Mark Bydder^{1}, Fadil Ali^{1}, Andres Saucedo^{1}, Chencai Wang^{1}, Akifumi Hagiwara^{1}, Alex D Pham^{1}, Jingwen Yao^{2}, and Ben Ellingson^{1}

^{1}UCLA, Los Angeles, CA, United States, ^{2}UCSF, San Francisco, CA, United States

The present article develops an understanding of how to choose optimal (or at least reasonable) parameter values for 3D radial density adapted sampling. This has a practical role in designing clinical protocols for short TE non-Cartesian imaging.

A variant of cones referred to in Ref 1 as constant polar angle constant sample density (and in the present study as corkscrew) is represented in

Tessellating a sphere of radius k

N = 16πk

The value π matrix

Practical scan times limit N to values well below Nyquist. E.g. for an imaging matrix of 128, Eq 1 requires ~50000 spokes. With fewer spokes, some aliasing is to be expected but numerical simulations also reveal a large change in the PSF. An approximately linear decrease in full width at half maximum (FWHM) is observed with N (

A reasonable criterion for k

k

At k

i. The distance between points on the same spoke decreases rapidly after k

Δk

ii. Equal spacing between points on neighboring spokes may be achieved by setting Δk

r = (1+sin(Φ/2))

iii. Expressing the Nyquist criterion as Δk

Φ = 2 acsc( sqrt(π/N) matrix - 1 )

which evaluates to 53.8° for the example in Figure 3.

The FWHM was numerically simulated from Φ = 0 to 90° for different numbers of spokes. Results in

This can be recognized in

The expression in Section 1.4(iii) can be rearranged to give an estimate for the Nyquist number of spokes for corkscrew (for n = 4).

N = [ sin(Φ/2) / (1+sin(Φ/2)) ]

This evaluates to around 0.13 matrix

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DOI: https://doi.org/10.58530/2022/2450