Analysis of spatiotemporal fidelity in quantitative 3D firstpass perfusion cardiovascular magnetic resonance
 Lukas Wissmann^{1}View ORCID ID profile,
 Alexander Gotschy^{1, 2, 3},
 Claudio Santelli^{1},
 Kerem Can Tezcan^{1},
 Sandra Hamada^{2, 4},
 Robert Manka^{1, 2, 5} and
 Sebastian Kozerke^{1, 6}Email author
DOI: 10.1186/s129680170324z
© The Author(s). 2017
Received: 2 September 2016
Accepted: 11 January 2017
Published: 27 January 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.
Keywords
Firstpass myocardial perfusion Myocardial blood flow Modulation transfer function kt PCA kt SPARSESENSE 3DMTF Wholeheart perfusionBackground
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.
followed by Fourier transformation to the xt domain.
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
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
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).
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.
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
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
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.
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
Declarations
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.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
 Windecker S, Kolh P, Alfonso F, et al. 2014 ESC/EACTS Guidelines on myocardial revascularization. Eur Heart J. 2014;35:2541–619.View ArticlePubMedGoogle Scholar
 Panting JR, Gatehouse PD, Yang GZ, JeroschHerold M, Wilke N, Firmin DN, Pennell DJ. Echoplanar magnetic resonance myocardial perfusion imaging: parametric map analysis and comparison with thallium SPECT. J Magn Reson Imaging. 2001;13:192–200.View ArticlePubMedGoogle Scholar
 Sakuma H, Suzawa N, Ichikawa Y, Makino K, Hirano T, Kitagawa K, Takeda K. Diagnostic accuracy of stress firstpass contrastenhanced myocardial perfusion MRI compared with stress myocardial perfusion scintigraphy. AJR Am J Roentgenol. 2005;185:95–102.View ArticlePubMedGoogle Scholar
 Schwitter J, Wacker CM, van Rossum AC, et al. MRIMPACT: comparison of perfusioncardiac magnetic resonance with singlephoton emission computed tomography for the detection of coronary artery disease in a multicentre, multivendor, randomized trial. Eur Heart J. 2008;29:480–9.View ArticlePubMedGoogle Scholar
 Schwitter J, Wacker CM, Wilke N, et al. MRIMPACT II: Magnetic Resonance Imaging for Myocardial Perfusion Assessment in Coronary artery disease Trial: perfusioncardiac magnetic resonance vs. singlephoton emission computed tomography for the detection of coronary artery disease: a comparative. Eur Heart J. 2013;34:775–81.View ArticlePubMedGoogle Scholar
 Ahmad IG, Abdulla RK, Klem I, Margulis R, Ivanov A, Mohamed A, Judd RM, BorgesNeto S, Kim RJ, Heitner JF. Comparison of stress cardiovascular magnetic resonance imaging (CMR) with stress nuclear perfusion for the diagnosis of coronary artery disease. J Nucl Cardiol. 2016;23:287–97.View ArticlePubMedGoogle Scholar
 Schwitter J, Nanz D, Kneifel S, et al. Assessment of myocardial perfusion in coronary artery disease by magnetic resonance: a comparison with positron emission tomography and coronary angiography. Circulation. 2001;103:2230–5.View ArticlePubMedGoogle Scholar
 Pärkkä JP, Niemi P, Saraste A, et al. Comparison of MRI and positron emission tomography for measuring myocardial perfusion reserve in healthy humans. Magn Reson Med. 2006;55:772–9.View ArticlePubMedGoogle Scholar
 FritzHansen T, Hove JD, Kofoed KF, Kelbaek H, Larsson HBW. Quantification of MRI measured myocardial perfusion reserve in healthy humans: A comparison with positron emission tomography. J Magn Reson Imaging. 2008;27:818–24.View ArticlePubMedGoogle Scholar
 Morton G, Chiribiri A, Ishida M, et al. Quantification of absolute myocardial perfusion in patients with coronary artery disease: comparison between cardiovascular magnetic resonance and positron emission tomography. J Am Coll Cardiol. 2012;60:1546–55.View ArticlePubMedGoogle Scholar
 Jaarsma C, Leiner T, Bekkers SC, Crijns HJ, Wildberger JE, Nagel E, Nelemans PJ, Schalla S. Diagnostic Performance of Noninvasive Myocardial Perfusion Imaging Using SinglePhoton Emission Computed Tomography, Cardiac Magnetic Resonance, and Positron Emission Tomography Imaging for the Detection of Obstructive Coronary Artery Disease. J Am Coll Cardiol. 2012;59:1719–28.View ArticlePubMedGoogle Scholar
 Bikiri E, Mereles D, Voss A, Greiner S, Hess A, Buss SJ, Hofmann NP, Giannitsis E, Katus HA, Korosoglou G. Dobutamine stress cardiac magnetic resonance versus echocardiography for the assessment of outcome in patients with suspected or known coronary artery disease. Are the two imaging modalities comparable? Int J Cardiol. 2014;171:153–60.View ArticlePubMedGoogle Scholar
 Mordi I, Stanton T, Carrick D, McClure J, Oldroyd K, Berry C, Tzemos N. Comprehensive Dobutamine Stress CMR Versus Echocardiography in LBBB and Suspected Coronary Artery Disease. JACC Cardiovasc Imaging. 2014;7:490–8.View ArticlePubMedGoogle Scholar
 Bamberg F, Marcus RP, Becker A, et al. Dynamic myocardial CT perfusion imaging for evaluation of myocardial ischemia as determined by MR imaging. JACC Cardiovasc Imaging. 2014;7:267–77.View ArticlePubMedGoogle Scholar
 AlSaadi N, Nagel E, Gross M, Bornstedt A, Schnackenburg B, Klein C, Klimek W, Oswald H, Fleck E. Noninvasive detection of myocardial ischemia from perfusion reserve based on cardiovascular magnetic resonance. Circulation. 2000;101:1379–83.View ArticlePubMedGoogle Scholar
 Shin T, Hu HH, Pohost GM, Nayak KS. Three dimensional firstpass myocardial perfusion imaging at 3T: feasibility study. J Cardiovasc Magn Reson. 2008;10:57.View ArticlePubMedPubMed CentralGoogle Scholar
 Vitanis V, Manka R, Giese D, Pedersen H, Plein S, Boesiger P, Kozerke S. High resolution threedimensional cardiac perfusion imaging using compartmentbased kt principal component analysis. Magn Reson Med. 2011;65:575–87.View ArticlePubMedGoogle Scholar
 Chen L, Adluru G, Schabel MC, McGann CJ, Dibella EVR. Myocardial perfusion MRI with an undersampled 3D stackofstars sequence. Med Phys. 2012;39:5204–11.View ArticlePubMedPubMed CentralGoogle Scholar
 Shin T, Nayak KS, Santos JM, Nishimura DG, Hu BS, McConnell MV. Threedimensional firstpass myocardial perfusion MRI using a stackofspirals acquisition. Magn Reson Med. 2013;69:839–44.View ArticlePubMedGoogle Scholar
 Manka R, Jahnke C, Kozerke S, Vitanis V, Crelier G, Gebker R, Schnackenburg B, Boesiger P, Fleck E, Paetsch I. Dynamic 3dimensional stress cardiac magnetic resonance perfusion imaging: detection of coronary artery disease and volumetry of myocardial hypoenhancement before and after coronary stenting. J Am Coll Cardiol. 2011;57:437–44.View ArticlePubMedGoogle Scholar
 Jogiya R, Morton G, De Silva K, Reyes E, Hachamovitch R, Kozerke S, Nagel E, Underwood SR, Plein S. Ischemic burden by 3dimensional myocardial perfusion cardiovascular magnetic resonance: comparison with myocardial perfusion scintigraphy. Circ Cardiovasc Imaging. 2014;7:647–54.View ArticlePubMedGoogle Scholar
 Manka R, Wissmann L, Gebker R, et al. Multicenter Evaluation of Dynamic ThreeDimensional Magnetic Resonance Myocardial Perfusion Imaging for the Detection of Coronary Artery Disease Defined by Fractional Flow Reserve. Circ Cardiovasc Imaging. 2015;8:e003061.View ArticlePubMedGoogle Scholar
 Sharif B, Dharmakumar R, Arsanjani R, Thomson L, Bairey Merz CN, Berman DS, Li D. NonECGgated myocardial perfusion MRI using continuous magnetizationdriven radial sampling. Magn Reson Med. 2014;72:1620–8.View ArticlePubMedPubMed CentralGoogle Scholar
 Sharif B, Arsanjani R, Dharmakumar R, Bairey Merz CN, Berman DS, Li D. Allsystolic nonECGgated myocardial perfusion MRI: Feasibility of multislice continuous firstpass imaging. Magn Reson Med. 2015;74:1661–74.View ArticlePubMedPubMed CentralGoogle Scholar
 Motwani M, Kidambi A, Uddin A, Sourbron S, Greenwood JP, Plein S. Quantification of myocardial blood flow with cardiovascular magnetic resonance throughout the cardiac cycle. J Cardiovasc Magn Reson. 2015;17:4.View ArticlePubMedPubMed CentralGoogle Scholar
 Gatehouse PD, Elkington AG, Ablitt NA, Yang GZ, Pennell DJ, Firmin DN. Accurate assessment of the arterial input function during highdose myocardial perfusion cardiovascular magnetic resonance. J Magn Reson Imaging. 2004;20:39–45.View ArticlePubMedGoogle Scholar
 Wissmann L, Niemann M, Gotschy A, Manka R, Kozerke S. Quantitative threedimensional myocardial perfusion cardiovascular magnetic resonance with accurate twodimensional arterial input function assessment. J Cardiovasc Magn Reson. 2015;17:108.View ArticlePubMedPubMed CentralGoogle Scholar
 Breton E, Kim D, Chung S, Axel L. Quantitative contrastenhanced firstpass cardiac perfusion MRI at 3 tesla with accurate arterial input function and myocardial wall enhancement. J Magn Reson Imaging. 2011;34:676–84.View ArticlePubMedPubMed CentralGoogle Scholar
 Patel AR, Antkowiak PF, Nandalur KR, West AM, Salerno M, Arora V, Christopher J, Epstein FH, Kramer CM. Assessment of advanced coronary artery disease: advantages of quantitative cardiac magnetic resonance perfusion analysis. J Am Coll Cardiol. 2010;56:561–9.View ArticlePubMedPubMed CentralGoogle Scholar
 Panting JR, Gatehouse PD, Yang GZ, Grothues F, Firmin DN, Collins P, Pennell DJ. Abnormal Subendocardial Perfusion in Cardiac Syndrome X Detected by Cardiovascular Magnetic Resonance Imaging. N Engl J Med. 2002;346:1948–53.View ArticlePubMedGoogle Scholar
 JeroschHerold M, Wilke N, Stillman AE. Magnetic resonance quantification of the myocardial perfusion reserve with a Fermi function model for constrained deconvolution. Med Phys. 1998;25:73–84.View ArticlePubMedGoogle Scholar
 Goldstein TA, JeroschHerold M, Misselwitz B, Zhang H, Gropler RJ, Zheng J. Fast mapping of myocardial blood flow with MR firstpass perfusion imaging. Magn Reson Med. 2008;59:1394–400.View ArticlePubMedGoogle Scholar
 Hautvast G, Chiribiri A, Zarinabad N, Schuster A, Breeuwer M, Nagel E. Myocardial blood flow quantification from MRI by deconvolution using an exponential approximation basis. IEEE Trans Biomed Eng. 2012;59:2060–7.View ArticlePubMedGoogle Scholar
 Broadbent DA, Biglands JD, Larghat A, Sourbron SP, Radjenovic A, Greenwood JP, Plein S, Buckley DL. Myocardial blood flow at rest and stress measured with dynamic contrastenhanced MRI: Comparison of a distributed parameter model with a fermi function model. Magn Reson Med. 2013;70:1591–7.View ArticlePubMedGoogle Scholar
 Pack NA, DiBella EVR. Comparison of myocardial perfusion estimates from dynamic contrastenhanced magnetic resonance imaging with four quantitative analysis methods. Magn Reson Med. 2010;64:125–37.View ArticlePubMedPubMed CentralGoogle Scholar
 Zarinabad N, Chiribiri A, Hautvast GLTF, Ishida M, Schuster A, Cvetkovic Z, Batchelor PG, Nagel E. Voxelwise quantification of myocardial perfusion by cardiac magnetic resonance. Feasibility and methods comparison. Magn Reson Med. 2012;68:1994–2004.View ArticlePubMedGoogle Scholar
 Zarinabad N, Hautvast G, Sammut E, Arujuna A, Breeuwer M, Nagel E, Chiribiri A. Effects of tracer arrival time on the accuracy of highresolution (voxelwise) myocardial perfusion maps from contrastenhanced firstpass perfusion magnetic resonance. IEEE Trans Biomed Eng. 2014;61:2499–506.View ArticlePubMedGoogle Scholar
 Tsao J, Boesiger P, Pruessmann KP. kt BLAST and kt SENSE: dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn Reson Med. 2003;50:1031–42.View ArticlePubMedGoogle Scholar
 Huang F, Akao J, Vijayakumar S, Duensing GR, Limkeman M. kt GRAPPA: a kspace implementation for dynamic MRI with high reduction factor. Magn Reson Med. 2005;54:1172–84.View ArticlePubMedGoogle Scholar
 Lustig M, Santos JM, Donoho DL, Pauly JM. kt SPARSE: high frame rate dynamic MRI exploiting spatiotemporal sparsity. In: Proceedings of the 14th ISMRM. 2006. p. 2420.Google Scholar
 Chao TC, Chung HW, Hoge WS, Madore B. A 2D MTF approach to evaluate and guide dynamic imaging developments. Magn Reson Med. 2010;63:407–18.View ArticlePubMedPubMed CentralGoogle Scholar
 Pedersen H, Kozerke S, Ringgaard S, Nehrke K, Kim WY. kt PCA: temporally constrained kt BLAST reconstruction using principal component analysis. Magn Reson Med. 2009;62:706–16.View ArticlePubMedGoogle Scholar
 Otazo R, Kim D, Axel L, Sodickson DK. Combination of compressed sensing and parallel imaging for highly accelerated firstpass cardiac perfusion MRI. Magn Reson Med. 2010;64:767–76.View ArticlePubMedPubMed CentralGoogle Scholar
 Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58:1182–95.View ArticlePubMedGoogle Scholar
 Samsonov AA, Kholmovski EG, Parker DL, Johnson CR. POCSENSE: POCSbased reconstruction for sensitivity encoded magnetic resonance imaging. Magn Reson Med. 2004;52:1397–406.View ArticlePubMedGoogle Scholar
 Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math. 2004;57:1413–57.View ArticleGoogle Scholar
 Kim D, Dyvorne HA, Otazo R, Feng L, Sodickson DK, Lee VS. Accelerated phasecontrast cine MRI using kt SPARSESENSE. Magn Reson Med. 2012;67:1054–64.View ArticlePubMedGoogle Scholar
 Sourbron SP, Buckley DL. Classic models for dynamic contrastenhanced MRI. NMR Biomed. 2013;26:1004–27.View ArticlePubMedGoogle Scholar
 JeroschHerold M. Quantification of myocardial perfusion by cardiovascular magnetic resonance. J Cardiovasc Magn Reson. 2010;12:57.View ArticlePubMedPubMed CentralGoogle Scholar
 Henningsson M, Mens G, Koken P, Smink J, Botnar RM. A new framework for interleaved scanning in cardiovascular MR: Application to imagebased respiratory motion correction in coronary MR angiography. Magn Reson Med. 2015;73:692–6.View ArticlePubMedGoogle Scholar
 Ogg RJ, Kingsley PB, Taylor JS. WET, a T1 and B1insensitive watersuppression method for in vivo localized 1H NMR spectroscopy. J Magn Reson B. 1994;104:1–10.View ArticlePubMedGoogle Scholar
 Messroghli DR, Radjenovic A, Kozerke S, Higgins DM, Sivananthan MU, Ridgway JP. Modified LookLocker inversion recovery (MOLLI) for highresolution T1 mapping of the heart. Magn Reson Med. 2004;52:141–6.View ArticlePubMedGoogle Scholar
 Wissmann L, Santelli C, Segars WP, Kozerke S. MRXCAT: Realistic numerical phantoms for cardiovascular magnetic resonance. J Cardiovasc Magn Reson. 2014;16:63.View ArticlePubMedPubMed CentralGoogle Scholar
 Broadbent DA, Biglands JD, Ripley DP, Higgins DM, Greenwood JP, Plein S, Buckley DL. Sensitivity of quantitative myocardial dynamic contrastenhanced MRI to saturation pulse efficiency, noise and t 1 measurement error: Comparison of nonlinearity correction methods. Magn Reson Med. 2016;75:1290–300.View ArticlePubMedGoogle Scholar
 Burchell TR, Boubertakh R, Mohiddin S, Miquel ME, Westwood MA, Mathur A, Davies LC. Adenosine Stress Perfusion Cardiac MRI: Improving Image Quality Using a 32Channel Surface Coil. Open J Med Imaging. 2011;1:21–5.View ArticleGoogle Scholar