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Topics spatial encoding - part 2

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Slice Selection z y x 0 imaging plane z gradient

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Slice Selection slice thickness is determined by gradient strength RF bandwidth t1t1t1t1 t2t2t2t2 t3t3t3t3

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Slice Selection Selection of an axial slice is accomplished by the z gradient. z gradient direction graph of the z magnetic gradient z-axis

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Slice Selection slice location is determined by the null point of the z gradient RF bandwidth slice 1 slice 2slice 3

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Frequency Encoding Within the imaging plane, a small gradient is applied left to right to allow for spatial encoding in the x direction. Tissues on the left will have a slightly higher resonance frequency than tissues on the right. The superposition of an x gradient on the patient is called frequency encoding. Frequency encoding enables spatial localization in the L-R direction only.

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Frequency Encoding z y x x gradient higher frequency lower frequency L R

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Frequency Encoding RF signal from entire slice A/D conversion, 256 points 1 line of k-space

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Phase Encoding An additional gradient is applied in the y direction to encode the image in the remaining direction. Because the x gradient alters the frequencies in the received signal according to spatial location, the y gradient must alter the phase of the signal. Thus, the points of k-space are revealed by recording the digitized RF signal after a phase encoding gradient application.

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Phase Encoding The technique of phase encoding the second dimension in the imaging plane is sometimes referred to as spin warping. The phase encoding gradient is “stepped” during the acquisition of image data for a single slice. Each step provides a unique phase encoding. For a 256 x 256 square image matrix, 256 unique phase encodings must be performed for each image slice. The second 256 points in the x direction are obtained by A to D conversion of the received signal.

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Phase Encoding z y x y gradient, phase step #192 y gradient, phase step #64

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Phase Encoding 2D k-space matrix gradient strength +128 RF in RF out A/D conversion gradient strength N RF in RF out A/D conversion gradient strength -128 RF in RF out A/D conversion END BEGIN line 128 line N line -128

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Spin Echo Imaging RF z gradient echo echo echo y gradient x gradient slice select phase readout

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Spin Echo Imaging view -128 view -55 view 40 k-space 256 x 256 points row 40 row -55 row -128 A/D, 256 points k x = frequency k y = phase

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Acquisition of spatially encoded data as described allows for reconstruction of the MR image. The frequency and phase data are acquired and form points in a 2D array. Reconstruction of the image is provided by 2D inverse Fourier transform of the 2D array. This method of spatially encoding the MR image is called 2D FT imaging. MR Image Reconstruction

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Discrete Fourier Transform F(k x,k y ) is the 2D discrete Fourier transform of the image f(x,y) x y f(x,y) kxkx kyky k-space F(k x,k y ) MR image

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Image Resolution and Phase Encoding Resolution is always maximum in the frequency encoding direction because the MR signal is always digitized into 256 points. Resolution can vary in the phase encoding direction depending on the number of phase steps used to acquire the image. Because each phase encoding requires a separate 90 and 180 degree pulse, image acquisition time is proportional to the number of phase encode steps.

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Image Acquisition Time

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Example, TR 2000, 192 phase steps, 1 NEX imaging time = 6.4 minutes At this rate, it would take 128 minutes to do an average 20 slice exam. Because TR is typically much longer than TE, we can acquire the data for the other slices between the 90 degree RF pulses. Image Acquisition Time

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Multi-slice Imaging echo echo echo echo slice 1 slice 2 slice 3 TR TE

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The maximum number of slices that can be obtained in a single acquisition is calculated as follows: Multi-slice Imaging

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k-space Traversal The most important phase encoding information is centered around the middle of k-space. Typically, k-space is filled in an orderly manner, beginning with the returned echos obtained at the maximum negative y gradient strength and continuing to the maximum positive value.

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For images obtained with less than 256 views, the number of phase encodings is evenly divided between positive and negative values centered around zero. Images reconstructed with less than 256 phase encodings have less detail in the phase encoding direction. k-space Traversal

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kxkx kyky decreased resolution

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Because k-space is symmetrical, one half of the space can be determined from knowledge of the other half. Imaging time can be reduced by a factor of 2 by collecting either the positive or the negative phase encodings and filling the remainder of k-space with the mirrored data. Half Fourier Imaging

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kxkx kyky kxkx kyky full resolution

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This technique is sometimes referred to as ‘half NEX’ imaging or ‘PCS’ (phase conjugate symmetry). Penalty: reduced signal decreases the signal to noise ratio, typically by a factor of Half Fourier Imaging

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The frequency half of k-space can also be mirrored. This technique is called fractional echo or ‘RCS’ (read conjugate symmetry). Decreased read time enables more slices per acquisition at the expense of reduced signal. Half Fourier Imaging

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kxkx kyky kxkx kyky normalphase symmetry kxkx kyky read symmetry

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kxkx kyky ? kxkx kyky kxkx kyky kxkx kyky

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3D Acquisition 3D is an extension of the 2D technique. advantages: true contiguous slices very thin slices (< 1 mm) no partial volume effects volume data acquisition disadvantages: gradient echo imaging only (3D FSE now available) motion sensitive

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3D Acquisition no slice select gradient entire volume of tissue is excited second phase encoding gradient replaces the slice select gradient after the intial RF pulse ( ), both y and z gradients are applied, followed by application of the x gradient during readout (echo)

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the z gradient is changed only after all of the y gradient phase encodes have generated an echo, then the z gradient is stepped and the y gradient phase encodes are repeated 3D Acquisition

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3D Imaging RF z gradient echo y gradient x gradient slice select phase readout

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3D Imaging kxkx kyky z step 1 z step 4 z step N

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