{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/42656"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/42656","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Mathematical Modeling of Vascular Tumor Growth and Development","abstract":"Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98).","abstract_html":"Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98).","abstract_has_math":false,"creators":["Cooper, Michele"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Science and Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Puri, Ishwar K."],"committee_members":["De Vita, Raffaella","Finkielstein, Carla V.","Tanaka, Martin L."],"year":2010,"date_issued":"2010-05-12","date_published":"2010-05-12","updated_at":"2026-07-22T22:19:21Z","subjects":["mathematical model","angiogenesis","vascular tumor","tumorigenesis"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05142010-104541"],"render_values":[{"text":"etd-05142010-104541","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/42656","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Puri, Ishwar K."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["De Vita, Raffaella","Finkielstein, Carla V.","Tanaka, Martin L."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Cooper, Michele"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:36:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:36:10Z","2010-06-16"]},{"key":"dc:date.issued","label":"Date","values":["2010-05-12"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Science and Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematical model","angiogenesis","vascular tumor","tumorigenesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05142010-104541"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/42656"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Mathematical Modeling of Vascular Tumor Growth and Development"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Puri, Ishwar K."],"dc:contributor.committeemember":["De Vita, Raffaella","Finkielstein, Carla V.","Tanaka, Martin L."],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Cooper, Michele"],"dc:date.accessioned":["2014-03-14T21:36:10Z"],"dc:date.available":["2014-03-14T21:36:10Z","2010-06-16"],"dc:date.issued":["2010-05-12"],"dc:description.abstract":["Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98)."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-05142010-104541"],"dc:identifier.uri":["http://hdl.handle.net/10919/42656"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["mathematical model","angiogenesis","vascular tumor","tumorigenesis"],"dc:title":["Mathematical Modeling of Vascular Tumor Growth and Development"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering Science and Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:21Z"}