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This paper presents a nonlinear profile order scheme for three-dimensional (3D) hybrid radial acquisition applied to self-gated, free-breathing cardiac cine magnetic resonance imaging (MRI). In self-gated, free-breathing cardiac cine MRI, respiratory and cardiac motions are unpredictable during acquisition, especially for retrospective reconstruction. Therefore, the non-uniformity of the k-space distribution is an issue of great concern during retrospective self-gated reconstruction. A nonlinear profile order with varying azimuthal increments was provided and compared with the existing golden ratio-based profile order. Optimal parameter values for the nonlinear formula were chosen based on simulations. The two profile orders were compared in terms of the k-space distribution and phantom and human image results. An approximately uniform distribution was obtained based on the nonlinear profile order for persons with various heart rates and breathing patterns. The nonlinear profile order provides more stable profile distributions and fewer streaking artifacts in phantom images. In a comparison of human cardiac cine images, the nonlinear profile order provided results comparable to those provided by the golden ratio-based profile order, and the images were suitable for diagnosis. In conclusion, the nonlinear profile order scheme was demonstrated to be insensitive to various motion patterns and more useful for retrospective reconstruction.
Two-dimensional (2D) cardiac cine MRI using multiple slices to cover the heart volume is widely employed in clinical practice.[1,2] During 2D cine scanning, multiple breath holds and electrocardiographic (ECG) gating are needed. Varying breath-holding positions causes slice misregistration error (gaps or overlaps between successive slices).[3] In addition, some patients have breath-holding incapability,[4] which will cause motion artefacts. Using ECG gating to synchronise heart motion prolongs patient preparation time and may be infeasible due to magnetohydrodynamic interference.[5,6] In recent years, free breathing, three-dimensional (3D), self-gated techniques without breath holding and ECG gating have been developed and widely studied.[7–17]
Self-gating techniques derive motion signals from internal organs without using peripheral equipment to synchronise respiratory and cardiac motion. There are two primary methods used to obtain respiratory and cardiac self-gating motion signals in cine MRI. First, k-space center data, which can reflect changes in image volumes, have been collected to derive respiratory and cardiac motion signals.[9,12–14] Self-gating signals can also be calculated from the image data themselves, but these signals require image reconstruction and registration calculation throughout the cardiac circle.[8,15–17] However, most self-gating methods require breath holds or ECG to avoid the complexity of separating respiratory and cardiac motions.[18,19] A hybrid radial sampling method that uses appropriate band-pass filters to separate respiratory and cardiac motions has been used in both respiratory and cardiac self-gated 3D cine MRI.[7,20] Motions are detected using the centerlines in the slice encoding direction (a process referred to as Cartesian acquisition), and radial sampling of each slice encoding is performed to ensure that k-space centerlines are acquired repeatedly. This technique does not require any extra data to obtain self-gating signals. However, the uniformity and stability of the k-space distribution is a great concern in retrospective cine MRI.
In this study, a nonlinear angle increment profile order for free-breathing respiratory and cardiac self-gated cardiac cine MRI was put forward. Optimal parameter values for the nonlinear formula were chosen based on simulation results. The proposed profile order was compared with the existing golden ratio-based profile order in terms of the k-space distribution and phantom and human image results.
Three-dimensional hybrid radial sampling was used to obtain self-gating signals and acquire k-space data simultaneously. As shown in Fig.
The purpose of determining the optimal profile order was to obtain an approximately uniform k-space distribution for each cardiac phase. In the aforementioned hybrid radial scheme, the profile angle is related to the profile number by
![]() | (1) |
![](cpb_26_1_018701/cpb_26_1_018701_ieqn2.gif)
![](cpb_26_1_018701/cpb_26_1_018701_ieqn3.gif)
In cine MRI, images are reconstructed from multiple cardiac cycles (see Fig.
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![](cpb_26_1_018701/cpb_26_1_018701_ieqn7.gif)
![](cpb_26_1_018701/cpb_26_1_018701_ieqn8.gif)
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![](cpb_26_1_018701/cpb_26_1_018701_ieqn10.gif)
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![](cpb_26_1_018701/cpb_26_1_018701_ieqn11.gif)
![](cpb_26_1_018701/cpb_26_1_018701_ieqn12.gif)
![]() | (4) |
![]() | (5) |
Compared with a uniform distribution, the sample density along the azimuthal direction is not homogeneous, which may affect the image signal-to-noise ratio (SNR). The ratio of the non-uniform SNR
![]() | (6) |
![](cpb_26_1_018701/cpb_26_1_018701_ieqn15.gif)
The optimal values of the variables α and β were determined by simulation to minimize SE for a cardiac frequency range of 0.6–3 Hz, and a breath frequency range of 0.1–0.5 Hz. Ranges of α (0–2) and β (0–1) values in increments of 0.01 were evaluated. The coefficient of variation (CV) was used to evaluate the SE for different cardiac and breath frequencies.
Ten normal volunteers (eight male and two female, mean age of 32 years ± standard deviation of 7 years), without any history or symptoms of cardiac disease, were studied. Cardiac cine imaging was performed in the supine position using a 1.5-T GE HDx scanner (maximum gradient amplitude 33.0 mT/m, slew rate 120 T/m/s, Excite 14 M5 software version; GE Healthcare, Waukesha, WI, USA). All subjects provided written informed consent, and the study was approved by the local institutional ethics review board at Weill Cornell Medical College. An eight-channel cardiac phased-array coil was used for signal reception.
Two separate scans were executed in random order using the same imaging parameters. The typical imaging parameters were as follows: TR/TE=4.4/1.3 ms, flip angle is
It was impossible to ensure that the volunteers maintained the same breathing and heart rate patterns during the two continuous scans. To compare the two profile orders using the same standards, the SEs calculated using Eq. (
The optimised nonlinear profile order was compared with the golden ratio-based profile order. A phantom was sampled using these two profile orders. The original k-space data for the phantom were selected based on self-gating signals from the ten volunteers. Twenty phantom images obtained using these two methods were compared in terms of the SNR.
Image quality metrics, including the blood SNR, myocardium-blood contrast, contrast-to-noise ratio (CNR), and image sharpness,[8] were calculated from a mid-ventricular slice for each volunteer. The two methods were compared using a nonparametric Wilcoxon signed-rank test. All of the tests were two-sided, and
Figure
Image reconstruction was performed for the ten subjects, for one of whom the golden ratio method had failed. Figure
![]() | Fig. 4. (a), (b) Images of mid-ventricular slices obtained with golden ratio-based profile order and (c), (d) nonlinear profile order in nine healthy volunteers. |
![]() | Table 1.
Metrics of image quality of the two methods |
Figure
The SNRs determined for phantom images of golden ratio-based and nonlinear profile orders were 164.45 ± 22.81 and 176.55 ± 23.83, respectively. Figure
It has been demonstrated that a self-gated approach permits accurate and reliable assessment of right-ventricle (RV) and left-ventricle (LV) cardiac dimensions without using ECG triggers and respiratory monitors.[7,20] In free-breathing, self-gated cardiac cine MRI, respiratory and cardiac motions are unpredictable before acquisition. Therefore, non-uniform k-space distribution is a major problem in retrospective self-gated reconstruction. In this study, a nonlinear profile order with varying azimuthal increments was proposed as an alternative to the golden ratio-based profile order.
Approximately uniform distributions were obtained for individuals with different heart rates and breathing patterns in both simulations and clinical acquisition of self-gating signals. The acquisition scheme for the golden ratio-based profile failed to provide the nearly uniform profile distribution in 3D hybrid radial SSFP acquisition in the study subjects. In the 3D hybrid radial acquisition scheme, interbeat (R–R) intervals limited the profile number to a range of 15–22, which was equal to the number of cardiac phases
The primary advantage of the nonlinear profile order is its insensitivity to the heart rate and breathing rate. Because the minimal CV of the SE (Eq. (
The proposed profile order was constructed and simulated on the basis of a specified hybrid radial profile order and was specified for use in retrospective cine MRI. For these circumstances, the golden ratio-based profile order was found to be unstable for different persons. This finding is not in conflict with other applications based on golden means. Fewer total profile numbers could be used to reduce the total scan time by using compressed sensing (CS) reconstruction. However, the optimal α and β values will differ from other total profile numbers. The simulation should therefore be repeated for other total profile numbers. Although this requirement is a clear limitation of the nonlinear profile order method, additional research will be conducted to establish the optimal α and β values for the usual profile numbers.
In conclusion, this paper presents a nonlinear profile order for 3D hybrid radial acquisition for use in cardiac and respiratory self-gated cine MRI. A more stable profile distribution is obtained during retrospective reconstruction using the proposed profile order than using a golden ratio-based profile order. Three-dimensional short-axis-view cine imaging with the proposed profile order achieves image quality comparable to that achievable with the existing golden ratio-based profile order.
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