SNR-optimized myocardial perfusion imaging using parallel acquisition for effective density-weighted saturation recovery imaging

Available online at www.sciencedirect.com

Magnetic Resonance Imaging 28 (2010) 341 – 350

SNR-optimized myocardial perfusion imaging using parallel acquisition for effective density-weighted saturation recovery imaging☆,☆☆ Marcel Gutberlet a,⁎, Oliver Geier b , Daniel Stäb a , Christian Ritter a , Meinrad Beer a , Dietbert Hahn a , Herbert Köstler a a Institut für Röntgendiagnostik, Universität Würzburg, 97080 Würzburg, Germany Department of Medical Physics, Rikshospitalet University Hospital, N-0027 Oslo, Norway Received 3 March 2009; revised 28 July 2009; accepted 26 November 2009

b

Abstract The concept of density-weighted imaging and parallel acquisition for effective density-weighted (PLANED) imaging was transferred to saturation recovery (SR) sequences, in order to increase the SNR in first-pass myocardial perfusion imaging. Filtering in combination with density-weighted imaging allows SNR-optimized data weighting and the free choice of the corresponding spatial response function (SRF) simultaneously. This method was evaluated in simulations and applied successfully to phantom and in vivo first-pass myocardial perfusion studies. Unfiltered, Cartesian sampled images were compared to images acquired with SR-PLANED, which has been adjusted to result in an identical SRF as the Cartesian imaging. SNR-optimized SR-PLANED imaging improved the SNR up to 15% without changing acquisition time, the SRF or the field of view (FOV). The presented method provides high image quality and optimized SNR for first-pass myocardial perfusion imaging. © 2010 Elsevier Inc. All rights reserved. Keywords: First-pass myocardial perfusion imaging; Density-weighted imaging; Parallel imaging; Spatial response function; Signal-to-noise ratio

1. Introduction Fast low-angle shot (FLASH) [1] or steady-state free precession (SSFP) [2] single-shot SR sequences are commonly used in first-pass myocardial perfusion imaging. These single-shot SR sequences suffer from a low signal-tonoise ratio (SNR) because of the reduced net magnetization due to the magnetization preparation and short acquisition times of typically less than 200 ms per image. To achieve an optimal SNR in a single-shot SR image, a proper data weighting of the acquired echoes is required. This can be ☆ This manuscript was approved by all contributing authors and they attested that the manuscript represents honest work. All authors fulfill the requirement for authorship. This manuscript has not been and will not be published in any other journal. There is no conflict of interest for any of the contributing authors. ☆☆ Grant sponsor: Deutsche Forschungsgemeinschaft (DFG). Grant numbers: KO 2938/1-2, KO 2938/2-1. ⁎ Corresponding author. Tel.: +49 931 201 34328; fax: +49 931 201 34471. E-mail address: [email protected] (M. Gutberlet).

0730–725X/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.mri.2009.11.007

accomplished by application of a k-space filter in the postprocessing [3]. The spatial response function (SRF) [4] describes the spatial origin of the signal contributing to a position in the image. Corresponding terms used in imaging are point spread function or impulse response. The Fourier transform of the SRF is the modulation transfer function (MTF). In MRI, the MTF corresponds to the k-space weighting. It is determined by the signal weighting caused by the magnetization preparation, the sampling density used in the acquisition and the filter applied in the postprocessing. In this context, the term “signal weighting” is used for the varying signal amplitude generated by the magnetization preparation. In saturation recovery (SR) sequences, the signal weighting is determined by the T1 relaxation during the acquisition after the application of a 90° preparation pulse. For example, sampling the k-space with constant sampling density in reverse centric order [5] leads to a triangularly shaped k-space weighting for short acquisition times. Here, the resulting signal weighting, induced by the magnetization preparation, works like a low-pass filter, leading to an SRF with reduced side lobes. However, if an SNR optimizing

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filter is applied in the postprocessing, the SRF degrades, leading to blurring and Gibbs ringing artifacts. Gibbs ringing seems to be a cause of the dark rim artifact [6], which was noticed in first-pass myocardial perfusion imaging. The severity of Gibbs ringing artifacts depends on the amplitude of the side lobes of the SRF. Therefore, a side lobe reduction of the SRF should decrease the Gibbs ringing. In addition to postprocessing filtering and changing the acquisition order in prepared sequences, there are several other techniques allowing SRF manipulation. Signal weighting by varying RF-pulse amplitudes [7] or a varying sampling density, like in acquisition [3,4,8–11] and density-weighted (DW) imaging [12,13], has been used for imaging sequences with constant signal weighting to improve the SRF in phase-encoding direction. In case of a Cartesian sampling for an imaging sequence with constant signal weighting, postprocessing filtering can be applied in order to improve the SRF. As all samples have the same noise, the data must be weighted uniformly in the reconstruction to achieve the optimal SNR. For example, for a Hanning p shaped ffiffiffiffiffiffiffiffi filter (Fig. 1) the noise increases by a factor of 3=2c1:22 due to the inappropriate data weighting caused by filtering. In acquisition weighted imaging, the k-space is sampled on a Cartesian grid and the SRF is changed by varying the number of acquisitions per phase-encoding step proportional to the favored k-space weighting (Fig. 1). Because a constant filter is applied in the postprocessing, all samples are weighted equally, resulting in an optimal SNR. However, since acquisition weighting requires several scans of the same phase-encoding steps, it is useful in applications where averaging is needed, such as in 31P chemical shift imaging [9].

Fig. 1. For imaging sequences with constant signal weighting using a Cartesian sampling, a k-space filter (gray line) is applied in the postprocessing, which is proportional to the favored k-space weighting w (k) (black dashed line), resulting in an improved SRF. In acquisition weighted imaging (ACS), the same SRF is achieved by choosing the number of measurements at the sampled k-space positions proportional to the favored k-space weighting. In DW imaging, k-space is sampled with a nonCartesian sampling density, which is proportional to the favored k-space weighting. In acquisition and DW imaging, the SNR is not degraded because all samples are uniformly weighted in the reconstruction.

In DW imaging, the SRF is adjusted by acquiring k-space with a sampling density, which is proportional to the favored k-space weighting (Fig. 1). As a constant filter is used in the reconstruction, the optimal SNR is achieved. But because of the varying sampling intervals in k-space in DW imaging, either the Nyquist criterion is violated in some regions of kspace, reducing the effective field of view (FOV), or the minimum total acquisition time is longer than in the corresponding Cartesian imaging sequence. Parallel acquisition for effective DW (PLANED) imaging [14] overcomes this problem by reconstructing the undersampled k-space intervals with parallel imaging techniques [15–18]. The SRF can also be improved by acquiring data in kspace on non-Cartesian trajectories like spirals [19,20]. The major problem of these techniques is their sensitivity to artifacts. In contrast, all methods using constant and equal gradients during all readouts, similar to spin-warp sequences, are more robust against these artifacts. Consequently, this work concentrates on SRF improvement in phase-encoding direction for sequences with constant readout gradients. Therefore, the aim of this work was to transfer the concept of PLANED imaging to the signal weighted SR sequences allowing SNR optimization by postprocessing filtering without degrading the SRF. The method was evaluated in simulations and phantom studies and applied to first-pass myocardial perfusion imaging. 2. Theory Single-shot SR sequences start with a 90° preparation pulse and crusher gradients to spoil the magnetization. During the recovery of the longitudinal magnetization a fast imaging sequence is applied. The recovery of the longitudinal magnetization results in an exponential [21,22] signal weighting of the consecutively measured echoes. For acquisition times that are short compared to the apparent relaxation time T1⁎, this signal can be approximated  increase4  by a linear function: Si = 1−exp−ti =T1 cti =T1⁎ . Since the acquisition times in single-shot SR myocardial perfusion imaging are very short, this work focuses on a linearly increasing signal in SR sequences. The signal acquired in k-space is a product of the Fourier transform Mk of magnetization distribution Mr in the object and the signal weighting function, induced by the magnetization preparation. Sk at position k depends on the relaxation and the order of the sampling. The reconstructed image IrCart is given by the Fourier transform of the acquired signal in k-space: IrCart =

X

Mk Sk e−ikr = Mr TSRFr

ð1Þ

k

P where ‘⁎’ the convolution, Mr = k Mk e−ikr , P denotes SRFr = Sk e−ikr and the sum extends over the Cartesian k

sampling k. The lower index k or r indicates the

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corresponding variable in k-space or image domain. The shape of the SRF is influenced by the signal evolution and the order of the sampling in k-space. Acquiring the k-space in reverse centric order [5] with constant sampling density and applying no filtering in the postprocessing lead to a symmetric, triangularly shaped signal weighting of k-space w(k) (Fig. 2A). The advantage over a linear sampling is a reduction of the contamination, which can also be seen from the reduced side lobes of the corresponding SRF (Fig. 2C). For this reason, reverse centric reordering is considered in the following description. The noise in the reconstructed image ΔIrCart is given by the number of phase-encoding steps N and the noise σk of the acquired echoes: DIrCart =

rX ffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi r2k = r0 N

ð2Þ

k

Here, a constant noise σ0 is assumed for each measurement. Because of the linear signal increase, the SNR of each phase-encoding step is proportional to the signal weighting Sk. To achieve a maximum SNR of the image, the measured echoes must be weighted proportional to their own SNR by application of a postprocessing filter. Fig. 2B shows the SNR optimization for SR sequences by applying a triangularly shaped filter to the signal weighting. The resulting k-space

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weighting w(k) is quadratic. A loss of spatial resolution can be seen clearly from a broadening of the main lobe of the corresponding SRF (Fig. 2D). Additionally, a severe amplification of contamination appears as increased amplitude of the SRF outside the voxel limits. Consequently, the application of no filter in SR sequences results in SNR loss due to suboptimal data weighting. However, the application of an SNR optimizing filter leads to massive blurring. DW imaging [12,13] allows manipulating the SRF by varying the sampling intervals between the acquired phaseencoding steps. In contrast to the common reconstruction of non-Cartesian sampled data, in the reconstruction of conventional DW imaging a density compensation filter [23–26] is unnecessary, as the k-space density in DW imaging is optimized to result in a favorable SRF. This can be utilized in the application of DW imaging to SR sequences: filtering can be used to optimize the SNR. Simultaneously, the sampling density is chosen in a way that, in combination with filtering and signal weighting, the desired SRF is obtained. The non-Cartesian DW data can be reconstructed by discrete Fourier transform (DFT): X Irdw = fk VSk VMk Ve−ik Vr = SRFdw ð3Þ r TMr kV

The set of k′ represents the non-Cartesian sampling and denotes the postprocessing filtering coefficients. In DW

Fig. 2. Comparison of unfiltered Cartesian and SNR-optimized filtered Cartesian single-shot SR imaging with reverse centric ordered acquisition of k-space: If no filtering is applied (A), the k-space weighting by signal weighting and filtering S(k)×f(k) is triangularly shaped. Because of the constant sampling density in Cartesian imaging, the total k-space weighting w(k) is identical to the weighting by the signal weighting and filtering S(k)·f(k). The corresponding SRF (C), calculated from the Fourier transform of w(k), has small positive side lobes. The gray area under the SRFs indicates the voxel size obtained from the Raleigh criterion [9]. In SNR-optimized Cartesian SR imaging, a triangularly shaped filter is applied resulting in a quadratically increasing k-space weighting w(k). The corresponding SRF (D) is broadened and shows a severe increase of contamination.

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imaging for SR sequences, the SRFrdw is determined by the signal weighting, the filter coefficients and the non-Cartesian sampling k′. The signal weighting Sk′ is defined by the relaxation of the magnetization. The filter coefficients fk′ must be chosen proportional to the SNR and, consequently, to the signal weighting for SNR-optimized reconstruction, i.e., fk′∼Sk′ The free parameter in SNR-optimized DW imaging is the sampling density, which can be chosen to generate the desired SRF. This is illustrated in Fig. 3: Fig. 3A shows the varying k-space intervals of the sampling leading to a changed weighting curve by signal weighting Sk′ and SNR optimizing filtering fk′ (Fig. 3B) in comparison to Cartesian-sampled SNR-optimized imaging (Fig. 2B). Because of the nonconstant sampling density, the k-space weighting w(k) is triangularly shaped (Fig. 3B) resulting in an identical, unblurred SRF (Fig. 3C) as in Cartesian, unfiltered imaging (Fig. 2C). For an investigation of the SNR improvement by filtering, an SNR comparison is accomplished between a Cartesian sampled, unfiltered image and an SNR-optimized filtered DW image. The sampling density in DW imaging is chosen to result in an identical shape of the SRF as in the Cartesian, unfiltered imaging, i.e., the

norm normalized SRFs (SRF r/SRF Pr =SRF P r=0) of both techniCart; norm norm ques: SRFr = ð Sk e−ikr Þ=ð Sk Þ and SRFdw; = r k k P P ð fk VSk Ve−ik Vr Þ=ð fk VSk VÞ must be identical:

kV

kV

ð4Þ

= SRFCart;norm SRFdw;norm r r

The statistical error of the filtered, DW image can be calculated by: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rX ffiffiffiffiffiffiffiffiffiffiffiffiffi X ð5Þ fk2Vr2k V = r0 fk2V DIrdw = kV

kV

With the condition of identical normalized SRFs (Eq. (4)), an SNR comparison can be made: X fk VSk V pffiffiffiffi pffiffiffiffi dw dw N SNRr SRFr 4Mr r0 N kV ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffi X = rX = rX ð6Þ Cart Cart SNRr Sk r0 fk2VSRFr TMr fk2V kV

kV

k

By derivation of Eq. (6), it can be shown easily that an optimal SNR gain, depending on the filter coefficients fk′, is achieved if every phase encoding step is weighted proportional P 2 to its own SNR: fk′=aSk′ with the normalization a= fk V. Hence, SNR-optimized filtered DW imaging kV

provides the maximum SNR for a given SRF. For SR sequences, the maximum available SNR gain of a DW, SNR-optimized acquisition compared to a Cartesian sampled, unfiltered acquisition with identical SRFs and equal number of phase-encoding steps can be approximated by replacing the discrete sum in Eq. (6) by an integral: X X aSk2 pffiffiffiffi Sk2 pffiffiffiffi dw N N SNRr k k X = rX ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiX = rX Cart SNRr Sk Sk a2 Sk2 Sk2 k

k

Z

k

1

1

x2 dx 0 c sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z Z 1

x2 dx 0

Fig. 3. (A) shows the inverse sampling density for SR-DW and SRPLANED. The k-space sampling intervals increase from the k-space edges to the center (A). In contrast to SNR-optimized Cartesian imaging (Fig. 2B), the k-space weighting by signal weighting and SNR optimizing filtering S(k)·f(k) is changed by the nonconstant sampling density to the triangularly shaped k-space weighting w(k) (B), resulting in the identical contaminationreduced and unblurred SRF (C) as the Cartesian unfiltered acquisition (Fig. 2C).

k

sffiffiffiffiffiffiffiffiffiffiffiffiffi Z dx 0 1

xdx

=

2 pffiffiffi 3c1:155: 3

ð7Þ

0

Hence, the application of the SNR optimizing filter increases the SNR by about 15%. The considerations above are made for the application of DFT in the reconstruction of the non-Cartesian sampling. As DFT is a time-consuming operation in practice, images are reconstructed with gridding [23], making use of fast Fourier transform. The non-Cartesian sampling is extrapolated onto a Cartesian grid by convolution with a gridding kernel, which is a small, finite window in k-space. Identical results are achieved for the SNR considerations above when using a gridding algorithm instead of DFT. However, the mapping onto a Cartesian grid may lead to additional artifacts. Nevertheless, the artifact power can be reduced by an appropriate choice of the gridding kernel [24–26].

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As already stated, the effective FOV in DW imaging is reduced [12] because of the varying sampling density. In PLANED imaging [14], parallel imaging is used to increase the FOV of DW data. Consequently, the SNR of SRPLANED imaging is additionally affected by the application of parallel imaging. Spatially varying noise amplification, depending on the coil configuration, occurs in parallel imaging and can be described for each pixel by the geometry (g) factor [15]. For this reason, in SR-PLANED, a g-factor map calculation is required to evaluate the ratio between the SNR gain by filtering and the noise amplification of parallel imaging.

3. Methods and material In order to investigate the influence of an exponential signal increase on the SNR and the shape of the SRF in comparison to a linear approximation, simulations with different relaxation times T1, typically appearing in in vivo measurements, were performed. The assumption for the approximation in the Theory section is that the signal increases linearly for SR sequences, i.e., the acquisition time is much shorter than the relaxation time T1. Typically, acquisition times in myocardial perfusion imaging are less than 200 ms, while T1 times of tissue in the human heart are about 1.2 s. Since in the presence of the contrast agent the relaxation time of blood and tissue is shortened, the condition of short acquisition times compared to T1 may be compromised. For this reason, simulations were performed for both a linearly increasing signal and an exponentially increasing signal with different relaxation times T1 and constant acquisition time. The calculations were implemented in the IDL programming environment (CREASO, Gilching, Germany). The consecutive signals were postprocessed with a linearly increasing filter and ordered reverse centric in k-space. For all simulations, the DW sampling (Fig. 3A) was used, which results in a triangularly shaped k-space weighting for a linear signal increase and application of a filter with linearly increasing filter coefficients. The SRFs were calculated from the filtered signals using gridding [23–26] without density compensation. The relative SNR was calculated from Eq. (6), using a filter with linearly increasing filter coefficients and both a linearly increasing signal and an exponentially increasing signal. All measurements were performed on a 1.5-T scanner (Magnetom Symphony, Siemens Medical Solutions, Erlangen, Germany) using a 12-channel body array coil and eight independent receiver channels. Data were recorded using a single-shot SR-turbo-FLASH sequence and a protocol typical for myocardial perfusion imaging (TE=1.4 ms, TR=2.8 ms, delay between SR-preparation pulse and FLASH sequence=12 ms, flip angle=15°, matrix-size=64×128, FOV in phase-encoding direction was 75% of FOV in read direction, slice thickness=8 mm, bandwidth=620 Hz/pixel).

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This study was approved by our institution's ethics committee, and written informed consent was obtained from all volunteers. In order to investigate the SNR gain of DW imaging in comparison to Cartesian imaging, a series of images of a phantom were acquired with Cartesian sampling, and images from these data were reconstructed using no filtering. Additionally, a second series of images were recorded using a DW sampling and an SNR optimizing filter in reconstruction. The DW sampling was adjusted to result in the identical normalized SRF as in the Cartesian imaging. The same number of phase-encoding steps and, accordingly, equal acquisition times were used in both acquisitions. Since the k-space density in the DW acquisition was calculated to result in a triangularly shaped k-space weighting, the normalized SRF of the SNR-optimized DW imaging equals the normalized SRF of the Cartesian sampling. The phase-encoding steps of the DW acquisition were calculated similarly to the method for one-dimensional density weighting proposed by Greiser and von Kienlin [12]: the one-dimensional k-space density ρk,i at position ki is defined as qk;i = D1k;i = ki −k1 i−1 . The area under the desired triangularly shaped k-space weighting function w(k) is divided into as many parts as phase-encoding steps are acquired. The ratio of the area of each part to the total area of the weighting function must equal the ratio of the corresponding weight of the phase-encoding step, generated by signal weighting andR filtering, toPthe sum ofPall these Rk kmax weights: kii + 1 wðk Þ= kmin wðk Þ = kkii + 1 Sk fk = kkmax Sk f k . min From this condition, the integral limits can be calculated, providing the k-space density, which is required to generate a k-space weighting w(k) in the presence of the signal weighting Sk and the postprocessing filter fk. In addition to the phantom studies, in vivo first-pass myocardial perfusion imaging studies were performed using SR-PLANED imaging with the protocol described above (FOV=430 mm, 6 ml Gd-BOPTA contrast agent [MultiHance, Bracco Diagnostics, Milan, Italy] at a flow rate of 4 ml/s into an antecubital vein followed by a flush of 20 ml saline [27]). Forty images were acquired in a breath-hold to record the passage of the contrast agent bolus through the heart of a healthy volunteer. After applying the SNR optimizing triangularly shaped filter to the non-Cartesian DW raw data, reconstruction was accomplished with two different methods: (a) conventional gridding [23] and (b) PLANED imaging [14]. In both reconstructions, no density correction was applied. The reconstruction was accomplished for each coil data set and finally combined to a single image by a square root of sum of squares operation. In PLANED reconstruction, a non-Cartesian GRAPPA/PARS algorithm [17,18] was used after SNR optimization by filtering. The GRAPPA factors were determined in a separate prescan using a Cartesian sampling. SRFs of both techniques were obtained by imaging a sharp edge and by derivation of the edge spread functions

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[28]. The SNR was assessed with the pseudo multiple replica approach by Robson et al. [29]. The required noise samples were acquired in addition to the phantom and in vivo studies. Ten thousand measurements were simulated in order to calculate the SNR pixel by pixel. Additionally, in SRPLANED, geometry factor maps were calculated in order to analyze noise amplification by parallel imaging.

4. Results The simulations showed that in SNR-optimized DW, for an exponential signal increase with acquisition times in the order of the relaxation time T1, the shape of the SRF is affected marginally and the SNR gain is very slightly reduced. For an acquisition time of 0.5 T1, the SRFs for a linear and an exponential signal increase are shown in Fig. 4. Their shapes are nearly identical and show only slight differences. The calculated SNR gain by DW imaging is reduced to 13%. Fig. 5 shows the images of the phantom study, comparing the standard Cartesian imaging using no filtering (Fig. 5A) with SNR-optimized DW. The DW images were reconstructed with two different reconstruction algorithms: Fig. 5B was reconstructed without parallel imaging and Fig. 5C with parallel imaging reconstruction, i.e., PLANED imaging. As in the DW acquisition, the Nyquist criterion is violated in some regions of k-space, and undersampling artifacts occur in the gridded images. A twofold FOV in phase-encoding direction was reconstructed to demonstrate the different effective FOVs: in the gridded image, the aliasing reduces the FOV (Fig. 5B), which is recovered in PLANED imaging (Fig. 5C), using parallel imaging to reconstruct the undersampled regions of k-space. In SNR-optimized DW, the phase-encoding steps are chosen to result in the same SRF as in the unfiltered Cartesian imaging. The corresponding SRFs (Fig. 6) determined in the phantom study are identical within the experimental errors. The central part of the SRF is identical for both PLANED and gridded DW imaging, while the outer parts of the SRF of SR-PLANED (not shown here), causing

Fig. 4. Comparison of the simulated SRFs of a filtered, DW sampling (Fig. 3A) assuming a linear (solid line) and an exponential signal increase with Tacq=0.5 T1 (dashed curve). The discrepancy from the linear signal increase causes a very slight change in the shape of the SRF.

Fig. 5. (A) shows the Cartesian sampled, unfiltered image of a phantom. The DW, SNR-optimized filtered image of the phantom reconstructed with conventional gridding is shown in (B) and the PLANED reconstruction, i.e., using parallel imaging, in (C). To demonstrate the effective FOV, all images were reconstructed with the twofold FOV. Phase-encoding direction is chosen from left to right. SRFs were calculated from the edge spread functions (white line). All images have equal SRFs (Fig. 6) for the reduced FOV.

the undersampling artifacts, are free of aliasing energy inside the increased FOV. The results of the SNR measurements in the phantom study are given in Fig. 7. Relative SNR maps comparing both DW imaging and SR-PLANED with unfiltered Cartesian imaging were calculated from the SNR maps simulated with the pseudo multiple replica approach [29]. The relative SNR between gridded DW imaging and the Cartesian unfiltered reconstruction is constant over the object, while the SNR between SR-PLANED and unfiltered Cartesian imaging has a low spatial variation with a slightly reduced mean value caused by the application of parallel imaging. In order to evaluate the influence of parallel imaging on the SNR in SR-PLANED, a histogram of the relative SNR was calculated from the pixels in the object (Fig. 7). In the gridded DW image, an SNR gain of 15% was found, while in SR-PLANED, the mean SNR gain was 13% with a standard deviation of 4%. The noise amplification by parallel imaging reduces the mean SNR by about 2%, but in comparison to Cartesian unfiltered imaging, it does not

Fig. 6. Center of the SRFs in phase-encoding direction of the phantoms shown in Fig. 5. The SRFs were determined from the edge spread functions of a sharp edge [28] (see white line Fig. 5). The black dashed line shows the SRF for the unfiltered, Cartesian sampling, and the gray solid line indicates the SRF of the DW data reconstructed with gridding and the SRF for SR-PLANED. The SRFs are identical within the experimental errors in the displayed region.

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Fig. 7. In the phantom studies, SNR maps of the DW data reconstructed with gridding and SR-PLANED were calculated and compared pixel by pixel to the SNR of unfiltered Cartesian imaging. Additionally, a histogram of the relative SNR was calculated from the pixels of the homogeneous object. In gridded DW, a mean SNR gain of 15% in comparison to Cartesian imaging was found. In SR-PLANED, the mean SNR was slightly reduced to 13% because of noise amplification by parallel imaging.

exceed the SNR gain by SR PLANED anywhere in the image. Fig. 8 shows an image of the in vivo first-pass perfusion imaging study reconstructed with gridding (Fig. 8A) and with SR-PLANED (Fig. 8B). The drastically reduced FOV of the gridded image demonstrates the essential application of SR-PLANED. In Fig. 9, three out of 40 SR-PLANED images acquired at 40 consecutive heart beats are displayed.

Fig. 8. The same data from an in vivo myocardial perfusion study were reconstructed with gridding (A) and SR-PLANED (B). The gridded image shows massive aliasing artifacts, while in SR-PLANED the whole FOV is available.

The images show different phases of the passage of the contrast agent through the heart. After the injection, the contrast agent passes through the right (Fig. 9A) and the left ventricle (Fig. 9B). Subsequently, the myocardium clearly emerges in the image (Fig. 9C). The reduced contamination and the increased SNR are reflected in the high image quality for 1.5 T single-shot SR-FLASH images. Since imaging in in vivo studies must be performed in breath-hold, a direct SNR comparison between unfiltered Cartesian imaging and SR-

Fig. 9. In vivo myocardial perfusion study using SR-PLANED. Three out of 40 images are demonstrated, showing different phases of contrast agent passage through the heart.

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Fig. 10. g-Factor map from an in vivo perfusion study reconstructed with SR-PLANED. The distribution of the g-factors is shown for pixels in the heart as shown in the g-factor map. With a mean g-factor of 1.01, very low noise amplification was noticed, resulting in an effective SNR gain of 14% of SR-PLANED in comparison to unfiltered Cartesian SR imaging.

PLANED may be problematic. In order to test for noise amplification by parallel imaging, geometry factors were calculated directly from the SR-PLANED data as described by Robson et al. [29] (Fig. 10). A histogram of the g factor in the area of the heart was calculated. Noise amplification with a mean g factor of 1.01 with standard deviation of 0.03 was observed. This is very low compared to the SNR gain of 15% by SNR optimizing filtering and results in a mean SNR gain of 14% in the in vivo SR-PLANED study.

5. Discussion The concept of PLANED imaging was transferred to SR sequences, used in first-pass myocardial perfusion imaging, allowing the generation of an unblurred and contaminationreduced SRF additionally to an SNR improvement by postprocessing filtering. In addition to several other techniques, acquisition [3,4,8–11] and DW [12,13] imaging have been used for SRF manipulation in sequences with constant signal weighting. Compared to postprocessing filtering, the advantage of these methods is that the SNR is not reduced by suboptimal data weighting. In acquisition weighted imaging, k-space weighting is accomplished by a repeated measurement of phase-encoding steps. An optimal SNR is achieved by the application of a filter with constant filter coefficients, so that all samples are weighted equally in reconstruction [3]. In DW imaging, k-space weighting is obtained by variation of the k-space intervals during the data acquisition. As every phase-encoding step is acquired only once, applying no filter, not even for density compensation in reconstruction, results in an optimal SNR. However, with the use of magnetization preparation like in single-shot SR imaging, an additional evolution of the magnetization is causing a varying signal weighting during the acquisition. A postprocessing filter with coefficients proportional to the signal weighting by magnetization preparation is required to obtain an optimal SNR in the resulting image. Since SNR optimizing filtering accompa-

nies a degradation of the SRF, image quality is severely reduced. In DW imaging, this is compensated by using a nonconstant sampling density. The varying k-space density is adjusted to result in a favorable SRF in combination with the k-space weighting by signal weighting and filtering. Hence, in SR-PLANED, SRF manipulation simultaneously with SNR optimization is obtained by a combination of postprocessing filtering and density weighting. An SNR comparison of SR-PLANED with unfiltered, Cartesian imaging provided a significantly higher SNR for SR-PLANED. The experimentally measured SNR gain of 13-14% is in agreement with the value of 15% predicted for ideal g factors of 1.00. The SRFs of the compared methods were identical, so that the SNR gain clearly originates from SNR optimizing filtering. This is in contrast to conventional acquisition and DW imaging, where an SNR improvement, observed in comparison to an unweighted sequence with the same width of the main lobe of SRF, is object dependent and originates from a contamination reduction. In the phantom and the in vivo studies of this work, a triangularly shaped k-space weighting was chosen, resulting in an SRF with only positive side lobes producing very moderate contamination. However, the presented method allows a free choice of the SRF in principle. For example, a Hanning-weighting function can reduce contamination additionally in comparison to the triangularly shaped weighting used in this work. Because of the nonconstant sampling density in DW imaging, the Nyquist criterion may be violated in some regions of k-space, reducing the effective FOV. In PLANED imaging [14], the undersampled intervals are reconstructed by parallel imaging [15–18]. The slightly reduced SNR gain of SR-PLANED, in comparison to the predicted value, can be explained by noise amplification caused by parallel imaging. SNR and geometry factor maps were calculated in order to determine the influence of parallel imaging on the SNR. With a maximum sampling distance of 1.5Δk0 and a mean sampling density of 1, no excessive noise amplification appeared in this application. The SNR calculations and the measurement of an identical SRF in the reduced FOV for

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the PLANED and the gridding reconstruction support this statement. The histogram of the SNR gain over the homogeneous phantom reflects the low spatial variation of the geometry factor. As already described by Robson et al. [29], the intrinsic regularization of the GRAPPA reconstruction may lead to g factors less than 1 in some regions of the image. This may be an additional explanation for the low noise amplification found in the GRAPPA-reconstructed phantom and in vivo studies. An assumption for a successful operation of SRPLANED is a linear increase of the signal amplitude. For FLASH sequences, signal evolution remains linear with short acquisition times for a perturbation with RF pulses of constant flip angle [21]. Simulations showed that even for times T1 in the range of the acquisition time the SRF and the SNR of SR-PLANED are affected only slightly. This validates the application of the presented technique to firstpass myocardial perfusion imaging where T1 may be shortened in the presence of contrast agent. Moreover, the high image quality of SR-PLANED in the in vivo study supports the feasibility of the application of SR-PLANED to clinical routine studies. Typically, a Cartesian sampling is used in first-pass myocardial perfusion imaging. In addition to the acquisition of k-space in reverse centric order, a linear or centric ordered sampling can be used [30]. The last two sampling schemes result in contaminated SRFs. A postprocessing filter can be used to reduce the contamination. However, the filtering increases the SNR loss by suboptimal data weighting. Instead, the method of SR-PLANED can also be transferred to the linear and centric ordered acquisition allowing SRF improvement at an optimal SNR. However, here the correction of the k-space weighting by the sampling density may result in very low sampling densities at some k-space positions, which may exceed the maximum acceleration factor of parallel imaging or may increase the g-factor. Radial sampling [31] is an alternative trajectory used in first-pass myocardial perfusion imaging. Its advantage is the rapid acquisition of the center of k-space and its moderate artifact characteristics due to undersampling of k-space. Because the radial sampling results in a massively blurred SRF, the k-space density in radial imaging requires density compensation in the reconstruction. However, the filter used for density compensation in order to improve the SRF does not correspond to the filter for SNR-optimized data weighting. The represented method of DW imaging uses a variation of the phase-encoding sampling. In radial imaging, the readout gradients must be changed to apply DW imaging. Therefore, a simultaneous optimization of the SRF and the SNR is much more complex. A further SNR increase in first-pass myocardial perfusion imaging can be achieved at higher field strengths [32, 33] and by using SSFP [2] instead of FLASH imaging. The method of SR-PLANED can also be used at higher field strengths and with SSFP sequences as described in this work.

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