Table of contents
1. General steps of phase difference map reconstruction and the main value range of arctangent function
MRI is a phase-sensitive imaging modality , and each pixel value in the complex image after Fourier transform of the original MR data has a mode and a phase . Standard modulo reconstruction discards the phase and builds the image using only the values. However,There is useful information encoded in the phase.
For example, the phase map can generate B0 uniformity information, which can be used for shimming; it can also generate fluid flow information, which can be used for phase-sensitive angiography; phase information can also be used for in vivo MR temperature distribution measurement and MR elastography.
Collect two independent data sets, and then form a phase difference map , justCan solve the phase map pollution problem. The so-called phase difference map is obtained by subtracting a pair of phase image pixels one by one . The purpose is to highlight the desired phase and cancel the harmful phase at the same time .
Extracting physical parameter values from phase images is not a simple matter. becauseMany factors contribute unwanted phase to the phase image, such as gradient eddy currents , chemical shifts , magnetic susceptibility changes , and accompanying fields , etc. These unwanted contributions make the phase map polluted and difficult to interpret, and the desired information is often overwhelmed by these harmful phases.
phase difference reconstructionThe core of is to perform an arctangent operation on each voxel to generate a phase image (map). The output of the arctangent function is defined in a limited range, called the principal value range . In the field of MRI, the phase range is generally extended to (-π, π] by a four-quadrant arctangent function. Phase values outside the range of principal values are represented by a value within the principal value, calledAliasing(alias). Aliasing in the phase map is accompanied by discontinuities (jumps at ±π) , calledphase wrapping.
To improve computational efficiency and minimize the number of phase warpings, an optimal phase difference reconstruction should perform only one arctangent operation per pixel. Also, because of the discontinuity, it is desirable to perform operations such as phased array multi-coil data combination operations and concomitant field phase correction operations before computing the arctangent.
Second, the arctangent operation
Assume that two K-space data have been collected and want to generate a phase difference map. The data sets are first sign-alternated and zero-filled, and then undergo Fourier transforms separately to generate two independent complex images .
The process of restoring the phase difference value in the range (-π,π] to its true value is calledphase unwrapping.
Because eddy currents depend on the design and calibration of the MR hardware, it is often difficult to predict the exact spatial dependence of the resulting phase error.
3. Correction of predictable phase error and accompanying field
After the phase difference image is formed, harmful phase errors often remain . Phase contamination, such as that caused by gradient vortices, is problematic for phase contrast angiography. Such phase errors are therefore often corrected by experimental fit .
For example, in a region where there should be zero phase difference, such as stationary tissue in a phase contrast angiogram, a constant phase and linear phase can be determined by polynomial fitting of the phase difference image. Since the fitted phases are presumably entirely due to system imperfections such as eddy currents, postprocessing can be used to remove them.
Other phase errors , such as those arising from accompanying fields, can be predicted precisely becauseThey are fundamental physical effects (can be described by Maxwell's equations), and it is advantageous to correct for these phase errors before computing the arctangent.
Another advantage of applying the image warp correction separately to the real and virtual images before the arctangent operation is that any transformation of the image intensity caused by the warp correction algorithm does not affect the phase difference map .
4. Graphic deformation correction
Correction operations for image distortion caused by gradient nonlinearity can also be used for phase difference images . For multi-coil combinations, it is even more advisable to apply image distortion correction before the arctangent operation. This is because the image warping correction is an orthographic projection using an interpolation method such as cubic splines . If image distortion correction is applied after the arctangent operation, phase wrapping will be encountered and the discontinuity of its transitions in the image will cause unwanted overshoot.
A drawback of the interpolated phase image : If the phase image is interpolated (such as image distortion correction or rectangular field of view reduction), overshoot (arrow) will occur at the aliasing boundary, and this interpolated phase image is not suitable for solution Winding treatment .It is preferable to interpolate the real and virtual images before the arctangent instead of interpolating the phase image。