mechanics for a cylindrical tumor growing within a ductal membrane is used to determine the buildup of residual stress due to growth. These results can have possible implications for tumor growth rates and morphology.
Type:
text; Electronic Dissertation
Keywords:
cancer; chemotherapy; immune; immunotherapy; mathematical; model
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Goriely, Alain; El-Kareh, Ardith
Committee Chair:
Goriely, Alain

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleMathematical Models of Tumor Growth and Therapyen_US
dc.creatorRobertson-Tessi, Marken_US
dc.contributor.authorRobertson-Tessi, Marken_US
dc.date.issued2010en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA number of mathematical models of cancer growth and treatment are presented. The most significant model presented is of the interactions between a growing tumor and the immune system. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector-T-cell-mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for.The model is applied to tumors of different growth rates and antigenicities to gauge the relative importance of the various immunosuppressive mechanisms in a tumor. The results suggest that there is an optimum antigenicity for maximal immune system effect. The immunosuppressive effects of further increases in antigenicity outweigh the increase in tumor cell control due to larger populations of tumor-killing effector T cells. The model is applied to situations involving cytoreductive treatment, specifically chemotherapy and a number of immunotherapies. The results how that for some types of tumors, the immune system is able to remove any tumor cells remaining after the therapy is finished. In other cases, the immune system acts to prolong remission periods. A number of immunotherapies are found to be ineffective at removing a tumor burden alone, but offer significant improvement on therapeutic outcome when used in combination with chemotherapy.Two simplified classes of cancer models are also presented. A model of cellular metabolism is formulated. The goal of the model is to understand the differences between normal cell and tumor cell metabolism. Several theories explaining the Crabtree Effect, hereby tumor cells reduce their aerobic respiration in the presence of glucose, have been put forth in the literature; the models test some of these theories, and examine their plausibility.A model of elastic tissue mechanics for a cylindrical tumor growing within a ductal membrane is used to determine the buildup of residual stress due to growth. These results can have possible implications for tumor growth rates and morphology.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectcanceren_US
dc.subjectchemotherapyen_US
dc.subjectimmuneen_US
dc.subjectimmunotherapyen_US
dc.subjectmathematicalen_US
dc.subjectmodelen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGoriely, Alainen_US
dc.contributor.advisorEl-Kareh, Ardithen_US
dc.contributor.chairGoriely, Alainen_US
dc.contributor.committeememberSecomb, Timothyen_US
dc.contributor.committeememberTabor, Michaelen_US
dc.contributor.committeememberEl-Kareh, Ardithen_US
dc.identifier.proquest11122en_US
dc.identifier.oclc752260980en_US
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