TITLE:
Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme
AUTHORS:
Omotayo Bamidele Awojoyogbe, Oluwaseun Michael Dada, Karem Boubaker, Omoniyi Adewale Adesola
KEYWORDS:
Bloch NMR Flow Equations; Boubaker Polynomial Expansion Scheme (BPES); Magnetic Resonance Imaging (MRI); Adiabatic Condition
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.5,
November
12,
2013
ABSTRACT: Computational techniques are
invaluable to the continued success and development of Magnetic Resonance
Imaging (MRI) and to its widespread applications. New processing methods are
essential for addressing issues at each stage of MRI techniques. In this study,
we present new sets of non-exponential generating functions representing
the NMR transverse magnetizations and signals which are mathematically designed
based on the theory and dynamics of the Bloch NMR flow equations. These signals
are functions of many spinning nuclei of materials and can be used to obtain
information observed in all flow systems. The Bloch NMR flow equations are
solved using the Boubaker polynomial expansion scheme (BPES) and analytically
connect most of the experimentally valuable NMR parameters in a simplified way
for general analyses of magnetic resonance imaging with adiabatic condition.