Quiescent frame, contrast-enhanced coronary magnetic resonance angiography reconstructed using limited number of physiologic frames from 5D free-running acquisitions

Abstract

Background:

5D, free-running imaging resolves sets of 3D whole-heart images in both cardiac and respiratory dimensions. In an application such as coronary imaging when a single, static image is of interest, computationally expensive offline iterative reconstruction is still needed to compute the multiple 3D datasets.

Purpose:

Evaluate how the number of physiologic bins included in the reconstruction affects the computational cost and resulting image quality of a single, static volume reconstruction.

Study type:

Retrospective

Subjects:

15 pediatric patients following Ferumoxytol infusion (4mg/kg)

Field strength/Sequence:

1.5T/Ungated 5D free-running GRE sequence

Assessment:

The raw data of each subject were binned and reconstructed into a 5D (x-y-z-cardiac-respiratory) images. 1, 3, 5, 7, and 9 bins adjacent to both sides of the retrospectively determined cardiac resting phase and 1, 3 bins adjacent to the end-expiration phase are used for limited frame reconstructions. The static volume within each limited reconstruction was compared with the corresponding full 5D reconstruction using the structural similarity index measure (SSIM). A non-linear regression model was used to fit SSIM with the percentage of data used compared to full reconstruction (% data). A linear regression model was used to fit computation time with % raw data used. Coronary artery sharpness is measured on each limited reconstructed images to determine the minimal number of cardiac and respiratory bins needed to preserve image quality.

Statistical tests:

The coefficient of determination (R²) is computed for each regression model.

Results:

The % of data used in the reconstruction was linearly related to the computational time (R² = 0.99). The SSIM of the static image from the limited reconstructions is non-linearly related with the % of data used (R² = 0.85). Over the 15 patients, the model showed SSIM of 0.9 with 22% of data, and SSIM of 0.95 with 45% of data. The coronary artery sharpness of images reconstructed using no less than 5 cardiac and all respiratory phases is not significantly different from the full reconstructed images using all cardiac and respiratory bins.

Data conclusion:

Reconstruction using only a limited number of acquired physiological states can linearly reduce the computational cost while preserving similarity to the full reconstruction image. It is suggested to use no less than 5 cardiac and all respiratory phases in the limited reconstruction to best preserve the original quality seen on the full reconstructed images.

INTRODUCTION

Coronary magnetic resonance angiography (MRA) has the potential to have a significant impact on the diagnosis and therapeutic management of patients with coronary artery disease, but its clinical use is currently limited. The technical reasons for the limited use of coronary MRA can be primarily attributed to: 1) physiological motion due to respiration and myocardial contraction degrading image quality, 2) the complex three-dimensional geometry of the coronary vasculature requiring a large field of view within an isotropic imaging volume, and 3) the small size of coronary vessels requiring a high image resolution. The conventional approach to overcome motion is to use a stack of oblique 2D images over multiple breath-holds, either as a single-shot acquisition or temporally gated using the patient’s electrocardiogram (ECG) [1–3]. Such 2D approaches, however, do not adequately capture the tortuous geometry exhibited by the coronary arteries. Whole-heart 3D coronary MRA[4] overcomes the problems with limited coverage of the coronary vasculature but requires other means of motion compensation, such as navigator–echo gating. Though this approach can be successful [5], it requires significant planning to correctly time the ECG acceptance window and position the respiratory navigator and determine the respiratory acceptance window. Furthermore, variable respiratory patterns or respiratory drift can result in unpredictably long scan times and inconsistent image quality. Finally, the requirement of high spatial resolution inevitably increases scan time in 3D ECG and navigator echo–gated scans.

Recent efforts have been made to develop alternatives to these prospective motion compensation techniques, including the use of prospective ECG-gated self-navigation to retrospectively compensate for respiratory motion following image acquisition [6, 7] and a self-gated, free-running framework in which data are acquired without any prospective ECG or respiratory gating [8–10]. In the free-running techniques, image data are acquired and used to obtain a physiological motion signal to allow for retrospective motion compensation. In the fully self-gated approach, data are acquired continuously, and the cardiac and respiratory motions are part of the signal variations. By separating these two signals [10], the data can be binned along both a dimension encoding for cardiac phases and a respiratory position dimension, allowing for the generation of a 5D image (x-y-z-cardiac-respiratory) using a previously published method of compressed sensing reconstruction[9]. Without the need for prospective gating, data acquisition can be performed with minimal planning from the operator over a large volume and with a known, fixed scan time. This technique requires the use of a T1-shortening contrast agent with a prolonged half-life, ensuring its efficacy throughout the scan. Ferumoxytol, an iron-based contrast agent, fulfills this requirement.

Though these techniques reduce the scan time and improve ease-of-use for image acquisition, the tradeoff is a significantly greater computational cost during reconstruction. Using compressed sensing–based reconstruction requires an iterative solution, as the linear system is underdetermined. Furthermore, separating each data interleave according to their relative cardiac and respiratory position creates a very large amount of data which must be held in memory and then repeatedly transformed into and out of Fourier space to arrive at an acceptable solution [9]. This process is very time consuming—on the order of 10s of hours—and requires powerful computing hardware. These drawbacks currently impede clinical implementation of these techniques.

The ability to resolve an image volume at multiple cardiac and respiratory states may allow for many diagnostic advantages; however, there are some applications wherein only a static volume is necessary. For coronary MRA, the temporal domain is not usually of interest as only the quiescent image volume defined when the heart is most stationary is necessary for most diagnostic visualization and measurement. Therefore, to substantially reduce the computational cost of the reconstruction, one might only reconstruct highly selected and specific data corresponding to this stationary time point. The optimization equation used to find a solution to the undersampled data, however, works through both a minimization of the error in the solution when compared to the original data (data consistency) and a minimization of the total variation within each dimension (regularization) [11]. The regularization allows for data to be implicitly shared between dimensions, filling in gaps for static regions and enforcing continuity in regions exhibiting motion. Reducing this problem to a purely 3D reconstruction removes these attributes of the algorithm, leaving only a single volume of data which is expected to yield a suboptimal solution.

Because these intra-dimensional comparisons are only directly made between immediately adjacent volumes, it is expected that, for a given volume, the benefit associated with each additional bin within that dimension would exhibit a diminishing marginal utility. Therefore, we propose to evaluate 5D reconstruction using limited number of adjacent physiologic data bins. Rather than use all of the discretized cardiac phases and respiratory positions, the reconstruction would use only those bins including and surrounding the image volume of interest. We hypothesize that there exists an optimal number or percentage of bins that can reduce the needed computation while still providing an acceptable final image.

METHODS

Data acquisition

The study was performed using data on 15 consecutive pediatric subjects with age of 16+/− 14, 10 female and 5 male ratio, heart rate of 72 +/− 18 BPM, and respiratory rate of 16 +/− 4.2 who received IV ferumoxytol (Fereheme, AMAG pharmaceutical) contrast at a concentration of 4 mg/kg. The study was approved by the Institutional Review Board and written informed consent was obtained from the legal guardians prior to CMR scanning. Images were acquired on a 1.5T scanner (MAGNETOM Sola, Siemens Healthcare, Erlangen, Germany), using an 18-channel body coil placed over the heart. Data were acquired with a previously described[10, 12], prototype, continuous, free-running (ECG free, navigator free) golden-angle radial spiral phyllotaxis[13] GRE sequence over a 220 × 220 × 220 mm³ field-of-view (FOV) with 192 samples per readout, giving an isotropic spatial resolution of 1.1 mm³. RF Excitation used a 15° flip angle. All fat saturation pulses and ramp-up RF excitations were removed. A total of 124,344 radial lines were acquired with 12 segments (radial lines) per interleaf. Acquisition of each interleaf occurred over 34 ms with TR/TE of 2.8/1.6 ms, and the time required to sample all 10,362 interleaves was 5 minutes and 54 seconds. Following acquisition, the raw data were exported offline for reconstruction [10, 14].

Physiologic signal extraction and binning

For all data sets, cardiac and respiratory motion signals were extracted from the raw data and subsequently binned using a previously reported methodology using MATLAB (MathWorks) [10]. A brief summary of this methodology is presented here. Principal component analysis of the temporally-resolved superior-inferior projections of each interleaf of data produced a physiological motion signal which spanned the duration of the sequence acquisition and represented a superposition of the cardiac and respiratory motion signals. These two signals were separated through a power spectrum density analysis. Once the signals were successfully identified and separated, data were binned into four respiratory states and a variable number of cardiac phases determined such that each phase represented a 50 ms window without view sharing consistent with the previously published 5D free-running approach [10] (Figure 1).

Figure 1:

Overview of data acquisition, physiologic signal extraction and separation, data binning, and 5D image reconstruction.

Image reconstruction

Total variation–regularized, compressed sensing–based image reconstruction of the highly undersampled data sets was performed using the alternating direction method of multipliers (ADMM) algorithm by exploiting sparsity in the cardiac, respiratory, and spatial dimensions [15, 16]. The reconstruction solved the following unconstrained optimization problem,

$$x=\underset{x}{\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}\frac{1}{2}\parallel Ax-b{\parallel }_2^2+{\lambda }_s{∥{\nabla }_{s}x∥}_1+{\lambda }_c{∥{\nabla }_{c}x∥}_1+{\lambda }_r{∥{\nabla }_{r}x∥}_1$$

where $x$ is the five-dimensional image; $A$ is the nonuniform fast Fourier transform operator scaled by the coil sensitivity map; $b$ is the $k$-space data; ${\nabla }_s$, ${\nabla }_c$, and ${\nabla }_r$ are the finite difference operators along the spatial, cardiac, and respiratory dimensions; and $\lambda$ are the corresponding regularization weights.

For each reconstruction, the ADMM algorithm comprised 10 iterations, within which the conjugate gradient algorithm was repeated four times to minimize the convex quadratic function. The regularization weights were chosen as 1e-4 for the spatial, 0.02 for the respiratory, and 0.02 for the cardiac dimensions, and the augmented Lagrangian parameter was set as 0.06. All calculations were performed in MATLAB on a server equipped with two 24-core CPUs, 24 × 32 GB RAM, and an 11-GB NVIDIA GPU on Linux system CentOS 7.6 OS.

Full reconstruction and Cardiac Quiescent phase determination

For each subject, a full 5D reconstruction (x-y-z-cardiac-respiratory) was performed utilizing all four respiratory bins and all cardiac bins. Following reconstruction, the temporal phase which exhibits the least cardiac motion was determined by a consensus reading between two MR scientists, one with 4 years’ experience and one with 25 years’ of experience in CMR by reviewing mid-short-axis cine at the end-expiration 3D image in cardiac dimension and choosing the central quiescent period. End-expiration phase was determined by review of the respiratory phases on a coronal view of the heart and liver dom at end-diastole. Because this analysis was performed using the final image calculated from the compressed sensing–based reconstruction, this methodology provides a retrospective approach for determination of the cardiac quiescent phase. For all of the subjects, this quiescent phase was determined to be in mid-diastole.

Limited reconstructions

In each subject, the image volume associated with the cardiac quiescent phase during end-expiration was recorded and used as the 3D reference volume. This 3D reference volume came from a full 5D reconstruction using all of the acquired data, including all cardiac phases (Figure 2a: all cardiac phases) and all respiratory bins (Figure 2b: all four respiratory positions). A series of limited reconstructions were then performed using the same raw data but with a variable number of total cardiac (Figure 2a: 1, 3, 5, 7, 9, and all cardiac phases) and respiratory bins (Figure 2b: 1, 3, and 4 respiratory positions). In total, there were 18 reconstructions (six combinations of cardiac bins and three combinations of respiratory bins) for each subject, 17 of which were limited reconstructions and one of which was a full reconstruction. The computational cost of each reconstruction was recorded as the amount of time (hours) to solve the inverse problem. In the case where only one cardiac phase was utilized, the problem reduced to a 4D reconstruction (x-y-z-respiratory). In the case where only one respiratory bin was used with multiple cardiac phases, the problem again reduced to a 4D reconstruction (x-y-z-cardiac); similarly, when only one cardiac phase and one respiratory position were used, the problem further reduced to a 3D reconstruction (x-y-z). For each of these, the cardiac quiescent phase was chosen retrospectively from the cardiac dimension of the full 5D reconstruction.

Figure 2:

Limited reconstruction bin utilization. (a) Data are acquired continuously across the cardiac cycle and are binned according to their relative temporal position. When all cardiac phases are used in the reconstruction, only the image volume corresponding to the cardiac quiescent phase was evaluated. For each limited reconstruction, the quiescent phase was always included, and a variable number of adjacent phases were also included. (b) Data are acquired during free-breathing and are binned according to their respiratory position. When all respiratory positions are included, only the position corresponding to end-expiration was evaluated. For each limited reconstruction, the end-expiration phase was always included, and a variable number of adjacent phases were also included.

Coronary artery sharpness measurement

To compare diagnostic value of limited reconstructions versus the full reconstruction, coronary artery vessel wall sharpness was evaluated. Images were reformatted to show a section of the proximal left anterior descending artery (Figure 3a). A line was drawn across the artery and sharpness was measured by fitting the intensity values in the normal direction of the centerline to a double sigmoid function (Figure 3b)[17] where the average of the two slopes parameters a₁ and a₂ is the fitted coronary sharpness value. Example measurements of proximal LAD sharpness on the full reconstruction and a single cardiac and respiratory phase reconstruction are shown in Figure 3. Student T-test is used to compare the significance of the sharpness difference, and a p value less than 0.05 is considered statistically significant.

Figure 3:

Proximal left descending artery (LAD) sharpness measurement using double sigmoid fitting on segments normal to the coronary centerline. (a) Normal segments along proximal LAD shown in red and measured sharpness on the full reconstruction image (top) and single cardiac and respiratory phase limited reconstruction image (bottom). (b) double sigmoid function fitted (red) to intensity changes on the normal segments versus distance (blue dots), where parameters a1 and a2 are two slopes of the fitted curve. Overall sharpness is the average of slope 1 and slope 2.

Structural Similarity Measure

Each limited reconstruction was compared against the full reference reconstruction by calculation of the 3D structural similarity index measure (SSIM) index of the image volume associated with the cardiac quiescent phase and end-expiration in both. This measure produces a value from 0 to 1, with 1 indicating exact structural similarity and 0 indicating no structural similarity [18]. These indices were then plotted against the ratio of total bins used in the limited reconstruction as compared with the full reconstruction. Nonlinear regression analysis was performed to fit a curve to the data. The absolute and relative time required for each reconstruction was plotted against the absolute and relative bins used in the reconstruction, respectively, to determine if a linear relationship existed between these values. Student T-test is used to compare the significance of the SSIM difference, and a p value less than 0.05 is considered statistically significant.

RESULTS

For the 15 subjects, the total number of reconstructed cardiac phases using the free-running framework were 17 +/− 4. The number of phases was determined such that each cardiac phase covered approximately 50 ms, so the values was dependent on heart rate. With four respiratory positions reconstructed for each subject, this resulted in a total number of adjacent physiologic bins of 67 +/− 14, to be used in the full reconstructions, yielding 1–3% of the Nyquist sampling limit per image volume. The time required to complete each of these three reconstructions monotonically increased with the total number of bins. By looking at the combined group of all limited reconstructions and full reconstructions, the relationship between number of bins and time was strongly linear, with approximately 13 minutes needed for each additional bin (Figure 4a).

Figure 4:

Computational cost and similarity analysis for image reconstruction with variable total bins. (a) The total time needed for reconstruction was seen to be directly proportional to the total number of bins used. Linear regression analysis produced a line with slope 0.22 hours per total bins included in the reconstruction and a coefficient of determination of 0.99 (N = 270, n = 18). (b) For each limited reconstruction, the SSIM index was calculated against the full reconstruction and was plotted over the relative number of bins used in the reconstruction. The 15 data points highlighted by orange arrow are reconstructed using single end-expiration respiratory phase and all cardiac phases (25% bins used). A nonlinear parametric function of the form y=1-exp(−ax^b+1)/c was fitted to the data, where a, b, and c were calculated to be 6, 0,73, and 5.3, respectively, giving a coefficient of determination of 0.8. The intersections of the modeled line and SSIM of 0.9, 0.96, and 0.98 were observed to be at 18%, 30%, and 42% total bins, respectively (N = 270, n = 18). (c) For each limited reconstruction, the percentage of total bins used in the reconstruction was plotted against the relative time needed for the reconstruction. The slope of the line was seen to be 0.99 with a coefficient of determination of 0.99. The intersections of this line and the lines representing 18%, 30%, and 42% total bins used in the reconstruction were seen to lie at 18%, 30%, and 42% of the reconstruction time, respectively (N = 270, n = 18).

For each limited reconstruction, the image volume corresponding to the cardiac quiescent phase during end-expiration was compared against the same volume from the full reconstruction using the SSIM index. These SSIM indices were plotted against the percentage of total bins used in each limited reconstruction in reference to the full reconstruction, and a non-linear model was fitted with a coefficient of determination of 0.8 (Figure 4b). The intersection of this model with SSIM indices of 0.90, 0.96, and 0.98 were observed to be at 18%, 30%, and 42% of the total bins, respectively, which correspond to using 3 cardiac and 4 respiratory bins (18 +/− 4.3% of total bins, n = 15), 5 cardiac and 4 respiratory bins (30 +/− 7.2% of total bins, n = 15), and 7 cardiac and 4 respiratory bins (42 +/− 11% of total bins, n = 15) in limited reconstructions, respectively. The data points that fall off the fitted non-linear model (Figure 4b: green) are from limited reconstructions of which a single respiratory state and all cardiac phases are used (25% bins used).

The ratio of bins used in each limited reconstruction were then compared against the relative time required to complete the calculation (Figure 4c), and again a strongly linear relationship was observed with a coefficient of determination of 0.99. The 18%, 30%, and 42% bin utilizations were seen to intersect with this line at 18%, 30%, and 42% calculation duration, respectively. The use of a single respiratory phase has a large effect on image quality, with SSIM indices of 0.86 +/− 0.1 (n = 15). The SSIM index of different combinations of respiratory and cardiac bins is plotted in Figure 5 to visualize the pattern of relative impact of the number of adjacent cardiac phases versus respiratory phases.

Figure 5:

Impact of the number of cardiac and respiratory bins utilized to the SSIM index. Structural similarity index measure (SSIM) was assessed for quiescent frame reconstructed using 1, 3, 5, 7, and all cardiac phases within 1, 3, and 4 (all) respiratory bins conditions.

The relationship between the number of cardiac and respiratory bins and the functional performance of the resulting reconstruction can be appreciated by visually comparing the same slice in each reconstruction performed on a single raw data set (Figure 6). One can see that using only one cardiac and respiratory bin produces an image in less than 1% of the time required for the full reconstruction, but with a noticeable degradation in quality and a reported SSIM index of 0.38. In this case, using five cardiac and four respiratory bins allowed for an image to be reconstructed in less than 30% the total calculation time but with negligible quality loss and an SSIM index of 0.97.

Figure 6:

Representative comparison of image quality for a single subject. For each combination of total cardiac and respiratory bins, the image was reconstructed and the SSIM index was computed in reference to the full reconstruction. For each reconstruction, the SSIM index and the time required to complete the calculation are displayed.

A similar comparison was made on other data sets with in-plane views of the right and left coronary arteries in three separate reconstructions (Figure 7), full reconstruction, using 7 cardiac and all respiratory phases, and using 5 cardiac and all respiratory phases, respectively. This location was chosen as an example as it is the location where anomalous origin of the coronary artery is diagnosed. Both vessels are very easily identifiable and traceable in the full reconstruction and in the two limited reconstructions with high SSIM indices. Of the two limited reconstructions, the coronary arteries were easy to identify and follow, and using more cardiac phases in the limited reconstructions gives marginal improvement on the image quality as seen on SSIM compared to the full reconstruction.

Figure 7:

Representative comparison of coronary origins on three example subjects. Multiplanar reformation of images obtained with the full 5D reconstruction (left), first limited 5D reconstruction (center, 7 cardiac phases), and second limited reconstruction (right, 5 cardiac phases) to visualize the left and right coronary takeoffs on three example subjects.

Coronary artery sharpness comparison

The LAD artery’s sharpness on the full reconstruction has no significant difference with the limited reconstructions using 9, 7, 5 cardiac phases and all respiratory phases, with p-values equal to 0.30, 0.36, 0.70 respectively. However, the LAD artery’s sharpness on the full reconstruction is significantly different from the limited reconstructions using only 1 or 3 cardiac phases and all respiratory phases, with p-values equal to 0.0037, and 0.0037 respectively. This indicates that in order to preserve the coronary artery sharpness, no less than 5 cardiac phases and all respiratory phases are needed.

DISCUSSION

The ability to retrospectively gate MRA acquisitions using intrinsic image information to compensate for cardiac and respiratory motion represents a significant advancement in coronary imaging. One of the major drawbacks of this approach is that reconstruction of image volumes resolved across the cardiac and respiratory cycles can consume a considerable amount of computational power and time. The major findings of this study were:1) the reconstruction time for a self-gated image is directly determined by the total number of adjacent physiologic bins, 2) the image quality for a particular physiologic position is improved by each additional adjacency in the adjacent physiologic space, 3) each additional adjacency provides a diminishing marginal benefit toward the image quality, 4) to minimize reconstruction time and preserve image quality, no less than 5 cardiac and all respiratory bins are needed in 5D free running imaging for coronary static whole-heart imaging. Together, these findings indicate that for a static reconstruction of free-running coronary MRA data, the computational cost can be reduced through removal of physiologic bins while still preserving the image quality.

The full image reconstructions performed here required 15.4 +/− 2.7 hours to complete on a fairly powerful computer system. In this study, it was observed that with the same computational hardware, regularization parameters, and total iterations, the time required to complete 5D image reconstructions utilizing the ADMM algorithm followed a very linear behavior depending on the total number of adjacent physiologic bins included in the calculation. This result was expected, as every iteration of the algorithm requires a Fourier transform of each image volume and comparisons between the volume and those volumes adjacent to it in both the respiratory and cardiac dimensions. Therefore, the total time required for a given 5D reconstruction can be reduced linearly by removing additional bins from the calculation.

Each additional bin adjacent to a particular bin of interest improves the overall image quality but exhibits a diminishing marginal utility. This can be seen in the nonlinear relationship between the SSIM with the reference reconstruction and the relative number of bins used in the calculation. The modeled behavior of this relationship predicts that using as few as 18% of the total bins is expected to complete in 18% of the reference time and give an SSIM of 0.9. Using 30% of the total bins is predicted to complete in 30% of the reference time and give an SSIM of 0.96. However, when 42% of total bins are used, predicted to complete in 42% of the reference time, it gives marginal improvement to image quality with SSIM of 0.98. We can see that using 30% of total bins offers a very significant reduction in computation time with a high confidence of maintaining the original image quality of the full reconstruction. Similarly, the number of bins included in the reconstruction relates directly to the memory usage, allowing the calculation to be performed on systems with less total memory or freeing up resources for multiple calculations to be performed simultaneously.

We found that using a single respiratory phase results in a reduction in SSIM. This reduction in image quality occurs for every number of cardiac phases as seen in Fig. 4b. The use of one single respiratory bin in the reconstruction prevents the algorithm from exploiting sparsity in the respiratory dimension. Therefore, to best utilize the efficiency of the limited reconstruction and preserve similarities to the full reconstruction, it is prudent to use 3 or 4 respiratory phases. In this study, we tested the number of cardiac phases needed to preserve image quality and coronary artery sharpness when 4 respiratory phases are used, and found that when 5, 7, and 9 cardiac phases are used, the structural similarity indices are 0.97 +/− 0.01, 0.99 +/− 0.00, 0.998 +/− 0.00, and coronary artery sharpness are not significantly different from the full reconstruction, with p-value equal to 0.30, 0.36, 0.70. However, when only 1 and 3 cardiac phases are used, the structural similarity indices dropped to 0.74 +/− 0.07, 0.91 +/− 0.03, and coronary artery sharpness are significantly different from the full reconstruction, with p-values equal to 0.004 and 0.004. This could be seen from the learned nonlinear model of SSIM index with the percent of total bins used in the reconstruction (Figure 4b.). When 5 cardiac and 4 respiratory phases are used in the limited reconstruction, corresponding to using 30 % of total bins, a SSIM of 0.96 is achieved. Using 7 cardiac and 4 respiratory phases, corresponding to using 42% of total bins, only gives marginal benefit that the SSIM is 0.98. On the other hand, if only 3 cardiac and 4 respiratory phases are used, using 18 % (n=15) of total bins, SSIM drops to 0.9. Although an SSIM of 0.9 indicates good agreement between the limited reconstruction with the full reconstruction, its image quality is not sufficient to preserve the coronary artery sharpness from the full reconstruction. Therefore, to sufficiently minimize reconstruction time while best preserve image quality, at least 5 cardiac phases are needed in the limited reconstruction.

Prospective gating suffers when physiologic patterns are difficult to anticipate or are inconsistent throughout the duration of a scan, and this can result in unpredictably long scan times or unreliable image quality. Through the free-running scheme, data acquisition is performed independently of the cardiac phase or respiratory position, allowing for gating to occur retrospectively with full consideration of the physiologic behavior exhibited by the subject over the duration of the acquisition. This provides a constant, known acquisition time—under seven minutes in this study—with very minimal planning needed from the operator. Clinical implementation of whole-heart, motion-resolved acquisitions is currently limited by its computational cost, but the results presented here indicate that removal of adjacent physiologic bins can reduce this cost while still preserving image quality.

The determination of the cardiac quiescent period was done through estimating the temporal variation in the final 5D reconstruction computed with all adjacent physiologic bins. The purpose of this study was to investigate how altering the number of included adjacent physiologic bins would affect the reconstructed image, and therefore this retrospective approach was used. However, for this technique to offer any real performance improvement, this determination needs to be made prospectively. With only fifteen subjects, this cannot be adequately validated to work in all cases, but a simple approach would be to acquire a 2D cine of the subject’s heart immediately before or after the image acquisition, and quantitatively assess the timing to determine approximately where in the cardiac cycle the heart is quiescent [19–21]. This method has been used clinically for prospective cardiac gating, so it is possible that it could be applied to this as well. Another possibility would be to determine the cardiac quiescent phase directly through analysis of the physiologic motion signal. This motion signal is already extracted from the image data to correctly bin each interleave along the respiratory and cardiac dimensions (Figure 1). It is possible to determine the relative temporal position of each interleave using this cardiac motion signal [10], therefore it may also be possible to identify the cardiac quiescent phase as well. Further studies would be needed to validate or optimize any or all of these approaches.

Several challenges are introduced to coronary MRA when data are being sampled continuously. For prospective ECG-gated acquisitions, several preparatory pulses are applied which work to saturate the myocardial tissue, suppress epicardial fat signal, and suppress the motion of the anterior chest wall which can interfere with motion detection and create radial streaking artifacts [7, 22–24]. The total time necessary for these preparatory pulses—approximately 100 to 150 ms—is usually negligible when acquisition is limited to only once per cardiac cycle. When data acquisition is occurring continuously to fully resolve images across the cardiac cycle, however, these preparatory pulses can reduce the effective temporal resolution of the acquisition by more than half. Because of this, we chose to remove these preparatory pulses and instead amplify the blood signal through the use of ferumoxytol. Ferumoxytol is a superparamagnetic iron oxide–based drug which has been primarily used to treat anemia but has shown great potential for off-label diagnostic use as a T₁ shortening contrast agent for cardiovascular MRA [25]. At a concentration of 4 mg Fe / kg body weight, the T₁ of blood has been shown to decrease from 1990 ± 573 ms to 80 ± 42 ms, with an in vivo R₁ relaxivity of 12 mM⁻¹ s⁻¹ at 1.5 T [26]. By comparison, the R₁ relaxivities of gadolinium-based agents are usually in the range of 4 to 5 mM⁻¹ s⁻¹ at 1.5 T [27]. In this study, we modified the prototyped ECG-free, free-breathing bSSFP sequence to instead use a spoiled-GRE, T₁-weighted acquisition. The GRE sequence preferentially enhances blood signal intensity in the images because of the presence of IV ferumoxytal and also lowers the RF deposition in the pediatric cohorts. Furthermore, the particle size of ferumoxytol is substantially larger, preventing it from leaving the vasculature. Without redistribution into the extravascular space, the concentration differential between blood and myocardium is maintained, and plasma elimination half-life in humans is approximately 10 to 14 hours [26] allowing the signal amplification to remain constant throughout the data acquisition. Therefore, the properties of ferumoxytol make it particularly well-suited for use in continuously-acquiring, self-gated MRA.

The motivation of this study is to obtain a single, static 3D volume from the free-running 5D reconstruction with significantly reduced computational time. Here, we used limited number of bin from the entire collection of resolved cardiac and respiratory bins to reduce the computational cost in the iterative reconstruction. We demonstrated that our method can reduce the reconstruction time while preserving the image quality of the 3D cardiac quiescent frame when a specific number of cardiac and respiratory bins are used. Another method that reconstructs the 3D image from the full 5D acquisition[28] uses similarity analysis on the SI projection data and groups the data collected near the same physiologic state together. The most populated group is used in the final reconstruction. This method would be beneficial if one physiologic state is longer than the others and therefore more data can be grouped in such state and potentially eliminate the need for the under-sampled reconstruction. Future work will compare the two methods using the same datasets.

This study has limitations. As implemented in this study, the determination of the cardiac quiescent phase occurs retrospectively after reconstructing the full 5D image. This process deviates from the proposed desired workflow. We realize a prospective approach is essential for implementing quiescent frame reconstruction in real-world applications. The purpose of this study was to show the feasibility of the approach. Though many reconstructions were repeated for each subject, the number of raw data sets was fairly small, and not necessarily representative of adult cardiac disease patients on whom this technique may be applied. Another implicit limitation within this analysis is the assumption that the full reconstructions using all physiologic bins are the reference standard for all cases, while the reference images will have some blurring due to motion, the regularization, and potentially residual effects after reconstruction optimization process. The motion binning and gating method in this study assigned the temporal resolution of each cardiac phase to be 50 ms, which is two standard deviations less than the length of the quiescent period during mid-diastole (72+/− 5%) found in a previous study[29], therefore the residual motion will be minimal in the reference images. In addition, there have been studies showing that the binning method used here provides superior image quality to standard respiratory gating [30, 31]. In this study, we do not have data to show the comparison since the acquired 5D free-running raw data was in clinical subjects and scan time did not permit the standard ECG and diaphragm respiratory gating data to be acquired. For the residual motion that could be present in the reference images, there are ways to further compensate for motion within the respiratory and cardiac bins. A recent technique using inter-bin and intra-bin respiratory motion compensation method also demonstrated further improvement on the sharpness in the 5D free-running acquisition scheme and this method could be combined with the technique presented in the current study[32]. We did not examine other methods to speed up the reconstruction (i.e., DL-based reconstruction), since it was beyond the scope of this paper. For each volume, the intra-dimensional adjacencies are used to enforce continuity which can compensate for the artificial undersampling used during the physiologic binning. Therefore, a reconstruction using all physiologic bins will have more information available for the calculation which would likely be the better image. This was visually observed for the cases tested in this study; however, it is possible that for some data sets a limited reconstruction may produce a better image set than the full reconstruction. The total number of respiratory physiologic bins, using 4 respiratory bins in the full reconstruction in this study, can be adjusted by changing the temporal resolution during data binning. However, we only examined the effect of using a subset of physiologic bins of the 4 respiratory phases following the suggestion from a previous result shows that sorting the raw data into 4 respiratory bins achieves the optimal image quality and is less computationally expensive than using 6 or 8 bins[7].

CONCLUSION

The computational cost associated with reconstructing images from a fully self-gated 5D coronary MRA free-running framework was found to be directly proportional to the number of adjacent physiologic bins included in the calculation. For a static 3D image reconstruction at end-expiration and the cardiac quiescent phase, the adjacent image volumes along these physiologic dimensions were seen to provide a nonlinear contribution to the overall image quality; each additional image volume provided a diminishing benefit to the static image reconstruction. Therefore, the computational cost of reconstructing a static image volume can be reduced substantially while negligibly affecting the image quality if an optimal number of physiologic positions are selected. At least 5 cardiac and 4 respiratory phases are needed in the limited reconstruction to preserve the high coronary artery sharpness in the costly full reconstruction. These findings have the potential to reduce the logistical hurdles associated with clinical implementation of this 5D MRA framework in cases where only a static image volume is desired.