Coupled Flow and Transport in an Organ and its Vasculature

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dc.contributor.advisorRiviere, Beatriceen_US
dc.contributor.advisorFuentes, Daviden_US
dc.creatorTzolova, Bilyanaen_US
dc.date.accessioned2024-08-30T18:37:43Zen_US
dc.date.available2024-08-30T18:37:43Zen_US
dc.date.created2024-08en_US
dc.date.issued2024-08-08en_US
dc.date.submittedAugust 2024en_US
dc.date.updated2024-08-30T18:37:43Zen_US
dc.description.abstractIn contrast to many other types of cancer, the incidence of liver cancer, specifically hepatocellular carcinoma (HCC), is on the rise. For most patients, surgical intervention is not a viable option, leaving them reliant on chemotherapy treatments, particularly transarterial chemoembolization (TACE), for relief. Our study aims to understand how these treatments function within the liver and their impact on tumor growth. Building upon existing research, we model the flow and transport of chemotherapy drugs and embolic agents in the liver using the miscible displacement equations. Utilizing CT images from liver cancer patients, we extract a 1D centerline of the hepatic vascular structures that deliver blood to the tumors, and then construct a 3D mesh from the liver segmentations. We employ the singularity subtraction technique to create a finite element model for the flow of blood in the liver, specifically focusing on areas affected by the TACE treatment. We extend the singularity subtraction technique to the time-dependent advection-diffusion equation to model the concentration of chemotherapy drugs in the liver and tumors. We first solve the time-dependent non-conservative advection-diffusion equation using the finite element method. To address instabilities arising when the model is advection dominated, we then utilize the discontinuous Galerkin method to solve the time-dependent conservative advection-diffusion equation. We couple the models for blood flow following the injection of an embolic agent with the transport of chemotherapy to develop a comprehensive model based on the miscible displacement equations in the liver. We then apply the simulation to data from MD Anderson patients diagnosed with hepatocellular carcinoma who have undergone transarterial chemoembolization treatment. This final model enables us to provide insights into the evolving dynamics of TACE within the liver.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationTzolova, Bilyana. Coupled Flow and Transport in an Organ and its Vasculature. (2024). PhD diss., Rice University. https://hdl.handle.net/1911/117836en_US
dc.identifier.urihttps://hdl.handle.net/1911/117836en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectadvection-diffusionen_US
dc.subjectflowen_US
dc.subjecttransporten_US
dc.subjectporous mediaen_US
dc.subjectfinite elementen_US
dc.subjectmiscible displacementen_US
dc.titleCoupled Flow and Transport in an Organ and its Vasculatureen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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