Closed form solution of improved Bloch NMR fluid flow equation using Elzaki transform method
Year: 2026
Type: article
Abstract: The primary objective of this research work is to develop a novel closed-form solution for the improved Bloch NMR fluid flow equation, which models the magnetization generated by nuclear spins of the spinning nuclei, which can be quantified and measured. This novel magnetization signal equation incorporates previously unaddressed parameters associated with NMR blood flow, such as the strength of the external magnetic field in the NMR spectrometer and the precessional frequency of the spinning nuclei. To further our understanding of how nuclear spins behave in arterial, venous, and capillary blood samples, the impact of transverse relaxation time on the magnetization of the spinning nuclei was investigated. The Elzaki transform method, Complex inversion integral, and Cauchy’s residue theorem were employed to obtain the analytical solution of the improved Bloch NMR fluid flow equation. MATLAB and Origin software tools were used to generate and simulate data. The simulated results show that when the transverse relaxation times of the arterial, venous, and capillary blood samples, respectively, increase, the magnetization of blood-spinning nuclei represents 3D curved surfaces. These imply that the phase coherence of the spinning nuclei flowing along the human blood vessel changes due to the random interactions among the spinning nuclei.
Institutions: Modibbo Adama University of Technology, Yazd University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,470
OpenAlex ID: W7135170484