Nonlinear simulation of tumor growth and chemotherapy

  • Paul Macklin

    Student thesis: Master's ThesisMaster of Science


    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.
    Date of Award2003
    Original languageEnglish
    Awarding Institution
    • University of Minnesota Twin Cities
    SponsorsNational Science Foundation
    SupervisorJohn S. Lowengrub (Supervisor)


    • Tumour growth
    • Chemotherapy

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