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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
Phase Diagram01:19

Phase Diagram

The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
Phase Diagram01:24

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...

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Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
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Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Extended phase graphs with anisotropic diffusion.

M Weigel1, S Schwenk, V G Kiselev

  • 1University Hospital Freiburg, Department of Radiology, Medical Physics, Breisacher Strasse 60a, 79106 Freiburg, Germany. Matthias.Weigel@uniklinik-freiburg.de

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|June 15, 2010
PubMed
Summary
This summary is machine-generated.

The extended phase graph (EPG) calculus now models anisotropic diffusion in magnetic resonance imaging (MRI). This computational method efficiently quantifies echo intensities in complex sequences with varying gradients and diffusion effects.

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In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Biophysics
  • Computational Physics

Background:

  • The extended phase graph (EPG) calculus provides an efficient method for analyzing magnetization behavior in multi-pulse MRI sequences.
  • EPG calculus allows for efficient quantitation of echo intensities, even in complex sequences with arbitrary flip angles.
  • Modeling diffusion effects in MRI is crucial for understanding tissue microstructure.

Purpose of the Study:

  • To extend the EPG calculus to incorporate anisotropic diffusion effects in the presence of arbitrary gradients.
  • To develop a computational framework for efficient and accurate analysis of diffusion-weighted MRI signals.
  • To validate the extended formalism against known examples and apply it to multi-echo sequences.

Main Methods:

  • Extension of the EPG concept to include RF pulses with arbitrary flip angles and phases.
  • Incorporation of anisotropic diffusion as a linear operator acting on magnetization states.
  • Development of an algorithm for integrating diffusion anisotropy effects into the EPG framework.
  • Validation of the formalism using established literature examples.

Main Results:

  • The developed algorithm successfully integrates anisotropic diffusion effects into the EPG calculus.
  • The method allows for the representation of diffusion effects as specific weightings of magnetization pathways.
  • The formalism was validated on known examples, demonstrating its accuracy and applicability.
  • The study successfully calculated effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.

Conclusions:

  • The extended EPG calculus provides an efficient and accurate method for analyzing diffusion-weighted MRI signals, particularly in the presence of anisotropic diffusion and complex pulse sequences.
  • This computational approach facilitates the quantitation of echo intensities and the understanding of diffusion effects in various MRI scenarios.
  • The validated formalism offers a powerful tool for researchers investigating tissue microstructure and developing advanced MRI techniques.