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Phase Encoding Gradient MRI | MRI Signal Localisation | MRI Physics Course #9
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Phase Encoding Gradient MRI | MRI Signal Localisation | MRI Physics Course #9

Introduction and Slice Selection Gradient

In this section, the speaker introduces the topic of localizing signal within an MRI image. They discuss how a specific slice along the z-axis can be selected using a slice selection gradient.

Slice Selection Gradient

  • A slice selection gradient is used to select a specific slice along the z-axis in an MRI image.
  • Spins within the selected slice resonate or process in phase with one another.

Frequency Encoding Gradient

This section focuses on creating a frequency differential along the x-axis of the selected slice using a frequency encoding gradient.

Frequency Encoding Gradient

  • A frequency encoding gradient is applied over the time that signal is being sampled.
  • The spins process faster at one end of the x-axis compared to the other end, resulting in a gradient of frequencies along that axis.
  • The net magnetization vector of the entire slice is measured during data acquisition time, which occurs during the frequency encoding gradient.
  • The analog signal obtained during data acquisition is converted into discrete digital values through multiple sampling.
  • The number of samples determines the number of frequencies that can be delineated along the x-axis.

Data Acquisition and Inverse Fourier Transformation

This section explains how data acquisition occurs during the frequency encoding gradient and how an inverse Fourier transformation can be performed on the recorded signal.

Data Acquisition and Digital Signal Conversion

  • The net magnetization vector signal obtained during data acquisition represents different frequencies contributing to it.
  • Multiple samples are taken to convert this analog signal into a digitized or digital signal.

Inverse Fourier Transformation

  • A one-dimensional inverse Fourier transformation calculates the frequencies responsible for generating the net magnetization vector.
  • The change in net magnetization vector over time is unique to specific frequencies with varying amplitudes.
  • The frequencies obtained from the net magnetization vector signal are placed along the x-axis, corresponding to different x-axis locations.

Rephasing and Defacing

This section clarifies the concept of rephasing and defacing in relation to the 180-degree radio frequency pulse and its impact on signal processing.

Rephasing and Defacing

  • The 180-degree radio frequency pulse used in slice selection causes spins to dephase and then rephase at a specific time (te).
  • This results in an increase in signal followed by free induction decay.
  • The increase in signal helps account for local magnetic field inhomogeneities, making it more similar to true T2 decay.

Sampling Frequencies and Image Encoding

This section discusses the sampling of analog signals during data acquisition and how frequencies are organized to encode an image.

Sampling Frequencies

  • Analog signals can be sampled multiple times during data acquisition, typically using 128 or 256 samples.
  • The frequencies contributing to the signal remain the same based on the x-axis frequency encoding gradient.

Image Encoding

  • The combination of different frequencies obtained from sampling is used to delineate those frequencies along the x-axis.
  • By ordering frequencies from low to high, an entire column signal along the selected slice's x-axis can be obtained.
  • A one-dimensional Fourier transformation encodes these specific frequencies contributing to the image.

One-Dimensional Inverse Fourier Transformation

This section explains how a one-dimensional inverse Fourier transformation is used to create an image based on data acquired during frequency encoding gradient.

One-Dimensional Inverse Fourier Transformation

  • Using the data acquired during the frequency encoding gradient, an image can be created based on the signal from the entire column at different x-axis locations.
  • The frequencies are ordered from low to high, providing signals for the selected slice's x-axis.
  • This transformation is an inverse one-dimensional Fourier transformation.

Localization Along Y-Axis

This section explores how signals can be delineated based on their y-axis location within a slice.

Spins in Slice without Frequency Encoding Gradients

  • When no frequency encoding gradients are applied, spins within a slice resonate in phase with each other at the same frequency.
  • At this time, only the main magnetic field affects magnetization in the slice.

Conclusion

The speaker concludes by highlighting that further exploration will focus on delineating signals based on their y-axis location within a slice.

Future Focus

  • Delineating signals along the y-axis will be explored in subsequent talks.

Calculation of Y-Axis Contributions to Net Magnetization Vector

This section explains how to calculate the y-axis contributions to the net magnetization vector.

Calculating Y-Axis Contributions

  • The signal represents the net magnetization vector over time.
  • Phase encoding is applied in the y-axis direction.
  • The anatomy being imaged remains unchanged, only the amount of phase introduced into the y-axis changes.
  • One-dimensional inverse Fourier transformation can be used to calculate x-axis locations and signal amplitude for each x-axis location.
  • Increasing the phase encoding gradient along the y-axis leads to further dephasing and a reduction in signal.

Phase Encoding and Localization in Y-Axis Direction

This section discusses phase encoding and localization in the y-axis direction.

Increased Phase Encoding Gradient

  • Increasing the phase encoding gradient along the y-axis results in more dephasing and a further reduction in signal.
  • Spins closer to null points experience less phase change, while those near the periphery of the slice experience more phase change.
  • The degree of phase change helps localize signals from different y-axis locations.

Opposite Direction Phase Encoding Gradient

  • Applying a phase encoding gradient in the opposite direction causes dephasing in the opposite direction as well.
  • Signal loss occurs, but one-dimensional inverse Fourier transformation can still be used to obtain x-axis locations with specific signals.

Multiple Phase Encoding Steps for Resolution

This section explains how multiple phase encoding steps are used to achieve resolution in the y-axis direction.

Repeating Sequence for Each Phase Encoding Step

  • To add resolution in the y-axis direction, each additional phase encoding step requires repeating the sequence.
  • Longer time is needed as each cycle includes a different phase encoding gradient before acquiring data at frequency encoding gradients.

Determining Number of Pixels

  • The number of phase encoding steps determines the number of pixels that can be delineated in the y-axis of the image.

Organization of Acquired Data

This section discusses how acquired data is organized.

Using Different Phase Strengths

  • Different magnitudes of phase encoding are applied to generate different signals.
  • Grayscale values represent numerical data points, not pixels.
  • By convention, unfazed samples are acquired first, followed by small amounts of positive and negative phase for each cycle.

Summary and Conclusion

This section provides a summary and conclusion.

Generating Signals for Y-Axis Resolution

  • Multiple phase encoding steps with different magnitudes are used to acquire data points for y-axis resolution.
  • The organization of acquired signals is based on the amount of phase used.
  • Each cycle introduces a small amount of positive or negative phase to generate different lines of data.

Number of Phase Encoding Steps

In this section, the speaker discusses the number of phase encoding steps and their relationship to the data acquisition process.

Phase Encoding Steps

  • The number of phase encoding steps is equal to the number of times the phase encoding gradient is applied during data acquisition.
  • These phase encoding steps affect the re-phasing of spins and contribute to the overall signal generation.

Frequency Encoding Gradient

This section focuses on the frequency encoding gradient and its impact on spin re-phasing.

Frequency Encoding Gradient

  • Before applying the frequency encoding gradient, spins are allowed to re-phase as their frequencies change.
  • At the midpoint of this gradient, all spins will be perfectly in phase with each other.
  • The assumption is made that a specific amount of phase application can cause two pixels to be perfectly out of phase with each other.

Signal Values and Data Acquisition

Here, the speaker explains how signal values are obtained during data acquisition and emphasizes the importance of considering both k-space data and frequency encoding data.

Signal Values and Data Acquisition

  • The acquired data represents all measured signals throughout the entire data acquisition period.
  • The k-space data, along with frequency encoding data, is used to determine signal contributions from specific locations at given periods of time.
  • Two-dimensional Fourier transformation combines these datasets to create images displayed on computer screens.

Practical Example Using Signal Contributions

This section provides a practical example demonstrating how signal contributions from different pixels are calculated using k-space and frequency encoding data.

Practical Example

  • By using k-space and frequency encoding data, measurable signals can be calculated from specific x-axis columns.
  • The assumption is made that the signal contribution comes only from two pixels, although it actually comes from multiple pixels along the y-axis.
  • Signal values are assigned numerical values, such as 14, to represent their amplitudes.

Amplitude Calculation and Phasing Gradient

In this section, the speaker discusses how amplitude calculations are affected by phasing gradients.

Amplitude Calculation and Phasing Gradient

  • The net magnetization vectors of signals at the same frequency but different phases are combined to calculate the measured signal's amplitude.
  • By applying a specific phasing gradient, signals can become 180 degrees out of phase with each other.
  • The amplitude of the total signal is obtained by adding or subtracting the amplitudes of individual signals.

De-phasing and Signal Calculation

This section explores how de-phasing affects signal calculation and introduces a formula for determining signal amplitudes.

De-phasing and Signal Calculation

  • Signals that have undergone de-phasing due to a phase encoding gradient will result in lower amplitudes compared to the original signals.
  • The frequencies remain the same, but they are now 180 degrees out of phase with each other.
  • A formula is used to calculate the measured signal's amplitude based on subtracting one signal's amplitude from another.

Conclusion

The transcript provides an explanation of phase encoding steps, frequency encoding gradients, data acquisition processes, and signal calculations. It emphasizes the importance of considering both k-space data and frequency encoding data in obtaining accurate measurements.

Pixel Values

This section discusses the pixel values in the transcript.

Pixel Values

  • We have a pixel value of 10 here.
  • Another pixel value is mentioned as 4.

The transcript does not provide any further information about the significance or context of these pixel values.

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