Computational fluid dynamics simulations guided by Fourier velocity encoded MRI

Introduction: Fourier velocity encoding (FVE) is a promising MRI method for assessment of cardiovascular blood flow. FVE provides considerably higher signal-to-noise ratio (SNR) than phase contrast (PC) imaging, and is robust to partial-volume effects. On the other hand, FVE does not directly provide velocity maps. These maps are useful for calculating the blood flow through a vessel, or for guiding computational fluid dynamics (CFD) simulations. PC-driven CFD has been previously demonstrated, and can be useful for reducing scan time, improving spatial resolution, and/or denoising the MRI data. This work introduces a method for using FVE data (rather than PC data) to guide CFD simulations. Methods: Simulated FVE data was derived from 3DFT FGRE PC data from a pulsatile carotid flow phantom (Phantoms by Design, Inc., Bothell, WA). PC imaging was performed on a 3T GE Discovery MR750 system (50 mT/m, 200 T/m/s), using a 32-channel head coil. Scan parameters: resolution = 0.5×0.5×1.0 mm; FOV = 16×12×7.5 cm; Venc = 50 cm/s; TR = 11.4 ms; flip angle = 8.5; temporal resolution = 91.2 ms; scan time = 40 minutes; 9 NEX; pulse cycle 60 bpm). The spin-density map (magnitude image), m(x,y), and the through-plane velocity map, pc , , corresponding to a temporal frame at midsystole, were used to simulate a spiral FVE spatial-velocity distribution, according to the signal model: , , = , ∙ sinc pc , ∗ jinc , where x and y are the in-plane spatial coordinates, w is the through-plane velocity, and δr and δw are FVE’s spatial and velocity resolutions, respectively. The spatial blurring effects of the jinc kernel were reduced using a deconvolution algorithm to obtain ̃ , , . Then, an estimate of the true velocity at a given spatial coordinate (xo,yo) was estimated from ̃ , , as: , = arg min ̃ , , , − sinc . Finally, CFD calculations were performed using a modified version of the SIMPLER algorithm, in which , was used to constrain the CFD calculation. The phantom’s bloodmimicking fluid (viscosity 5 mPa.s, density 1100 kg/m) was assumed to be Newtonian, isothermal, and incompressible. The simulation grid was designed with 0.5×0.5×1.0 mm resolution, and a computational time step δt = 0.25 ms was used. Finally, the estimated flow field was compared quantitatively and qualitatively with both a pure CFD solution and the PC-measured flow field. This process was repeated for different values of δr (1 or 2 mm); and for each slice along the z axis. The velocity resolution, δw, was 10 cm/s. Results and Discussion: The spin-density maps in Fig. 1a illustrate the spatial blurring associated with each value of δr, for a slice perpendicular to the phantom’s bifurcation. Fig. 1b presents the FVE-estimated velocity maps, , for each spatial resolution value, while Fig. 1c shows the associated errors (relative to the PC map, wpc). The results show that lower error levels were obtained when FVE data with finer spatial resolution was used. In this slice, the absolute error was greater than 5 cm/s for only 10% of the voxels when δr = 1 mm was used; while 31% of the voxels presented error greater than 5 cm /s when δr = 2 mm was used. Fig. 2 shows (i) the PC-measured velocity field; and the CFDsimulated velocity fields, obtained using (ii) pure CFD, (iii) FVE-driven CFD (δr = 1 mm), and (iv) FVE-driven CFD (δr = 2 mm). Considerable qualitative improvement — with respect to agreement with the PC reference — can be appreciated in the FVE-driven results, when compared with the pure CFD result. Table 1 presents the measured signal-toerror ratio (SER) relative to the PC reference, for the CFD results shown in Fig. 2. Both FVE-driven solutions achieved higher SER than the pure CFD approach, when evaluating the three-dimensional velocity vector = , , ; the SER gain (relative to pure CFD) was 1.49 dB when δr = 1 mm was used, and 0.80 dB when δr = 2 mm was used. When evaluating only the y-axis velocity component (v), there was a 0.11–0.35 dB loss in SER with the proposed method. This may be a positive effect of denoising, since the velocities along that axis are extremely low (vpc’s total energy is 15.7 dB lower than that of wpc). Nevertheless, the SER gains for the u and w components more than compensate for this. Conclusion: This work presented a method for using FVE data to guide CFD simulations. We showed that FVE-driven CFD achieves better agreement with a PC-measured velocity map than pure CFD solutions. This is an important result, since a 1-mm resolution spiral FVE dataset could be acquired in the same scan time as 1 NEX of a 0.5-mm resolution PC dataset with the above parameters; however the FVE dataset would have an SNR 23 dB higher than that of PC (for a 2-mm resolution spiral FVE, scan time would be 3 times Figure 1: (a) Spin-density maps for PC (0.5 mm spatial resolution), FVE with 1 mm spatial resolution, and FVE with 2 mm spatial resolution, for a slice perpendicular to a carotid phantom’s bifurcation; (b) corresponding velocity maps; and (c) absolute error for the FVEestimated velocity maps, relative to the PC reference.