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Spatial and Temporal Resolution in Cardiovascular MR Imaging: Review and Recommendations¹

¹ From the Applied Science Laboratory, GE Medical Systems, Baltimore, Md (G.S.S.); and Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, MRI Room 143 (Nelson Basement), 600 N Wolfe St, Baltimore, MD 21287 (G.S.S., D.A.B.). Received December 10, 2003; revision requested February 19, 2004; revision received April 12; accepted May 24. Address correspondence to D.A.B. (e-mail: dbluemke@jhmi.edu).

View larger version (20K): [in a new window]   Figure 1. Schematic of the k-space representation of MR raw data.

View larger version (31K): [in a new window]   Figure 2a. (a) Hypothetical one-dimensional object consisting of only two spatial sinusoids. (b) Continuous Fourier transform of the object contains nonzero values only at the frequencies of the two sinusoids. (c) The k-space raw data are essentially a sampled version of the Fourier transform in b. Imaging parameters determine the frequency and extent of the sampling. In this case, the spatial resolution was chosen such that sampling was performed only out to kxmax = ±32; therefore, the high-frequency information at kx = ±40 are not present in the raw data. (d) Plot of the DTFT of the data in c (dark curve). The DTFT function (Eq [13]) represents the sampled raw data with infinite spatial resolution; however, it does not contain the high-frequency components present in the original object (light curve and part a).

View larger version (14K): [in a new window]   Figure 2b. (a) Hypothetical one-dimensional object consisting of only two spatial sinusoids. (b) Continuous Fourier transform of the object contains nonzero values only at the frequencies of the two sinusoids. (c) The k-space raw data are essentially a sampled version of the Fourier transform in b. Imaging parameters determine the frequency and extent of the sampling. In this case, the spatial resolution was chosen such that sampling was performed only out to kxmax = ±32; therefore, the high-frequency information at kx = ±40 are not present in the raw data. (d) Plot of the DTFT of the data in c (dark curve). The DTFT function (Eq [13]) represents the sampled raw data with infinite spatial resolution; however, it does not contain the high-frequency components present in the original object (light curve and part a).

View larger version (13K): [in a new window]   Figure 2c. (a) Hypothetical one-dimensional object consisting of only two spatial sinusoids. (b) Continuous Fourier transform of the object contains nonzero values only at the frequencies of the two sinusoids. (c) The k-space raw data are essentially a sampled version of the Fourier transform in b. Imaging parameters determine the frequency and extent of the sampling. In this case, the spatial resolution was chosen such that sampling was performed only out to kxmax = ±32; therefore, the high-frequency information at kx = ±40 are not present in the raw data. (d) Plot of the DTFT of the data in c (dark curve). The DTFT function (Eq [13]) represents the sampled raw data with infinite spatial resolution; however, it does not contain the high-frequency components present in the original object (light curve and part a).

View larger version (26K): [in a new window]   Figure 2d. (a) Hypothetical one-dimensional object consisting of only two spatial sinusoids. (b) Continuous Fourier transform of the object contains nonzero values only at the frequencies of the two sinusoids. (c) The k-space raw data are essentially a sampled version of the Fourier transform in b. Imaging parameters determine the frequency and extent of the sampling. In this case, the spatial resolution was chosen such that sampling was performed only out to kxmax = ±32; therefore, the high-frequency information at kx = ±40 are not present in the raw data. (d) Plot of the DTFT of the data in c (dark curve). The DTFT function (Eq [13]) represents the sampled raw data with infinite spatial resolution; however, it does not contain the high-frequency components present in the original object (light curve and part a).

View larger version (16K): [in a new window]   Figure 3a. (a) The ideal reconstruction of f[x] = {1, 1, 1, 1, 1, 1} with use of the DTFT is a continuous and periodic function of x (periodicity not shown). (b) Six-point DFT reconstruction of the same data.

View larger version (8K): [in a new window]   Figure 3b. (a) The ideal reconstruction of f[x] = {1, 1, 1, 1, 1, 1} with use of the DTFT is a continuous and periodic function of x (periodicity not shown). (b) Six-point DFT reconstruction of the same data.

View larger version (13K): [in a new window]   Figure 4a. By using the same six-point "raw data" as in Figure 3, increasing the size of the DFT to (a) eight points, (b) 16 points, (c) 32 points, and (d) 64 points causes the reconstructed image to more closely resemble the ideal reconstruction in Figure 3a.

View larger version (16K): [in a new window]   Figure 4b. By using the same six-point "raw data" as in Figure 3, increasing the size of the DFT to (a) eight points, (b) 16 points, (c) 32 points, and (d) 64 points causes the reconstructed image to more closely resemble the ideal reconstruction in Figure 3a.

View larger version (20K): [in a new window]   Figure 4c. By using the same six-point "raw data" as in Figure 3, increasing the size of the DFT to (a) eight points, (b) 16 points, (c) 32 points, and (d) 64 points causes the reconstructed image to more closely resemble the ideal reconstruction in Figure 3a.

View larger version (25K): [in a new window]   Figure 4d. By using the same six-point "raw data" as in Figure 3, increasing the size of the DFT to (a) eight points, (b) 16 points, (c) 32 points, and (d) 64 points causes the reconstructed image to more closely resemble the ideal reconstruction in Figure 3a.

View larger version (44K): [in a new window]   Figure 5a. Phantom images demonstrate the effect of DFT size. Both images were acquired with identical imaging parameters (256 x 256 acquisition matrix, 20-cm FOV, 0.78-mm nominal resolution). (a) Reconstruction with a 256 x 256 DFT. (b) Reconstruction with a 512 x 512 DFT and zero filling. The zero-filled reconstruction is a better representation of the acquired resolution than is the 256 x 256 DFT.

View larger version (51K): [in a new window]   Figure 5b. Phantom images demonstrate the effect of DFT size. Both images were acquired with identical imaging parameters (256 x 256 acquisition matrix, 20-cm FOV, 0.78-mm nominal resolution). (a) Reconstruction with a 256 x 256 DFT. (b) Reconstruction with a 512 x 512 DFT and zero filling. The zero-filled reconstruction is a better representation of the acquired resolution than is the 256 x 256 DFT.

View larger version (31K): [in a new window]   Figure 6a. View sharing. (a) Two segmented cine acquisitions (VPS = 8) performed with identical imaging parameters. Temporal resolution t equals VPS · TR. The only difference is that data acquisition and hence the cardiac phase images in acquisition 2 (Acq 2) are delayed by t/2 with respect to acquisition 1 (Acq 1). (b) Offset data from acquisition 2 in a can be created from data from acquisition 1. By regrouping cardiac phase data, additional data points (phases 1, 2, and 3) can be reconstructed between original data points (phases 1, 2, 3, and 4). Although the effective time between adjacent reconstructed images is t/2, the temporal resolution for each cardiac phase image is still t.

View larger version (21K): [in a new window]   Figure 6b. View sharing. (a) Two segmented cine acquisitions (VPS = 8) performed with identical imaging parameters. Temporal resolution t equals VPS · TR. The only difference is that data acquisition and hence the cardiac phase images in acquisition 2 (Acq 2) are delayed by t/2 with respect to acquisition 1 (Acq 1). (b) Offset data from acquisition 2 in a can be created from data from acquisition 1. By regrouping cardiac phase data, additional data points (phases 1, 2, and 3) can be reconstructed between original data points (phases 1, 2, 3, and 4). Although the effective time between adjacent reconstructed images is t/2, the temporal resolution for each cardiac phase image is still t.