Pavan Poojar^{1}, Sairam Geethanath^{1,2}, Ashok Kumar Reddy^{3}, and Ramesh Venkatesan^{3}

Rapid prOtotyping of 2D non-CartesIan K-space trajEcTories (ROCKET) aims to aid researchers interested in rapid development and testing of new MR methods starting from pulse sequence design to image analysis. This was achieved by utilizing Pulseq for pulse sequence design and graphical programming interface for image reconstruction and analysis. ROCKET was demonstrated on two non-Cartesian k-space trajectories – FID based radial and spiral. Each trajectory was tailored into three different trajectories based on rotating angle – standard, golden angle and tiny golden angle. All studies were performed on Siemens scanner demonstrated on in-vitro phantom and in-vivo healthy brain acquisitions and SNRs were computed.

The FID based radial trajectory was designed using equation $$$k_x=k_{width}cos\theta$$$ and $$$k_y=k_{width}sin\theta$$$, where $$$k_{width}$$$ is the maximum extent of k-space and defined as $$$k_{width}=N\delta k$$$, *N* is matrix size and $$$\delta k=1/FOV$$$, FOV is the field of
view. The general spiral trajectory was defined by equation^{3} $$$k(\tau)=\lambda \tau^{\alpha}e^{j\omega\tau}$$$ where, τ- function of time, α is the variable density
factor, λ=N/(2*FOV), N is
matrix size, ω=2πn, n is number of turns. As α increases, the density factory also increases. The
designed spiral trajectory is the modified version of the code^{4}. Each trajectory was designed for three
rotating angles – standard, Golden Angle (GA) and Tiny Golden Angle (TGA). GA is obtained by dividing 180^{0} by the golden ratio of
1.618. The acquired data is spaced by a constant azimuthal increment of 111.26^{0}.
The limiting factor of GA is the rapid change of eddy currents. TGA provides
smaller angular increments by inheriting all the properties of GA.
ROCKET was demonstrated on two non-Cartesian
k-space trajectories (namely, FID based radial and spiral) with three rotating
angles. The standard rotating angle for radial/spiral was obtained by
dividing 360^{0} with the total number of spokes/interleaves. The GA and TGA angles were obtained by using equations from the paper^{5,6}.
The radial/spiral GRE pulse sequence were designed with six different
gradient waveforms, and all were scanned on in-vivo healthy brain and in-vitro
Disease Neuroimaging Initiative (ADNI) phantom (Phantom laboratory, New York). The acquisition
parameters were shown in table 1. Figure 1 shows the rapid prototyping using
ROCKET. The non-Cartesian GRE pulse sequences were designed in Pulseq and the seq files were generated. Each seq
file is typically converted to the vendor specific files by using an
interpreter. Here, all the scans were performed on a Siemens 3T Prisma. The generated
seq files were exported directly to the MR scanner and raw data was
obtained. The trajectory and the k-space data were given as input to the GPI
network and images were reconstructed. Finally, line intensity profile was
plotted using GPI script (GPI/Recon.net)^{7} to compare the resolutions
of the reconstructed images obtained from in-vitro and in-vivo studies.

Table 1: Acquisition parameters for 2D radial and spiral
based GRE sequence. Same acquisition parameters were employed for *in-vivo* and *in-vitro*
data.

Figure 1:
Block diagram representing the ROCKET pipeline.

Figure 2: Radial trajectories for three rotating
angles - standard, GA and TGA along with gradient waveforms for all three
variants. Third row shows the pulse sequence diagram for 1TR.

Figure 3: Spiral trajectories for three rotating angles -
standard, GA and TGA along with representative gradient waveforms. Third row
shows the pulse sequence diagram for 1TR.

Figure 4:
Reconstructed images of radial in-vitro and in-vivo shown first
two columns for all the three variants (standard, TGA and GA). Spiral in-vitro
and in-vivo reconstructed images shown in third and fourth column for all the
three variants. The line intensity plots are shown in fourth row.