Radial-acquisition(RA) imaging is suitable for lung imaging because it allows a very short TE and a desirable degree of motion insensitivity. Despite its tolerance to motion artifacts, respiratory motion is still a major reason of causing image artifacts in lung imaging such as blurring and some streak artifacts. To minimize the motion artifacts, respiratory gating is performed in lung imaging in a prospective or a retrospective way [1]. Prospective gating usually takes more time than retrospective gating since the expected number of samples are to be acquired with the length of acquisition window fixed. In contrast, retrospective gating can maintain the scan time constantly and provide a flexibility in choosing any respiratory phase to be reconstructed. In retrospective gating, it is an important issue to keep the k-space as uniform as possible after gating. Recently we suggested that use of many interleaves in the k-space trajectory work for this purpose [2]. In this study, we address how many number of interleaves would be optimal to maintain the uniformity of k-space coverage after retrospective gating in consideration of different breathing patterns.

In ref.2, we showed that increasing the number of interleaves(i_max) could significantly reduce non-uniformity of k-space coverage after retrospective gating. What is then an optimal condition for attaining as uniform k-space coverage as possible after gating in various respiratory patterns? For discussion, the respiratory-signal form is assumed to be a sinusoidal function ranging from 1 and -1. Gated samples are assumed to be selected below the threshold set to 0. The gated period of one respiratory cycle and the duration of one interleaf are dubbed T_gating and T_interleaf, respectively. With respect to T_gating and T_interleaf, three cases can be thought of as possible references: T_gating>T_interleaf (Case I), T_gating=T_interleaf (Case II), T_gating<T_interleaf (Case III). Figure 1 illustrates the sampling uniformity of each case when respiratory-gated data are selected during every T_gating. As shown in Fig. 1b, Case II is most probable to provide a nearly uniform sample distribution when compared to Case I and Case III. Since T_interleaf = TR×p_max(= # of views per one interleaf) and N_views = i_max×p_max, Case II is rewritten in terms of TR and p_max:

$$optima\ p_{max} = \frac{T_{gating}}{TR}$$

$$optimal\ i_{max} = \frac{N_{views}\cdot TR}{T_{gating}}$$

Simulation was performed to see how the gated-sample uniformity changes with respect to p_max using an in-vivo respiratory signal. p_max varied from 130 to 1,180 by an increment of 50. The total number of views N_views = 157,000. Uniformity was evaluated by the distribution of the number of points (N_circle) inside an imaginary circle around each point on the surface of k-space sphere. If sample points are more uniformly distributed, N_circle would have a smaller variation throughout the entire points. Phantom and in-vivo human lung were scanned at Siemens 3T(Trio) to evaluate the effect of k-space non-uniformity on image quality. The gradient-echo-based ultrashort-TE sequence, CODE(Concurrent Dephasing and Excitation), was used for experiments[3]. 89,830 views were selected out of N_views = 160,200 through retrospective gating. Two cases of p_max = N_views and optimal p_max = 900 were compared. Scan parameters were given in Table 1.

Simulation shows that the optimal p_max(=630) provides the minimum standard deviation of N_circle, indicating the highest uniformity of k-space coverage (Fig.2). The weak dependence on the statistics of T_gating shows that the proposed sampling scheme can maintain the sample uniformity over a range of variation in breathing patterns expected in actual in-vivo scans. Figure 3 shows the selected axial slices of phantom and human lung imaging. Ringing and striped image artifacts appear in the images obtained with a single-spiral acquisition(p_max=N_views) due to the non-uniform sample density in k-space and are well suppressed in the images obtained with the optimal p_max due to the improved sample uniformity.We suggested here the optimal condition that uniformity of k-space coverage is well maintained after retrospective-respiratory gating, that is, the length of one interleaf be equal to the gating length in one respiratory cycle. Numerical simulation showed that the proposed condition maximized the sample uniformity as validated by the smallest standard deviation of the number of neighboring samples. Phantom and human lung experiments also demonstrated that the proposed method combined with retrospective-respiratory gating can significantly suppress streak artifacts as well as motion-related blurring. Although our sampling strategy was based on the 3D radial trajectory proposed by Wong’s et al.[4], it can also be applied to other interleaved sampling functions such as the golden-angle-ordered readout in a spiral phyllotaxis pattern[5].