Dynamic Regularized Adaptive Cluster Optimization (DRACO) for Quantitative Cardiac Cine MRI in Complex Arrhythmias

Abstract

BACKGROUND:

Irregular cardiac motion can render conventional segmented cine MRI non-diagnostic. Clustering has been proposed for cardiac motion binning and may be optimized for complex arrhythmias.

PURPOSE:

To develop an adaptive cluster optimization method for irregular cardiac motion, and to generate the corresponding time-resolved cine images.

STUDY TYPE:

Prospective.

SUBJECTS:

13 with atrial fibrillation, 4 with premature ventricular contractions, 1 patient in sinus rhythm.

FIELD STRENGTH/SEQUENCE:

free-running balanced steady state free precession (bSSFP) with sorted golden-step, reference real-time sequence.

ASSESSMENT:

Each subject underwent both the sorted golden-step bSSFP and the reference Cartesian real-time imaging. Golden-step bSSFP images were reconstructed using the Dynamic Regularized Adaptive Cluster Optimization (DRACO) method and k-means clustering. Image quality (4-point Likert scale), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), edge sharpness, and ventricular function were assessed.

STATISTICAL TESTS:

Paired t-tests, Friedman test, regression analysis, Fleiss’ Kappa, Bland–Altman analysis. Significance level p<0.05.

RESULTS:

The DRACO method had the highest percent of images with scores ≥3 (96% diastolic frame, 93% systolic frame, and 93% multiphase cine) and the percentages were significantly higher compared to both the k-means and real-time methods. Image quality scores, SNR, and CNR were significantly different between DRACO vs k-means and between DRACO vs real-time. Cardiac function analysis showed no significant differences between DRACO vs the reference real-time.

CONCLUSION:

DRACO with time-resolved reconstruction generated high quality images and has early promise for quantitative cine cardiac MRI in patients with complex arrhythmias including atrial fibrillation.

INTRODUCTION

Cine MRI is the reference standard for quantitative evaluation of cardiac morphology and function [1]. In settings of complex arrhythmias such as atrial fibrillation, irregular cardiac motion can result in imaging artifacts and sometimes premature scan termination [2]. Notably, atrial fibrillation has a prevalence of 1–2% in the United States and the estimated lifetime risk for atrial fibrillation is 1 in 3 for white and 1 in 4 for black individuals [3]. The high incidence of atrial fibrillation provides strong motivation for the development of techniques to manage highly irregular and non-periodic cardiac motion in quantitative MRI. Although self-gating methods have been developed to relieve the dependency on electrocardiogram (ECG)-gating, typical self-gating methods [4–7] often assume periodic or quasiperiodic cardiac motion or that cardiac motion is within a specified frequency range. These assumptions often fail when capturing irregular cardiac motion for quantitative assessment [8].

In complex arrhythmias, the non-periodic nature of cardiac motion demands more flexible data-driven methods, and clustering algorithms represent one possible solution [9–11]. In general, clustering approaches partition data into multiple groups, and drive group association based on definitions of similarity between the data points [12]. Although clustering algorithms have been used in cardiac MRI postprocessing including segmentation [13] and automatic disease detection [14], they are rarely used in the processing of raw image data and subsequent reconstruction steps. For handling of cardiac motion, k-means [15] has been applied in several MRI frameworks [16–18], including ECG-free 2D cine MRI for quantitative evaluation of cardiac function in sinus rhythm. However, this method had limitations in some patients with atrial fibrillation, specifically flickering artifacts and unstable image quality across different phases, which was attributed to temporal inconsistencies [18]. Another limitation, intrinsic to k-means clustering, is arbitrary indexing, which does not provide any specific temporal ordering to reflect cardiac phase relationships [18]. The temporal continuity of cardiac motion is therefore neither fully leveraged nor represented when a simple k-means approach is used.

In this study, a method called Dynamic Regularized Adaptive Cluster Optimization (DRACO) is developed to cope with complex arrhythmias and to generate cine images that can be used for quantitative evaluation of cardiac morphology and function. We hypothesized that a) cluster indexing of cardiac motion binning should be continuous along the natural time dimension and b) the centroids of temporally-adjacent clusters should be close in the image or projection dimension. We aimed to evaluate the performance of our proposed DRACO imaging framework relative to k-means clustering for handling complex arrhythmias in cardiac cine MRI using a sorted golden step pulse sequence.

MATERIALS AND METHODS

Data acquisition and pre-processing

With approval from the local Institutional Review Board and in compliance with the Health Insurance Portability and Accountability Act, seventeen patients with arrhythmias (n=13 atrial fibrillation (AF), n=4 premature ventricular contractions (PVC)) and one subject with sinus rhythm were recruited to undergo cardiac MRI. All participants provided written informed consent prior to participation. All AF and PVC patients had arrhythmias during the scan. All scans were performed on a 3.0T clinical scanner (Skyra; Siemens Healthcare, Erlangen, Germany) with an 18-channel phased-array body coil. Using both the sorted Cartesian golden-step sequence [19] and a commercially available reference real-time sequence, ten to 12 imaging slices in the ventricular short-axis orientation (covering the entire ventricle) were acquired. The reference real-time sequence has a Cartesian balanced steady-state free precession (bSSFP) readout and inline reconstruction provided by the commercial entity. Representative sequence parameters are shown in Table S1. The acquisitions were performed with breath-holding to minimize respiratory-motion related differences between the sorted Cartesian golden-step and the reference real time images. The ECG signal was simultaneously recorded during the data acquisition and used for timing in the DRACO algorithm.

The sorted golden step sequence with additional navigators has been previously described [18]. Briefly, additional k-space center lines were introduced after every n^th TR to a free-running Cartesian sequence with sorted golden-step trajectory [19] and bSSFP readout. The additional k-space center lines act as motion navigators and were combined as one single matrix with dimension $N_{\mathrm{c}\mathrm{o}\mathrm{i}\mathrm{l}}{N}_{\mathrm{e}\mathrm{n}\mathrm{c}}\times T,$ where $N_{\mathrm{c}\mathrm{o}\mathrm{i}\mathrm{l}}$ is the number of receive coils, $N_{\mathrm{e}\mathrm{n}\mathrm{c}}$ is the number of data points in the frequency encoding direction, and $T$ is the number of navigators along the time dimension. The Inverse Fast Fourier Transform (IFFT) was applied in the frequency encoding direction to convert frequency information to 1D spatial projections. The first order difference of the projections was calculated and the first order differences from multiple coils were concatenated to a new data matrix $X$ with dimension ${N_{\mathrm{c}\mathrm{o}\mathrm{i}\mathrm{l}}N}_{\mathrm{e}\mathrm{n}\mathrm{c}}\times T$. Principal component analysis (PCA) was applied along the coil direction at each time point to generate a compact matrix $𝒴\in {\mathbb{C}}^{N_{\mathrm{f}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s}}\times T}$, which can be used in either of the subsequent clustering algorithms.

Clustering of cardiac motion states

The k-means clustering approach for handling cardiac motion states has been previously described [18]. In brief, k-means clustering was applied to the compressed motion navigator matrix $𝒴$ and data points representing similar cardiac motion states were assigned to clusters based on similarity of motion information from k-space navigator lines. Navigator lines in the same cluster were considered to have similar motion. We chose 25 clusters to yield a temporal resolution of ~40 ms, and cluster assignments were based on minimizing the sum of in-cluster distances among all clusters. The cluster assignments were used for data binning in the reconstruction step whereby the data within each cluster were assumed to reflect one cardiac phase.

Figure 1 shows the proposed DRACO imaging framework. In contrast to conventional clustering approaches, DRACO is designed to estimate probabilistic associations between k-space data at each time point and the intrinsic cardiac phase (time-phase association of mechanical cardiac motion states). This feature enables depiction of a smooth transition between dynamic motion states regardless of the cardiac rhythm and enables iterative adaptation. To provide a flexible mechanism for integration of varying cardiac motion patterns and sequential temporal ordering, regularization is imposed on the clustering geometry. Finally, the optimization-driven adaptive scheme provides a single framework to handle both periodic and non-periodic cardiac motion patterns. This 3-prong approach provides a convenient and comprehensive way to represent both morphologic and physiological prior assumptions in a unified manner. A detailed explanation of DRACO along with its cost function is described in the Supplemental Material. In brief, the time-phase association is described as matrix $ℳ$ of size $K\times T$ such that its ${(k,t)}^{\text{th}}$ component describes the likelihood and corresponding level of contribution of the sampled data at time t to the cardiac phase $k$. In our experimental setting, $K$ is typically 25 and $T$ is typically 1290. Each cardiac phase is represented as cluster centroids. The association $ℳ$ and cluster configurations are achieved by minimizing a cost function that includes (1) a data fidelity term that reflects the goodness of fit between observed data and the clusters, (2) a regularization term to encourage piecewise smoothness during cardiac motion state transitions that relate to the underlying cardiac rhythm such as atrial fibrillation or premature ventricular contractions, and (3) a regularization term to encourage adjacency and intrinsic ordering of the clustering centers for smooth cluster transition. Although others have used a more passive but causal way to impose closeness in time-resolved reconstruction [20], the similarity term in the DRACO method imposes motion state adjacent clusters to be closer to each other.

Figure 1.

Imaging framework for Dynamic Regularized Adaptive Cluster Optimization (DRACO). (A) In the data acquisition step, navigator data Y_nav and image data Z_img are acquired using the sorted golden step pulse sequence. (B) During cluster analysis, navigator data Y_nav is separated from the image data Z_img. Navigator data Y_nav serves as the input into the clustering algorithm to generate cluster matrix M, which represents cardiac motion. Cluster matrix M describes the likelihood probability that motion from the navigator data at each time frame belongs to a specific cluster, which helps to resolve irregular motion. Regularization of the similarity between adjacent clusters and adjacent time frames is performed to get the final M. (C) In the “time-resolved” reconstruction step, cluster matrix M is applied to order and weight the unsolved image in a pseudo-real-time formulation, and to mimic the nonperiodic motion pattern. Sensitivity maps in S are calculated based on the image data and the sampling operator Ω is defined based on the data acquisition pattern. To generate the final images, total variation regularization is applied along the temporal dimension.

Image reconstruction

In sinus rhythm, cardiac motion is regular and periodic. However, in arrhythmias, the pattern of cardiac motion varies with the duration of the RR interval, which reflects the cycle length for each heartbeat. In some instances, the RR interval is so short that only a few cardiac phases (motion states) exist.

For the k-means approach, image reconstruction for sinus rhythm and arrhythmias was performed as previously described [18] using the ESPIRiT reconstruction method [21]. Briefly, ESPIRiT was applied to every cluster bin to generate the cine images. To generate a video of the reconstructed data, the temporal order for the patient with sinus rhythm was based on the recorded ECG. For patients with arrhythmias, the temporal order was generated based on the sequential time stamp from the navigator data such that images with a shorter time stamp are ordered earlier and images with longer time stamp are ordered later in the cardiac cycle.

For the proposed DRACO reconstruction step, we employed the time-cluster association matrix $ℳ$ to generate images from uncertain motion patterns during arrhythmias. The reconstructed images result from minimizing a cost function that includes terms to enforce fidelity of the k-space data and total variation (TV) regularization. K-space data fidelity is enforced by taking into account under-sampling, coil sensitivity maps, Fourier transform, and $ℳ$. The cluster matrix $ℳ$ governs how k-space data from different cardiac cycles are softly combined at each time point to render the corresponding images. The weight parameter $\lambda$ is used in the TV regularization term and reflects the balance between k-space data fidelity and dynamic cardiac motion states. The parameter $\lambda$ requires fine tuning for specific patient cohorts. In the current dataset, the best $\lambda$ was either 0.0003 or 0.0005. When generating pseudo “real-time” videos, the cluster having the largest cluster value at each time point is the one responsible for the image at that specific time point. Through an iterative process for each time point, a pseudo “real-time” video consisting of images from $I$ is produced. See Supplemental Material for detailed mathematical expressions.

For comparison purposes, real-time images were also reconstructed from the sorted golden step pulse sequence acquisition. In the latter case, each phase of the real-time images was directly generated using the temporally adjacent k-space data.

Assessment of image quality and measures of ventricular function.

To assess image quality, three readers (KLN, 10 years of cardiac MR experience; AP, 3 years of cardiac MR experience; JPF, 20 years of cardiac MR experience) independently graded the image quality using a 4-point Likert scale (Supplemental Material, Table S2). Images from DRACO, k-means, and reference real-time methods were randomized and shown to all readers, who were blinded to the methodology. Representative end-systolic (ES) and end-diastolic (ED) images in the left ventricular base, mid, and apical slices from all subjects (n=17) were scored first because the systolic and diastolic frames are most important for cardiac function analysis. Multiphase images of the ventricular base, mid, and apical slices were then scored in real-time cine mode. A total of 51 slices (17 patients × 3 slices) at ES and at ED and cine videos (n=51) from the three methods were evaluated and compared.

Quantitative image quality metrics including signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and edge sharpness were also compared. To calculate SNR, regions of interest (ROIs) were drawn (ZM, 5 year of cardiac MR experience) within the mid-ventricular blood pool, myocardium, and air (outside the body but within the field of view). Mean signal intensity (SI) was recorded in blood and myocardium, and the standard deviation (SD) of the SI was assessed in air to quantify image noise. The SNR of all tissue types was calculated as: $\mathrm{S}\mathrm{N}\mathrm{R}=\frac{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\left({\mathrm{S}\mathrm{I}}_{\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{e}}\right)}{\mathrm{S}\mathrm{D}\left({\mathrm{S}\mathrm{I}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)}$. The CNR between blood and myocardium was computed as: $\mathrm{C}\mathrm{N}\mathrm{R}=\frac{{\mathrm{S}\mathrm{I}}_{\mathrm{b}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{d}}-{\mathrm{S}\mathrm{I}}_{\mathrm{m}\mathrm{y}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{m}}}{\mathrm{S}\mathrm{D}\left({\mathrm{S}\mathrm{I}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)}$. To assess the relative impact of DRACO vs k-means on image noise, we computed the corresponding SNR and CNR ratios for DRACO and k-means reconstruction:

$$SNRratio=\frac{{DRACO}_{SNR}}{{k-means}_{SNR}}$$ (Eq 1)

$$CNRratio=\frac{{DRACO}_{CNR}}{{k-means}_{CNR}}$$ (Eq 2)

To compare the edge sharpness of images generated from the DRACO and k-means methods, a signal intensity profile was plotted along a line across the right ventricle (RV), interventricular septum, and left ventricle (LV) of the ES and ED mid-ventricular images. The slope between the 25^th and 75^th percentile of the intensity values at the blood pool and interventricular septal edges was computed. The average slope values in $\frac{1}{\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}}$ from the ES and ED images were used to compare the edge sharpness between the two methods. A larger average slope value represents sharper edges.

In atrial fibrillation, significant beat-to-beat variation in ventricular function exists and the effect of the RR intervals on LV ejection fraction is more pronounced than in sinus rhythm [22]. Notably, the cycle length of the preceding RR interval has been shown to be related to the stroke volume [23] and in atrial fibrillation, the effect of the preceding RR interval on LV stroke volume is strongest at higher heart rates [24]. Therefore, to evaluate ventricular function derived from DRACO, the relationship between the preceding RR intervals and the LV area changes in the mid ventricular slices were analyzed. Specifically, curves of LV area change over time for the mid-ventricular slice of each patient were generated from the DRACO-reconstructed “real-time” videos. The maximum and minimum ventricular areas were identified for each curve and the LV area change reflected the difference between the maximum and minimum LV area over multiple heartbeats. A regression analysis was then performed between the preceding RR interval and the LV area change.

For both the DRACO and reference real-time images, commercially available software (Medis Suite 4.0, Medis Medical Imaging, Leiden, Netherlands) was used to quantify ejection fraction (EF), end-diastolic volume (EDV), end-systolic volume (ESV) of the RV and LV as well as LV mass from a full stack of 10–12 ventricular short-axis slices. DRACO-reconstructed images had 25 phases per slice. The ventricular volumes and EFs were calculated by averaging diastolic and systolic volumes across three consecutive heartbeats.

Statistical analysis

Statistical analysis was performed using MATLAB version 2021a (MathWorks, Natick, MA, USA). Categorical variables are summarized as frequencies or percentages. Continuous variables are summarized as mean±SD or median and interquartile range (IQR) as appropriate. The Kolmogorov-Smirnov test was used to test normality of the data. For group comparisons, a two-tailed paired sample t-test was performed on normally distributed data. The Friedman test was performed for multiple non-parametric image quality score comparisons (DRACO method, k-means method, and reference method) with subsequent post-hoc group analysis using Tukey’s test. Inter-reader agreement of image scoring was calculated using Fleiss’ Kappa. Fleiss’ Kappa value is interpreted as: ≤0 no agreement, 0.01–0.20 slight agreement, 0.21–0.40 fair agreement, 0.41– 0.60 moderate agreement, 0.61–0.80 substantial agreement, and 0.81–1.00 almost perfect agreement. Two group comparisons were performed with the Wilcoxon rank sum test. Linear regression analysis was performed to evaluate ventricular function using the preceding RR intervals and LV area change curves. A p value of < 0.05 was considered statistically significant. Bland–Altman analyses were applied to assess the mean bias for biventricular EDV, ESV and EF values derived from the DRACO approach and the reference real-time approach.

RESULTS

Seventeen subjects with arrhythmias (68 ± 14 years, n=17 males, n=13 atrial fibrillation, n=4 PVCs) and one subject (53 years, female) in sinus rhythm underwent imaging at 3.0T. The average heart rate was 71 ± 23 BPM.

Illustrations of qualitative performance on clustering behavior

Figures 2 and 3 illustrate a patient with a run of premature ventricular contractions (PVCs) and a patient with atrial fibrillation during image acquisition, respectively. In both figures, representative behavior of the cluster value matrix $ℳ$, the binning results, and the cluster centroid matrix $C$ are shown for k-means and DRACO. For the cluster value similarity matrices, the y-axis indicates the cluster index number and the color scale indicates similarity values for the data points within the cluster. A similarity value of zero represents no similarity, whereas a value of one represents 100% similarity.

Figure 2.

Comparison between k-means and DRACO for a patient with PVCs. (A) A recorded ECG tracing belonging to a patient with predominantly sinus rhythm and a short period of PVCs. (B) Cluster value similarity matrices showing that DRACO can deal with the variation in motion patterns including shifts between abnormal heartbeats (PVC run) and normal heartbeats (sinus beats). Both cluster matrices for k-means and DRACO show different temporal patterns during sinus and during the PVCs. However, the results for DRACO show more variation in the similarity values across the clusters at each time point than k-means, which fits well with the shift in periodicity shown in the section of the ECG recording with PVCs. (C) Cluster binning results showing that DRACO is more effective at suppressing abrupt changes during binning than k-means. The separation of motion states along the x-axis is more well-defined for DRACO. (D) Relative to k-means, the cluster centroid matrix for DRACO showed improved continuity of cluster positions, which is beneficial for subsequent image reconstruction. In contrast, the centroid values of k-means show a noise-like pattern along the cluster index dimension. The cluster centroid values for DRACO have a smooth shift along this dimension. ECG, electrocardiogram; PVC, premature ventricular contraction; DRACO, dynamic regularized adaptive clustering optimization.

Figure 3.

Comparison between k-means and DRACO for a patient with atrial fibrillation. (A) A recorded ECG tracing belonging to a patient with atrial fibrillation (time-varying RR intervals). (B) Cluster value similarity matrices showing that DRACO can handle the time-varying motion patterns that are intrinsic to atrial fibrillation. There is a wider range of similarity scores across the clusters generated from DRACO. (C) Cluster binning results showing that DRACO can suppress abrupt changes during binning. (D) Relative to k-means, the cluster centroid for DRACO showed improved continuity of cluster positions in the setting of varying RR intervals, which is beneficial for subsequent image reconstruction. The cluster centroid values for k-means show an abrupt, pixelated, and noisy pattern along the cluster index dimension. In contrast, the cluster centroid values from the DRACO method have smooth shifts along the cluster dimension. ECG, electrocardiogram; DRACO, dynamic regularized adaptive clustering optimization.

In the setting of PVCs (Figure 2), a brief, continuous period corresponding to the run of PVCs is seen in the middle while longer periods at the beginning and the end corresponds to sinus rhythm seen on the simultaneously recorded ECG signal (Figure 2A). Two different motion patterns can be appreciated in the illustrations of the cluster value similarity matrix (Figure 2B) and cluster binning (Figure 2C). Apparent in the clustering binning results (Figure 2C), DRACO successfully reduced abrupt temporal changes that sometimes occur during cluster binning. Unlike the abrupt patterns seen for k-means, locations of adjacent clusters are also more continuous in the DRACO cluster centroid matrix (Figure 2D). These differences in the behavior or performance reflect intrinsic differences between k-means clustering and the proposed DRACO method. In k-means clustering, the cost function contains only the data fidelity term. In contrast, DRACO had two additional regularization terms that enforce smoothness of motion state transitions and smoothness in cluster transitions. The $ℳ$ in k-means was a matrix with a binary value (0 or 1), whereas DRACO had a probability-like matrix. Moreover, the DRACO reconstruction included a temporal TV regularization term, whereas the k-means method used ESPIRiT reconstruction without TV regularization. These features contributed to the better performance of the DRACO approach relative to k-means.

For the patient with atrial fibrillation, variations in the RR interval can be clearly observed on the recorded ECG (Figure 3A). Relative to k-means, DRACO showed better disaggregation of cluster index values (Figure 3B), and DRACO cluster binning (Figure 3C) suppressed the abrupt temporal changes while achieving temporal sensitivity that captured the irregular cardiac motion inherent to atrial fibrillation. The continuity of adjacent clusters in the DRACO centroid matrix (Figure 3D) is also consistent with our premise that the regularization step for the current atrial fibrillation dataset should be cluster-continuous. Notable in both Figures 2 and 3 is the performance of the DRACO method to better distribute the high values along the time dimension relative to k-means. Unlike the k-means approach which defines cluster membership in a binary fashion, the probability-like matrix $ℳ$ in DRACO facilitates a probability distribution of motion states that is more akin to the underlying cardiac rhythm.

Figure 4 shows the recorded ECG and corresponding self-correlation maps of the cluster matrix for sinus rhythm, PVCs, and atrial fibrillation. The self-correlation map for sinus rhythm shows repetitive and highly correlative values as a result of periodic cardiac motion, as illustrated by dense yellow parallel lines. In the setting of PVCs, multiple yellow parallel and diagonal lines are also present on the self-correlation map, but these lines are less dense than those for sinus rhythm. The time points are still highly correlated with each other and the motion of these PVCs maintained a specific degree of periodicity. In this example, between 8 to 11 secs, there are several separate diagonal lines with larger gaps between each other. This suggests that the motion pattern between 8–11 secs is different from that at other time points, but that the motion remains quasiperiodic within that 8–11 sec period. In the correlation map for atrial fibrillation, there are almost no subdiagonal lines, which is consistent with the nonperiodic nature of the cardiac motion.

Figure 4.

Self-correlation maps for subjects with sinus rhythm, PVCs, and atrial fibrillation. Recorded ECGs for sinus rhythm patient, PVCs, and atrial fibrillation are shown in the top row. Self-correlation maps of cluster matrices over time are shown in the bottom row. The self-correlation maps illustrate the behavior of the cluster matrix and their correlation over time. In the sinus rhythm patient, the dense parallel yellow diagonal lines indicate that cardiac motion is highly correlated in the time dimension and is periodic. In the setting of PVCs, the multiple parallel yellow diagonal lines show that the cardiac motion remains relatively periodic, but less so. In atrial fibrillation, few diagonal lines can be seen, which is consistent with the inherent irregular motion of atrial fibrillation. ECG, electrocardiogram; PVC, premature ventricular contraction.

Image quality, SNR, CNR, and edge sharpness

Table 1 provides a summary of the qualitative and quantitative results. There were significant differences in the quality of single-phase images among the methods. Based on a 4-point Likert scale, DRACO had a higher percentage of single-phase (diastolic, systolic) images with image quality score ≥3 relative to k-means and reference real-time cine. A significant difference was found between single-phase image quality scores for DRACO vs k-means and for DRACO vs reference real-time (Friedman test, all p values <0.001). The systolic and diastolic single-phase images generated by DRACO had no severe image artifacts. Figure 5 shows that DRACO + 1D TV is able to generate excellent quality images whereas those reconstructed by k-means have some artifacts. The 1D profiles of images generated using DRACO + 1D TV show continuous shape change, while the 1D profiles of those from k-means show abrupt changes over time.

Table 1.

Summary of quantitative and qualitative metrics

Methods	DRACO	k-means	Real-time
SNR	137.2 ± 91.6	70.1 ± 48.0	╲
CNR	92.2 ± 59.5	47.1 ± 28.9	╲
Edge sharpness (pixel−1)	1.01 ± 0.62	0.71 ± 0.45	╲
Image score: diastole	3.72 ± 0.50	3.21 ± 0.82	3.16 ± 0.84
Image score: systole	3.64 ± 0.54	3.13 ± 0.70	3.03 ± 0.80
Image score: multi-phase	3.61 ± 0.52	2.38 ± 0.58	2.94 ± 0.79
Percent of images with quality scores ≥3: diastole (%), N=51	96	73	70
Percent of images with quality scores ≥3: systole (%), N=51	93	73	66
Percent of images with quality scores ≥3: multi-phase (%), N=51	93	27	62

CNR, contrast-to-noise ratio; SNR, signal-to-contrast ratio

Figure 5.

Ventricular short axis images across several representative phases and 1D profiles across the interventricular septum vs time. The images and 1D profiles belong to a patient (age=68y, average heart rate=60 BPM) who was in atrial fibrillation throughout the scan. Shown are basal and mid ventricular short axis images across seven of 25 frames reconstructed using k-means, k-means with “time resolved” total variation (k-means + 1D TV), DRACO, and DRACO with “time resolved” total variation (DRACO + 1D TV). The systolic and diastolic frames from the k-means received an image quality score of 2 while the frames from DRACO + 1D TV received a score of 3. The multiphase (cine) image quality score for DRACO + 1D TV was 4 for both the base and mid ventricular slice. The image quality score for k-means was 2 for both base and mid ventricular images. A movie file of the images is available as Video S1 (see Supplementary Material). BPM, beats per minute; TV, total variation; DRACO, dynamic regularized adaptive cluster optimization.

There were significant differences in the quality of multi-phase cine images among methods. For cine images generated by DRACO, a total of 93% received a score of ≥3, compared to 27% for k-means and 62% for the reference real-time method. A significant difference was also found between multiphase image quality scores for DRACO vs k-means and for DRACO vs reference real-time. Illustrative cine video examples of the case in Figure 5 are shown in Video S1 where it can be seen that DRACO reduced the flickering artifacts that typically degraded the images generated by k-means. Inter-reader agreement analysis of image quality scores was moderate (Fleiss’ kappa values of 0.57 for diastolic phase, 0.51 for systolic phase, and 0.43 for multiphase images).

Figure 6 shows DRACO and real time images from a subject with sinus rhythm and two patients with atrial fibrillation. One patient with atrial fibrillation had a low average heart rate (~45 BPM) and the other had a higher average heart rate (~95 BPM). Cine videos of the corresponding subjects are shown in Video S2. DRACO generated diastolic and systolic images with almost no artifacts in all three subjects (Figure 6A), whereas some artifacts were present on the reference real-time images, particularly the systolic images from the subjects with atrial fibrillation. Figure 6B shows the simultaneously recorded ECG signal with corresponding data points that were clustered for the corresponding systolic and diastolic phases. Without prior information from the ECG signals, DRACO consistently clustered the data points immediately before the R peak within one cluster (diastole) and data points immediately after the R peak in another cluster (systole) regardless of the differences in the QRS morphology.

Figure 6.

Comparison of DRACO and reference real-time approaches for sinus rhythm and atrial fibrillation with low and high heart rates. (A) Systolic and diastolic images belonging to patients with sinus rhythm and atrial fibrillation with low heart rate (average ~ 45 BPM) and high heart rate (average ~ 95 BPM). Images for DRACO were acquired with the sorted golden-step sequence and reconstructed using the DRACO algorithm and time resolved reconstruction. Reference images were acquired using the reference real-time bSSFP sequence with inline reconstruction. (B) Corresponding recorded ECG signals in the subjects with sinus rhythm, low-heart-rate atrial fibrillation and high-heart-rate atrial fibrillation. The R peaks are marked by the gray arrowheads. Points chosen by the DRACO method are depicted in blue and red. In general, blue points are binned into the systolic cluster while red points are binned into the diastolic cluster. The time duration for the systolic and diastolic periods is marked by the blue and red rectangles, respectively. A movie file is available as Video S2. DRACO, dynamic regularized adaptive cluster optimization; SAX, short axis; BPM, beats per minute, bSSFP, balanced steady-state free precession.

The ratio of the DRACO SNR to that of the k-means SNR was 1.97±1.23. The ratio of the DRACO CNR to that of the k-means CNR was 2.07±1.31. Paired t-tests found significant differences in the SNR and CNR values for DRACO vs k-means. The edge sharpness was higher (1.01±0.62 pixel⁻¹) for DRACO than for k-means (0.71±0.45 pixel⁻¹ for k-means (paired t-tests, p=0.052, 95% confidence interval [0.003, 0.566]).

LV area change vs preceding RR interval as a marker of ventricular function

Figure 7 shows a plot of the LV area change vs the duration of the preceding RR interval in 11 atrial fibrillation patients. Two patients with atrial fibrillation who received contrast injection were excluded. A regression analysis of the LV area change vs preceding RR interval showed a nonlinear relationship between LV area change and the preceding RR interval ($R^2$ of 0.419, p<0.05). The correlation coefficient between left ventricular area change and preceding RR interval was 0.647.

Figure 7.

Relationship between the preceding RR interval and the temporal left ventricular area change. Shown are data points from the mid ventricular short-axis images of 11 patients with atrial fibrillation. The correlation coefficient between left ventricular area change and preceding RR interval was 0.647. Two patients with contrast agent injection were excluded. Each color represents a unique patient.

Bland-Altman analyses of cardiac function derived from DRACO and real-time

Paired t-tests found no significant difference between metrics of cardiac function derived from the DRACO method and real-time method (Table 2). Bland–Altman analyses of DRACO and real-time derived EF, ventricular volumes, biventricular mass in arrhythmia subjects showed clinically negligible mean bias values (Figure 8, Table 2). A total of 94% of data points were within the 95% limits of agreement. In the 17 subjects, LV EF was 30.1% ± 9.71% (DRACO) versus 28.9% ± 9.58% (reference), and RV EF was 27.7% ± 8.31% (DRACO) versus 27.9% ± 9.42% (reference).

Table 2.

Comparison of cardiac functional metrics derived from DRACO relative to reference real-time cine MRI

Parameter	Mean bias*	95% confidence interval**	P **
LV EF (%)	1.2	[−1.2, 3.6]	0.30
LV EDV (mL)	−3.5	[−9.5, 2.4]	0.22
LV ESV (mL)	−3.8	[−8.4, 0.8]	0.10
LV mass (g)	2.5	[−3.9, 8.9]	0.43
RV EF (%)	−0.26	[−2.4, 1.8]	0.80
RV EDV (mL)	−3.4	[−8.6, 1.7]	0.18
RV ESV (mL)	−2.3	[−6.8, 2.2]	0.29

^*Mean bias and 95% confidence intervals are derived from Bland–Altman analyses.

^**Group comparisons using paired t-tests with corresponding 95% confidence intervals.

EF, ejection fraction; EDV, end-diastolic volume; ESV, end-systolic volume; g, grams; LV, left ventricular; mL, milliliters; RV, right ventricular

Figure 8.

Bland–Altman plots comparing (A) left ventricular and (B) right ventricular metrics of cardiac function. The metrics were assessed using the proposed DRACO method and reference real-time pulse sequence. The dotted horizontal lines represent the 95% limit of agreement. LV, left ventricle; RV, right ventricle.

DISCUSSION

Cine cardiac MRI is an important method for evaluation of cardiac morphology and function, but approaches that enable quantitative evaluation of ventricular function in complex arrhythmias are lacking. In this study, DRACO was proposed for clustering and time-resolved TV reconstruction to address irregular cardiac motion. Compared to k-means and the reference real-time methods, a significantly higher percentage of DRACO-generated images achieved image quality scores ≥3 on a 4-point Likert scale. SNR and CNR were also significantly higher for DRACO-generated images. Edge sharpness was also improved but this did not achieve statistical significance. Lastly, the nonlinear relationship between the LV area change and the preceding RR interval supports further work to enable an adaptive heartbeat as a quantitative representation of ventricular function in atrial fibrillation.

The novelty of our proposed pipeline lies in 1) usage of a probability-like cluster matrix to represent motion state, 2) customization of regularization terms for soft motion binning, and 3) time-resolved reconstruction based on the cluster matrix without the need for the ECG during reconstruction. Unlike conventional self-gating methods [4,5,7] that force binary associations between time frame and cardiac phase, the cluster matrix, based on several features, evaluates the membership likelihood of the motion signal from each frame. This probabilistic cluster matrix allowed more flexibility for the subsequent reconstruction step and had good correspondence to the recorded ECG regardless of intra-slice and inter-slice variation of the cardiac motion pattern. Relative to k-means methods [16–18] where only one data fidelity term is used for motion clustering, the individually-tailored regularization terms along the temporal dimension and the centroid dimension in DRACO provided fidelity for temporal ordering of the cluster index and reduced the abrupt temporal changes of the clustering results. Subsequently, to generate a pseudo-real-time video, the time-resolved reconstruction weighted and permuted 25 images for different cardiac phases to multiple pseudo-real-time-images based on the cluster matrix and solved the problem with 1D TV regularization. The result is a pseudo-real-time video that preserves the fidelity of the motion pattern in cases of atrial fibrillation and PVCs while generating fewer images for quantification than conventional real-time imaging. Post-processing of the images for quantification of ventricular morphology and function is more feasible with fewer images (~25 frames) than the larger number of images (~300–400 frames) in a typical 20 sec cine MRI acquisition from the real-time method [25].

In prior work [18], the k-means method generated reasonable images for sinus rhythm subjects but showed artifacts for arrhythmia patients. The better performance of DRACO in the current work can again be attributed to the effectiveness of the customized regularization terms in DRACO and supports our hypothesis that the temporally continuous assumption in the time dimension and the cluster centroid spatial dimension generalize well for complex arrhythmias. The real-time approach only makes use of the temporal continuity of cardiac motion and the k-means approach just focuses on the spatial similarity of motion signal, whereas the DRACO method considers both temporal continuity and spatial similarity. This generalization may improve the current clinical workflow for atrial fibrillation and PVCs as well as situations where prospective ECG gating, manual tuning, and/or settings to exclude abnormal heartbeats fail.

DRACO also performed significantly better than the k-means method [18] in terms of SNR and CNR because the customized regularization terms reduced the abrupt temporal changes of the clustering and the time-resolved 1D TV reconstruction suppressed the potential flickering artifact. In contrast, the k-means method relies on a single data fidelity term for motion binning and used ESPIRiT [21] reconstruction without the TV term. Both terms reduced the noise level and contributed to the significantly higher SNR and CNR for DRACO. By reducing the flickering and blurring artifacts that affect the blood pool–myocardial border, DRACO achieved higher average edge sharpness values at the blood pool-septal interface.

Prior studies have shown a correlation between the preceding RR interval duration and LV stroke volume [22–24]. We observed a similar relationship for DRACO-generated images with RR intervals between 400–1200 msec. The regression analysis of LV area change vs preceding RR interval showed a low $R^2$ value suggesting non-linearity in the relationship; this observation is in line with findings from earlier studies [26–27]. Another study [28] suggested a logarithmic relationship along with a correction for both the preceding and pre-preceding RR intervals for quantitative assessment of ventricular function. Exclusion of data points for a pre-preceding RR interval <500 ms improved the correlation between RR interval and ventricular function [28].

More recent strategies to address the problem of ventricular function quantification in arrhythmias, especially atrial fibrillation, include compressed sensing real time [29–30] and XD-GRASP [4]. Compressed sensing real time makes use of a specialized k-space sampling pattern and sparsity in certain domains of images to reconstruct images from under-sampled data but does not bin k-space data into different phases based on the motion signal prior to image reconstruction. In contrast, our DRACO framework focuses on temporal continuity of cardiac motion, generates adaptive motion representation for the cardiac motion signal, bins k-space data based on the motion presentation, and performs the reconstruction using TV regularization. Meanwhile, XD-GRASP performs k-space data binning using motion signals, but the binning is generally based on specific frequency ranges (e.g. 0.5 – 2.5 Hz). DRACO employs an adaptive mechanism within the clustering algorithm. Although XD-GRASP can exclude data from atypical cardiac cycles in patients with PVCs, the exclusion strategy fails for atrial fibrillation and multiple reconstructions would be needed in order to cope with the variation in cardiac cycle lengths for atrial fibrillation [31]. In DRACO, both PVCs and atrial fibrillation can be handled by the adaptive clustering algorithm without additional reconstruction requirements.

LIMITATIONS

First, because the approach is posed as a regularized optimization problem, further work is needed to better characterize the sensitivity and general applicability of our hyperparameter choices. Ideally, tabulation and self-tuning models would be more desirable for automation and easier deployment in clinical settings. Second, the cohort of 17 patients with arrhythmias is small given the range of complexity in atrial fibrillation and PVCs. Although representative results from patients with both low and high heart rate atrial fibrillation are shown, the heart rate range remains limited. For better hyperparameter tuning, a wider spectrum of heart rate range would be beneficial. Third, all the scans were performed under breath holding conditions in the current patient cohort. To enable free-breathing acquisitions, respiration motion could be distinguished from cardiac motion prior to reconstruction or an additional regularization term could be used in the clustering algorithm for respiration motion. Fourth, because of the inherent temporal irregularity of arrhythmia especially atrial fibrillation, only short-time average performance of arrythmia can be acquired and there is not a perfect gold-standard approach for it. In this work, the most available real-time approach was used as a reference. In further work, the results of DRACO can be compared with more reference approaches such as segmented cine bSSFP with arrythmia rejection and more advanced real-time imaging mentioned in [25]. Finally, the scan time for each 2D slice is longer than the conventional segmented cine or real-time imaging approaches that make use of acceleration by parallel imaging techniques such as GRAPPA [32]. In the current DRACO method, no acceleration was used. Future work to accelerate the framework could include under-sampling and filling-in of unacquired data using acquired calibration lines similar to GRAPPA or adding regularization terms in the image reconstruction for under-sampled data.

CONCLUSIONS

DRACO with time-resolved TV reconstruction may be an effective framework for handling irregular cardiac motion, with early results showing robust performance for patients with atrial fibrillation and PVCs. Compared with k-means clustering and the reference real-time cine MRI, the proposed framework generates significantly better single-phase diastolic and systolic images as well as cine images with minimal to no flickering artifacts. With further testing and optimization in a larger cohort with a wider spectrum of heart rate variability, DRACO with time-resolved TV reconstruction has potential to provide a general workflow for resolving cardiac motion in the setting of complex arrhythmias.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the authors upon reasonable request.