Buildup of Image Quality in View-Shared Time-Resolved 3D CE-MRA

Abstract

Time-resolved 3D contrast-enhanced MR angiography (CE-MRA) often relies on view sharing of peripheral k-space data to enable acquisition of angiograms with both high spatial resolution and a rapid frame rate. It is typically assumed that k-space will be fully sampled during passage of the contrast bolus arterial phase. However, this is not the case when view sharing is incomplete, for example at the leading edge of an enhancing vessel or if acquisition time is limited as in fluoroscopic tracking for multi-station bolus chase MRA. Incomplete view sharing will degrade image quality, for example by reducing vessel signal and sharpness and increasing undersampling artifacts. In this work, the evolution of angiogram quality with view sharing is quantitatively assessed in phantom experiments and in vivo CE-MRA calf studies. It is demonstrated that there are multiple sets of sequence parameters that can yield a target image update time, but the choice of parameters can profoundly affect how image quality evolves with view sharing. A fundamental tradeoff between vessel signal and sharpness and its relationship to the sequence temporal footprint is investigated and discussed.

INTRODUCTION

Time-resolved 3D contrast-enhanced MR angiography (CE-MRA) often relies on segmented sampling of k-space and view-shared reconstruction to achieve high spatiotemporal resolution. Although acceleration techniques such as partial Fourier (1,2) and parallel acquisition (3–5) allow a greatly reduced acquisition time for a given targeted spatial resolution, these techniques alone are typically insufficient to provide the short frame times desired for time-resolved imaging. To further reduce the frame time, a segmented acquisition can be used in which only a portion of k-space is sampled each time frame. However, such undersampling by itself can degrade angiogram quality by reducing SNR, decreasing vessel sharpness, or increasing artifact (6). View sharing (7), which enables full sampling of k-space by concatenating the most recently sampled k-space region with previous measurements of the other regions, is a commonly used reconstruction technique to reduce these adverse spatial effects but can be accompanied with some loss of temporal fidelity (8).

In some situations, the complete sampling of segmented k-space is not always achieved or even desired. Such undersampling due to incomplete view sharing can occur for a variety of reasons. First, immediately upon arrival of the contrast bolus within a vessel of interest, no prior contrast-enhanced data are available for view sharing, and therefore the initial contrast-enhanced time frames are undersampled. All view-shared CE-MRA acquisitions experience this effect. Second, if high temporal fidelity is desired, particularly in portraying the leading or trailing edge of the contrast bolus, view sharing may be disabled, causing all time frames to be undersampled (9). This technique may be used to assess rapid, complex flow as might be seen in regions of rapid arterial-to-venous transit. Lastly, if the time to image a vessel of interest is restricted, either due to interrupted imaging or a limited duration of the bolus arterial phase, full k-space sampling might not be achieved. This is the case for fluoroscopic tracking (10), an approach for 3D bolus chase MRA of the peripheral vasculature that uses rapidly-acquired time-resolved images to allow real-time triggering of table advance from proximal to distal stations. If bolus transit across a proximal station is rapid, then the time-resolved acquisition at that station must be terminated to advance the table and keep pace with the bolus. Consequently, images formed at the proximal station might be acquired with incomplete k-space sampling, and the resultant image quality will depend on the extent of k-space filling allowed prior to moving the table.

Many 3D CE-MRA time-resolved approaches, such as keyhole (11), TRICKS (12), CAPR (13), and TWIST (14), use similar Cartesian k-space segmentation strategies that employ view sharing. The most common approach is to segment the k_Y-k_Z phase encoding plane into two regions: a central low-spatial-frequency region and a peripheral high-spatial-frequency region. Typically, the central region is fully sampled every time frame and the peripheral region is less frequently sampled, thus the density of samples per frame in the peripheral region is less than that in the central region. With this allowance for two regions, and ignoring any differences in how the peripheral region might be further subdivided, the k_Y-k_Z segmentation for view sharing can be defined using only two parameters: the size of the central region and the sampling density of the peripheral region. For a given target frame time, there are multiple combinations of these parameters that can be used. For example, the time needed to sample a larger central region can be offset by sampling the peripheral region with a lower density. However, the choice of segmentation parameters can profoundly affect the quality of initial contrast-enhanced time frames and how angiogram quality evolves in time as k-space becomes more fully sampled with view sharing.

The consequences of view sharing for angiogram image quality have been previously investigated in a number of studies. These include the effects of contrast bolus dynamics (8,15,16) and evaluations of different sequence parameters for specific imaging protocols (17–19). Although these studies have contributed to the understanding of view sharing tradeoffs, they consider specific imaging scenarios and target particular quality metrics. The purpose of this work is to provide a broader quantitative assessment of how 3D time-resolved CE-MRA image quality is impacted by progressive view sharing and the selection of generalized k-space segmentation parameters. Phantom experiments are used to study how vessel signal, sharpness, and undersampling artifact magnitude evolve in time with view sharing for an array of sequence parameters. The observed experimental trends are corroborated with analysis of in vivo 3D time-resolved CE-MRA calf studies, and implications of the results are discussed. We believe that the conclusions drawn from this work are applicable to all vascular regions and provide general guidance for selection of parameters for view-shared time-resolved 3D CE-MRA sequences.

METHODS

View-Shared Sampling Parameters

To study the effects of incomplete view sharing on angiogram quality, a time-resolved sampling pattern was used that employs common characteristics of view-shared sequences (Figure 1). It is assumed that the readout direction is fully sampled along the k_X direction, orthogonal to the plane of the figure, and view sharing is restricted to the peripheral region of the k_Y-k_Z phase encoding plane shown. A specific sampling pattern is described by a central region of size C and peripheral region with sampling density D (Figure 1a). C is defined as the ratio of the diameter of the central region to that of the combined central and peripheral region and is assumed to be the same for both the k_Y and k_Z directions. D is defined as the ratio of the sampling density of the peripheral region compared to the central region. C and D are referred to as segmentation parameters and are expressed as percentages. Consistent with many CE-MRA sampling strategies, the corners of the k_Y-k_Z phase encoding plane are not sampled (20). For this work, sampling of the peripheral region is done randomly to reduce the coherence of aliasing artifacts caused by undersampling (21).

FIG. 1.

(a) k_Y-k_Z phase encoding plane with a fully-sampled central region (orange) and a partially-sampled (D=50%) peripheral region (black). In this example, C=31%, meaning the diameter of the central region is nearly a third of that of the combined central and peripheral region. (b) Progressive view sharing with initial peripheral sampling density of D₀=25%. View sharing results in progressive filling of the peripheral region, from D₀=25% to D=100%. The data that would be included in reconstructing each frame is shown on the time axes, with orange and black blocks corresponding to center and peripheral region samples, respectively. Initially, only the central region and one-quarter of the peripheral region are sampled, constituting an image update. The time at which sampling of the image update begins is indicated by the black arrowhead. The next frame resamples the center region as well as a different quarter of the peripheral region. The quarter of the peripheral region from the prior image update is included in the reconstruction, shown to the left of the arrowhead. This continues, and eventually the peripheral region is filled. The extent of temporal information included in the reconstruction of the D=100% frame is referred to as the temporal footprint and is indicated by the red arrowheads.

The progressive filling of k-space due to view sharing can be modeled by a linear increase in D. For example, in Figure 1b, if a time-resolved sampling pattern has a base density (D₀) of 25%, then the first image of a contrast bolus initially entering a blood vessel within some field-of-view (FOV) will be formed with sampling of the k-space center and only 25% of peripheral k-space. Subsequent time frames of the view-shared time series will be sampled with D=50%, 75%, and 100%. A view-shared sequence can be described by two temporal parameters: (i) the image update time, defined as the time to sample the base sampling pattern comprised of peripheral k-space with density D₀ and the center with full density; and (ii) the temporal footprint (13), defined as the temporal extent of view-shared information used in a given reconstruction. In this work, an elliptical-centric temporal ordering is assumed, whereby for each image update the central region is acquired first followed by the peripheral region. As shown in Figure 1b, if the image update time is 5 sec and D₀=25%, then complete view sharing will occur after 20 sec, which is the temporal footprint plus the time to sample the initial central region.

Time Comparisons

The relative sampling times of view-shared sequences can be compared using a plot of temporal footprint vs. image update time. For this work these times were calculated in arbitrary units (au). The fully-sampled case, corresponding to C=100%, was assigned to have an image update time of 100 au. Because this case in effect corresponds to no view sharing, the temporal footprint is also equal to 100 au. The image update times and temporal footprints of all other sampling patterns were calculated based on the relative number of sampled phase encodes compared to this reference. Note that since C is defined as the ratio of k-space distances, the sampling times will be proportional to C² or the area of the phase-encoding plane sampled by C. Also note that as C increases, the time to sample the peripheral region with a given relative sampling density D₀ will be reduced. Figure 2a shows a plot of temporal footprint vs. frame time using the au timescale. In Figure 2b results are shown for the case in which 2× partial Fourier acceleration is additionally applied to the peripheral k-space region. In both cases, starting at the far right of the plots and following along the outermost curve corresponds to progressively smaller base densities (D₀) for the fixed C of 30%. Reduction of D₀ results in less peripheral k-space being sampled per time frame, and the image update time decreases. However, as D₀ decreases more updates are required to fully sample k-space, causing the temporal footprint to increase. For smaller C the curve scales toward the origin, and additional curves are shown for the cases of C=20%, 10%, and 5%. In this work, to assess how vessel image quality evolves in time with view sharing, several sequences that yielded the same target image update time (e.g., dashed lines in Fig. 2) were compared using experimental data generated from vial phantoms as well as results from in vivo studies.

FIG. 2.

Plots of temporal footprint vs. image update time for a number of sequences with distinct segmentation parameters. Separate plots are shown (a) without and (b) with 2× partial Fourier acceleration of the peripheral region. The size of the central region C and initial sampling density of the peripheral region D₀ are indicated. For a given image update time, there are a number of sequences that can be used (e.g., dashed lines), each with a different temporal footprint. The temporal footprint and image update time are expressed in arbitrary units relative to the time it would take to sample a sequence with C=100% (100 au). Due to partial Fourier acceleration, sequences in (b) have shorter update times and temporal footprints than the equivalent sequences in (a), but the 100 au reference time is the same for both plots.

Phantom Experiments

To determine the effects of varying the segmentation parameters C and D on image quality, binary sampling patterns like those in Figure 1 were generated and used to mask isotropically-sampled 256 × 256 k_Y-k_Z phase encoding planes of a set of images representing three different vessel sizes. The vessel images were created using axial 2D spin echo imaging of water-filled vial cross-sections of different diameters (4, 6, and 12 mm) with an FOV of 25.6 × 25.6 cm² and 1.0 mm² isotropic resolution. These vessel diameters and FOV correspond to those encountered in CE-MRA of the peripheral vasculature. The vials were imaged individually and no signal sources were present in the background. The resultant spin echo images were 2D fast Fourier transformed (FFTed) to produce assumed fully-sampled phase encoding planes. After masking the k-space data by a sampling pattern, a 2D-FFT was applied to produce the undersampled vessel image. All images were 3× sinc-interpolated to improve sampling resolution for quantitative assessment and visualization. For each vessel image, C was varied from 5% to 100% and D from 12.5% to 100%. Note that in this experimental setup the contrast bolus profile is assumed to be constant and the effects of bolus dynamics are not considered. Also, the phantom images only consider signal from the vials and thus represent ideal sparsity. Artifacts originating from other signal sources such as background tissue or the compounding effects of undersampling multiple vessels are not taken into account.

In Vivo CE-MRA Studies

Nine healthy volunteers were enrolled for participation in an institutional review board-approved HIPAA-compliant study. Each subject provided written informed consent. The calf vessels of the volunteers were imaged using one of three different time-resolved 3D CE-MRA sampling patterns listed in Table 1 (three volunteers per pattern). Results were retrospectively evaluated to assess how vessel image quality evolves with progressive view sharing. All studies were acquired using a 3T imaging system (Signa; GE Healthcare; Waukesha, WI) with a fast 3D GRE sequence in a coronal format with 1.0 mm isotropic spatial resolution. Slice encoding (Z) was anterior/posterior (A/P) and phase encoding (Y) was left/right (L/R). The phase encoding plane was accelerated using 2D SENSE with R = R_Y × R_Z = 4 × 2 = 8 and 2D partial Fourier acquisition. A power injector (Spectris Solaris; Medrad; Indianola, PA) was used to deliver 20 mL of gadobenate dimeglumine contrast material (MultiHance; Bracco Diagnostics; Princeton, NJ) followed by 20 mL saline flush, both at 3.0 mL/sec. Angiograms were reconstructed with zero-filling and 2× density compensation of the peripheral region of the axial phase-encoding plane. The CAPR sampling pattern (13) was used, which only differs from the more general pattern used for the phantom experiments in this work in that the peripheral region is segmented into slender vanes to resemble projection-like sampling as opposed to random-like sampling. The projection-like sampling creates subtle coherent streaking artifacts like those typical of radial sampling as opposed to incoherent noise-like artifacts (2).

Table 1.

Time-resolved sampling patterns used for calf time-resolved CE-MRA in vivo studies. Sequences 1, 2, and 3 all provided 1 mm isotropic resolution, encompassed a typical FOV of 40 (S/I) × 32 (L/R) × 13.2 (A/P) cm³, and were acquired with R=8 2D SENSE and partial Fourier undersampling.

Sequence:	1: Large C	2: Medium C	3: Small C
Center Size (C)	31%	21%	10%
Base Sampling Density (D0)	25%	12.5%	20%
Image Update Time (sec)	5.0	2.5	2.5
Temporal Footprint (sec)	17.7	19.0	12.1

Vessel Image Quality Assessment

Image quality of the undersampled vessel phantom images was quantitatively assessed using four metrics: (i) peak signal; (ii) peak sharpness; (iii) peak-signal-to-mean-background ratio (SMBR); and (iv) peak-signal-to-peak-background ratio (SPBR). Peak signal was measured as the maximum signal intensity of the vessel. Peak sharpness, which indicates how well the vessel edge is defined, was measured by calculating the maximum slope of the vessel edge along a line profile passing through the center of the vessel. Prior to measuring peak sharpness, the line profile was scaled to have a maximum value of 1.0 so as to eliminate the dependence of sharpness on vessel signal. SMBR and SPBR, which indicate the magnitude of undersampling artifacts in the image background, were respectively measured as the ratios of the measured peak vessel signal to the mean and to the maximum background intensities in a region of interest (ROI) placed outside the vicinity of the vessel. SMBR and SPBR were selected as opposed to, for example, signal-to-noise ratio, since the background can have notable structure even with random-like undersampling, particularly for low D values, and may not have typical noise-like statistics.

For the in vivo studies six target vessel cross-sections in the axial phase encoding plane were evaluated in each leg of each study, yielding 36 trials per sampling pattern. The target arterial segments were selected to provide a range of vessel sizes and consisted of the popliteal artery, tibioperoneal trunk, and proximal and middle anterior and posterior tibial arteries. For reference these axial segments are identified in the full maximum-intensity projection (MIP) CE-MRA result shown in Figure 3d. For each target vessel, the second time frame in which contrast material was present was identified and reconstructed without view sharing. Use of the second frame insures that the central k-space region is sampled while contrast material is present in the vessel. The base sampling density, either D₀=25%, 12.5%, or 20% depending on the sampling pattern used, was assumed for this frame, and D increased linearly with view sharing in subsequent frames up to D=100%. The trials for each sampling pattern were grouped into three categories according to vessel diameter as measured by the full-width at half-maximum (FWHM): (I) 1.5 to 3.0 mm; (II) 3.0 to 4.5 mm; and (III) 4.5 to 6.0 mm. The FWHM was measured using the line profile of the first fully-sampled time frame. Image quality of target vessel segments was assessed using two of the same metrics, peak signal and peak sharpness, defined above for the phantom studies. This is illustrated in Figures 3a–c, which show the evolution of signal and sharpness with D. The line profiles used to assess vessel sharpness were drawn through each vessel cross section so as to minimize blurring due to the coherent radial-like undersampling artifacts generated by use of the CAPR pattern. SMBR and SPBR were not evaluated in the in vivo studies due to confounding factors such as spatially-dependent noise amplification from 2D SENSE reconstruction and undersampling artifacts originating from enhanced vessels other than the target. Individual trials were excluded if the vessel diameter did not fit into one of the categories or if insufficient contrast-enhanced time frames were available to achieve full view sharing, as was the case in some studies with interrupted acquisition. The mean peak signal and sharpness of each vessel category for every sampling pattern and peripheral sampling density D were calculated.

FIG. 3.

(a) Zoomed axial sections of the proximal posterior tibial artery taken from a time series formed in vivo using Sequence 2. The cumulative peripheral region sampling density D and cumulative sampling time are indicated for each time frame. (b) Time series of a similar artery cross section from a different subject imaged with Sequence 3. (c) Line profile plots through the center of each vessel with the first frame plotted in red and the last frame plotted in blue. The non-scaled plots (top row) show the buildup of vessel signal, and the scaled plots (bottom row) are useful for visualizing sharpness. The more rapid buildup of signal and sharpness using Sequence 3 vs. Sequence 2 is apparent. (d) MIP of a select in vivo calf MRA result time frame with Sequence 3. Approximate locations of vessel segment line profiles used for analysis, as demonstrated in (a–c), are indicated with red lines.

RESULTS

Phantom Experiments

The evolution of relative peak signal vs. increased view sharing D is illustrated in Figure 4 for C ranging from 5% to 30%. Results are shown in Figs. 4a-b-c for the three different vial sizes (4, 6, and 12 mm diameters) with line profile FWHM values of 2.4, 4.2, and 9.4 mm, respectively. The fully-sampled (D=100%) images are taken as the reference. Data points for a given C value are fit with a linear trendline. As D increases, the increasing peak signal reflects the fact that each image update in the view-shared sequence provides more sampling of k-space while the vessel is contrast-filled. To illustrate, for an acquisition done with D₀=12.5%, the points in the figure for D=12.5% correspond to the first image of the time series, those for D=25% the second image, etc. For acquisitions performed with other values of D₀ the signal values follow the same trendlines but with appropriate spacing. For example, for a sequence using D₀=33% the first update would correspond to D=33%, the second with D=67%, and the third with full 100% sampling. In some cases, if C is sufficiently large, it alone can sample 100% of the vessel peak signal, as can be seen for C≥20% for the 12 mm vial. The corresponding peak signal center sizes for the 4 and 6 mm vials are approximately C≥70% and C≥45%, respectively (data not shown).

FIG 4.

Vial phantom relative peak signal vs. cumulative peripheral region sampling density D for various central region sizes C. Plots are shown for the (a) 4 mm, (b) 6 mm, and (c) 12 mm vials.

The evolution of relative peak vessel sharpness with increased D is shown in Figure 5. Trends for a given C are shown by fitting the data points to a 3^rd-degree polynomial. Sampling patterns with small C (e.g., 5% and 10%) produce sharper images when undersampled; i.e. images with cumulative D values less than about 80%. Sharpness tends to decrease as C increases up until about C=30%, and then the trend reverses (not shown). The trends are similar for all vial sizes, with sharpness generally decreasing for a given C as the vial diameter increases.

FIG. 5.

Vial phantom relative peak sharpness vs. cumulative peripheral region sampling density D for various central region sizes C. Plots are shown for the (a) 4 mm, (b) 6 mm, and (c) 12 mm vials.

SPBR vs. D is plotted in Figure 6. With undersampling, SPBR increases with C up until about C=30%, at which point the trend reverses (not shown). SPBR is highest when C is just large enough to fully sample the vessel signal (e.g., C=20% for the 12 mm vial). For these cases where the center samples the bulk of the vessel signal, progressive sampling of the peripheral region with increasing D adds noise power to the background without contributing much signal to the vessel image. Conversely, when this does not hold, as with smaller C, then the SPBR improves as D increases. Plots of SMBR vs. D are not shown since the trends were identical to those for relative peak signal vs. D (see Fig. 4) as a result of the mean background magnitude being approximately constant for all D.

FIG. 6.

Vial phantom peak-signal-to-peak-background ratio (SPBR) vs. cumulative peripheral region sampling density D for various central region sizes C. Plots are shown for the (a) 4 mm, (b) 6 mm, and (c) 12 mm vials.

In Vivo CE-MRA Studies

Figures 7 and 8 show the evolution of measured signal and sharpness with D for the in vivo results, similar to the plots for the vial phantoms in Figs. 4 and 5. However, note that in Figs. 7 and 8 D is expressed as cumulative sampling time (sec) as opposed to cumulative peripheral sampling density (%) as in Figs. 4 and 5. Plots are shown for all three sequences listed in Table 1 and for all three vessel size groups (I-II-III in parts a-b-c of Figs. 7 and 8). For comparison, results from the vial phantom experiments using the same segmentation parameters C and D as the in vivo sequences are shown as dashed lines in Figs. 7a–b and 8a–b. The vial measurements were placed in the appropriate group plots as determined by their FWHM values (group I: 2.4 mm vial; group II: 4.2 mm vial). The trends of vessel signal and sharpness vs. C and D observed with the in vivo data are similar to those observed in the phantom experiments as described above.

FIG. 7.

Plots of average relative vessel signal vs. time for the three in vivo study sequences. Results are shown for each vessel size group (I, II, and III): (a) 1.5–3.0 mm, (b) 3.0–4.5 mm, and (c) 4.5–6.0 mm FWHM. (a–b) show corresponding vial phantom experiment results as dashed lines with matching color. The 4 mm vial with 2.4 mm FWHM was used in (a), and the 6 mm vial with 4.2 mm FWHM was used in (b). There is excellent agreement between the phantom and in vivo results.

FIG. 8.

Plots of average relative vessel sharpness vs. time for the three in vivo study sequences. The plots are laid out as in Fig. 7. The discrepancy between the vial phantom and in vivo results is attributed to the low SNR of the in vivo studies, particularly in early time frames, which can obscure blurring of the vessel. Despite these differences in relative magnitude, the overall trends are similar for the phantom and CE-MRA studies.

Figure 9 shows images of the vasculature of the left calf for each of the three volunteers studied with the medium-C Sequence 2 (a-b-c) and the small-C Sequence 3 (d-e-f) of Table 1. Both of these sequences had an update time of 2.5 sec. The inset for each figure part shows the progressive degree of k-space sampling used to generate that image, approximately corresponding to the time over which the proximal vessels were filled with contrast material. A movie comparing the image evolutions of Sequences 2 and 3 is provided in Supplemental Movie #1.

FIG. 9.

Comparison of in vivo CE-MRA time series for Sequences 2 and 3. (a–c) Time series MIPs for the three studies acquired with medium-C Sequence 2. The time post-contrast injection and the peripheral region sampling density D are indicated. The degree of sampling of the k_Y-k_Z plane is indicated by the inset CAPR patterns. Full sampling is achieved after eight frames. (d–f) Similar layout for the three small-C Sequence 3 studies, which reach full sampling after only five frames. The rapid improvement in vessel quality using Sequence 3 is evident.

DISCUSSION

This work has shown how vessel signal and sharpness evolve over the time series of a view-shared sequence as is commonly used for time-resolved CE-MRA. The dependence of these evolutions on the k_Y-k_Z sampling characteristics of the acquisition, specifically the size C of the fully-sampled k-space central region and the density D₀ of the less-frequently-sampled peripheral region, has been demonstrated. To our knowledge this is the first detailed study of these phenomena.

The results show that, for a set of view-shared sequences that have a given image update time, there is a tradeoff of vessel signal with vessel sharpness. This is consistently seen in the phantom studies in that curves with progressively larger C provide higher signal values (Fig. 4) but lower sharpness values (Fig. 5). This tradeoff occurs for all three vessel sizes studied in this work. These trends are also observed in the in vivo measurements in Figs. 7 and 8, in which the results demonstrate a similar tradeoff. This tradeoff can also be appreciated from the image comparison in Figure 9. The small-C Sequence 3, acquired with C=10% and D₀=20% (Figs. 9d-e-f) consistently provides only low signal in the first one or two frames but rapidly gains sharpness over these frames. On the other hand, the medium-C Sequence 2, formed with C=21% and D₀=12.5% (a-b-c), has relatively good signal in the first and second frames, but requires more 2.5 sec updates to gain sharpness equivalent to that for Sequence 3.

The above tradeoff can be explained as follows. For a given image update one can either more extensively sample the central k-space region (i.e., increase C and decrease D₀) to benefit from overall high signal level or more densely sample the peripheral region (i.e., increase D₀ and decrease C) for improved sharpness. In terms of k-space sampling, increasing C at the expense of D will effectively give greater weight to the central low spatial frequencies compared to the peripheral high spatial frequencies until D=100% when view sharing is complete. This preferential weighting of central vs. peripheral k-space causes the low spatial frequencies to dominate in the vessel image, effectively leading to a blurred low-resolution representation of the vessels and thus a reduction of vessel sharpness. Additionally, the choice of increasing C or D₀ is intrinsically linked to the sequence temporal footprint, as illustrated in Fig. 2. For a given image update time, increasing D₀ will reduce the number of image updates needed to fill k-space, thereby shortening the temporal footprint. Increasing C, on the other hand, will reduce D₀ and extend the temporal footprint. Given that the temporal footprint defines the time needed to fill k-space using view sharing, gaining signal by increasing C is costly in terms of the time it takes to improve vessel sharpness. This becomes ever more apparent as C gets larger, since more samples are needed to substantially increase the size of the k-space central region.

The degree to which an increase in C vs. D₀ is beneficial is determined in part by the size of the vessels under consideration. For example, referring to Fig. 4c, for a given vessel size, once C is adequately large there is little to gain by making it larger in an attempt to increase signal. This point of diminished improvement occurs approximately when the central region is large enough to substantially capture the full vessel signal in k-space (e.g., C≥20% for the 12 mm vial). On the other hand, if the vessels are small, as in Fig. 4a, increasing C provides relatively little gain in signal at the expense of a greatly extended temporal footprint. The size of C needed to fully sample the vessel signal can be estimated by calculating the width of the main lobe of the k-space sinc response to a rect-shaped vessel profile of a specific FWHM as given by Fourier transform properties. For the vial phantoms considered in this work, with FWHM values of 2.4, 4.2, and 9.4 mm and a nominal spatial resolution of 1.0 mm, the expected center sizes required for sampling 100% of the peak vessel signal are C=83%, 48%, and 21%, respectively, which agree well with the experimental results.

The presentation of image update time and temporal footprint in Figure 2 in arbitrary units can be used to facilitate the comparison of different sequences. The plot axes will scale as common imaging parameters such as TR, spatial resolution, and parallel imaging acceleration are adjusted. For example, the above-described Sequence 3 (C=10%; D₀=20%) used 2D SENSE acceleration of R=8 in generating the images shown in Fig. 9d-e-f. This sequence corresponds to an image update time and temporal footprint of (11 au, 52 au) in Figure 2b. If improved receiver coils were to allow increased SENSE acceleration of R=10, then an update time of 11 au and footprint of 52 au in Figure 2b would convert to an update and footprint 10/8× larger, or 14 au and 65 au, respectively. This would allow a modified view-shared sequence with C=20% and D₀=20%, essentially allowing both the high C and high D₀ seen to be desirable in Figure 9. As another example, if the 1.0 mm spatial resolution in both Y and Z used for Sequences 2 and 3 were slightly degraded to 1.2 mm, then the number of necessary phase encodings would be reduced by a factor of (1.2)², or 1.44. This, too, would scale the plot. The more forgiving resolution would allow the update time and footprint to be reduced for full sampling. Such analysis might be useful in adapting view-shared sequences to perfusion imaging using dynamic contrast enhancement, in which case the spatial resolution demands are typically less but the time resolution requirements are greater than for CE-MRA.

As a specific application of this work, the transit time of contrast material along the S/I extent of the thigh station in peripheral CE-MRA can be relatively short, often under 10 seconds (22). If fluoroscopic tracking is to be performed over this region, this short transit time dictates that the temporal footprint of the sequence is ideally no longer than this. For good precision in monitoring contrast passage, a small image update time is also desired, such as 2.5 sec or less. Sequences 2 and 3 of Table 1 both meet the target of the short frame time, but the reduced temporal footprint of the small-C Sequence 3 enabling rapid build-up of vessel signal and sharpness made it be our choice in spite of its shortcomings of reduced signal in early frames.

There are several limitations to this study. First, this work did not take into account the possible time-varying nature of the contrast bolus signal. If the signal modulation is extensive over the temporal extent of the image acquisition, then it would ideally be accounted for. This has been done previously with respect to studies of bolus timing in view-shared acquisition (15), spatial resolution limits in CE-MRA (23), and bolus administration (16). In the intervening time since these previous studies there has been considerable development of parallel acquisition, particularly as applied to CE-MRA. This has reduced the acquisition time for high resolution imaging to well under 20 sec. In this work a constant bolus signal was used for the phantom studies. For the in vivo studies, analysis of the luminal signal of the popliteal arteries from individual, non-view-shared, 2.5 (Sequences 2 and 3) or 5.0 sec (Sequence 1) time frames showed that after the first frame considered, the signal modulation was at most 20% of the maximum over the subsequent 25 sec. This modulation is relatively small, particularly in light of the small 12.1 to 19.0 sec temporal footprints of the sequences analyzed (Table 1). Use of a constant bolus serves as an idealized reference, but the observed bolus and limited acquisition time of the in vivo studies were well matched to this. For applications in which the contrast modulation is greater, such as modeling higher injection rates using diminished contrast volume, the methodology used for the phantom studies would likely need modification to allow a contrast bolus with greater modulation.

There are other limitations. Second, this work considered scenarios with essentially no background signal, which underestimates the consequences of undersampling when there are other signal sources in angiograms such as residual tissue from imperfect subtractions. As demonstrated in Figure 6 of this work, undersampling artifact will be more severe when using sequences with small center sizes. Third, it has been shown for static images that increasing the weighting of an undersampled k-space peripheral region can allow tradeoff of signal, sharpness, and undersampling artifact (6). Such an approach, although not currently practical for time-resolved CE-MRA, may allow a more favorable tradeoff of the effects of undersampling with appropriate post-processing. Lastly, zero-filling was used for all reconstructions, but there may be advantages to using post-processing techniques such as homodyne (1), HYPR (24), or compressed sensing (25) to better account for the unsampled portions of k-space.

In summary, we have developed a framework for the study of the evolution of signal and sharpness in time-resolved imaging using view sharing. The development is general in that the k-space sampling method considered encompasses many commonly-used contemporary techniques. For imaging at a fixed image update time we have shown the tradeoff of signal with sharpness with sequence parameters. Results were presented in phantom studies and corroborated with in vivo CE-MRA exams. The methodology can be scaled to account for alterations in such acquisition parameters as spatial resolution and degree of acceleration with parallel imaging.

Supplementary Material

Supp Movie S1

MOVIE 1: Rotating targeted MIPs (3× sinc-interpolated) of the left calf vasculature of two in vivo studies, one acquired with medium-C Sequence 2 (left side of movie) and the other with small-C Sequence 3 (right side of movie), corresponding to the time series in Figs. 9c and 9f, respectively. The first five frames with contrast are shown, updating every full rotation (2.5 sec). Higher vessel signal is seen in the early frames using Sequence 2, but the more rapid buildup of signal and sharpness is evident using Sequence 3.