Life Sciences Commons^™

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

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 …

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …