scholarly journals On necessity for analytical solution of the Bloch equations for nuclear magnetic resonance signals at condition express control of liquid medium

2021 ◽  
Vol 2086 (1) ◽  
pp. 012134
Author(s):  
M N Davydov ◽  
V V Davydov ◽  
V Yu Rud
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Analytical Solution ◽  
Liquid Medium ◽  
Bloch Equation ◽  
Control Medium ◽  
Bloch Equations ◽  
Medium Condition ◽  
Condition State ◽  
Nuclear Magnetic

Abstract The necessity of using express analysis methods to control medium condition is substantiated. It has been shown that the method of express control based on the phenomenon of nuclear magnetic resonance is one of the most preferable. It was found that to increase the information about the medium condition state obtained from the recorded NMR signal, it is necessary to use a mathematical model (based on analytical solutions of the Bloch equations). Two approaches are considered that are used to describe the NMR signal in a liquid medium. It is determined that in the classical approach in the system of Bloch equations it is possible to take into account the peculiarities of using radiotechnical methods of signal registration. The direction of the analytical solution of the Bloch equation is proposed. The experimental data are compared with the numerical solution.

Nuclear magnetic resonance studies of multi-site chemical exchange. I. Matrix formulation of the Bloch equations

1970 ◽  
Vol 48 (23) ◽  
pp. 3641-3653 ◽  
Author(s):  
L. W. Reeves ◽  
K. N. Shaw
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Chemical Exchange ◽  
Relaxation Times ◽  
Bloch Equations ◽  
Matrix Formulation ◽  
Exchange Processes ◽  
Site Exchange ◽  
Saturation Effects ◽  
Nuclear Magnetic

A concise matrix formulation of chemical exchange effects on a nuclear magnetic resonance (n.m.r.) spectrum using the Bloch equations is described. The method accommodates many-site exchange processes, site-dependent relaxation times, differing site populations, and saturation effects in a steady-state first-order spectrum. The simple two-site exchange system is analyzed in detail and saturation effects in this system are studied numerically. Alternative forms of the basic lineshape equation are derived, all of which are readily adapted to efficient computer calculations for complete lineshape fitting to obtain kinetic data for complicated chemical exchange processes.

A Numerical Algorithm to Capture Spin Patterns of Fractional Bloch Nuclear Magnetic Resonance Flow Models

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
R. C. Mittal ◽  
Sapna Pandit
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Grid Point ◽  
Operational Matrix ◽  
Computation Time ◽  
Haar Wavelet ◽  
Bloch Equation ◽  
Haar Wavelets ◽  
Test Problems ◽  
Nuclear Magnetic

Fractional Bloch equation is a generalized form of the integer order Bloch equation. It governs the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance (NMR). Scale-3 (S-3) Haar wavelet operational matrix along with quasi-linearization is applied first time to detect the spin flow of fractional Bloch equations. A comparative analysis of performance of classical scale-2 (S-2) and novel scale-3 Haar wavelets (S-3 HW) has been carried out. The analysis shows that scale-3 Haar wavelets give better solutions on coarser grid point in less computation time. Error analysis shows that as we increase the level of the S-3 Haar wavelets, error goes to zero. Numerical experiments have been conducted on five test problems to illustrate the merits of the proposed novel scheme. Maximum absolute errors, comparison of exact solutions, and S-2 Haar wavelet and S-3 Haar wavelet solutions, are reported. The physical behaviors of computed solutions are also depicted graphically.

scholarly journals A 31P Nuclear Magnetic Resonance Study of Intracellular pH of Plant Cells Cultivated in Liquid Medium

1982 ◽  
Vol 70 (4) ◽  
pp. 1156-1161 ◽  
Author(s):  
Jean-Baptiste Martin ◽  
Richard Bligny ◽  
Fabrice Rebeille ◽  
Roland Douce ◽  
Jean-Jacques Leguay ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Liquid Medium ◽  
Intracellular Ph ◽  
Plant Cells ◽  
Nuclear Magnetic Resonance Study ◽  
Magnetic Resonance Study ◽  
31P Nuclear Magnetic Resonance ◽  
Nuclear Magnetic

scholarly journals Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials

2020 ◽  
Vol 10 (8) ◽  
pp. 2850 ◽  
Author(s):  
Harendra Singh ◽  
H. M. Srivastava
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Jacobi Polynomials ◽  
Bloch Equation ◽  
Spin Resonance ◽  
Magnetic Resonance Imaging Mri ◽  
Mean Square Errors ◽  
Nuclear Magnetic

In the present paper, we numerically simulate fractional-order model of the Bloch equation by using the Jacobi polynomials. It arises in chemistry, physics and nuclear magnetic resonance (NMR). It also arises in magnetic resonance imaging (MRI) and electron spin resonance (ESR). It is used for purity determination, provided that the molecular weight and structure of the compound is known. It can also be used for structural determination. By the study of NMR, chemists can determine the structure of many compounds. The obtained numerical results are compared and simulated with the known solutions. Accuracy of the proposed method is shown by providing tables for absolute errors and root mean square errors. Different orders of the time-fractional derivatives results are illustrated by using figures.

An emerging technology: Nuclear magnetic resonance microscopy

1988 ◽  
Vol 46 ◽  
pp. 1000-1001
Author(s):  
M.J. Hennessy ◽  
E. Kwok
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Relaxation Times ◽  
Basic Research ◽  
Local Environment ◽  
Magnetic Resonance Images ◽  
Nmr Microscopy ◽  
Mri Scans ◽  
Temperature Relaxation ◽  
Nuclear Magnetic

Much progress in nuclear magnetic resonance microscope has been made in the last few years as a result of improved instrumentation and techniques being made available through basic research in magnetic resonance imaging (MRI) technologies for medicine. Nuclear magnetic resonance (NMR) was first observed in the hydrogen nucleus in water by Bloch, Purcell and Pound over 40 years ago. Today, in medicine, virtually all commercial MRI scans are made of water bound in tissue. This is also true for NMR microscopy, which has focussed mainly on biological applications. The reason water is the favored molecule for NMR is because water is,the most abundant molecule in biology. It is also the most NMR sensitive having the largest nuclear magnetic moment and having reasonable room temperature relaxation times (from 10 ms to 3 sec). The contrast seen in magnetic resonance images is due mostly to distribution of water relaxation times in sample which are extremely sensitive to the local environment.

Sign in / Sign up

Export Citation Format

Share Document