Publication Date

8-2023

Advisor(s) - Committee Chair

Richard Schugart, Mark Robinson, Lukun Zheng

Degree Program

Department of Mathematics

Degree Type

Master of Science

Abstract

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim to improve the accuracy of perfusion parameter measurements by implementing algebraic deconvolution methods based on singular value decomposition (SVD) with regularization. SVD is a commonly used computational technique, but it can yield poor parameter estimates when applied to noisy data, leading to distortions in the shape of the vascular residue function and inaccurate cerebral blood flow measurements. By introducing regularization techniques, we aim to mitigate these issues and enhance the reliability of the parameter measurements.

Furthermore, we explore the application of a non-linear regression method called boxcar nonlinear regression (boxNLR) as an alternative approach for measuring perfusion parameters from contrast-time curves obtained from CT imaging. The boxNLR method, when compared to SVDbased algorithms, offers potential improvements in accurately estimating perfusion parameters by reducing the impact of noise and artifacts. By comparing the results obtained from both the SVD with regularization and boxNLR methods, we evaluate the effectiveness and reliability of the boxNLR approach in enhancing perfusion parameter measurements.

Overall, this thesis aims to contribute to the field of dynamic contrast agent magnetic resonance perfusion imaging by addressing the challenges associated with parameter estimation. By comparing the effectiveness of SVD with regularization and boxNLR methods, in the future, we expect to compare these results to perfusion parameter measurements estimated from machine learning algorithms.

Disciplines

Applied Mathematics | Biology | Numerical Analysis and Computation | Other Applied Mathematics | Physical Sciences and Mathematics

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