Effects of Relaxation Times from the Bloch Equations on Age Related Changes in White and Grey Matter

  • S. I. Yusu Department of Engineering and Computing, Cosmopolitan University, Abuja, Nigeria.
  • D. O. Olaoye Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • M. O. Dada Department of Physics, Federal University of Technology, Minna, Niger State, Nigeria.
  • A. Saba Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • K. J. Audu Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
  • J. A. Ibrahim 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.
Keywords: Forcing function, Grey Matter, White matter, Spin lattice and Spin-spin relaxation

Abstract

This research work presented the analytical method of using T1 and T2 relaxation rates of white matter and grey matter to distinguish the passage of time on human organs. A time dependent model equation evolved from the Bloch Nuclear Magnetic Resonance equation was solved under the influence of the radio frequency magnetic field [rfB1(x, t) ̸= 0] and in the absence of radio frequency magnetic field [rfB1(x, t) = 0]. The general solution was considered in three cases. Analysis of the solutions obtained revealed that the rate of decrease of the white matter was faster than that of the grey matter. Between 100 and 400 seconds the difference is more noticeable.

Published
2024-03-06
How to Cite
Yusu, S. I., Olaoye, D. O., Dada, M. O., Saba, A., Audu, K. J., Ibrahim , J. A., & Jatto, A. O. (2024). Effects of Relaxation Times from the Bloch Equations on Age Related Changes in White and Grey Matter. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1), 93 - 105. Retrieved from http://ijmso.unilag.edu.ng/article/view/2058
Issue
Vol 10 No 1 (2024)
Section
Articles

Copyright (c) 2024 S. I. Yusu, D. O. Olaoye, M. O. Dada, A. Saba, K. J. Audu, J. A. Ibrahim , A. O. Jatto

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This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.