The Effect of Spiral Trajectory Correction on Pseudo-Continuous Arterial Spin Labeling with High-Performance Gradients on a Compact 3T Scanner

Abstract

Purpose:

To demonstrate the feasibility of pseudo-continuous arterial-spin-labeled (pCASL) imaging with 3D fast-spin-echo stack-of-spirals on a compact 3T scanner (C3T), to perform trajectory correction for eddy-current-induced deviations in the spiral readout of pCASL imaging, and to assess the correction effect on perfusion-related images with high-performance gradients (80 mT/m, 700T/m/s) of the C3T.

Methods:

To track eddy-current-induced artifacts with Archimedean spiral readout, the spiral readout in pCASL imaging was performed with five different peak gradient slew rate (S_max) values ranging from 70 to 500 T/m/s. The trajectory for each S_max was measured using a dynamic field camera, and applied in a density-compensated gridding image reconstruction in addition to the nominal trajectory. The effect of the trajectory correction was assessed with perfusion weighted (ΔM) images and proton-density-weighted images as well as cerebral blood flow (CBF) maps, obtained from ten healthy volunteers.

Results:

Blurring artifact on ΔM images was mitigated by the trajectory correction. The CBF values on the left and right calcarine cortices showed no significant difference after correction. Also, the SNR of ΔM images improved, on average, by 7.6% after correction (P < 0.001). The greatest improvement of 12.1% on ΔM images was achieved with a spiral readout using S_max of 300~400 T/m/s.

Conclusion:

Eddy currents can cause spiral trajectory deviation, which leads to deformation of the CBF map even in cases of low value S_max. The trajectory correction for spiral-readout-based pCASL produces more reliable results for perfusion imaging. These results suggest that pCASL is feasible on C3T with high-performance gradients.

Introduction

Arterial spin-labeled (ASL) perfusion MR imaging has been used to quantify cerebral blood flow (CBF) non-invasively. It has been validated as an alternative CBF measurement method to H₂¹⁵O PET perfusion imaging methods, which require exogenous contrast agents.^1–3 As a quantitative physiological parameter, ASL CBF has been shown to be an important clinical biomarker to detect cerebrovascular diseases and neurodegenerative disorders, such as dementia and brain cancer.^4–6 Also, ASL MR imaging has been applied to study aging, gender, and development in research subjects.^7,8

To capture perfusion signal arising from inflowing, labeled, arterial blood spins delivered to tissue, various implementation strategies have been developed for both spin-labeling and data acquisition.⁹ Much work on the spin-labeling task has been focused on improving its labeling efficiency and SNR. The pseudo-continuous ASL (pCASL) labeling method has been widely used in clinical settings, with advantages demonstrated over the CASL or the PASL methods.^9,10 pCASL takes advantage of reduced magnetization transfer effects, and is compatible with modern RF transmission hardware.^9,10 It also helps to reduce artifacts and perfusion signal loss by improving labeling efficiency. For data acquisition, the segmented 3D acquisition scheme combined with background suppression has been one of the techniques recommended for clinical use.^9,11,12 A spiral trajectory has the advantage of requiring fewer excitations than Cartesian trajectories, and is robust against motion and flow artifacts.^13–15 For these reasons, 3D fast-spin-echo (FSE) stack-of-spirals (SOS) has gained popularity for pCASL perfusion imaging.^16,17

A lightweight, low-cryogen, compact 3T MRI system (C3T) has been developed and reported in the literature.^18,19 It is equipped with high performance gradients, which can operate at 700 T/m/s simultaneously with an 80 mT/m maximum gradient amplitude on each gradient axis.^18–23 Typical whole-body MR scanners offer up to a 200 T/m/s gradient slew rate, and their performance may be further limited due to concerns about peripheral nerve stimulation (PNS).²⁴ The C3T can apply higher slew rates and gradient amplitudes because PNS is reduced due to its smaller bore diameter of 37 cm. Its 26 cm diameter of spherical volume is suitable for imaging heads, extremities and infants. The C3T has been shown to improve image quality for anatomical, functional and diffusion imaging when compared to conventional whole-body scanners.^25,26 Preliminary work reported the feasibility of the 3D spiral pCASL technique on the C3T without the need of a second RF transmitter.²⁷ Prior to this demonstration, the feasibility of pCASL on the C3T without the use of an additional transmitter was in question, because the smaller and shorter magnet geometry requires a labeling plane that is closer to the imaging volume when compared to a whole-body system.

Use of a higher slew rate and gradient amplitude can aggravate gradient eddy currents, especially with rapidly-varying waveforms like spiral readouts. Additionally, mismatches in group delay between the RF and gradient subsystems, can also lead to image distortion and/or deformation. To address eddy current effects, the actively shielded gradient coils^18,28 and gradient waveform pre-emphasis^29,30 are used on the C3T system. However, eddy current effects can remain, causing k-space trajectory deviations that are amplified during high spatial resolution acquisitions.^31,32 Gradient eddy current effects on the spiral readout have not been widely studied in ASL-based perfusion imaging using a spiral trajectory. This may be because the eddy-current-induced artifacts in ASL imaging at relatively low gradient slew rates can be confounded with other sources of errors, especially due to ASL’s intrinsically low SNR. However, as the effect becomes more obvious at higher slew rates, eddy currents are detrimental to ASL image quality. To measure the trajectory deviation, previous studies have proposed direct measurement of the current in each gradient channel,³³ use of point phantoms on different locations,³⁴ and use of specialized nuclear-magnetic-resonance (NMR) probes to measure the dynamic magnetic field.^35–37 In our study, a dynamic field camera consisting of dedicated NMR probes was used to measure spatiotemporally-varying magnetic fields, resulting in direct observation of actual trajectories.^38–40 A field camera can characterize inaccuracies in the gradient waveforms, and allow trajectory measurements without any modification of the pulse sequence. For the 3D FSE SOS pulse sequence, a field camera can capture the actual spiral readouts (in the presence of eddy currents, group delays, etc.) to improve the quality of reconstructed images.

In this paper, the feasibility of pCASL on a C3T scanner is demonstrated. Trajectories for the spiral readouts with various slew rates were tracked with a field camera, and then the trajectory correction for eddy-current-induced artifacts on pCASL perfusion imaging was assessed. This work was built on the preliminary results we reported previously.⁴¹

Methods

MRI data acquisition and scan protocol

All MR studies were conducted on a technology demonstrator C3T built by GE Global Research (Niskayuna, NY, USA).^18–23 The C3T included an integrated T/R RF coil for transmission, and an 8-channel brain coil (Invivo, Gainesville FL, USA) was used for reception. B0 frequency tracking and linear concomitant field pre-emphasis corrections were applied due to the asymmetric gradient design.^21,23

The system runs standard DV26 software (GE Healthcare, Chicago IL, USA), and the stock pulse sequence for pCASL perfusion imaging was based on a 3D FSE SOS with background suppression.^10–12 The spiral readouts were numerically generated with Archimedean spirals determined by a number of factors, including field-of-view (FOV), receiver bandwidth (±BW), maximal gradient amplitude (G_max), peak slew rate (S_max), number of spiral interleaves (N_itl) and number of spiral readout samples (N_s).¹³ To prevent undersampling along the spiral readout direction, G_max for all the spiral trajectories was determined by the azimuthal Nyquist sampling criterion^42–44: $G_{max}=\frac{2\pi }{\gamma }\cdot \frac{2BW}{FOV}$, which yields 50 mT/m for all studies where a maximum allowable BW of ±250kHz was chosen to push the gradient amplitude as high as possible during readout sampling. The S_max in conjunction with N_itl and N_s determines the in-plane resolution (Δx). In this study, N_itl was held constant to keep the same total scan time. A series of S_max values, including 70, 200, 300, 400 and 500 T/m/s, were used to observe the effect on pCASL imaging. N_s was chosen to target a 3.5 × 3.5 mm effective in-plane spatial resolution Δx. Higher values of S_max led to a reduced number of samples N_s. The imaging parameters are summarized in Table 1.

Table 1.

Sequence parameters of spiral trajectory for experiment^a

Experiment	# of interleaves, Nitl	TE (ms)	Readout duration per shot (ms)	TR (ms)	Gmaxb (mT/m)	Smaxc (T/m/s)	Receive BW (kHz)	# of samples per readout, Ns	Effective in-plane resolution, Δx (mm)	Acquisition time (min:sec)
pCASL	8	8.9	4.00	4563	50	70	±250	2000	3.52	4:06
		7.3	2.40	4491		200		1200	3.49	4:02
		6.9	2.00	4473		300		1000	3.44	4:01
		6.9	1.68	4473		400		840	3.51	4:01
		6.9	1.52	4473		500		760	3.49	4:01
High resolution imaging	16	8.9	4.00	4563	50	700	±250	2000	1.21	3:12

^aThe sequence had an in-plane FOV of 24 cm, acquired transverse slices with 44 k_z steps of 4 mm thickness and N_EX=3. For ASL imaging, a labeling duration and a post-labeling delay were 1.450 and 1.525 sec., respectively.

^bRestricted gradient amplitude of ||G_x + iG_y||.

^cRestricted slew rate of ||S_x + iS_y||, namely ||$\frac{d{G}_x}{dt}$ + i$\frac{d{G}_y}{dt}$||.

For perfusion imaging, a post-labeling delay (PLD) of 1.525 s, a labeling duration (LD) of 1.450 s, and 3 averages (N_EX) were used to acquire label and control images. Perfusion-weighted images (ΔM) were obtained by subtracting label from control images. Each pCASL acquisition produced ΔM and PDw images as well as a corresponding CBF map. The entire cerebrum was covered by the imaging volume, the center of which corresponded to the iso-center of the scanner.

Anatomical images were acquired with a T2-weighted FSE pulse sequence to cover the same volume as pCASL imaging (FSE: TR/TE 4466.0/91.7 ms, 0.43 × 0.43 × 4.0 mm with zero slice gap), and used as reference images for co-registration and segmentation of gray and white matter.

Ten healthy volunteers without known neurological disease (age = 34.4 ± 8.6 years, 5 females/5 males) were recruited and scanned under an Institutional Review Board-approved protocol, after providing written informed consent. The order of the five values of S_max was randomized for each subject to reduce a bias from subject fatigue and motion.

Measurement and correction of the spiral trajectory

In order to estimate the actual k-space trajectories in the presence of eddy currents and system delays, a dynamic field camera with sixteen ¹⁹F NMR field probes (Skope, Zurich, Switzerland) was used.^38–40 A plastic bracket holding the field camera probes (similar to Figure 1E in Ref. 38) was placed in the scanner bore. The time-varying magnetic fields of spiral readouts were acquired, from which the trajectories in (k_x, k_y) were derived. The trajectories were repeatedly measured for each interleave of the spirals and for each value of S_max. The acquisition duration of the field camera was adjusted to match the spiral readout length. The measured trajectories were obtained at a 1.0 MHz sampling rate and resampled to match the receiver bandwidth of ±250 kHz.

Figure 1.

High-resolution proton-density-weighted data of an ACR phantom and two volunteers (on Sept. 2018 and Mar. 2019) were obtained by a 3D fast-spin-echo stack-of-spirals pulse sequence, where a readout spiral was generated with 700 T/m/s of S_max, 50 mT/m of G_max and 16 interleaves. The images were reconstructed (A, B, C) without and (D, E, F) with the trajectory correction. In the uncorrected images, the imaging object was rotated and signals inside the object were blurred due to deviation in spiral trajectories. The same image display window level and width were used across the images. The trajectory deviation was illustrated (G) with the spiral-out beginning of 8 interleaves at a center of k-space and (H) at the end of a single interleaf among 16 spiral interleaves. (I) Pointwise deviations between nominal and measured trajectories were plotted over readout time. Δk denotes a distance on k-space determined by the Nyquist criterion (Ref. 13), which is used to quantify the deviation.

To apply the correction, density-compensated gridding image reconstruction was performed offline using the measured trajectories instead of the nominal trajectories. Image reconstruction was implemented in Matlab (The MathWorks, Inc., Natick MA, USA) using the Orchestra (GE Healthcare, Waukesha WI, USA) software development kit (SDK). To verify the trajectory correction in the high resolution PDw image, the American College of Radiology (ACR) MRI quality control phantom⁴⁵ and volunteer data were acquired by the imaging parameters as described in Table 1.

Data processing and analysis

A CBF map was calculated with:

$$\text{CBF}=\frac{6000\cdot \text{λ}\cdot {\text{S}}_{\Delta \text{M}}\cdot \text{exp}\left({\text{T}}_{\text{PLD}}/{\text{T}}_{1,\text{b}}\right)}{2\cdot \text{α}\cdot {\text{T}}_{1,\text{b}}\cdot {\text{S}}_{\text{PDw}}\cdot \left(1-\text{exp}\left(-{\text{T}}_{\text{LD}}/{\text{T}}_{1,\text{b}}\right)\right)} \left[\text{ml}/100\text{ g}/\text{min}\right],$$ (1)

where S_ΔM and S_PDw are signals from ΔM and PDw images obtained, respectively, from the pCASL sequence.⁹ The symbol λ denoted a blood-brain partition coefficient of 0.9 ml/g.⁴⁶ The labeling efficiency of α was set to 0.85 for pCASL.¹⁰ T_1,b was the longitudinal relaxation time in blood at 3T of 1650 ms.⁴⁷ T_PLD and T_LD were 1525 ms and 1450 ms for the ΔM images, respectively.

To minimize the mismatch between intra-subject data, image alignment was performed among pCASL images of the five S_max values, with and without trajectory correction. The corrected PDw image with the lowest S_max of 70 T/m/s was used as a reference. Rigid-body transformation between the reference and PDw images obtained with other S_max values was applied to the corresponding ΔM image and the CBF map. This preprocessing was performed on each subject’s data by using Statistical Parametric Mapping software (SPM12, Wellcome Trust Centre for Neuroimaging, UK). To evaluate SNR efficiency, five rectangular ROIs of 37.6 × 37.6 mm² were manually placed on the anterior, lateral, and posterior cerebral regions, as well as on the background area after image alignment (Figure 6A). Mean values of image intensities and noise variances were evaluated from the cerebral regions and the background area, respectively. Perfusion SNR efficiency was scaled by $1/\sqrt{T_{readout}}$, because, in general, we expect the image SNR to be proportional to the square root of the sampling time.

Figure 6.

(A) ROI for perfusion SNR of the ΔM image. The present image is the sum of the corrected ΔM images of 70-T/m/s slew rate across subjects. For SNR comparison with the corrected ΔM images, the ROIs were applied after their alignment to the corrected images. (a-d) Multiple brain ROIs were used to average the signal intensities. (e) Background ROI was used to estimate noise variance and chosen as far from the brain as possible within the circular clipping in order to minimize a blurred signal caused by off-resonance effect in the spiral trajectory. (B) Perfusion SNR of ΔM image depending on trajectory correction, sampled on four ROIs of ten volunteers and scaled by a square root of a readout duration. The trajectory correction constantly improved SNR of the perfusion image [P < 0.001; Wilcoxon signed rank test]. The error bar denotes standard deviations of the mean SNR (N=40).

For regional analysis with inter-subject data, pCASL-related images were registered to the corresponding anatomical image, and then spatially normalized and resampled to the Montreal Neurological Institute (MNI) brain template using SPM12. The Neuromorphometrics atlas in SPM (Neuromorphometrics, Inc., Somerville, MA, USA. under academic subscription, http://Neuromorphometrics.com/) was employed to define regions of interest in the spatially-normalized images. The unified segmentation routine implemented in SPM12 was used to segregate gray and white matter,⁴⁸ where the tissue probability maps were binarized at a threshold of 0.8 to discriminate gray or white matter. The MNI-normalized images and the segregation masks for gray and white matter were used for three types of quantitative analysis in this study: (1) To evaluate the effect of the artifact, S_max-related CBF values on gray matter of the anterior cingulate gyrus (Label index 100 and 101 in the Neuromorphometrics atlas, respectively) and the calcarine cortex (Label index 108 and 109 in the Neuromorphometrics atlas, respectively) were examined on the right and left hemispheres, independently. (2) To evaluate the CBF contrast ratio of the gray matter to the adjacent white matter, the two CBF means of gray and white matter segregated at each of the 98 regions (Label index 100 to 207 in Neuromorphometrics atlas) were evaluated and the mean of the ratios for each S_max was calculated across subjects. (3) To further observe the effect of S_max on trajectory-corrected MNI-normalized images, the signal enhancement was evaluated in the ΔM, PDw and CBF images. 98 regions of gray matter (Label index 100 to 207 in the Neuromorphometrics atlas) and 2 regions of cerebral white matter (Label index 44 and 45 in the Neuromorphometrics atlas) from each subject were considered.

Statistical analysis was performed using Matlab. The Wilcoxon matched-pairs signed rank test was used to assess differences between pCASL-related images reconstructed with and without trajectory correction. To study S_max dependence, the intensities of pCASL-related images were normalized to corresponding images obtained using the lowest slew rate of 70 T/m/s for each test subject in order to minimize subject-dependent factors. We measured the significance between 70 T/m/s and other S_max with the non-parametric t-test. Since all of the normalized values in 70 T/m/s were zero, one-sample Wilcoxon signed-rank test was applied with normalized values. Differences with P < 0.05 were considered significant.

Results

Correction of distortion on pCASL images

High-quality perfusion maps were obtained from all subjects on the C3T. After k-space trajectory correction using the field camera measurement, significant improvement in image quality was observed. To illustrate the effect of the trajectory corrections, PDw imaging with higher resolution than the perfusion imaging was used. Without correction (Figure 1A, 1B, and 1C), the images were rotated counter-clockwise and signals inside the brain were smeared, making the edges unclear. Moreover, the blurring artifacts caused hyper/hypo-intense signal boundaries at the edges or near the venous sagittal sinus (indicated by the yellow arrow in Figure 1). The trajectories measured by the dynamic field camera for S_max = 700T/m/s were plotted with nominal trajectories on a normalized k-space (k_max=±0.5 mm⁻¹) as shown in Figure 1G and 1H. Figure 1H shows that the deviation between the end points of the nominal and measured trajectories was 2.97Δk where Δk denotes a sampling distance on k-space to satisfy the radial Nyquist criterion. In the same way, pointwise trajectory deviations were plotted over spiral readout time in Figure 1I. Note that the deviation started at 0.1538Δk (±0.0148Δk, standard deviations) rather than zero, which could be caused by a timing mismatch between data acquisition and gradient transmission (i.e., mismatched group delay). Note that the observed trend of deviation change on k-space was similar to the gradients applied for spiral readout $\Vert G\Vert$ (see Supporting Information Fig. S1A and S1E). Also, the oscillating pattern in the deviation was considered to be caused by the x- and y-gradient difference. In addition, the trajectories previously measured with the field camera continued to work well for the scans of two volunteers acquired six months apart, as shown in Figure 1E and 1F.

As shown in Figure 2, rotational artifacts were also present in low-resolution perfusion images acquired, even with low values of slew rate S_max of 70 T/m/s. The signal boundary artifact observed in the high resolution images was not apparent in PDw images, but the ΔM images and the corresponding CBF maps clearly benefitted from the correction. In the magnified images (Figure 3), distortion can be observed in uncorrected ΔM images, e.g., counter-clockwise blurring in the anterior region. This distortion was worse in the uncorrected images acquired with the higher slew rate, and was not limited to the anterior part of the brain. Blurring can also be found in comparison of corrected and uncorrected CBF maps acquired with different slew rates. In a quantitative analysis, blurring artifact could cause signal contamination across hemispheres, if uncorrected. As shown in Figure 4B and 4D, the CBF differences between the left and right areas increased with increasing S_max without the trajectory correction. The calcarine cortex regions showed a large difference even with the lowest value S_max. With the correction, these differences were dramatically reduced.

Figure 2.

The unaligned pCASL-related images of (A, B) PDw, (C, D) ΔM and (E, F) CBF were presented with various values of S_max, where upper and lower rows of each contrast denoted the results (A, C, E) without and (B, D, F) with the trajectory correction, respectively. Since co-registration across images was not applied, a counter-clockwise rotation of the brain was observed in (A, C, E). The artifact became more severe as the maximum slew rate increased. The blurring artifact between inter-hemisphere in uncorrected images of both (C) ΔM and (E) CBF can be seen at both the anterior and the posterior parts of the brain. Further details are shown in the next two figures.

Figure 3.

Distorted signal patterns on the anterior part across two hemispheres in (A) ΔM and (C) CBF images, which were alleviated with the trajectory correction as shown in (B) and (D), respectively.

Figure 4.

CBF values of (A) the anterior cingulate cortices (ACC) and (C) the calcarine cortices (Calc) were evaluated with various values of S_max to demonstrate the effect of the trajectory correction. The ‘right – left’ differences of ACC and Calc regions were presented in (B) and (D), respectively, with Wilcoxon one-sample signed rank test. The CBF differences tended to increase along S_max for both regions without the field camera trajectory correction. However, the correction led the CBF difference to be mitigated independent of the value in S_max. The error bar denotes standard error of CBF means or CBF differences (N=10).

Artifact influenced the CBF values at a single hemisphere as well as the inter-hemisphere. In Figure 5, the profiles of the CBF maps were compared to that of the anatomical image. With the correction, the profiles from the CBF maps with five different values of S_max were more coherent with each other and with the anatomical profile in comparison with Figure 5C. When considering the peak displacement in Figure 5D, the distances from the CBF profiles to the anatomical profile were 3 mm in 70 to 300 T/m/s and 4.5 mm in 400 and 500 T/m/s with the uncorrected CBF maps. This value was almost as much as the in-plane resolution for pCASL imaging. This geometry mismatch between the CBF map and the corresponding anatomical image could cause misestimated CBF values. Figure 5E shows the CBF contrast ratios of gray matter to the adjacent white matter. The ratios with the trajectory correction tend to be larger than those without the correction for S_max of 200 to 500 T/m/s, because of better depiction of white matter in the CBF, reduced with correction (Supporting Information Fig. S2).

Figure 5.

Signal profile comparison of CBF maps and an anatomical image within a hemisphere. A ROI on (A) T2w anatomical image and (B) CBF map was chosen as indicated by the arrows. The profiles on the ROI were plotted (C) with and (D) without the trajectory correction. The coherence between anatomical image and CBF maps was improved with the trajectory correction regardless of S_max. (E) CBF contrast ratio of the gray matter to adjacent white matter depending on the trajectory correction and S_max. The ratios with the trajectory correction tended to be larger than those without correction on S_max of 200 to 500 T/m/s. The error bars denote the standard deviation of the ratio across subjects (N=10). Wilcoxon signed-rank test for matched pairs was performed (**; P < 0.01, n.s.; not significant).

Improvement in perfusion SNR by the trajectory correction

The signal and noise variances of pCASL images were quantitatively investigated at four different region and at a background region. The signal intensities and SNRs were averaged across four locations, ten subjects and five different values of S_max. In Table 2, the signal on ΔM images was improved by 7.7 % with the correction (P < 0.001), while the noise variance from background did not show any significant change (P = 0.5527). Thus, the overall perfusion SNR improved by 7.6 % (P < 0.001). The SNR of the PDw images seemed to be improved greatly due to the large reduction in noise variance. However, the high noise variance in the uncorrected PDw images was overestimated because of artifacts in the background of the uncorrected images. The actual SNR increase in PDw images is mainly attributed to an improvement of 9.8 % in image intensity (P < 0.001) the same as ΔM images. After the trajectory correction, some signal changes were observed in both of ΔM and PDw images. Since the signal changes in the ΔM images were smaller than those in PDw images, the corresponding CBF maps had slightly reduced values of −1.5% (P < 0.001).

Table 2.

The effect of the trajectory correction on ASL-derived images

ASL-derived images		w/ correction mean (SD)	w/o correction mean (SD)	Difference mean (SD) a	p-valueb	Percent change (%)
ΔM (×100)	Signal	2119.7 (395.4)	1967.4 (332.5)	152.3 (101.0)	<0.001	7.7
	Noise variance	85.3 (17.0)	85.1 (17.7)	0.3 (9.5)	0.5527	0.2
	pSNRc	17.4 (4.2)	16.2 (3.8)	1.1 (2.1)	<0.001	7.6
PDw	Signal	3334.1 (453.6)	3036.4 (342.0)	297.7 (152.6)	<0.001	9.8
	Noise variance	9.6 (4.3)	22.6 (10.2)	−13.1 (9.2)	<0.001	−57.5
	SNR	408.9 (161.5)	169.5 (96.9)	239.4 (158.4)	<0.001	141.2
CBF [ml/ 100g / min]		53.5 (6.6)	54.3 (6.7)	−0.9 (1.5)	<0.001	−1.5

^aAveraging of subtracting w/o correction from w/ correction at each S_max of each subject.

^bWilcoxon signed rank test for paired two samples.

^cThe perfusion SNR, namely pSNR, was scaled by $1/\sqrt{Readout \left(ms\right)}$.

In Figure 6B, perfusion SNR in the ΔM images was evaluated and scaled with the square root of the readout duration for each S_max. For all values of S_max, the correction significantly improved perfusion SNR. The improvement in perfusion SNR was more apparent for S_max above 200 T/m/s compared to 70 T/m/s. Perfusion SNR remains independent of S_max both before and after the trajectory correction showing no signal loss by S_max.

Signal dependence on S_max

Figure 7A and 7B show the gray matter and white matter signal intensity change in the ΔM, PDw and CBF images, respectively. The signal enhancement of the ΔM images increased by 12.1% and 11.2 % in gray and white matter for images acquired with S_max of 400T/m/s, respectively (P < 0.001 for both). The signal increase on ΔM images led to increased CBF values in gray matter (P < 0.001) while the CBF value in white matter began to increase when higher slew rates were used (400 and 500 T/m/s) (P = 0.003 and P = 0.005, respectively).

Figure 7.

Signal enhancements by S_max in ΔM, PDw and CBF images, which were normalized to S_max of 70 T/m/s on (A) gray matter and (B) white matter. CBF enhancement is at the peak when S_max of 400 T/m/s is used. The errors bar denotes standard deviations of the mean enhancement. Wilcoxon signed-rank test was performed with N = 980 and 20 for gray and white matters, respectively (*; P < 0.05, **; P < 0.01, ***; P < 0.001, n.s.; not significant).

Discussion and Conclusions

The trajectory correction for spiral readout improved the quality of the ΔM and the PDw images in pCASL imaging. Trajectory deviation was primarily caused by eddy currents and mismatch in group delay. A dynamic field camera was used to measure actual spiral trajectories. The measured trajectory provided robust artifact correction which alleviated the deformation, especially in the ΔM images over a range of S_max. Also, the trajectory correction improved SNR in both the ΔM and the PDw images and yielded better registration with anatomical images across all values of S_max.

We recorded dynamic magnetic fields of spiral readouts in 3D FSE SOS with the field camera only once. The dynamic field data was then reused, successfully, to correct all subject and phantom scans with the identical protocol over the subsequent 7 months. This suggests that the dominant contribution for reproducibility of the first-order eddy currents is possibly related to the design and structure of the gradient system rather than any specific property of a phantom or volunteer. However, a thermal change by high-gradient-duty-cycle scans can cause a temporary change in gradient characterization.^49,50 Our application of pCASL roughly consists of a 1.4 s labeling block, a 1.5 s waiting block, and a 0.3 s data acquisition block in 4.5 s repetitions. Although the acquisition block runs the gradients at a high temporal duty cycle, our experiment indicated that the waveforms were not sufficiently amplitude-intensive to cause significant thermal state variation in the gradient system. EPI readouts used by Wilm et al.,⁵⁰ using a gradient of ±30 mT/m, was 128 ms for a TR of 150 ms which was far more intensive compared with our 4-ms spiral readouts by 44 slice-encodings in 4.5 s TR. Therefore, it was considered that our pCASL sequence would not cause a significant change in gradient characterization by thermal variation.

Instead of using a dynamic field camera, a simple method to correct the spiral trajectory has been proposed for estimating the gradient time delay for each gradient axis.³² Although the gradient amplitude polarity reversal was used to estimate the delays in a previous study,³² we performed a time-shifting of nominal trajectories at 0.1 μs intervals and compared those with the corresponding measured trajectories to estimate time shifting. Timing delays, corresponding to the minimized mean square error between the shifted nominal trajectory and the measured trajectory, determined the characterized delay for the gradient axis (Supporting Information Fig. S3). Reconstructed with the shifted nominal trajectories, phantom and volunteer PDw images of 700 T/m/s in S_max did not show significant rotational or blurring artifacts (Supporting Information Fig. S4). However, there are some residual artifacts near edges and image non-uniformity was observed. In the CBF comparison, some artifacts at the brain boundary and overestimation of CBF values for white matter were observed with the shifted nominal trajectory (Supporting Information Fig. S5). This phenomenon became more severe with a higher slew rate. This suggested that solely using a timing delay correction for an Archimedean spiral trajectory generated with a high slew rate is probably not sufficient. We believe that this is likely because the Archimedean spiral trajectory used in this study contains a band of frequencies, rather than a dominant single frequency component present in a sinusoidal waveform (Supporting Information Fig. S1).

The SNR of spiral imaging has been known to be proportional to the square root of the total data sampling time, including spiral readout duration, number of spiral interleaves, and the number of averages. Figure 6B indicates that perfusion SNR scaled with the square root of each readout duration is expected to act like the intrinsic SNR of MRI data.⁵¹ In this study, while keeping the number of interleaves N_itl constant, the number of sampling points N_s was reduced so that the sampling window was shorter when a higher S_max was used. Another design choice was to reduce the number of interleaves N_itl while keeping the sampling points constant. In this way, the overall scan time could be reduced while maintaining the same SNR and effective in-plane resolution. Note that N_s in Cartesian is usually fixed by FOV and Δx. Hence, the spiral scan with a higher slew rate provided more freedom to adjust the total scan time, based on the choice of N_s and N_itl, with the caveat that a large number of samples N_s can cause off-resonance artifact on spiral imaging. However, the results in Figure 7 indicate that signal intensity in the ΔM images seemed to have changed with S_max, It was observed that S_max of 400 T/m/s produced the highest signal on the ΔM images.

The underlying reasons behind the signal behavior of S_max= 400 T/m/s are not known, and are an area for future study beyond the scope of this paper. We can, however, rule out some possibilities. A basic MR signal intensity would be proportional to a combined effect of the effective in-plane resolution (Δx) and TE, namely, $\Delta x^2\text{exp}\left(-TE/T_2\right)$. When evaluating this expression with the imaging protocol in Table 1 and 110 ms of T₂ in gray matter,⁵² MR signals are expected to be 100.0, 99.7, 97.3, 101.3 and 100.1 (in normalized values) for 70, 200, 300, 400 and 500 T/m/s of S_max, respectively. However, the calculation doesn’t fit the observed trend of signal enhancement for gray matter with various S_max, and it implies that 300 ~ 400 T/m/s might produce higher signals compared to 400 ~ 500 T/m/s if the values in 300 T/m/s could be obtained with the same condition of Δx and TE to make the MR signal be 100. Also, as mentioned in the Methods section, the acquisition order with S_max was randomized across the subjects. If scoring the scan order on a scale of 1 (first scan) to 5 (last scan), the averages of the scan order were 3.1, 3.1, 3.4, 2.4 and 2.9 for 70, 200, 300, 400 and 500 T/m/s of S_max, respectively. This suggests that the signal behavior for the S_max dependence was correlated with neither the acquisition order to apply S_max nor the effect of voxel size and TE.

As other possibilities, the B0 term of the eddy current is known as a source of artifact with spiral trajectory.⁵³ The zeroth-order dynamic field was measured by the field camera, and the B0 deviation on spiral readout data can be corrected by complex multiplication with the zeroth-order dynamic field prior to a gridding procedure in reconstruction.⁵³ Note that it differs from the B0 concomitant field correction, which was corrected in real time with frequency tracking.²¹ We did not apply an additional B0 eddy current correction here, beyond the system’s built-in feature, due to the relatively short readout duration (~4ms). Additionally, 16 NMR field probes of the field camera are capable of providing high-order dynamic fields. In principle, higher-order (i.e., higher degree) dynamic fields of 2^nd and 3^rd can be applied for more accurate image reconstruction with high-order reconstruction.^39,54 In this study, we did not attempt to correct for higher-order spatial terms, in part due to the smaller field of view of the compact system. The B0 deviation and high-order eddy currents with higher S_max could be more severe and cause more signal deformation, especially for higher S_max. If B0 and high-order eddy currents can be perfectly addressed, the signal intensities for higher S_max would be improved more.

Although it is generally expected that increasing slew rates should offer monotonic improvements in signal quality, we speculate that for complex trajectories, such as spirals operating at high slew rates (e.g., at S_max > 500 T/m/s), the small trajectory measurement errors may begin to dominate (e.g., the minor contribution for eddy currents originating from a phantom or volunteers, which was not concurrently measured in this study). On the other hand, we didn’t consider B1 field imperfection as a source of such signal behavior, because inhomogeneity in the B1 field is considered to be time-invariant and independent of the gradient slew rate. Both the cause of this behavior and a predictive understanding of signal behavior are areas for future study.

The amount of signal change for the ΔM and PDw images differed from each other above 200 T/m/s of S_max. The differences between the ΔM and PDw images were reflected in the derived CBF values as plotted in Figure 7, which tended to yield the relationship of $\text{\%CBF}=\left(\text{\%ΔM}-\text{\%PDw}\right)/\left(1+\text{\%PDw}\right)$. The effect was greatest at S_max of 300 ~ 400 T/m/s. The signal increase from the trajectory correction could suggest a criterion for determining an optimal S_max for pCASL imaging using spiral readouts at a pre-determined spatial resolution. The improved perfusion SNR could be beneficial for the pCASL-based applications, such as multiple-PLD arterial transit delay estimation.⁵⁵

In conclusion, the C3T scanner supported reliable pCASL without the need for a second RF transmitter. For pCASL imaging based on a 3D FSE SOS trajectory, correction with a dynamic field camera reduced image artifacts, improved perfusion SNR and, consequently, enhanced the quality of the perfusion map, regardless of maximum slew rate used, with the benefits generally increasing with slew rate. We note that the trajectory was only measured once with a dynamic field camera and the measured trajectories were effective at correcting the data obtained from all subjects. Finally, in these tests the image quality of ΔM was best at a maximum slew rate value of approximately 300 ~ 400 T/m/s.

Supplementary Material

Supp figS1-5

Supporting Information Figure S1. (A, B) Time course of gradient magnitude and slew rate for Archimedean spiral trajectories that were generated with parameters in Table 1. (C, D) Power spectral density of x- and y-gradient waveforms of a spiral interleave, respectively. (E) Displacement in normalized k-space (k_max = ±0.5 mm⁻¹) between a nominal and the corresponding measured trajectories of a spiral interleave as $\Vert k_{nominal}\left(t\right)-k_{measured}\left(t\right)\Vert$.

Supporting Information Figure S2. CBF means in (A) gray matter and (B) the adjacent white matter were plotted depending on correction and S_max, respectively.

Supporting Information Figure S3. Estimated gradient delays which were evaluated by minimizing mean square error between the shifted nominal trajectory and the measured trajectory. The error bars denote the standard deviation among spiral interleaves.

Supporting Information Figure S4. Effects of time-shifted trajectory on PDw images. The difference in PDw images (the last row) was evaluated by a subtraction of ‘shifted (3^rd row) – measured (2^nd row)’. The shifted trajectories did not produce the same type of rotational and blurring artifacts as the measured trajectories. However, unexpected signal drop on the object edge and non-uniformity in intensity were observed. These artifacts were reduced in the low-resolution and low-slew-rate image.

Supporting Information Figure S5. Effects of time-shifted trajectory on CBF maps to explore group delay errors. The difference in CBF was evaluated by CBF subtraction of ‘shifted – measured’. In a comparison with the measured trajectory, the shifted trajectory caused artifacts on the brain boundary and yielded underestimates to CBF. These effects become more severe with increasing slew rate, suggesting that group delay errors alone can’t account for all the artifacts corrected and reported in this paper.