Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Phasor Arithmetics01:13

Phasor Arithmetics

612
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...
612
Phasors01:12

Phasors

936
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...
936
Phasor Relationships for Circuit Elements01:16

Phasor Relationships for Circuit Elements

867
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:
867
Kirchoff's Laws using Phasors01:12

Kirchoff's Laws using Phasors

684
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....
684
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

1.9K
Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a...
1.9K
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

535
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
535

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

AI-based histopathology analysis predicts checkpoint inhibitor response in advanced melanoma and identifies patterns associated with response.

European journal of cancer (Oxford, England : 1990)·2026
Same author

Postoperative ischemia and neurological deficits after glioma resection: A systematic review and meta-analysis.

Neuro-oncology practice·2026
Same author

Negative impact of hippocampal radiotherapy dose on memory function in patients with brain metastases.

Neuro-oncology practice·2026
Same author

Structural Fiber Tract Alterations in Relation to Surgery in Children With a Posterior Fossa Tumor.

NMR in biomedicine·2026
Same author

Study protocol for a multicenter phase II prospective externally controlled non-inferiority trial of hypofractionated re-irradiation in patients with recurrent high-grade glioma (RISinG).

PloS one·2026
Same author

DeepMultiConnectome: Deep multi-task prediction of structural connectomes directly from diffusion MRI tractography.

NeuroImage·2026
Same journal

Reproducibility of Splanchnic Blood Flow Measured Using Phase-Contrast MRI.

NMR in biomedicine·2026
Same journal

Restriction-Weighted Q-Space Trajectory Imaging (ResQ): Toward Mapping Diffusion-Time Effects With Tensor-Valued Diffusion Encoding in Human Prostate Cancer Xenografts.

NMR in biomedicine·2026
Same journal

In Vivo Quantitative Detection of PEGylated Macromolecules by Magnetic Resonance Spectroscopy.

NMR in biomedicine·2026
Same journal

Metabolic Assessment in Human Pluripotent Stem Cell-Derived Cerebral Organoids Using HR-MAS NMR Spectroscopy.

NMR in biomedicine·2026
Same journal

Characterizing Metabolic and Compositional Heterogeneity of Calf Muscle Using CEST MRI at 3 T.

NMR in biomedicine·2026
Same journal

Estimating the Sodium Content: A Case Series of Benign and Malignant Renal Tumours Using <sup>23</sup>Na-MRI at 3 T.

NMR in biomedicine·2026
See all related articles

Related Experiment Video

Updated: Dec 14, 2025

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer
07:54

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

Published on: October 15, 2015

8.3K

Untangling the diffusion signal using the phasor transform.

Michael J van Rijssel1, Martijn Froeling1, Astrid L H M W van Lier1

  • 1Center for Image Sciences, UMC Utrecht, Utrecht, the Netherlands.

NMR in Biomedicine
|July 24, 2020
PubMed
Summary
This summary is machine-generated.

The phasor technique, adapted from microscopy, shows promise for analyzing diffusion-weighted MRI signals in glioblastoma. While not superior for all decay model fitting, it offers improved precision for intravoxel incoherent motion (IVIM) parameters.

Keywords:
diffusion fraction estimationdiffusion modelingintravoxel incoherent motionmulti-compartment diffusion modelingphasor representationtissue characterization

More Related Videos

Author Spotlight: Standardizing Spheroid Formation Methods for Metabolic and Oxygenation Analysis Using Fluorescence Lifetime Imaging Microscopy
08:43

Author Spotlight: Standardizing Spheroid Formation Methods for Metabolic and Oxygenation Analysis Using Fluorescence Lifetime Imaging Microscopy

Published on: August 9, 2024

1.6K
Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells
05:56

Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells

Published on: November 12, 2020

3.1K

Related Experiment Videos

Last Updated: Dec 14, 2025

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer
07:54

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

Published on: October 15, 2015

8.3K
Author Spotlight: Standardizing Spheroid Formation Methods for Metabolic and Oxygenation Analysis Using Fluorescence Lifetime Imaging Microscopy
08:43

Author Spotlight: Standardizing Spheroid Formation Methods for Metabolic and Oxygenation Analysis Using Fluorescence Lifetime Imaging Microscopy

Published on: August 9, 2024

1.6K
Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells
05:56

Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells

Published on: November 12, 2020

3.1K

Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Biomedical Optics
  • Medical Physics

Background:

  • Separating complex decay signals in diffusion-weighted MRI is challenging.
  • The phasor technique, successful in optical microscopy for separating signals based on lifetime, was recently proposed for diffusion MRI.
  • Investigating its utility for fitting decay models and visualizing decay rates is crucial.

Purpose of the Study:

  • To evaluate the added value of the phasor technique for fitting diffusion-weighted MRI decay models and visualizing decay rates.
  • To compare phasor-based fitting with established methods like linear least squares (LLS), nonlinear least squares (NLLS), and segmented fitting (SF).
  • To assess the phasor technique's performance in glioblastoma patients and simulated data.

Main Methods:

  • Phasor visualization applied to diffusion-weighted scans from five glioblastoma patients.
  • Simulations to assess the influence of diffusivity values and b-values on three-component model fitting ('unmixing') using phasor-based and LLS fits.
  • Comparison of phasor-based intravoxel incoherent motion (IVIM) fitting with NLLS and SF methods for accuracy and precision.

Main Results:

  • Phasor visualization revealed a distinct cluster in two glioblastoma patients, correlating with tumor enhancement on FLAIR images.
  • Phasor-based fitting demonstrated higher precision for IVIM parameters f (perfusion fraction) and D (diffusivity) compared to NLLS and SF.
  • Linear least squares (LLS) fitting slightly outperformed phasor-based fitting for 'unmixing' scenarios.

Conclusions:

  • The phasor technique offers valuable insights for diffusion-weighted MRI, particularly in identifying potential tumor regions through visualization.
  • While its utility for general decay model fitting is less pronounced, the phasor approach enhances precision for specific models like IVIM.
  • Further research may integrate phasor-derived information into advanced fitting routines for improved diagnostic capabilities.