Impact of Relaxation Time from Improved Bloch NMR Fluid Flow Equation on NMR Signal of Blood Proton Spins using Laplace Transform Method
Main Article Content
Abstract
Nuclear Magnetic Resonance (NMR) is a non-destructive spectroscopic technique in which the magnetization of a sample, such as human blood, changes by the application of both an external and radio frequency (RF) field to the sample. NMR is a non-invasive tool used in medicine and surgery for getting valuable information on blood flowing along the human blood vessels. In the existing work done on NMR signal, which is the transient state solution of the Bloch NMR fluid flow equation, it is noted that some NMR blood flow parameters, such as static magnetic field and Larmor precessional frequency of blood-spinning protons, are missing in the existing NMR signal equation. In order to solve this problem to generate accurate NMR signal results. This study developed a new NMR signal equation that contains the missing NMR parameter. Furthermore, the signal equation was used to investigate the effect of transverse relaxation times of arterial, venous, and capillary blood, respectively, on the NMR signal of blood proton spins. Laplace transform method was utilized to obtain the NMR signal, which is the closed-form solution of the improved Bloch NMR fluid flow time-dependent equation. MATLAB and Origin Pro software tools were utilized for the generation and simulation of data. Results of the simulation and analysis showed that for varied relaxation times of arterial, venous, and capillary blood, the NMR signal generated from the blood proton spins decreased with increasing time. This means that the blood proton spins gradually lose their alignment of magnetic moments, which is due to the interactions between neighboring blood proton spins. The results obtained from the simulations may be used as a means of validating the experimental results obtained from an NMR/Magnetic resonance imaging machine by providing a theoretical basis for comparison with the experimental data.
Downloads
Article Details
References
Abragam, A. (1961). The Principles of Nuclear Magnetism. Oxford University Press.
Awojoyogbe, O. B., Dada, O. M., Faromika, O. P., & Dada, O. E. (2011). Mathematical concept of the Bloch flow equations for general magnetic resonance imaging: A review. Concepts in Magnetic Resonance Part A, 38A(3), 85–101. https://doi.org/10.1002/cmr.a.20210
Carbajo, R. J., & Neira, J. L. (2013). Spectroscopic Parameters in Nuclear Magnetic Resonance. In R. J. Carbajo & J. L. Neira, NMR for Chemists and Biologists (pp. 31–52). Springer Netherlands. https://doi.org/10.1007/978-94-007-6976-2_2
Carbajo, R. J., Neira, J. L., Carbajo, R. J., & Neira, J. L. (2013). The Basis of Nuclear Magnetic Resonance Spectroscopy. NMR for Chemists and Biologists, 1–29.
Carlier, P. G., Bertoldi, D., Baligand, C., Wary, C., & Fromes, Y. (2006). Muscle blood flow and oxygenation measured by NMR imaging and spectroscopy. NMR in Biomedicine: An International Journal Devoted to the Development and Application of Magnetic Resonance In Vivo, 19(7), 954–967. https://doi.org/10.1002/nbm.
Chance, B., Nakase, Y., Bond, M., Leigh Jr, J. S., & McDonald, G. (1978). Detection of 31P nuclear magnetic resonance signals in brain by in vivo and freeze-trapped assays. Proceedings of the National Academy of Sciences, 75(10), 4925–4929. https://doi.org/10.1073/pnas.75.10.4925
Endre, Z. H., Kuchel, P. W., & Chapman, B. E. (1984). Cell volume dependence of 1H spin-echo NMR signals in human erythrocyte suspensions: The influence of in situ field gradients. Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, 803(3), 137–144. https://doi.org/10.1016/0167-4889(84)90003
Fabry, M. E., & San George, R. C. (1983). Effect of magnetic susceptibility on nuclear magnetic resonance signals arising from red cells: A warning. Biochemistry, 22(17), 4119–4125. https://doi.org/10.1021/bi00286a020
Gale, P. K., & Pierre, J. W. (1995). Prony analysis based parameter estimation of an NMR signal of blood plasma for cancer detection. 1995 International Conference on Acoustics, Speech, and Signal Processing, 2, 1185–1188. https://doi.org/10.1109/ICASSP.1995.480449
Gao, J.-H., Holland, S. K., & Gore, J. C. (1988). Nuclear magnetic resonance signal from flowing nuclei in rapid imaging using gradient echoes. Medical Physics, 15(6), 809–814. https://doi.org/10.1118/1.596197
Heidari, A., & Gobato, R. (2020). Spherical Paramagnetic Contribution to Shielding Tensor Analysis of Nuclear Magnetic Resonance Signals in Gum Cancer Cells, Tissues and Tumors. Dent Oral Maxillofac Res, 6(5), 1–2.
Horn, M., Kadgien, M., Schnackerz, K., & Neubauer, S. (2000). Spectroscopy: 31P-nuclear magnetic resonance spectroscopy of blood: A species comparison. Journal of Cardiovascular Magnetic Resonance, 2(2), 143–149. https://doi/abs/10.3109/10976640009148684
Hoult, D. I. (1981). An overview of NMR in medicine.
Jensen, J. H., & Chandra, R. (2000). Strong field behavior of the NMR signal from magnetically heterogeneous tissues. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 43(2), 226–236. https://doi.org/10.1002/(SICI)1522-2594(200002)43 .
Karseev, A., Vologdin, V., & Davydov, V. (2015). Features of nuclear magnetic resonance signals registration in weak magnetic fields for express–control of biological solutions and liquid medium by nuclear magnetic spectroscopy method. Journal of Physics: Conference Series, 643(1), 012108. https://doi.org/10.1088/1742-6596/643/1/012108.
Khan, D., Parveen, I., & Sharma, S. (2022). Design, Synthesis and Characterization of Aurone Based α, β-unsaturated Carbonyl-Amino Ligands and their Application in Microwave Assisted Suzuki, Heck and Buchwald Reactions. Asian Journal of Organic Chemistry, 11(1), Article 1. https://doi.org/10.1002/ajoc.202100638
Lindon, J. C., Holmes, E., Bollard, M. E., Stanley, E. G., & Nicholson, J. K. (2004). Metabonomics technologies and their applications in physiological monitoring, drug safety assessment and disease diagnosis. Biomarkers, 9(1), 1-31. https://doi.org/10.1080/13547500410001668379 .
Myazin, N. S., & Davydov, V. V. (2018). Features of formation of structure of a nuclear magnetic resonance signal in weak magnetic field. Journal of Physics: Conference Series, 1135(1), 012061. https://doi.org/10.1088/1742-6596/1135/1/012061
Prance, R. J., & Aydin, A. (2007). Acquisition of a nuclear magnetic resonance signal using an electric field detection technique. Applied Physics Letters, 91(4). https://doi.org/10.1063/1.27622
Rasheed, L., & Usman, A. (2023). Analytical solution of Bloch NMR fluid flow space–time-dependent equation using laplace transform and complex inversion integral. International Journal of Modern Physics B, 2450052. https://doi.org/10.1142/S0217979224500528
Rasheed, A. L., Usman, A., Timtere, P., & Agada, L. E. (2024). Effect of Relaxation Times on Magnetization of Blood Proton Spins at Steady State using Improved Bloch NMR Fluid Flow Equation. International Journal of Development Mathematics 1(4), 152-165. https://doi.org/10.62054/ijdm/0104.12
Theis, F. J., & Meyer-Bäse, A. (2010). Biomedical signal analysis: Contemporary methods and applications.
Torrey, H. C. (1956). Bloch equations with diffusion terms. Physical Review, 104(3), 563. https://doi.org/10.1103/PhysRev.104.563
Webb, A. (2016). The principles of magnetic resonance, and associated hardware. https://doi.org/10.1039/9781782623878-00001
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. https://doi.org/10.5281/ZENODO