Multi‐band Adiabatic Inversion Pulses for Use with the 8th‐order Hadamard Spectroscopic Imaging Technique

Abstract

Rf pulses with frequency responses which correspond to the rows of the 8th‐order Hadamard matrix are developed. These pulses can be used in the B1 insensitive Hadamard Spectroscopic Imaging multi‐volume localization technique. It is shown how any adiabatic rf pulse, which inverts spin population at a well defined frequency band, can be modified to invert populations at several frequency bands simultaneously. Conditions on the frequency and amplitude functions which allow such modifications are defined. For increasing amplitude the interaction between the bands produces nonlinear irradiation at several frequencies. By using an integrated form of the Floquet formalism and perturbation theory, the interaction between the bands is described analytically by an effective Hamiltonian. From this description the conditions which guarantee minimization of the unwanted irradiation are defined. The experimental results agree very well with the theoretical predications.

Two methods for peak RF power minimization of multiple inversion‐band pulses

“…As shown earlier (14,15), an inversion at w, will occur if the third term in H'(t) can be neglected. This requirement defines the condition: Idt') -&t -t ' ) + ( w 1 -wz)l >> 1yNt')I…”

“…We had also shown that when high amplitude is present, nonlinear interactions between the different bands distort the pulse frequency profile even when equation 6 is satisfied (14,15). Using perturbation and Floquet theories, we have shown that a correct choice of the reference phase in the { q ( t ) ) set, can minimize these nonlinear interaction (14,15).…”

“…To generate these pulses, we use linear response theory in the following way (13)(14)(15): 1) Defining a set of single inversion-band functions as follows:…”

“…Using perturbation and Floquet theories, we have shown that a correct choice of the reference phase in the { q ( t ) ) set, can minimize these nonlinear interaction (14,15).…”

Hybrid Three Dimensional (1D‐Hadamard, 2D‐Chemical Shift Imaging) Phosphorus Localized Spectroscopy of Phantom and Human Brain

“…Hadamard encoding for 3D multi-voxel spectral localization has been proposed recently by Goelman et al (15, 22,35). In HSI spatial information is encoded on the spins n times according to the rows (or columns) of a Hadamard matrix H, of order n. This is accomplished by applying shaped RF pulses in the presence of a field gradient and is demonstrated schematically for n = 4 in Fig. 2.…”