Bloch Simulations of UTE, WASPI and SWIFT for Imaging Short T2 Tissues

Introduction: Clinical MR is predominantly geared towards the imaging of “long” T2 species (T2’s greater than 10 ms). However, musculoskeletal (MSK) tissues of interest, such as ligaments (T2 ≈ 4-10 ms), tendons (T2 ≈ 2 ms) and cortical bone (T2 ≈ 0.5ms) often exhibit low signal intensity in images acquired using clinical MR sequences [1]. Three specialized sequences designed to overcome these limitations are Ultrashort TE (UTE) imaging [1,2], Water And Fat Suppressed Projection Imaging (WASPI) [3], and SWeep Imaging with Fourier Transformation (SWIFT) [4]. We present theoretical work including Bloch simulations to investigate the T2 blurring characteristics of these three techniques. Theory: To simplify our analysis, we will constrain our focus on 1D objects along the x-axis with spin density ρ(x). UTE can be performed either in 2D (using slice selective half RF pulses) [1] or 3D (using non-selective RF pulses) [2], while WASPI and SWIFT are exclusively in 3D form (using short non-selective hard RF pulses). UTE and WASPI are based on acquiring the Free Induction Decay (FID) of the MR signal as soon after the end of the RF pulse as possible (e.g. minimum TE ≥ 8μs). This is typically accomplished by using a radial center-out k-space trajectory and data sampling time TAQ on the order of a millisecond in duration (Fig.1a,b). In WASPI, the imaging gradient, G, is already applied during the RF pulse (Fig.1b). Therefore the RF pulse has to be kept short (~10μs, resulting in only a small flip angle) to avoid premature dephasing of the signal from the imaging gradient. In UTE the read gradient is zero during the RF pulse and is ramped up quickly during the readout, leading in part to radial ramp-sampling (Fig.1a). With either technique, magnitude images are reconstructed from the re-gridded k-space data. To model the effect of T2 decay, the FID signal in the time domain is multiplied by an exponential decay function. The T2 blurring in the image domain (1D) for WASPI and (to good approximation) for UTE is characterized by a convolution with a Lorenzian point-spread-function [2] (Eq.[1]). The SWIFT technique can be regarded as a member of the general class of Simultaneous Excitation and Acquisition (SEA) pulse sequences, in which small excitation pulses and data acquisition intervals are rapidly interleaved (Fig.1c). For SWIFT the amplitudes B1(t) of the small RF pulses follow a fast-sweeping hyperbolic secant function with phase modulation Φ(t). This results in a flat frequency response if the magnetization is tipped by a small flip angle. The Bloch equations including T2 decay (R2 ≡ 1/T2) can be solved for SWIFT in the small tip angle approximation using the following (standard) definitions: { }