MRI contrasts in high rank rotating frames

Abstract

Purpose MRI relaxation measurements are performed in the presence of a fictitious magnetic field in the recently described technique known as RAFF (Relaxation Along a Fictitious Field). This method operates in the 2nd rotating frame (rank n = 2) by utilizing a non-adiabatic sweep of the radiofrequency effective field to generate the fictitious magnetic field. In the present study, the RAFF method is extended for generating MRI contrasts in rotating frames of ranks 1 ≤ n ≤ 5. The developed method is entitled RAFF in rotating frame of rank n (RAFFn). Methods RAFFn pulses were designed to generate fictitious fields that allow locking of magnetization in rotating frames of rank n. Contrast generated with RAFFn was studied using Bloch-McConnell formalism together with experiments on human and rat brains. Results Tolerance to B0 and B1 inhomogeneities and reduced specific absorption rate with increasing n in RAFFn were demonstrated. Simulations of exchange-induced relaxations revealed enhanced sensitivity of RAFFn to slow exchange. Consistent with such feature, an increased grey/white matter contrast was observed in human and rat brain as n increased. Conclusion RAFFn is a robust and safe rotating frame relaxation method to access slow molecular motions in vivo.

Exchange-induced relaxation in the presence of a fictitious field

“…Following our nomenclature, H 1 is the effective field in first rotating frame (FRF), and thus upon convention the H 1 (here we adapted terminology used in [4]) is the vector sum of ω 1 (t) x⃗ ' and Δω ( t ) z⃗ '. Here, we present derivations of the exchange induced relaxations obtained in the SRF.…”

“…It can be seen that R 1ρ,H2 ( t ) and R 2ρ,H2 ( t ) relaxation rate constants resembles the modulation functions of RAFF2 pulses [4]. When the RAFF2 pulse with α 2 = π/4 acts on magnetization that is initially along the z ’ axis, R RAFF2 will be the average of T 1 ρ ,H2 −1 ( t ) and T 2 ρ ,H2 −1( t ) over the duration of the pulse as given by [4]: $$R_{\mathrm{normalR}\mathrm{normalA}\mathrm{normalF}\mathrm{normalF}2}=\frac{1}{2T_{\mathrm{p}}}\underset{0}{\overset{T_{\mathrm{normalp}}}{\int }}true(T_{1\mathrm{normal\rho },\mathrm{normalH}2}^{-1}false(tfalse)+T_{2\mathrm{normal\rho },\mathrm{normalH}2}^{-1}false(tfalse)true)dt.$$ Here T p is the duration of sine/cosine pulses used in RAFF2. Finally, in Figure 3 the calculations performed with Eqs.…”

“…Subsequently, we extended this method to higher rotating frames (3 ≤ n ≤ 5) by utilizing consecutive transformations to the rotating frame of rank n around y (n−1) and x (n−1) axes. The new method which is entitled RAFFn (with n indicating rank of the rotating frame), generates fictitious RF field components operating in the rotating frames of rank n. Here, the final effective field in the rotating frame n, H n , is the vector sum of D n−1 and C n−1 [4]. Note, in this work magnetic field vectors will be expressed in angular frequency units (i.e., ω 0 = γ B 0 z⃗ ).…”

“…By convention, the RF field ( B 1 ) is applied along the x axis ( x ') of the rotating frame and the RF field vector is ω 1 = γ B 1 x⃗ ', and the frequency offset Δω 0 ( t ) z⃗ . The non-adiabatic sweep of the effective RF field H 0 produces a fictitious field component ( C 1 =γ −1 d α 0 / dt y⃗ '), and the effective fictitious field H 1 in the second rotating frame is the vector sum of C 1 and the frequency offset D 1 [4]. Here, γ is the gyromagnetic ratio and α 0 is the time-dependent angle between H 0 and the first rotating frame quantization axis z '.…”

“…Inportantly, the method allows to significantly reduce the specific absorption rate (SAR). Motivated by the promising findings of our experimental study of RAFFn in the human and rat brain [4] which demonstrated great potential of RAFFn in characterization of tumors and indicated its exceptional sensitivity to myelin, here we provide a theoretical description of exchange-induced relaxation, which is critical for the understanding of the MRI contrast obtained with RAFFn in vivo [6]. In this work, the analytical solution for anisocronous two site exchange (2SX) (i.e., exchange between sites with different chemical shifts) in the fast exchange regime (FXR) during RAFF2 was derived.…”