Exact solution to the Bloch equations and application to the Hahn echo.

Summary of "Exact solution to the Bloch equations and application to the Hahn echo."

The exact symbolic solution of the Bloch equations is given in the Lagrange form and illustrated with R(2) experiments using a Hahn echo. Two different methods are also applied to approximately solve the Bloch equations, we find that splittings with effective-field interpretations are very substantially better than other approximations by comparing the errors. Estimates of transverse relaxation, R(2), from Hahn echos are effected by frequency offset and field inhomogeneity. We use exact solutions of the Bloch equations and simulations to quantify both effects, and find that even in the presence of expected B(0) inhomogeneity, off-resonance effects can be removed from R(2) measurements, when parallelomega parallel0.5gammaB(1), by fitting the exact solutions of the Bloch equations. Further, the experiments and simulations show that the fitting models with the exact solutions of the Bloch equations do not depend on the sampling density and delay times.


Department of Chemistry and Chemical Biology, McMaster University, 1280 Main St. W., Hamilton, Ontario, Canada L8S 4M1.

Journal Details

This article was published in the following journal.

Name: Journal of magnetic resonance (San Diego, Calif. : 1997)
ISSN: 1096-0856


DeepDyve research library

PubMed Articles [10939 Associated PubMed Articles listed on BioPortfolio]

Myocardial T1 mapping at 3.0 tesla using an inversion recovery spoiled gradient echo readout and bloch equation simulation with slice profile correction (BLESSPC) T1 estimation algorithm.

To develop an accurate and precise myocardial T1 mapping technique using an inversion recovery spoiled gradient echo readout at 3.0 Tesla (T).

Electron Dynamics and IR Peak Coalescence in Bridged Mixed Valence Dimers Studied by Ultrafast 2D-IR Spectroscopy.

Dynamic IR peak coalescence and simulations based on the optical Bloch equations have been used previously to predict the rates of intramolecular electron transfer in a group of bridged mixed valence ...

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population....

Statistical Physics Methods Provide the Exact Solution to a Long-Standing Problem of Genetics.

Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this Letter, we use such methods to solve a long-standing problem in statist...

Gd(III)-Gd(III) distance measurements with chirp pump pulses.

The broad EPR spectrum of Gd(III) spin labels restricts the dipolar modulation depth in distance measurements between Gd(III) pairs to a few percent. To overcome this limitation, frequency-swept chirp...

Clinical Trials [2104 Associated Clinical Trials listed on BioPortfolio]

A Phase 2 Study to Evaluate the Safety and Efficacy of CB-03-01 Solution, a Comparator Solution and Vehicle Solution in Males With Androgenetic Alopecia

In this proof-of-concept study, the safety and efficacy of a solution formulation will be investigated in male subjects with androgenetic alopecia (AGA) after twice daily application for u...

Tricuspid Regurgitation Study

The effect of cardiac pacing leads on tricuspid regurgitation is unclear. This study will determine whether using a smaller diameter leads and an alternate position in the ventricle, the p...

Measurement of Cerebral Oxygen Extraction Fraction Using MRI Technique

All images in this study were acquired on a 1.5 T Sonata whole body scanner (Siemens Medical Inc., Erlangen, Germany) using 2D multi-echo gradient echo/spin echo sequence and 2D single-sho...

Addressing Motion and Confounds Issues in Resting fMRI- Application of Multi-echo EPI Scanning

Resting state functional MRI is widely used for studying brain functional networks. However, in-scanner head movement and other non-neuronal noise can disproportionately bias connectivity ...

To Determine the Effects of Deodorant, Antiperspirant and Washing on the Pharmacokinetics of 2% Testosterone MD Lotion

Testosterone replacement treatment is the most effective way of treating hypogonadism in men. Acrux has a propriety testosterone replacement product, Testosterone MD-Lotion and this ...

Medical and Biotech [MESH] Definitions

Hypertonic sodium chloride solution. A solution having an osmotic pressure greater than that of physiologic salt solution (0.9 g NaCl in 100 ml purified water).

The application of technology to the solution of medical problems.

The application of mathematical formulas and statistical techniques to the testing and quantifying of economic theories and the solution of economic problems.

The pressure required to prevent the passage of solvent through a semipermeable membrane that separates a pure solvent from a solution of the solvent and solute or that separates different concentrations of a solution. It is proportional to the osmolality of the solution.

Solution that is usually 10 percent glucose but may be higher. An isotonic solution of glucose is 5 percent.

Quick Search

DeepDyve research library

Searches Linking to this Article