Liao Ying^{1}, Paul Kyu Han^{2}, Shuang Hu^{2,3}, Kui Ying^{4,5}, Chao Ma^{2}, and Georges El Fakhri^{2}

UTE allows imaging of rapidly decaying short-T_{2} components and are often combined with

When spatial encoding is performed by the phase-encoding gradients, the spatially resolved signal at a spatial location x and time t can be expressed as follows [7,8]:

$$I(x,t) = \rho(x)\cdot e^{-i(\phi_{B_0}(t)+\phi_{G}(t))}$$

$$\phi_{B_0}(t)=\gamma\cdot\triangle B_0\cdot t$$

$$\phi_G(t)=x\cdot\gamma\cdot\int_{t_0}^{t}G(\tau)d\tau=2\pi\cdot x\cdot k_G(t)$$

where $$$\rho(x)$$$ denotes the proton density, $$$\phi_{B_0}(t)$$$ denotes the phase accumulation due to field inhomogeneity ($$$\triangle B_0$$$ , $$$\gamma$$$ denotes gyromagnetic ratio, and $$$\phi_G(t)$$$ denotes the phase accumulation due to multi-echo gradient $$$G(t)$$$, and $$$k_G(t)$$$ denotes the k-space trajectory traversed by the multi-echo gradient. Thus, by acquiring scans with (Fig. 1a) and without (Fig. 1b) the multi-echo gradient, the phase accumulation due to field inhomogeneity ($$$\phi_{B_0}(t)$$$) can be eliminated and $$$k_G(t)$$$ can be derived via numerical fitting.

All experiments were performed on a whole-body PET/MR scanner (Biograph mMR, Siemens, Erlangen, Germany) using head coil for reception and body coil for transmission. 2D k-space trajectory calibration scan was performed on a water phantom to characterize the k-space trajectory traversed by a multi-echo UTE gradient sequence. The imaging parameters were: field-of-view (FOV) = 240 $$$\times$$$ 240 $$$mm^2$$$, matrix size = 128 $$$\times$$$ 256, slice thickness = 5 $$$mm$$$, TR/TE = 9.0/2.3 $$$ms$$$, and total scan time = 9 $$$min$$$ 50 $$$s$$$. The TR unit with (Fig. 1a) and without (Fig. 1b) the gradient structure of interest was acquired in an alternative fashion for each of the phase-encoding gradients.

3D UTE with multi-echo radial acquisition was performed on a resolution phantom and a healthy subject. The study protocol was approved by our local Institutional Review Board (IRB). The imaging parameters were: field-of-view (FOV) = 240 $$$\times$$$ 240 $$$\times$$$ 240 $$$mm^3$$$, matrix size = 128 $$$\times$$$ 128 $$$\times$$$ 128, number of spokes = 51472, TR = 10.0 $$$ms$$$, TEs = 70/1830/2710/3590/4470/5350/6230 $$$\mu s$$$, flip angle = 10$$$^\circ$$$, hard pulse duration = 100 $$$\mu s$$$, gradient ramp time = 120 $$$\mu s$$$ (gradient slew rate = 163.1 $$$mT/m/ms$$$), plateau gradient amplitude = 19.57 $$$mT/m$$$, dwell time = 2.5 $$$\mu s$$$, and total scan time = 8 $$$min$$$ 35 $$$s$$$.Image reconstruction was performed using the k-space trajectory calculated from the designed gradient structure of multi-echo UTE and the k-space trajectory measured using the calibration scan as the input for non-uniform fast Fourier transform (NUFFT) reconstruction algorithm [9].

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