Realtime phasecontrast flow cardiovascular magnetic resonance with lowrank modeling and parallel imaging
 Aiqi Sun^{1},
 Bo Zhao^{2, 3},
 Yunduo Li^{1},
 Qiong He^{1},
 Rui Li^{1}Email author and
 Chun Yuan^{1, 4}
DOI: 10.1186/s1296801703301
© The Author(s). 2017
Received: 5 January 2017
Accepted: 19 January 2017
Published: 10 February 2017
Abstract
Background
Conventional phasecontrast cardiovascular magnetic resonance (PCCMR) employs cinebased acquisitions to assess blood flow condition, in which electrocardiogram (ECG) gating and respiration control are generally required. This often results in lower acquisition efficiency, and limited utility in the presence of cardiovascular pathology (e.g., cardiac arrhythmia). Realtime PCCMR, without ECG gating and respiration control, is a promising alternative that could overcome limitations of the conventional approach. But realtime PCCMR involves image reconstruction from highly undersampled (k, t)space data, which is very challenging. In this study, we present a novel modelbased imaging method to enable highresolution realtime PCCMR with sparse sampling.
Methods
The proposed method captures spatiotemporal correlation among flowcompensated and flowencoded image sequences with a novel lowrank model. The image reconstruction problem is then formulated as a lowrank matrix recovery problem. With proper temporal subspace modeling, it results in a convex optimization formulation. We further integrate this formulation with the SENSEbased parallel imaging model to handle multichannel acquisitions. The performance of the proposed method was systematically evaluated in 2D realtime PCCMR with flow phantom experiments and in vivo experiments (with healthy subjects). Additionally, we performed a feasibility study of the proposed method on patients with cardiac arrhythmia.
Results
The proposed method achieves a spatial resolution of 1.8 mm and a temporal resolution of 18 ms for 2D realtime PCCMR with one directional flow encoding. For the flow phantom experiments, both regular and irregular flow patterns were accurately captured. For the in vivo experiments with healthy subjects, flow dynamics obtained from the proposed method correlated well with those from the cinebased acquisitions. For the experiments with the arrhythmic patients, the proposed method demonstrated excellent capability of resolving the beatbybeat flow variations, which cannot be obtained from the conventional cinebased method.
Conclusion
The proposed method enables highresolution realtime PCCMR at 2D without ECG gating and respiration control. It accurately resolves beatbybeat flow variations, which holds great promise for studying patients with irregular heartbeats.
Keywords
Cardiovascular imaging Phasecontrast CMR Cine Realtime flow imaging Modelbased reconstruction Lowrank modeling Parallel imagingBackground
Over the past few decades, phasecontrast cardiovascular magnetic resonance (PCCMR) has been developed into a powerful tool for quantification and visualization of blood flow dynamics in the heart and large vessels [1–5]. It has advanced the understanding and diagnosis of various cardiovascular diseases, such as atherosclerosis [6], aneurysms [7], and arteriovenous malformation [8]. Conventional PCCMR [9, 10] employs electrocardiogram (ECG) synchronized cine acquisitions with respiration control to acquire data from multiple cardiac cycles, from which averaged velocity maps are obtained. Although this approach has been widely used in biomedical research and clinical practice, it suffers from a number of wellknown limitations. For example, it often requires periodic or quasiperiodic cardiac motion to ensure efficient data acquisition; rejection of data caused by irregular cardiac motion often leads to prolonged acquisition time. Additionally, due to its underlying assumption, this approach only obtains averaged flow information over multiple cardiac cycles, failing to resolve beatbybeat flow variations associated with irregular cardiac motion (e.g., cardiac arrhythmia). Capturing physiological and/or pathological flow variabilities has long been an important goal of PCCMR research [11–14].
Realtime PCCMR [15, 16] without ECG gating and respiration control is a promising direction to address these limitations; however, it requires a much higher imaging speed, posing significant challenges for both data acquisition and image reconstruction. A number of techniques have been developed to advance realtime PCCMR. For example, advanced acquisition methods, such as echoplanar [17, 18], radial [19, 20], and spiral [21–24] acquisition schemes, have been employed for realtime PCCMR. In addition, realtime PCCMR also benefits from accelerated data acquisitions. For example, with the emergence of parallel imaging, sensitivity encoding (SENSE) [25] and generalized autocalibrating partially parallel acquisitions (GRAPPA) [26] have been applied to realtime PCCMR [27–32]. More recently, modelbased reconstruction methods [33, 34] using regularized nonlinear inversion [35] have been developed, achieving 2D realtime flow imaging with a spatial resolution of 1.5 mm and a temporal resolution of 25.6 ms by jointly reconstructing a proton density map, a phase map, and a set of coil sensitivities.
In this work, we present a new modelbased method for realtime PCCMR with sparse sampling. It is based on the integration of a novel lowrank model with parallel imaging. With temporal subspace modeling, the proposed method yields a convex optimization problem, thereby enabling efficient computation. The proposed method achieves realtime PCCMR without ECG gating and respiration control, and well resolves the beatbybeat flow variations that cannot be obtained from the conventional cine method. Compared with stateoftheart realtime PCCMR techniques, it provides higher temporal resolution. The effectiveness of the proposed method has been systematically evaluated in 2D realtime PCCMR using both phantom experiments and in vivo experiments. A preliminary account of this work was presented in [36, 37].
Theory
where ρ _{ v }(r, t) denotes the dynamic image associated with either the flowcompensated (i. e., v = 1) or flowencoded image sequence (i. e., v = 2, ⋯, N _{ v }), S _{ i }(r) the sensitivity map for the i th receiver coil (i = 1, 2, ⋯, N _{ c }), and d _{ v,i }(k, t) and η _{ v,i }(k, t) respectively the (k, t)space measured data and measurement noise. Here, the goal is to reconstruct ρ _{ v }(r, t) from the undersampled data {d _{ v,i }(k, t)}, and then calculate the velocity maps as \( \mathrm{V}\left(\mathbf{r}, t\right)=\frac{\varDelta \phi \left(\mathbf{r}, t\right)}{\uppi}\cdot \)VENC, where Δϕ(r, t) = ∠ ρ _{ v }(r, t) − ∠ ρ _{1}(r, t) denotes the phase difference between the flowencoded and flowcompensated image sequences, and VENC the prespecified encoding velocity. Since in realtime PCCMR, there is no data sharing with ECG gating, (k, t)space data is often highly undersampled. Direct inversion of {d _{ v,i }(k, t)} can incur significant aliasing artifacts and lead to inaccurate velocity measurements.
on which we enforce the lowrank structure, i.e., rank(C) ≤ L. There are a number of ways of imposing lowrank constraints [38, 40, 42, 43]. Here, we use an explicit rank constraint via matrix factorization, i.e., C = UV, where U ∈ ℂ ^{ N × L } and V ∈ ℂ ^{ L × M }. In this lowrank representation, the columns of U and rows of V respectively span the spatial subspace and temporal subspace of C.
Methods
We performed both phantom and in vivo studies to evaluate the performance of the proposed method for 2D realtime PCCMR. The experiments were conducted on a 3.0 T whole body MR scanner (Achieva, Philips Medical System, Best, The Netherlands), equipped with a 32channel cardiovascular coil. A gradientecho (GRE) based pulse sequence was adapted to implement the proposed realtime acquisition scheme as shown in Fig. 1. Here neither ECG gating nor respiration control was used to aid data acquisition. Additionally, we performed conventional cine PCCMR using a vendorprovided GREbased pulse sequence, in which retrospective ECG gating was used.
Second, in vivo experiments were performed to evaluate the proposed method. Ten healthy volunteers (7 males, age: 22–29 years, median: 25 years), who had no symptoms of cardiovascular diseases, were recruited. In addition, we performed a feasibility study of applying the proposed method for arrhythmia detection, and recruited two patients (2 males, age: 23year old and 72year old). This study was approved by the Institutional Review Board at Tsinghua University, and all the subjects gave written informed consent. Both the cine and realtime flow experiments were performed on the planes perpendicular to the ascending aorta (AAo) and descending aorta (DAo) during free breathing, and with one directional velocity encoding along the FH direction. For the cine acquisition, the retrospective ECG gating was set according to an estimate of each subject’s heartbeat period, and three averages were performed to mitigate respiratory motion artifacts. For both the cine and realtime imaging experiments, the following imaging parameters were used: FOV = 240 mm × 225 mm, matrix size = 132 × 124, spatial resolution = 1.80 mm × 1.80 mm, slice thickness = 5 mm, TR/TE = 4.5/2.8 ms, flip angle = 10°, and VENC = 200 cm/s. For the realtime flow imaging, the temporal resolution is 4 × TR = 18 ms, whereas for the cine imaging, the temporal resolution is around 36 ms (with 28 cardiac phases). The total acquisition time was around 94 s for both experiments.
For cine flow imaging, the flowcompensated and flowencoded images were simply reconstructed from the fullysampled data. For the proposed realtime flow imaging, we followed the procedure illustrated in Fig. 2. Specifically, we first performed the temporal interpolation and estimated the temporal subspace V from the training data. We then estimated the coil sensitivity maps S _{ i } from the temporally averaged (k, t)space measurements. We further determined the spatial subspace U by solving Eq. (6), followed by forming the timeseries images for flowcompensated and flowencoded images. To improve the computational efficiency, proper coil compression (e.g., [50]) can be adopted. After image reconstruction, phase correction [51] was performed to correct the phase offsets caused by eddy currents. The velocity maps were then extracted for quantitative flow analysis.
We analyzed the results of the phantom and in vivo experiments. For the phantom experiments, the flow waveforms obtained from the cine and realtime flow imaging methods were analyzed for both periodic and aperiodic flow patterns. For the in vivo experiments with healthy subjects, we evaluated the degree of agreement between the flow measurements from the cine method and those from the proposed method. Specifically, we performed a BlandAltman analysis, as well as a paired Student’s ttest, on the peak velocities and stroke volumes obtained from the two methods. Here the peak velocity is defined as the maximum velocity within one cardiac cycle, and the stroke volume is the integral of the flow velocity over one cardiac cycle within the ascending aorta. For the experiments with arrhythmic patients, we evaluated the flow variabilities captured by the proposed method with reference to an external ECG recording of cardiac motion.
To evaluate the effectiveness of imposing a lowrank constraint on the joint Casorati matrix \( \mathbf{C}=\left[\begin{array}{cc}\hfill {\mathbf{C}}_1\hfill & \hfill {\mathbf{C}}_2\hfill \end{array}\right] \), we performed a comparison with an alternative formulation, in which the lowrank constraint is enforced for each individual flow image sequence. The signaltonoise (SNR) and velocitytonoise (VNR) were calculated for the magnitude images and velocity maps, respectively. Here SNR was calculated as a ratio between the mean signal intensity over a region of interest (ROI) and the standard deviation of the background, whereas VNR was calculated as a ratio between the mean velocity for the same ROI and the standard deviation for a region in the stationary tissue [52].
Results
Representative results are shown to illustrate the performance of the proposed method. Figure 3 shows the flow waveforms for the phantom experiments obtained from the conventional cine method and the proposed realtime imaging method. Here the input flow waveforms for the pump were also shown. As can be seen, for the flow waveform (I) (i.e., periodic flow), both the cine and realtime imaging methods can capture the flow dynamics. In particular, the peak flows obtained from the two methods were accurate. However, for the flow waveform (II) (i.e., aperiodic flow), only the proposed method resolves the significant flow variations. The conventional cine method, which integrates data into a single cardiac cycle, fails to reconstruct the aperiodic flow dynamics (e.g., erroneous peak flows).
Discussion
In this work, we introduced a new realtime flow imaging method and systematically demonstrated its effectiveness with both flow phantom experiments and in vivo experiments. Here, it is worth reiterating the key characteristics of the proposed method. First, the proposed method can be used as a viable alternative to the conventional cine flow imaging method in that it provides comparable (if not superior) image quality and flow information for healthy subjects. Second, the proposed method is able to resolve beatbybeat physiological and/or pathological flow variations, which cannot be obtained from the conventional cine method based on ECG gating and respiration control. Such information is often clinically important (e.g., for assessing cardiac arrhythmia).
As with other modelbased methods, the proposed method involves model selection (i.e., selection of the rank L). Generally, the selection of L needs to balance the model representational power, the number of measurements (i.e., acquisition time), and signaltonoise ratio [40]. In this work, we manually selected L to trade off the above factors, and it consistently yielded good reconstruction performance, although it is worthwhile to investigate other principled model selection methods (e.g., [53, 54]) in future research.
The proposed formulation results in a convex optimization problem, which enables efficient computation. For example, the runtime for reconstructing an in vivo dataset (from 94 s realtime acquisition) takes around 10 min on a workstation with 64 GB RAM and 3.47 GHz CPU. The computational efficiency may be further improved by an implementation on graphical processing units. Such an investigation is beyond the scope of this paper, but is worthwhile to explore for future research.
In addition to rank constraint, sparsity constraint can also be incorporated to accelerate PCCMR. It has been demonstrated in [40, 43, 55] that joint lowrank and sparsity constrained reconstruction leads to improved performance for dynamic MRI. Along this line, we can extend the proposed realtime flow imaging method by exploiting our early work [56] in cine flow imaging, although such an extension will come with additional computational cost.
The flowcompensated and flowencoded images share similar magnitude but different phase differences. We can extend the proposed method to exploit such information and impose a stronger constraint in the modelbased reconstruction. However, the resulting formulation can involve a joint reconstruction of magnitude and phase images, which generally leads to a nonconvex optimization problem. To solve such a problem, specialized algorithms and proper initialization are often needed. In contrast, the proposed method here employs a lowrank model to exploit the spatiotemporal correlation between flow images, which leads to a simple convex problem formulation and efficient computation. Given that the two models may have different tradeoffs, comprehensively evaluating their advantages and drawbacks is a very interesting open problem to be explored in future work.
In this work, we demonstrate the performance of the proposed method for 2D realtime flow imaging, in which throughplane flow was imaged. Considering the complex flow patterns and blood vessel geometry, it is highly desirable to perform 3D realtime flow imaging. However, 3D realtime flow imaging generally involves a more challenging tradeoff between spatial resolution, temporal resolution, and imaging time, and a significantly more challenging computational problem. We are investigating an extension of the proposed method to 3D realtime flow imaging, and the results will be reported in future work.
This paper is focused on the development of a novel realtime flow imaging technique, which should serve as a foundation for our subsequent clinical studies. Given that the proposed method well resolves beatbybeat flow variations, it can provide more information on hemodynamics for patients with significant irregular heartbeats. In the future work, we plan to conduct systematic study of the proposed method for various potential clinical applications (e.g., atrial fibrillation, premature atrial contraction or congenital heart disease).
It is also worthwhile to remark on the potential limitations of the proposed method. First, note that the aforementioned spatial and temporal resolution both refer to nominal resolution. For a linear shiftinvariant reconstruction method (e.g., conventional Fourier reconstruction), the resolution can be characterized through the point spread function. However, for a nonlinear reconstruction method (e.g., sparsity [57] or lowrank constrained reconstruction [38, 40]), rigorously characterizing the resolution has been a longstanding open problem. In this work, we turn to reporting the nominal spatial and temporal resolution, although it is worthwhile to perform an indepth study of resolution characterization for these advanced image reconstruction methods in future research.
Second, it is useful to create gold standard data sets for studying realtime flow imaging. Due to the undersampling nature of realtime imaging experiments, it is often difficult to generate an ideal reference for systematic quantitative evaluation. For example, in the phantom experiments, the input flow waveforms for the pump deviate from the flow measurements during the constant flow due to the phantom response to the flow/pressure in the tubing system. In the future, we hope to build a more advanced flow imaging phantom, in which better reference data sets can be generated.
Conclusions
A new modelbased method was introduced for highresolution realtime PCCMR without ECG gating and respiration control. It integrates the novel lowrank model with parallel imaging, which enables highquality image reconstruction from highly undersampled (k, t)space data for realtime PCCMR. The effectiveness and utilities of the proposed method have been demonstrated for 2D realtime PCCMR with both phantom experiments and in vivo experiments. We expect that the proposed method will enhance the practical utility of realtime PCCMR for various clinical applications.
Abbreviations
 AAo:

Ascending aorta
 DAo:

Descending aorta
 ECG:

Electrocardiogram
 FOV:

Field of view
 GRAPPA:

Generalized autocalibrating partially parallel acquisitions
 PCCMR:

Phasecontrast cardiovascular magnetic resonance
 SENSE:

Sensitivity encoding
 TE:

Echo time
 TR:

Repetition time
 VENC:

Encoding velocity
Declarations
Acknowledgements
The authors thank Prof. ZhiPei Liang at the University of Illinois at UrbanaChampaign for insightful discussions. The authors also thank Dr. Zechen Zhou and Shuo Chen at Tsinghua University for the help with data acquisition.
Funding
This work was partially supported by the National Key R&D Program during the “13th FiveYear Plan” (2016YFC1301601), and National Institute of Health (NIHRO1EB013695).
Availability of supporting data
Not applicable.
Author’s contributions
AS conceived the study, developed the imaging technique, performed data collection and analysis, and drafted the manuscript. BZ conceived the study, developed the imaging technique, assisted in the interpretation of the results, and revised the manuscript. YL and QH assisted with the experimental study. RL participated in the design of experimental study, assisted in the interpretation of the results, and revised the manuscript. CY supervised the project and revised the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Written informed consent was obtained from all the subjects for publication of their individual details and accompanying images in this manuscript.
Ethical approval and consent to participate
This study was approved by the Institutional Review Board at Tsinghua University, and all the subjects gave written informed consent.
Authors’ information
The authors have no additional information to report.
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
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