Abstract

Breast cancer is one of the most common cancers in women and early detection is a key component in the treatment of cancer and can lead to drastic improvement of patient survival rates. Cancerous tissue is stiffer on average than healthy soft tissue, and in the presence of a compressive force, the stiffer areas tend to deform less than the softer areas. The problem being analyzed is based on a linear elasticity system that describes displacement in soft tissue under applied body forces in biomedical applications, specifically in the case of identifying soft tissue cancers. Elasticity imaging, or elastography, can be employed as a method of tumor identification by using imaging systems such as an ultrasound to measure tissue deformation. The task of identifying the tissue stiffness parameter is formulated as an optimization problem with a system of partial differential equations (PDEs) as a constraint. The optimization problem of estimating the tissue stiffness parameter, or the shear modulus, of the system is solved using iterative methods that require repeated solving of the underlying PDE system (linear elasticity system). This results in a high computational cost in general and makes these methods less feasible in clinical applications. The primary goal of this work is to develop a computational framework based on finite elements for the identification of a distributed parameter in a PDE system. We also propose an adaptive mesh refinement framework that provides the resolution needed for the recovery of the spatially varying parameter while improving the computational efficiency.

Publication Date

5-6-2024

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Department, Program, or Center

Mathematical Sciences, School of

College

College of Science

Advisor

Basca Jadamba

Advisor/Committee Member

Patricia Iglesias Victoria

Advisor/Committee Member

Akhtar Khan

Campus

RIT – Main Campus

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