Application of Diffusion Magnetic Resonance Imaging Equation to Compressible and Incompressible Fluid Particles in a Spherical Region

  • Ahmed Saba Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • S. I. Yusuf Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • D. O. Olaoye Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • A. O. Jatto Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
DOI: https://doi.org/10.6084/zenodo.13152986
Keywords: Spherical region, Compressible fluid, Incompressible fluid, Magnetization

Abstract

In the previous work, the response of viscous and non-viscous fluids to magnetic resonance was examined. In this research work, Diffusion magnetic resonance imaging, MRI, is used to study, analyse and compare the response of particles of compressible and incompressible fluids in a spherical region. The fluids considered are hydrogen gas and paraffin oil. The general flow equation was evolved from the fundamental Bloch equations. The general flow equation was
solved using the method of separation of variables and applied to spherical region leading to Legendre equation of the first and second kinds. From the results obtained, it can be concluded that the value of Magnetization for hydrogen gas ranges from 9.28819444503×1013 to 9.35×1014. However, appreciable change can be noticed when magnetization is 9.2881944500003 × 1013. For paraffin oil, the value of Magnetization ranges from 2.749305556000075×1014 to 2.75×1014
with appreciable change noticed at magnetization value of 2.7493055560000094 × 1014. The analytical solution of Diffusion MRI equation adopted in this research work has shown the difference in compressible (hydrogen gas) and incompressible (paraffin oil) fluids in a spherical region through the magnetization values that were generated. This is laying credence to the effectiveness and non-invasive properties of MRI.

Published
2024-05-25
How to Cite
Saba, A., Yusuf, S. I., Olaoye, D. O., & Jatto, A. O. (2024). Application of Diffusion Magnetic Resonance Imaging Equation to Compressible and Incompressible Fluid Particles in a Spherical Region. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), 10 - 30. https://doi.org/10.6084/zenodo.13152986
Issue
Vol 10 No 3 (2024)
Section
Articles

Copyright (c) 2024 Ahmed Saba, S. I. Yusuf, D. O. Olaoye, A. O. Jatto

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