Alexander Fyrdahl^{1,2}, Karen Holst^{1,2}, Martin Ugander^{1,2}, and Andreas Sigfridsson^{1,2}

Due to respiratory motion, cardiac imaging is performed during breath holding. Breath holding can be strenuous, or even impossible, for patients with heart disease. We suggest a method for respiratory self-gating using a Golden Angle radial k-space trajectory and principal component analysis. Radial trajectories sample the middle of k-space, which corresponds to the large structure content of the image, each repetition time. The respiratory motion can be detected from the

To evaluate the consitency of the proposed technique for CMR, a complete left ventricular stack of 2D short axis slices (11±1 slices, slice thickness 8 mm, distance factor 20%) was acquired during free breathing in healthy volunteers (n = 8, age 29 ± 5 years, 63% male) using radial balanced steady state free precession with golden angle ordering (flip angle 65 degrees, TR 3.2 ms, resolution 1.5x1.5 mm, 6667 radial spokes per slice). ECG and respiratory bellows signals were simultaneously acquired. The respiratory gating signal was estimated using the DC term of each radial spoke per coil element. Principal component decomposition was performed along the temporal dimension of this k-space center signal. The Fourier transform of the resulting components, which contained the most prominent peak in the range 0.1 to 0.5 Hz was selected and smoothed with a single-sided bandpass filter. The analytical representation $$$f_A$$$ of the real-valued function $$$f$$$ is defined as$$f_A = f - i\mathcal{H}(f)$$where $$$\mathcal{H}(f)$$$ denotes the Hilbert transform of $$$f$$$. It can easily be shown that nulling all negative frequencies will results in an analytical representation, thus applying a single-sided bandpass filter will result in an analytical representation of the respiratory signal. Importantly, the argument of the analytical signal describes the instantaneous phase of the respiration, thus inspiration could easily be distinguished from expiration. The duration of each respiratory cycle was measured for both the bellows and the derived respiratory gating signal by identifying the peaks of the two curves and measuring the peak-to-peak distance. An image was also reconstructed in end-diastole both with and without respiratory self-gating in end-expiration for comparison of image quality.

1. Santelli C, Nezafat R, Goddu B, et al. Respiratory bellows revisited for motion compensation: preliminary experience for cardiovascular MR. Magn Reson Med. 2011;65(4):1097-1102.

2. Holst K, Ugander M, Sigfridsson A. Respiratory Resolved Cardiac Cine Imaging using Self-Gated Golden Angle Radial Acquisition. Proc. Intl. Soc. Mag. Reson. Med. 23. 2015

Respiratory signals from a bellows (gray) and self-gating based on principal component analysis of the k-space center from 2D golden-angle radial acquisition.

ECG-gated short-axis image in end diastole with (a)
and without (b) respiratory self-gating based on principal component analysis
of the center of *k*-space from free-breathing 2D golden-angle radial cine
imaging in a healthy volunteer.

Correlation between respiratory cycle duration using bellows
and self-gating. R2 0.80, p<0.001, mean ± SD difference 10±295 ms.