Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Omotayo Bamidele Awojoyogbe, Oluwaseun Michael Dada, Karem Boubaker, Omoniyi Adewale Adesola

Department of Physics, Federal University of Technology, Minna, Nigeria.
UPDS/ESSTT/63 Rue Sidi Jabeur 5100, Mahdia, Tunisia.

DOI: 10.4236/jamp.2013.15011                

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.

Keywords

Bloch NMR Flow Equations; Boubaker Polynomial Expansion Scheme (BPES); Magnetic Resonance Imaging (MRI); Adiabatic Condition

Conflicts of Interest

The authors declare no conflicts of interest.

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