Binomial-like selective inversion sequences are commonly incorporated into WATERGATE [1] and Excitation Sculpting [2] based solvent signal suppression schemes (e.g., [3]). Compared to shaped/soft selective inversion pulses, the binomial-like sequences afford ease of setup and better selectivity with equal duration. Binomial-like sequences share the symmetric structure of binomial sequences (e.g., [4]), which consist of hard rectangular RF pulses with nutation angles in the ratios of binomial coefficients (e.g., 1:1, 1:2:1, and 1:3:3:1), while containing RF pulses with nutation angles in arbitrary ratios (e.g., a:b:b:a, a and b are positive real numbers). The two most widely applied binomial-like inversion sequences are the 3-9-19/W3 [5] and W5 [6] sequences. The further understanding and optimization of these sequences can be facilitated by the effective visualization of the magnetization evolution during the application of these sequences.
Each unit vector emanating from the origin can be transformed into a unique complex number through stereographic projection, i.e., a bulk magnetization of an ensemble of non-interacting spin-1/2 nuclei with a constant magnitude can be transformed into a unique complex number [7]. In this study, stereographic projection has been performed on the bulk magnetization during the application of a binomial or binomial-like selective inversion sequence in order to demonstrate a new way of visualizing magnetization evolution and hopefully gain better understanding of the working mechanisms of binomial and binomial-like sequences.