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Related Experiment Video

Updated: May 8, 2026

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes

Published on: October 4, 2018

The approach to steady state using homogeneous and Cartesian coordinates.

D F Gochberg¹, Z Ding

¹Department of Radiology and Radiological Sciences, Vanderbilt University Institute for Imaging Science. Vanderbilt University, Nashville, TN 37232-2675, USA. daniel.gochberg@vanderbilt.edu

Computational and Mathematical Methods in Medicine

|August 29, 2013

Summary

This summary is machine-generated.

Achieving a steady-state in magnetic resonance systems is possible through RF pulse sequences. This study enhances analytic methods for faster calculations by comparing homogeneous and Cartesian coordinate systems.

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Area of Science:

Magnetic Resonance Imaging
Quantum Mechanics
Physical Chemistry

Background:

Magnetic resonance systems reach a steady-state under repeated radiofrequency (RF) pulse and magnetic field gradient sequences.
Numerical methods can model this trajectory, but analytic solutions offer deeper insights and computational efficiency.
Previous work introduced analytic analysis using homogeneous coordinates.

Purpose of the Study:

To further develop analytic methods for understanding magnetic resonance steady-states.
To compare the advantages of homogeneous versus Cartesian coordinate systems in this analysis.
To provide a faster and more insightful approach to magnetic resonance system calculations.

Main Methods:

Developing analytic solutions for magnetic resonance system dynamics.
Utilizing homogeneous coordinates for system analysis.
Comparing analytic results obtained from homogeneous and Cartesian coordinate systems.

Main Results:

Analytic analysis provides superior insight and speed compared to numerical methods for magnetic resonance steady-states.
Homogeneous coordinate systems offer distinct advantages in the analytic treatment of these systems.
The study quantifies the relative merits of homogeneous versus Cartesian approaches.

Conclusions:

Analytic methods, particularly using homogeneous coordinates, offer significant advantages for understanding and calculating magnetic resonance system steady-states.
This work refines analytic techniques, enabling faster and more insightful magnetic resonance system analysis.
The comparison provides guidance on selecting appropriate coordinate systems for specific magnetic resonance applications.