Breath-hold or navigator-based MR acquisition has been widely used to remove the effect of motion from the images. However, breath holding can be challenging for patients. On the other hand, navigator-based methods suffer from lengthened acquisition time and the disturbance of magnetization history. In this respect, we will developed a self-gated free-breathing MR imaging method to obtain 4D MRI (3D spatial+1D respiratory phases) for deformable motion derivation.

A 3D stack-of-stars Golden Angle MRI sequence was previously proposed as a self-gated MR acquisition method [1]. Figure 1 illustrates the k-space sampling pattern. In this sequence, Cartesian encoding is utilized along the kz direction, forming a stack, while radial spokes are used in the kx-ky plane to form stars (hence the name stack-of-stars). For a given azimuthal angle, a stack-of-spokes is acquired first. After that, the next stack-of-spokes is acquired for another azimuthal angle. Thus, in Figure 1, the red stack of spokes is acquired for Angle 0, and then the blu stack of spokes is acquired for Angle 1. The golden angle (GA) is referred to as the 111.25° angular increment between two adjacent stack-of-spokes. The GA acquisition provides a rapid and nearly uniform coverage of the kx-ky space during any period of time. The typical acquisition time for each stack of spokes is Nz×TR and it usually ranges from 120 to 200 ms. Because respiration rate is slower than this sampling rate, it is assumed that all spokes in a stack of spokes are acquired at the same respiratory phase. Since every stack of spokes samples the k-space center (kx=ky=kz=0), signal variations across different radial angles at this point are assumed to be caused by respiratory motion and can be used to derive motion [2-4]. This type of approach is referred to as self-gated or self-navigated. Signal within the frequency range of 0.1–0.5 Hz and 0.5–2.5 Hz were assumed to represent respiratory and cardiac motion, respectively [3]. However, we have found that this assumption does not hold true. As Figure 2 clearly demonstrates, even in a stationary phantom, the pseudo-periodicity of the Golden Angle approach leads to a coherent signal pattern that can be misinterpreted as a motion signal. To overcome this problem, we developed a data acquisition scheme that generates a controlled frequency modulation pattern. The idea is to push all acquisition related frequency components to the far end of the spectrum. In this respect, we apply a scheme that is similar to amplitude modulation. First, the azimuthal angle $$$\phi$$$ is chosen as $$$\phi = \pi+(k\pi/N)cos(k\pi) $$$ where $$$ k = 0,1,...,N-1$$$ with $$$N$$$ being the number of radial lines. The modulation frequency is chosen so as to obtain the peaks at the highest possible location, that is, at the far end of the spectrum. However, in order to take advantage of the golden angles, each of the cosine-modulated angles were quantized onto the golden-angle grid. For instance, using $$$N=2216$$$ lines of cosine-modulated angles was enough to cover the grid for a 2000-line acquisition of the regular golden-angle acquisition after quantization. The remaining 216 lines were appended to the end of the acquisition and were later discarded.

For both acquisitions, the reconstruction was performed after filtering out the spectral content beyond 0.6 Hz, detrending and then binning the data.

Figure 3 shows the in-vivo spectra for the regular GA and the cosine-modulated acquisition. It can be clearly seen that the regular GA acquisition brings in numerous additional components that make it hard to distinguish the actual physiological signals. However, the cosine-modulated acquisition keeps the spectrum quite clean, opening up space for the respiratory content. Figure 4 shows the reconstructions by the two methods. The upper row shows the blurriness of the regular GA reconstruction whereas the bottom row shows the promise of the cosine-modulated scheme. [The red line is drawn to facilitate the differentiation of the 5 different phases.]The proposed scheme looks promising. Although it can be argued that the acquisition of additional lines that are later discarded is a waste of time, the ratio of such lines is quite small. For a 2000-line acquisition, they correspond to only 10% of the data. We tried different frequencies for the argument of the cosine; however, the most efficient quantization was obtained when the frequency was set to $$$\pi$$$.A new method is proposed that can better capture the frequency content of the respiratory motion. The results are promising.