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Related Concept Videos

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Phasors01:12

Phasors

Phasors are a powerful mathematical tool used to analyze alternating current (AC) circuits. They provide a complex number representation of sinusoids, with the magnitude of the phasor equating to the amplitude of the sinusoid and the angle of the phasor representing the phase measured from the positive x-axis.
One of the significant benefits of using phasors is that they simplify the analysis of AC circuits by eliminating the time dependence of the current and voltage. This transformation...
Phasor Relationships for Circuit Elements01:16

Phasor Relationships for Circuit Elements

Phasor representation is a powerful tool used to transform the voltage-current relationship for resistors, inductors, and capacitors from the time domain to the frequency domain. This transformation simplifies the analysis of alternating current (AC) circuits.
In the time domain, Ohm's law provides a fundamental relation between the current flowing through a resistor and the voltage across it:
Kirchoff's Laws using Phasors01:12

Kirchoff's Laws using Phasors

Analyzing AC circuits in electrical systems is a fundamental aspect of electrical engineering. In these circuits, AC power is supplied from a distribution panel and wired to various household appliances in parallel. To perform a comprehensive analysis, electrical engineers use Kirchhoff's voltage and current laws, which are equally applicable in AC circuits as in DC circuits.
Kirchhoff's voltage law (KVL) states that the sum of phasor voltages around a closed loop in an AC circuit equals zero.
Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular frequency.

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Related Experiment Video

Updated: Jun 19, 2026

Quantifying Mixing using Magnetic Resonance Imaging
07:33

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

Multi-component quantitative magnetic resonance imaging by phasor representation.

Frank J Vergeldt1,2, Alena Prusova1, Farzad Fereidouni3

  • 1Laboratory of Biophysics, Wageningen University & Research, Wageningen, The Netherlands.

Scientific Reports
|April 15, 2017
PubMed
Summary
This summary is machine-generated.

Phasor analysis in quantitative magnetic resonance imaging (qMRI) effectively separates signals from multiple tissue components. This novel, model-free method enhances data decomposition and quantification across various biological samples.

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Area of Science:

  • Biomedical Imaging
  • Quantitative Magnetic Resonance Imaging (qMRI)
  • Data Analysis

Background:

  • Quantitative magnetic resonance imaging (qMRI) is a powerful non-invasive technique for life, material, and medical sciences.
  • Challenges arise in qMRI when multiple components within a single pixel contribute to the signal, hindering accurate quantification of individual parameters.
  • Existing methods struggle to effectively disentangle complex signals in multi-component voxels.

Purpose of the Study:

  • To introduce and validate the concept of phasor representation for disentangling signals from multiple components in qMRI data.
  • To demonstrate the application of phasor analysis for decomposition, unmixing, segmentation, and quantification of in vivo qMRI data.
  • To assess the model-free, speed, and accuracy of the proposed phasor analysis method, including its performance on undersampled data.

Main Methods:

  • Development and application of phasor representation to qMRI data.
  • In vivo data acquisition from plant stems, human and mouse brains, and human prostates.
  • Phasor plotting for signal decomposition, unmixing, and segmentation.

Main Results:

  • Successful decomposition and quantification of multi-component signals in diverse biological samples using phasor analysis.
  • Identification of 3 main T2 components and 3 apparent diffusion coefficients in human brain images.
  • Distinction of 5 main contributing spectral shapes in human prostate images.
  • Demonstration of the method's applicability to undersampled qMRI data.

Conclusions:

  • Phasor representation offers a novel, model-free approach to effectively disentangle and quantify signals from multiple components in qMRI.
  • The method is fast, accurate, and versatile, showing successful application across various biological tissues and imaging conditions, including undersampled data.
  • Phasor analysis significantly advances the capabilities of qMRI for precise biological and medical investigations.