{"id":{"repo_id":"dundee","oai_identifier":"oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"},"canonical_url":"https://search.dev.ndltd.org/etd/dundee/oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0","repository":{"repo_id":"dundee","name":"University of Dundee","base_url":"https://discovery.dundee.ac.uk/ws/oai"},"display":{"title":"Nonlinear simulation of tumor growth and chemotherapy","abstract":"We implement numerically a model for free boundary necrotic and non-necrotic tumor growth and chemotherapy, where the tumor-healthy tissue interface is a moving deformable boundary. In the process, we improve upon existing techniques and develop new finite difference and ghost fluid / level set methods to attain full second-order accuracy for the first time in the context of afully-coupled, nonlinear moving boundary problem. Our new methods include a robust boundarycondition-capturing Poisson solver, improved discretizations of the normal vector and curvature, anew technique for extending variables beyond the zero level set, and a new application of Gaussianfilter technology ordinarily associated with image processing. We conduct some parameter studies on 2D necrotic and non-necrotic tumor growth with and without chemotherapy, and we conclude with a 2D simulation of tumor breakup while undergoing chemotherapy.","abstract_html":"We implement numerically a model for free boundary necrotic and non-necrotic tumor growth and chemotherapy, where the tumor-healthy tissue interface is a moving deformable boundary. In the process, we improve upon existing techniques and develop new finite difference and ghost fluid / level set methods to attain full second-order accuracy for the first time in the context of afully-coupled, nonlinear moving boundary problem. Our new methods include a robust boundarycondition-capturing Poisson solver, improved discretizations of the normal vector and curvature, anew technique for extending variables beyond the zero level set, and a new application of Gaussianfilter technology ordinarily associated with image processing. We conduct some parameter studies on 2D necrotic and non-necrotic tumor growth with and without chemotherapy, and we conclude with a 2D simulation of tumor breakup while undergoing chemotherapy.","abstract_has_math":false,"creators":["Macklin, Paul"],"institution":"University of Minnesota Twin Cities","degree_name":"Master of Science","degree_level":"Master's Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lowengrub, John S."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-24T02:07:25Z","subjects":["Tumour growth","Chemotherapy"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"],"render_values":[{"text":"oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0","href":null,"code":true}]}]},"links":{"outbound_url":"https://discovery.dundee.ac.uk/en/studentTheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lowengrub, John S."]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["National Science Foundation"]},{"key":"dc:creator","label":"Author","values":["Macklin, Paul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2003"]},{"key":"dc:date.issued","label":"Date","values":["2003"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Minnesota Twin Cities"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://discovery.dundee.ac.uk/en/studentTheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Master's Thesis"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Tumour growth","Chemotherapy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0","https://discovery.dundee.ac.uk/en/studentTheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We implement numerically a model for free boundary necrotic and non-necrotic tumor growth and chemotherapy, where the tumor-healthy tissue interface is a moving deformable boundary. In the process, we improve upon existing techniques and develop new finite difference and ghost fluid / level set methods to attain full second-order accuracy for the first time in the context of afully-coupled, nonlinear moving boundary problem. Our new methods include a robust boundarycondition-capturing Poisson solver, improved discretizations of the normal vector and curvature, anew technique for extending variables beyond the zero level set, and a new application of Gaussianfilter technology ordinarily associated with image processing. We conduct some parameter studies on 2D necrotic and non-necrotic tumor growth with and without chemotherapy, and we conclude with a 2D simulation of tumor breakup while undergoing chemotherapy."]},{"key":"dc:title","label":"Title","values":["Nonlinear simulation of tumor growth and chemotherapy"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lowengrub, John S."],"dc:contributor.sponsor":["National Science Foundation"],"dc:creator":["Macklin, Paul"],"dc:date":["2003"],"dc:date.issued":["2003"],"dc:description.abstract":["We implement numerically a model for free boundary necrotic and non-necrotic tumor growth and chemotherapy, where the tumor-healthy tissue interface is a moving deformable boundary. In the process, we improve upon existing techniques and develop new finite difference and ghost fluid / level set methods to attain full second-order accuracy for the first time in the context of afully-coupled, nonlinear moving boundary problem. Our new methods include a robust boundarycondition-capturing Poisson solver, improved discretizations of the normal vector and curvature, anew technique for extending variables beyond the zero level set, and a new application of Gaussianfilter technology ordinarily associated with image processing. We conduct some parameter studies on 2D necrotic and non-necrotic tumor growth with and without chemotherapy, and we conclude with a 2D simulation of tumor breakup while undergoing chemotherapy."],"dc:identifier":["oai:discovery.dundee.ac.uk:studenttheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0","https://discovery.dundee.ac.uk/en/studentTheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"],"dc:language":["eng"],"dc:publisher.department":["Mathematics"],"dc:publisher.institution":["University of Minnesota Twin Cities"],"dc:relation.isreferencedby":["https://discovery.dundee.ac.uk/en/studentTheses/81baf877-f5ff-4a49-9d1b-4b6ea4445fe0"],"dc:subject":["Tumour growth","Chemotherapy"],"dc:title":["Nonlinear simulation of tumor growth and chemotherapy"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Master's Thesis"],"dc:type.qualificationname":["Master of Science"]},"updated_at":"2026-07-24T02:07:25Z"}