First, to investigate the effects of acquisition every other heartbeat on both the AIF and myocardial signals, five scans using radial 2D SMS and 3D SoS acquisitions were performed every heartbeat. Four of the five scans were analyzed using either only the even or the odd time frames, to understand how well an alternating beat acquisition would perform. Then, an alternating 2D/3D saturation-recovery sequence was implemented, and both phantom and in-vivo data of seven dogs (10 rest and 4 stress studies) and two human subjects were acquired and processed to study the differences and comparable aspects of the 2D SMS and 3D SoS methods.
2.1 Pulse Sequence
All scans were performed at 3T using a Prisma MRI system (Siemens Medical Solutions, Erlangen, Germany).
2.1.1 Every heartbeat acquisition
Both 2D SMS and 3D SoS sequences were performed as separate free-breathing acquisitions with “standard” every-beat ECG-gated acquisitions. The 2D SMS acquisition had a single saturation pulse each beat and then a short 20msec recovery time before using radial RF-spoiled gradient echo readouts. The readouts continued until the next R-wave trigger was detected. A continuous golden angle increment was used for all the rays. One slice group with a multi-band factor of 3 was acquired throughout each heartbeat. There was a slice gap equal to one slice thickness. The 2D SMS acquired ~300 rays per heartbeat (for a heart rate of ~80 beats per minute). The first 24 rays were used to reconstruct images for the AIF. Retrospectively, rays for the reconstruction of the tissue curves were selected as those acquired around systole. This was typically 25-96 rays, starting at approximately ray 40, depending on the heart rate. Selection of rays is detailed in the Reconstruction section below.
A 3D SoS acquisition every beat was also acquired. The pulse sequence consisted of a 2D saturation recovery AIF acquisition followed by a ~200msec 3D SoS acquisition as in . In each beat, the 2D AIF was acquired from 24 rays starting 20msec after a saturation pulse. Then another saturation pulse was performed and after recovery, the 3D readout started. Though a longer saturation recovery time (SRT), typically 150msec, was desired in terms of better contrast, a shorter SRT, like 100msec, was applied due to high heart rates, especially during stress. Scan parameters for 3D SoS: 92 rays each heartbeat, variable density in kz with 24 rays in the center section and six partitions acquired in total (eight slices reconstructed due to zero-padding in the k-space and center six slices used for analysis).
Saturation pulses as in  were used. The main imaging parameters used in 2D SMS and 3D SoS sequences are listed in Table 1.
2.1.2 Effects of acquisition every other beat on the AIF and myocardial signals
Data acquisitions were obtained in two subjects for 2D SMS and three subjects for 3D SoS, as described next. In these datasets, data with large variance possibly caused from motion were discarded. To be specific, if myocardial tissue signal intensities in two neighboring time frames in a slice of every-beat data differed by more than 20% for 10 consecutive frames, that subject was not analyzed. One 3D subject was left out for this reason, so two 2D SMS and two 3D SoS every-beat datasets were analyzed.
The effect of every-other-beat acquisition was investigated using every-beat data. The analysis was performed by comparison between data with every-beat (EB) acquisition, called the EB group, and using every-other-beat, (the EOB group), in both 2D SMS and 3D SoS subjects. To focus on the undersampling and minimize errors caused by reconstruction and post-processing, an “ideal” scenario was investigated first. That is, the EB data was reconstructed and registered, then divided into two EOB groups (odd and even) equally and processed in the following manner: (1) the same proton density (PD) signal intensities were used for both the EB and the EOB data; (2) the same myocardial region-of-interest (ROI) contours and shift adjustments were applied for both EB and EOB group; (3) gadolinium concentration ([Gd]) curves from the EB group were divided into two EOB sets.
However, actual data with other effects can be more complicated. Respiratory and cardiac motion, for example, might result in larger heart motion displacement between two neighboring image frames in an EOB acquisition compared to that of an EB acquisition. Such motion and fewer time frames relative to EB can reduce the performance of the reconstruction methods that include temporal regularization.
In this work, we included the practical “non-ideal” case, where the reconstruction and the processing of 2D SMS and 3D SoS data in the alternating 2D/3D acquisition were done independently, which is different from the ideal case described above. Thus, EB k-space data was separated into the even and odd EOB groups, and then each group was reconstructed, registered and quantified individually. To reduce variability, the same contour from EB data was applied to EOB data processing. In addition, the same proton density images were also used for EB and EOB data processing.
The overall workflow of acquisition, reconstruction and data processing is shown in Figure 1. The next section details the reconstruction and conversion to [Gd] for quantification of EB and EOB data.
Both 2D SMS and 3D SoS datasets were reconstructed by a joint spatial and temporal constrained reconstruction (STCR) method [16, 38, 39]. The STCR reconstruction minimized a cost function that consisted of an L2 data fidelity term between the estimated image and the undersampled data and L1 terms of spatial and temporal total variations (TV) as in equation (1). Pre-interpolation with GRAPPA operator gridding (GROG) was used to convert the radial sampling data onto a Cartesian grid as an initial step . The cost function used for the 3D SoS data reconstruction is:
2D SMS data required an additional step prior to reconstruction to select the range of rays to use for systole (or diastole or any cardiac phase, though only systole was reconstructed in this work). First, a preliminary sliding-window reconstruction was performed to obtain images with a temporal footprint of 55 msec/frame (24 rays). Such a reconstruction was repeatedly created after sliding by three rays (~7msec). Then we manually identified the most systolic images. The rays corresponding to those systolic images were used to perform the final reconstruction.
The work here only used the 3D data acquired near systole, although if heart rate allowed another 3D dataset was acquired each beat at diastole as in .
To compensate for respiratory motion, both rigid and deformable registration were applied. Rigid registration was performed on both PD images and perfusion images. A coarse mask was manually selected to encompass the whole heart and used as input to the registration step. Then a Fourier-based cross-correlation method was applied to iteratively register neighboring frames . Model-based deformable registration was then applied to perfusion images as in . That is, a series of motion-free synthetic images were first generated from fitting a two-compartment model to the images. The fitted images were essentially motion-free and used as the reference in each frame to register the reconstructed images. For the alternating 2D/3D datasets, registration was done for each sequence separately (neighboring frames were redefined as every other beat).
In an image frame generated by the summation of all perfusion frames, a small region was manually drawn within the blood pool area to obtain AIF signal intensity (SI) curves. Lines were drawn conservatively on the summed image to represent the endo- and epicardial border. The myocardial tissue SI curves were obtained from six equiangular myocardial segments in each slice .
2.4 Conversion from signal intensities to [Gd]
T1 values of different time frames were estimated by modeling. A Bloch simulation was used to generate a look-up-table (LUT), which converted the measured signal intensities to T1 values. The ratio between perfusion images and the first PD weighted image was the input to the LUT . The Bloch simulation used the prescribed scan parameters and accounted for the slice profile in each excitation RF pulse. For the 2D SMS acquisitions, the slice profile spanning the five slice thicknesses (3 slices plus gaps) was discretized into 1000 samples in the slice direction and the signal evolution of each sample was simulated. Signal intensities from all 1000 samples were summed to give the signal intensity of a specific slice, assuming equal contribution from each radial line readout, and including the appropriate CAIPIRINHA phase modulation  for each ray. For 3D imaging, the magnetization signal was simulated, and an extra kz encoding step was applied to account for readout of each kz partition. The k-space signal intensity of each kz partition was averaged and the unacquired kz partitions (partial Fourier) were kept zero, and then a Fourier transform was applied along kz to obtain the image space signal intensity for each slice.
Conversion from T1 values to [Gd] curves was then performed by the following equation.
T1 comes from the look-up-table (LUT) calculated from the previous step shown above. T1pre is the pre-contrast T1 where native tissue T1 was used either in the blood or myocardium. R is the T1 relaxivity constant, 3.7 mmol−1s−1 for Gadoteridol .
PD images were acquired using the same gradient echo sequences without the saturation recovery pulse, so the PD images were not truly independent of T1. Such T1 weighting of PD images has been reported to have negligible effects on the PD image signal intensity . A Bloch simulation was performed here to verify that the use of the first PD image did not bias the conversion to [Gd].
All quantitative MBF results were then calculated with a two-compartment model and an implicit assumption that the extraction fraction is unity.
2.5 Evaluation of every other beat flow values
After quantification, a difference ratio was calculated between EB group and EOB group, as described in the equation below.
2.6 Alternating 2D/3D acquisitions
For these acquisitions, the 2D hybrid radial SMS acquisition and the 3D SoS acquisition were applied in an alternating manner as illustrated in Figure 2.
The 2D SMS and 3D SoS EOB acquisitions used the same parameters as the EB sequences described above. The SRT applied before the 2D SMS acquisition was 20msec as was the SRT for the 2D AIF acquired in the same beat as the 3D SoS acquisition. The SRT applied before the 3D centric readout was 100msec. The reconstruction of 2D SMS and 3D SoS alternating acquisitions each used the same STCR method as given above for the EB data. The regularization weights were also the same as for the EB data. One special circumstance is that flow values were different between 2D SMS and 3D SoS methods due primarily to the AIF differences in two out of four stress datasets. Therefore, a composite AIF was created by combining the AIFs in each beat into a single AIF, after conversion to [Gd]. This AIF was then used with EOB tissue curves interpolated to the same temporal resolution in the four stress studies. Though not displayed in this paper, using a composite AIF for the resting cases caused negligible effects on the quantification.
A 9-vial phantom developed for T1 mapping and ECV standardization (T1MES)  was used to validate T1 estimates from the alternating 2D/3D sequence. All of the time frames were averaged. The same conversion method using a LUT as described above was used to estimate T1 values in each vial.
Alternating 2D/3D scans were done in 7 dogs (rest: n=10, adenosine stress: n=4) and 2 human subjects (male, age 73, 69 years; rest: n=2) with 0.05-0.075mmol/kg gadoteridol. The adenosine induced stress cases were performed in four dogs with ~280 microgram/kg/min. Another human study was also performed but the ECG triggering was poor, so that dataset was not used. A quantitative perfusion analysis of absolute MBF for each scan and MPR for the subjects with stress scans was performed followed by Bland-Altman and linear regression. Pearson’s correlation coefficient was used to calculate the region-wise relationship between 2D SMS and 3D SoS methods.