 Research
 Open Access
 Published:
Analysis of spatiotemporal fidelity in quantitative 3D firstpass perfusion cardiovascular magnetic resonance
Journal of Cardiovascular Magnetic Resonance volume 19, Article number: 11 (2017)
Abstract
Background
Wholeheart firstpass perfusion cardiovascular magnetic resonance (CMR) relies on highly accelerated image acquisition. The influence of undersampling on myocardial blood flow (MBF) quantification has not been systematically investigated yet. In the present work, the effect of spatiotemporal scan acceleration on image reconstruction accuracy and MBF error was studied using a numerical phantom and validated invivo.
Methods
Up to 10fold scan acceleration using kt PCA and kt SPARSESENSE was simulated using the MRXCAT CMR numerical phantom framework. Image reconstruction results were compared to ground truth data in the kf domain by means of modulation transfer function (MTF) analysis. In the xt domain, errors pertaining to specific features of signal intensitytime curves and MBF values derived using Fermi model deconvolution were analysed. Invivo firstpass CMR data were acquired in ten healthy volunteers using a dualsequence approach assessing the arterial input function (AIF) and myocardial enhancement. 10x accelerated 3D kt PCA and kt SPARSESENSE were compared and related to nonaccelerated 2D reference images.
Results
MTF analysis revealed good recovery of data upon kt PCA reconstruction at 10x undersampling with some attenuation of higher temporal frequencies. For 10x kt SPARSESENSE the MTF was found to decrease to zero at high spatial frequencies for all temporal frequencies indicating a loss in spatial resolution. Signal intensitytime curve errors were most prominent in AIFs from 10x kt PCA, thereby emphasizing the need for separate AIF acquisition using a dualsequence approach. These findings were confirmed by MBF estimation based on AIFs from fully sampled and undersampled simulations. Average invivo MBF estimates were in good agreement between both accelerated and the fully sampled methods. Intravolunteer MBF variation for fully sampled 2D scans was lower compared to 10x kt PCA and kt SPARSESENSE data.
Conclusion
Quantification of highly undersampled 3D firstpass perfusion CMR yields accurate MBF estimates provided the AIF is obtained using fully sampled or moderately undersampled scans as part of a dualsequence approach. However, relative to fully sampled 2D perfusion imaging, intravolunteer variation is increased using 3D approaches prompting for further developments.
Background
Diagnosis of ischemia in patients with known or suspected coronary artery disease (CAD) is increasingly being performed using cardiovascular magnetic resonance (CMR) firstpass perfusion imaging. Perfusion CMR outperforms other imaging techniques such as positron emission tomography (PET) and single photon emission computed tomography (SPECT) in terms of spatial resolution and operates without ionizing radiation. Compared to coronary angiography and the assessment of fractional flow reserve, perfusion CMR is noninvasive and has been proven suitable for patients with intermediate probability of significant CAD [1]. Numerous authors have compared the diagnostic performance of perfusion CMR to SPECT [2–6] and PET [7–10], and found that CMR performs at least comparably to these methods [11]. Studies comparing perfusion CMR to stress echocardiography and perfusion computed tomography report similar results [12–14].
Detection of small ischemic regions such as subendocardial perfusion defects is enabled by the high spatial resolution offered by CMR [15]. In addition to sufficient spatial resolution, wholeheart coverage is desired to accurately assess the size and extent of perfusion deficits [16]. These demands have triggered the development of threedimensional (3D) scanning techniques employing advanced undersampling strategies for efficient data acquisition [17–19]. The importance of wholeheart imaging has further been stressed by authors evaluating the volumetric ischemic burden as a marker of significant CAD [20–22]. Optimization of scanning efficiency has also been made in the temporal domain. Multiple authors have proposed perfusion CMR throughout the cardiac cycle to assess differences in perfusion between heart phases and to combine cine and perfusion imaging into a single scan [23–25]. Alternatively, interleaved acquisition at different heart phases may be used to separately capture blood pool and myocardial enhancement for improved perfusion quantification [26, 27] or framebyframe T1 mapping [28].
Absolute quantification of perfusion CMR has gained significant attention in the past decade since clinical advantages have been pointed out [29, 30]. Several technical aspects of myocardial blood flow (MBF) estimation from reconstructed images have been investigated mostly using single or multislice 2D imaging. Special focus has been put on the development of mathematical models for MBF estimation [31–34] and comparison between them [35, 36]. Zarinabad et al. have compared voxelwise vs. spatially averaged (sectorwise) estimation of MBF [36] and highlighted the importance of accurate bolus arrival time estimation [37]. Most recently, the feasibility of 3D CMR perfusion quantification has been demonstrated [25, 27].
Perceived image quality and deviation from a fully sampled reference image have traditionally been used as direct measures to validate spatiotemporal scan acceleration methodology [38–40]. A more general approach is the use of the modulation transfer function (MTF) concept to characterize the ability of a MR system to correctly capture spatial and temporal frequencies [41]. A perturbation of the system combined with linear regression is used yielding the MTF derived from the slope, and an artefact map based on the ratio of slope and intercept of the linear fit. This method is well suited for linear reconstruction methods, but application to nonlinear reconstruction techniques such as compressed sensing is also feasible if linearization about a suitable expansion point is used. Consequently, the MTF approach can be employed to compare spatiotemporal performance of linear and nonlinear reconstruction algorithms, such as kt PCA and kt SPARSESENSE [42, 43].
The present study introduces a linearized MTF approach to evaluate kt PCA and kt SPARSESENSE in the context of highly accelerated, fully quantitative 3D myocardial perfusion imaging. MTF maps derived from numerical phantoms and invivo data are used to investigate changes of spatiotemporal fidelity introduced by undersampling. Furthermore, errors in signal intensitytime curves are analysed and their influence on MBF estimation is highlighted. MRXCAT simulation of a subendocardial lesion reveals the ability of the proposed methodology to identify small ischemic territories. Finally, simulation results are validated invivo comparing 3D kt PCA, 3D kt SPARSESENSE and fully sampled 2D imaging.
Theory
kt PCA and kt SPARSESENSE
kt PCA and kt SPARSESENSE are reconstruction methods based on differing principles both suited for highly accelerated MRI.
In kt PCA, data is acquired on a Cartesian grid, which is shifted in kspace for each time frame as in kt SENSE [38]. The centre of kspace is fully sampled in all time frames, providing an image series with low spatial and high temporal resolution termed as training data. Before further processing, the data matrix D originally acquired in kt space is Fourier transformed to the xf domain,
F_{ kt→xf } denotes the Fourier transform from kt to xf space. The training data are used to determine the temporal principal components (PCs) of the dataset by transforming data from xf space to xpc space using principal component analysis (PCA),
where P and W are matrices representing the data in xf and xpc space, respectively, and matrix B contains the PCs. By assuming spatial invariance of the PCs, the same PCs can be used to unfold the aliased data. The reconstruction problem can then be solved via [42]
where w _{ x } and p _{ x } are vectors representing the rows of W and P at position x. w _{ x } contains the weights of the aliased voxels in p _{alias,x }, M ^{2} is the signal covariance, Ψ indicates the noise variance, and E is the encoding matrix. The dagger represents the MoorePenrose pseudoinverse and superscript H the conjugate transpose. The reconstructed image i _{ xf } in xf space is obtained using
followed by Fourier transformation to the xt domain.
In contrast to kt PCA, data in kt SPARSESENSE are pseudorandomly undersampled with a higher sampling density near the kspace centre decreasing towards the edge [44]. The reconstruction problem reads
with the encoding matrix E as above, the data d expressed as a vectorised form of D, and i the image to be reconstructed. Φ represents a sparsifying transform and λ is the regularization parameter. In kt SPARSESENSE, the reconstruction equation is minimized using a POCSlike algorithm alternating between data consistency and softthresholding [45, 46] leaving the acquired data unchanged, or nonlinear conjugate gradient optimization [44]. Common choices for Φ include the temporal Fourier transform (FT), temporal PCA or a mixture of both starting with the temporal FT for the first iterations, followed by PCA for the remaining iterations [47].
Spatiotemporal modulation transfer functions
Traditionally, modulation transfer functions (MTF) are used to describe an imaging system’s ability to portray an object. Chao et al. [41] have adopted the concept for the evaluation of accelerated MRI. The relationship between the object ρ and its image i can be formulated as
with the modulation transfer function H and noise n. Explicit calculation of H for large imaging problems, such as dynamic 3D imaging, can be infeasible or computationally too expensive. To address this issue, a perturbation approach
can be used. A small perturbation ξ is added repeatedly to the object ρ. ρ _{ ξ } and i _{ ξ } are the perturbed object and image, respectively. H _{ B } and h _{ A } are analogous to the MTF and noise in eq. (6). Multiple realizations of eq. (7) with different perturbations can be solved for h _{ A } and H _{ B } using linear regression, which results in slope H _{ B } and intercept h _{ A }. This MTF formalism can be applied to study the effects of scan acceleration. To this end, the image i _{ R=1} reconstructed from fully sampled data is used as the true object and the reconstructed image i _{ R>1} from undersampled data is its imaged version. The adapted version of eq. (7) reads
Instead of the 2D MTF [41], a 3D MTF H _{ B }(k _{ y } ,k _{ z } ,f) portraying two spatial and the temporal frequency directions is necessary for Cartesian dynamic 3D imaging. The frequency encoding direction k _{ x } can be omitted, or used for averaging, since no undersampling is applied and thus the MTF is constant along this direction. The MTF can be computed as [41]
where N _{ x } is the number of readout profiles. Similarly, the signaltoartefact map (S2A) can be derived relating the MTF to the intercept of the linear regression and to the object itself:
While the formalism is directly valid for the linear kt PCA in eq. (3), for kt SPARSESENSE (eq. (5)) an approximately linear relationship between fully sampled and accelerated imaging is assumed based on linearization about a suitable expansion point. This expansion point corresponds to the magnitude of the unperturbed object at each position in k _{ y } k _{ z } f space.
In the original interpretation of the MTF formalism a true object and its imaged version are compared. The natural upper bound for the MTF is 1, indicating that a certain voxel in kf space perfectly reproduces the corresponding object part. Lower values of the MTF indicate image degradation by the imaging system. Note that this strict physical constraint not necessarily applies to scan acceleration. Especially at the kfspace edges, where the signaltonoise ratio (SNR) is low, the effect of undersampling and subsequent reconstruction might also increase kf space magnitudes, resulting in MTF values above 1. Therefore, only the central kfspace parts of the MTF should be evaluated.
Myocardial blood flow quantification
There are a number of methods estimating myocardial blood flow (MBF) from firstpass perfusion CMR. The most direct approach is to derive MBF estimates from the relationship between contrast agent concentrations at the inlet c _{AIF}(t), referred to as arterial input function (AIF), and in the myocardial tissue c _{MYO}(t), using [48].
The flowweighted impulse response function R _{ F } = F · R(t) comprises the MBF estimate F and a normalized, decaying function R, with R _{ F }(t = 0) = F. The impulse response function can either be explicitly computed by modelfree deconvolution, or approximated using a suitable mathematical representation. The most common choice for R _{ F } is approximation using the 3parameter Fermi model [27, 31],
In this equation, F is the MBF estimate, and α, β are further fitting parameters. Note that the units of measurement for c _{AIF}(t) and c _{MYO}(t) are mmol/mL, while the amount of contrast agent in the myocardium measured by indicator dilution theory is in units of mmol/g of tissue. This discrepancy is implicitly corrected by scaling F by the myocardial tissue density of 1.05 g/mL [49].
Methods
Invivo measurements
Invivo CMR experiments were performed in 10 healthy volunteers (4 males) on a Philips Achieva 1.5 T scanner (Philips Healthcare, Best, The Netherlands) using a 5channel cardiac coil array. Volunteers had an average age of 26.2 ± 4.7 years and underwent CMR upon written informed consent in accordance with ethics regulations approved by the local ethics committee. Dynamic contrast enhanced CMR was conducted twice per volunteer and at least 20 min apart. Gadobutrol (Gadovist, Bayer Schering Pharma, Germany) at 0.075 mmol/kg b.w. dose was injected as contrast agent, followed by a 30 mL saline flush at 4 mL/s. Volunteers were measured during instructed breathholding.
A saturationrecovery dualsequence spoiled gradient echo sequence with ECGtriggering was used to acquire one image pair per heartbeat. The interleaved acquisitions [50] consisted of a 2D aortic scan for arterial input function (AIF) assessment and an endsystolic leftventricular scan to capture myocardial enhancement, as proposed earlier [27]. Myocardial enhancement was assessed using 3D imaging accelerated by kt PCA (N = 7 measurements), kt SPARSESENSE (N = 7), and fully sampled singleslice 2D imaging (N = 6) for comparison. To limit the amount of contrast agent administered and the examination time per volunteer, only two injections per volunteer were carried out. This resulted in three groups of volunteers, allowing comparison of kt PCA or kt SPARSESENSE with fully sampled 2D imaging (N = 3 for both), and direct intercomparison between the accelerated sequences (N = 4).
All myocardial enhancement scans were run with WET saturation preparation [51] using a saturation to acquisition time (T _{SAT}) of 150 ms. Accelerated 3D imaging parameters were: nominal scan acceleration: 10x, net acceleration factor without partial Fourier: 7.4–7.8, 11×7 training profiles in k _{ y } and k _{ z }, spatial resolution: 2.3×2.3×10 mm^{3}, 10 contiguous slices, typical fieldofview: 320×320×80 mm^{3}, flip angle: 15°, acquisition window: 189–216 ms, T _{ R }: 1.89–1.93 ms, T _{ E }: 0.74–0.78 ms. 62.5% and 75% partial Fourier sampling was applied in frequency and in both phase encoding directions, respectively. An elliptical kspace shutter was used on both the undersampled grid and the training portion. Equal undersampling rates were used in kt PCA and kt SPARSESENSE. Examples of sampling patterns as applied invivo for both kt methods are illustrated in Fig. 1. Fully sampled 2D myocardial enhancement scans were run with the following parameters: spatial resolution: 2.3×2.3 mm^{2} inplane, slice thickness: 10 mm, flip angle: 15°, acquisition window: 188–225 ms. T _{ R }, T _{ E } and partial Fourier factors were the same as for 3D imaging, resulting in comparable acquisition windows.
2D AIF imaging was planned orthogonally to the ascending aorta in transverse view, with a separate WET saturation preparation pulse. An ultrashort T _{SAT} of 3.7 ms was enabled using a centralout profile order, i.e. acquisition started at the kspace centre, continued outwards and concluded at the most distant point from the centre. Further 2D scan parameters were: 3x kt PCA acceleration, 11 training profiles, spatial resolution: 3.5×3.5 mm^{2}, slice thickness: 10 mm, fieldofview: 260×300 mm^{2}, flip angle: 15°, acquisition window: 40–48 ms, T _{ R }: 1.67 ms, T _{ E }: 0.58 ms.
In addition to contrastenhanced imaging, baseline T _{1} values were measured in all volunteers using modified LookLocker inversion recovery (MOLLI) imaging [52]. MOLLI acquisitions were done before the first and second contrast administration. Population average precontrast myocardial and leftventricular T _{1} values for the first and second injection were determined from these MOLLI T _{1} maps. These average T _{1} values were subsequently used for signal intensity to contrast agent concentration conversion, as outlined below.
Image reconstruction
kt PCA and kt SPARSESENSE reconstructions were implemented in ReconFrame (Gyrotools LLC, Zurich, Switzerland) and Matlab R2014a (MathWorks, Natick MA, USA). Sensitivity maps were derived from a separately acquired reference scan. The kt SPARSESENSE implementation comprised soft thresholding and a combination of temporal FT (10 iterations) and PCA (iteration 11 onwards) as sparsifying transforms [47]. Reconstruction voxel sizes of 2×2 mm^{2} and 1.25×1.25×5 mm^{3} were achieved using zerofilling of the 2D AIF image and the accelerated 3D scan, respectively. All reconstructed invivo images were manually segmented to yield regional signal intensitytime curves.
Modulation transfer function analysis
Numerical simulations were performed to compare images reconstructed from undersampled data with fully sampled references using MTFs. A fully sampled 3D numerical phantom was created using the MRXCAT simulation framework [53]. Phantom parameters were: spatial resolution: 2.3×2.3 mm^{2}, slice thickness: 5 mm, 10 slices, T _{ R } /T _{ E }: 2.0/1.0 ms, flip angle: 15°, contrast agent dose: 0.075 mmol/kg b.w., 5 receive coils, myocardial blood flow (MBF): 1 mL/g/min. 64 noise realizations with equal noise statistics were performed, each comprising 11 different perturbations for 4 different acceleration factors (cf. below). In each realization, 11 identical datasets were generated, which were individually perturbed by multiplication with factors 0.95–1.05 in steps of 0.01, and subsequent degradation by noise (SNR = 20). Scaling was done to ensure that a certain signal intensity range was covered for linear regression analysis. Compared to completely random perturbations without scaling, this approach ensured a spread of signal values at every kspace position. This resulted in a drastically reduced number of iterations required to probe linearity at all spatiotemporal frequency positions.
Fully sampled and undersampled numerical phantoms were reconstructed using kt PCA and kt SPARSESENSE. Undersampling factors were 2, 5 and 10 excluding training data, corresponding to net factors of 1.9, 4.4, and 7.6 when including the central 11×7 training ellipse. Because of a steep decline of kspace magnitudes away from the centre, noise becomes dominant towards the edges of kspace. To mitigate this effect, 64 realizations of each set of simulations were done and the average reconstructed images were used for MTF analysis. The reconstructed images from undersampled data were compared to the fully sampled reference in kf space using linear regression as detailed in eq. (8). MTFs and corresponding artefact measures were computed (cf. eqs. (9), (10)). To account for the drastic decrease of data magnitudes towards the kspace edges, MTFs were masked using thresholding on corresponding signaltoartefact maps (S2A). The S2A threshold was empirically set to 3 for 3D MTF maps; a value which best separates parts of the MTF with low and high artefact proportion. The different steps employed for MTF analysis are illustrated in Fig. 2.
Timing constraints prohibit acquisition of a fully sampled 3D dataset during the firstpass of the contrast agent invivo. Hence, reference single slice 2D data were used for invivo MTF analysis. MTF calculations were performed using the same undersampling factors and procedure as for the MRXCAT phantom. In contrast to the MRXCAT case, training consisted of 11 profiles in k _{ y } only, resulting in different net acceleration factors (1.9, 3.8, and 5.9), and the S2A threshold was set to 2.5.
Imagetime domain analysis
In addition to MTF analysis in kf space, signal intensity vs. time curves extracted from MRXCAT images were investigated. Direct comparison of accelerated scanning simulations with fully sampled reference data allows for estimation of data fidelity upon undersampling during contrast enhancement. Furthermore, specific features of the signal intensitytime curve such as the precontrast baseline, peak enhancement and upslope can be compared. Errors in these features will directly propagate into the estimated myocardial blood flow upon signaltoconcentration conversion or deconvolution fitting.
Myocardial blood flow quantification
Estimation of myocardial blood flow (MBF) was performed in two steps. First the image signal intensity vs. time curves from the blood pool and myocardium were converted to concentration vs. time curves using the signal model of the form [31]
S represents the signal intensity, T _{SAT} the saturation delay, T _{ R } the repetition time and n the number of profiles acquired between the acquisition start and the central kspace portion. R _{1} = 1/T _{1} is the dynamic relaxivity and the term a = cos α · exp(−R _{1} T _{ R }) additionally contains the flip angle α. The baseline time frames were used to determine the scaling factor S _{0} using precontrast T _{1} values. These values were either known for the MRXCAT simulations, or measured using MOLLI imaging for invivo data. Since S _{0} can be assumed unaffected by the Gadolinium administration, the dynamic T _{1} can be calculated with this S _{0} for each time frame. The relaxivity R _{1} is given by
where T _{1,0} is the baseline T _{1} in the absence of contrast agent, and r the materialspecific relaxivity of the contrast agent. Resolving eq. (14) yields the concentration c of the contrast agent.
Baseline ranges for signaltoconcentration conversion were set to time frames 1–5 for the AIF and 1–10 for the myocardial curves in all MRXCAT simulations. Since baseline length, timing of acquisition and contrast agent injection vary invivo, baseline range selection was done manually in each volunteer dataset. Invivo population average precontrast T _{1,0} values derived from MOLLI imaging were: 1590 ms for the left ventricle and 1020 ms for the myocardium at the first contrast agent injection. T _{1,0} before the second injection were 640 ms and 680 ms, respectively.
In a second step, the concentration vs. time curves c _{AIF} and c _{MYO} from the blood pool and the myocardium, respectively, were related to estimate the MBF using Fermi model deconvolution as detailed in eqs. (11) and (12), and reference [27].
Subendocardial Ischemic lesion simulation
The ability of the proposed 3D methods to reveal small ischemic defects was probed by MRXCAT simulation of subendocardial ischemia. Ischemia was introduced in a single slice of the MRXCAT phantom with a healthy rest MBF of 1 mL/g/min. The ischemic region in a midventricular slice covered a circumferential lateral sector spanning 60°, and a transmural subendocardial layer of 1–2 voxels. In this ischemic territory, contrast enhancement was suppressed such that the signal intensities remained around the baseline level during all time frames. Ischemic MRXCAT data were reconstructed without undersampling and at 10x scan acceleration using both kt PCA and kt SPARSESENSE. Subsequently, MBF quantification was performed.
Results
MTF simulation results are shown in Fig. 3. Thresholds in signaltoartefact maps (S2A) were used to mask out regions with low SNR in MTF maps. 3D and 2D MTF maps were set to zero if the corresponding signaltoartefact values were below 3 and 2.5, respectively. For 3D MRXCAT the MTF spans a 3D space in k _{ y } k _{ z } f.
Figure 3a displays a k _{ y } f slice of the MRXCAT MTF map at k _{ z } = 0 for kt PCA and kt SPARSESENSE at nominal acceleration factors of 2, 5, and 10. A k _{ z } f slice at k _{ y } = 0 of the MRXCAT MTFs is shown in Fig. 3b. For both reconstruction methods at all acceleration factors, the nonzero MTF values lie around the main axes, i.e. along the different direct current (DC) regions. In the temporal DC region, data at most spatial frequencies k _{ y } and k _{ z } are partially restored upon undersampling. Similarly, at spatial DC, all temporal frequency components are restored to a certain degree. MTF values decrease with increasing distance from the DC axes. For kt PCA at different undersampling factors, the shape of the MTF remains similar with slight narrowing of the nonzero regions near the DC axes. At R = 10, the MTF is noisier than at lower acceleration indicating noise amplification at certain spatiotemporal frequencies. Compared to kt SPARSESENSE, kt PCA restores offDC temporal frequencies on a relatively narrow range. As a consequence, MTFs from kt SPARSESENSE have a larger nonzero area, but exhibit larger changes when increasing R. MTF values >1 away from the DC axes signify deviation from linear behaviour due to the nonlinearity of the reconstruction algorithm. A number of spatial frequency components along k _{ y } is not restored using 10x kt SPARSESENSE. This leads to a loss of inplane spatial resolution in the reconstructed image.
MTF results derived from 2D invivo data are illustrated in Fig. 3c, revealing similar patterns as for the 3D simulation along the DC axes. In contrast to 3D, 2D results exhibit lower signaltoartefact ratios, yielding smaller nonzero MTF areas despite the slightly reduced signaltoartefact threshold. As in the 3D simulation at maximum undersampling rate R = 10, kt SPARSESENSE exhibits a loss of spatial resolution in phaseencoding direction.
AIFs extracted from central leftventricular regions of the reconstructed 3D MRXCAT images for R = 1, 2, 5, 10 are presented in Fig. 4a,b. AIFs appear perfectly aligned for all R except for the baseline. A closeup of the baselines and corresponding error plot as a function of R reveals 16.5 ± 2.0% reduced baseline signal intensities at R = 10 for kt PCA compared to the reference, while the baseline error is – 4.1 ± 1.4% for 10x kt SPARSESENSE (Fig. 4c,d). Errors in the AIF upslope and maximum signal intensity are depicted in Fig. 4e,f, and remain below ±2% at all acceleration factors.
Figure 5 highlights myocardial signal intensitytime curves extracted from a septal segment at a midventricular level of 3D MRXCAT simulations. Reference (R = 1) and R = 2, 5, 10 undersampled acquisitions are shown. Overall agreement between curves at all acceleration factors is good. Baseline errors are visible at R = 10 for both reconstruction methods, with increased signal intensity in the first time frames for kt PCA, and an elevated baseline shortly before bolus arrival for kt SPARSESENSE. As Fig. 5c reveals, these errors almost cancel out by averaging the baseline across the first 10 time frames. Mean baseline errors and standard deviations for 10 realizations of the simulations and 10fold undersampling were 1.4 ± 4.3% for kt PCA and 2.4 ± 2.4% for kt SPARSESENSE. The myocardial upslope changes by – 0.9 ± 1.0% and – 9.4 ± 3.4% for 10x kt PCA and SPARSESENSE, respectively. The peak signal intensity error stays below ±2% at all undersampling factors.
Errors in estimated MBF were evaluated in 8 slices and 6 angular sectors of the 3D MRXCAT simulation with an AIF extracted from the undersampled image representing standard noninterleaved acquisition. In order to model interleaved scanning with separate AIF assessment, MBF quantification errors were also determined using an AIF derived from a fully sampled reference. Detailed results are depicted in the form of Bull’s eye plots in Fig. 6, and summarized in Fig. 7 as mean MBF errors and standard deviations across the 8×6 regions. Mean MBF errors remain below 3% for all evaluations at R = 2 and R = 5. In contrast, if the AIF is extracted from the undersampled data itself, MBF at 10x undersampling is underestimated by 43.1 ± 2.3% for kt PCA, and 15.6 ± 6.2% for kt SPARSESENSE. Underestimation is removed when the AIF from fully sampled data is employed for quantification, with average MBF errors of 0.8 ± 4.3% and 0.9 ± 7.9% for 10x kt PCA and kt SPARSESENSE, respectively. The variation of MBF errors across the myocardium rises alongside increasing the acceleration factor.
Figure 8 displays example MRXCAT images of healthy and diseased simulations. While in the healthy case dynamic contrast enhancement is homogeneous in all myocardial slices, a small subendocardial defect was introduced in the lateral segment of the midventricular slice of the ischemia simulation. The ischemic lesion is very distinct in the fully sampled case and 10x kt PCA, but less perceptible in 10x kt SPARSESENSE. MBF estimation in the segment affected by ischemia yielded MBF = 0.46 mL/g/min for R = 1, 0.45 mL/g/min for 10x kt PCA and 0.73 mL/g/min for 10x kt SPARSESENSE. Due to the transmural averaging of myocardial signal including subendocardial ischemic and epicardial healthy voxels, the resulting MBF is larger than zero.
Invivo images comparing 10x accelerated kt PCA and kt SPARSESENSE are illustrated in Fig. 9. Five different slices from apex to base are displayed at time points of maximum contrast enhancement in the right ventricle, left ventricle, and myocardium. One slice was omitted inbetween slices thereby spanning nine slices. Both images display similar contrast enhancement, but while kt PCA images display sharp tissue boundaries, kt SPARSESENSE images appear more blurred.
Figure 10 shows example MBF estimates derived from invivo 3D kt PCA and kt SPARSESENSE images acquired with 10x undersampling. Average MBF values across 8 slices and 6 sectors per slice in the first volunteer were 0.93 ± 0.16 mL/g/min for kt PCA and 1.06 ± 0.39 mL/g/min for kt SPARSESENSE. For the second volunteer shown, mean MBF and standard deviations amounted to 0.86 ± 0.17 mL/g/min and 0.94 ± 0.30 mL/g/min, respectively. The larger standard deviations of MBF in kt SPARSESENSE appear as increased inhomogeneity in MBF values across the Bull’s eye plots.
A summary of average MBF and standard deviations for all volunteers is provided in Fig. 11. Volunteers were grouped according to the firstpass perfusion techniques to enable side by side comparison between acquisition methods within volunteers. In addition to wholeheart evaluation of 3D images, quantification was also performed in a midventricular region consisting of two averaged slices of the 3D images. The averaged region with effective slice thickness of 10 mm corresponded to the 2D imaging region. This step was done to increase comparability between 3D R = 10 and 2D MBF values. Average MBFs ranged from 0.64 and 1.22 mL/g/min and agreed well between methods. Ratios between mean kt PCA and kt SPARSESENSE MBF ranged from 0.88 to 1.08. Comparison between accelerated kt and 2D R = 1 methods yielded factors of 0.88 to 1.30 for kt PCA and 0.90 to 1.14 for kt SPARSESENSE. MBF standard deviations within volunteers normalized to the corresponding mean MBF were 16.3 ± 4.7% for 2D, 25.2 ± 5.5% for 10x kt PCA, and 32.5 ± 3.2% for 10x kt SPARSESENSE. MBF standard deviations were higher in accelerated 3D scans than in fully sampled 2D images. Comparison of the two accelerated methods yielded lower MBF variation in kt PCA than kt SPARSESENSE.
Discussion
The feasibility of MBF estimation from highly undersampled firstpass myocardial perfusion MRI has been investigated and presented in this work. Effects were examined by means of kf space based MTFs, imagetime domain analysis of signal intensity, and by deconvolution using Fermi function modelling for MBF estimation. The MRXCAT framework [53] was employed for simulation, and complemented by invivo assessment of perfusion using accelerated 3D kt PCA, 3D kt SPARSESENSE and fully sampled 2D reference data.
The concept of the MTF describing the relationship between an imaged object and its image has been adapted to portray undersampled firstpass perfusion CMR. Thereby, the MTF represents the relationship in kf space between the fully sampled and the undersampled data upon image reconstruction. Implementation in MRXCAT allowed for quantification of errors relating the accelerated imaging simulation to the corresponding fully sampled reference. The reduction in MTF area with increasing acceleration factor and the appearance of noise therein provide insights into the performance of the undersampling and reconstruction strategy.
For kt PCA, the k _{ y } f portion with MTF close to 1 remains almost unchanged from R = 2 up to R = 10, suggesting adequate performance of image reconstruction at all examined R. The increased noiselike patterns in 10x kt PCA MTFs indicate that this acceleration factor is close to the maximum achievable R without major loss of data fidelity. On the other hand, kt SPARSESENSE MTFs exhibit larger nonzero areas for all temporal frequencies further away from the spatial DC. MTF shapes at R = 2 and R = 5 are similar, but a sudden dropoff at high k _{ y } is observed at R = 10, indicating that data at higher spatial frequencies are not properly restored. This yields a loss in effective spatial resolution, which can be observed invivo comparing kt PCA and kt SPARSESENSE images in Fig. 9.
Starting from the original definition of the MTF as a relationship between the object and its image, the MTF may assume values between 0 and 1 because information about the object is only lost and never gained with bandlimited, linear imaging methods. However, when applied to the characterization of undersampling, MTF > 1 is possible indicating noise amplification at the corresponding kf position by regularized reconstruction. This phenomenon is most prominent at high undersampling rates, e.g. in the k _{ y } f MTF map for 10x kt PCA. Around spatial DC, some temporal frequencies exceed 1 resulting in the noiselike MTF appearance. In contrast, MTF values vastly exceeding 1, as observed only in kt SPARSESENSE MTF maps at higher k _{ y }, may not be explained by noise amplification alone. Presumably, these errors stem from the treatment of nonlinear compressed sensing reconstruction with the linear MTF formalism. The assumption of linearity between images from fully sampled and undersampled acquisitions is violated at higher frequencies, which is in line with previous statements [41]. The discrepancy between linear and nonlinear reconstruction algorithms treated with the MTF formalism was corrected for using masking with a fixed threshold in the signaltoartefact map.
Simulated signal intensitytime curves from the blood pool and the myocardium were examined at all acceleration factors R. The AIFs for different R agree well when upslopes and peak signal are compared, as well as for the baseline up to R = 5. Underestimation of the baseline at R = 10 is most prominent in kt PCA with almost 20% error. The myocardial curves up to R = 5 agree well with the reference, but exhibit deviations from ground truth at the beginning (kt PCA) or at the end of the baseline (kt SPARSESENSE). These errors are reflected in the myocardial baseline error, which can be reduced if the time frames selected for baseline averaging are optimally chosen. Based on these findings, the first time frames might be excluded when determining the baseline in kt PCA. Accordingly, for kt SPARSESENSE, the last time points before contrast agent arrival should be discarded. The septum was chosen for myocardial signaltime analysis due to its strategic position between the right and left ventricle. Aliasing of components from left and right ventricles and the myocardium is expected in the septum upon undersampling, as these three compartments are aligned along the foldover direction. Resolving the aliased data at this location should be more challenging than anywhere else in the myocardium [17].
The percentage errors upon MBF quantification using AIFs extracted from the undersampled image and from a fully sampled reference were compared. Global MBF underestimation up to 43% was observed at R = 10 with the AIF from undersampled data, an error not present when using the AIF from reference image. This finding indicates that the AIF baseline error may be the main source of inaccuracy. A remedy to address this issue invivo is interleaved AIF acquisition at small acceleration factors using dualsequence imaging, thereby markedly reducing the AIF baseline error. Exact knowledge of sequence parameters included in the corresponding signal model was assumed in this simulation, alongside with perfect saturation efficiency. As previously shown, errors in parameter estimation as well as inefficient saturation may additionally distort the estimated MBF [54]. In addition, signal intensity to concentration nonlinearity effects may further degrade quantification accuracy for singlesequence acquisition schemes.
Identification of subendocardial ischemia is a key criterion for the clinical utility of novel myocardial perfusion scan and postprocessing methodology. MRXCAT simulations of fully sampled and 10x accelerated imaging including a small ischemic lesion were performed to investigate this question. Quantification of 10x kt PCA data yielded MBF values in good agreement with the fully sampled reference both in healthy and ischemic regions. In contrast, MBF values derived from the 10x kt SPARSESENSE differed from the reference in healthy segments, with increased MBF variation. In the ischemic territory MBF reduction due to ischemia was less pronounced than in the reference. This latter effect may be related to the loss of effective spatial resolution observed in 10x kt SPARSESENSE MTF analysis.
Invivo data were measured using a dualsequence acquisition framework enabling separate images mapping blood pool and myocardial enhancement [27]. For 3x kt PCA the AIF baseline error remained below 2% as confirmed by our simulations up to R = 5. In addition, dualsequence imaging enabled separately optimized saturation delays for the interleaved scans, thereby eliminating the signal vs. concentration nonlinearity concerns.
The range of average MBF values found invivo at rest was in line with previous findings. Variations of MBF across different volunteers are expected based on physiological differences. The change in mean MBF between different acquisition techniques is lower than the intravolunteer MBF variation, and standard deviations in MBF around 20% compare well to previous work. This variation represents a persistent limitation of MBF quantification in part caused by the illposed nature of deconvolution fitting [49]. The increased intravolunteer variation observed in highly accelerated vs. fully sampled reference data can be explained in part by the loss in data fidelity and SNR caused by undersampling. To enhance MBF estimation precision, increasing the contrasttonoise ratio by high dose firstpass imaging is an option [27]. Furthermore, parallel imaging with up to 32 receive channels has been demonstrated to enhance image quality [55]. Moreover, in accelerated firstpass perfusion CMR accurate segmentation of the myocardium is crucial. For instance, the sectorwise myocardial signal intensitytime curve in the septum may be severely distorted if a single voxel from the right ventricle or multiple voxels affected by partial volume effects are included in the segmentation. These challenges need to be addressed in order to adopt fully quantitative perfusion CMR in clinical routine.
In addition to solving the aforementioned implementation challenges, further validation is needed before clinical introduction of the proposed methods. Future studies could include patients with subendocardial ischemia to investigate the ability to detect small, localized lesions. In addition, patients with triple vessel disease or microvascular disease potentially benefit from quantitative methods and may be included in clinical studies. In these pathologies, healthy remote myocardium may be absent as a reference for qualitative or semiquantitative approaches.
Conclusion
Combined modulation transfer function and signaltoartefact ratio analysis is a useful means of studying the performance of accelerated 3D firstpass perfusion CMR acquisition in a linearized regime, correctly predicting losses in spatial and temporal resolution. Highly accelerated perfusion CMR enables estimation of myocardial blood flow provided an unbiased arterial input function is acquired, e.g. using dualsequence acquisition. The accuracy of blood flow quantification from undersampled imaging is maintained compared to fully sampled reference images, whereas the precision measured by intravolunteer variation is reduced prompting for further improvements of wholeheart 3D perfusion imaging approaches.
Abbreviations
 AIF:

Arterial input function
 CAD:

Coronary artery disease
 CMR:

Cardiovascular magnetic resonance
 DC:

Direct current
 FT:

Fourier transform
 MBF:

Myocardial blood flow
 MTF:

Modulation transfer function
 PC:

Principal component
 PCA:

Principal component analysis
 PET:

Positron emission tomography
 S2A:

Signaltoartefact map
 SNR:

Signaltonoise ratio
 SPECT:

Single photon emission computed tomography
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Funding
This project was funded by the Swiss National Science Foundation, grant #CR3213_132671/1. Research support from Philips Healthcare, Best, The Netherlands is gratefully acknowledged.
Availability of data and materials
The MRXCAT framework used for numerical simulations contained in this study is available for download in source code format under www.biomed.ee.ethz.ch/mrxcat. Invivo data used in this study are available from the corresponding author on request.
Authors’ contributions
LW: Study design; realization of simulations and invivo CMR; volunteer recruiting and preparation; implementation and processing of image reconstruction, segmentation, quantification; authoring and revision of the manuscript. AG, SH: preparation and information of volunteers; CMR scanning. CS: Implementation and support for kt SPARSESENSE reconstruction. KCT: Study design and planning; CMR scanning; manuscript revision. RM: invivo CMR supervision; responsibility for ethics regulations. SK: Study design and supervision; advice on postprocessing; manuscript revision. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Consent to publish data from individual volunteers was obtained from all participants.
Ethics approval and consent to participate
The study was approved by the Ethics Committee of the Canton of Zurich (KEK); reference number EK1294. All volunteers gave written informed consent for study participation.
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Wissmann, L., Gotschy, A., Santelli, C. et al. Analysis of spatiotemporal fidelity in quantitative 3D firstpass perfusion cardiovascular magnetic resonance. J Cardiovasc Magn Reson 19, 11 (2017). https://doi.org/10.1186/s129680170324z
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Keywords
 Firstpass myocardial perfusion
 Myocardial blood flow
 Modulation transfer function
 kt PCA
 kt SPARSESENSE
 3DMTF
 Wholeheart perfusion