Probabilistic Streamline Estimation from Accelerated Fourier Velocity Encoded Measurements

Introduction Cine phase-contrast flow measurements allow for the non-invasive assessment of blood velocity in the cardiovascular system. Streamline estimation based on three-dimensional velocity vector field data is a common visualization method of blood flow patterns. Velocity encoded phase data are assumed to reflect mean velocity information of voxels superimposed by noise. Partial volume effects, however, distort the intra-voxel velocity distribution near vessel walls and in complex velocity fields, for example. Accordingly, velocity distributions are skewed and no longer follow a normal distribution. To this end, an estimated streamline using phase-contrast data represents one possible realization of the flow field. To consider all possible streamlines, a probabilistic streamline representation has been proposed [1]. This method does, however, assume normal noise distribution. In Fourier velocity encoding [2], spectral velocity distributions of voxels are measured and provide information of the true velocity scattering. In this work, the combination of k-t PCA [3] accelerated Fourier velocity encoding and probabilistic streamline estimation is proposed. Using computer simulations and in-vivo data acquired in the femoral artery of healthy subjects it is demonstrated that streamline estimation from Fourier velocity encoded data is significantly improved relative to visualizations based on conventional phase-contrast data. Methods Three-dimensional Fourier velocity encoding (FVE) was implemented on a 3T Philips Achieva system (Philips Healthcare, Best, The Netherlands). Twelve velocity encoding steps per dimension and a non-encoded reference scan were acquired in the femoral artery of healthy subjects. Five-fold undersampling in k-t space was applied yielding a net scan time reduction of 4.2. Remaining scan parameters were as follows: cardiac triggered segmented gradient echo sequence, number of slices: 15, number of heart phases: 20, spatial resolution: 1.5x1.5x1.5 mm, temporal resolution: 41 ms, velocity encoding range: ±180 cm/s, 0.75% partial Fourier sampling along ky and kz, TR: 8.1 ms, TE: 5.2 ms. The undersampled data were reconstructed using the k-t PCA method implemented in Matlab (Mathworks, Natick, USA) and run on standard PC hardware yielding time-resolved data in the space-velocity domain (Figure 1a-b). Velocity spectra for each voxel were interpolated and values below the noise level measured were suppressed (Figure 1c). Streamline estimation was performed using Monte Carlo (MC) simulations with repeated velocity integration (Figure 2a). In each of the total of 1000 iterations, the velocity for every voxel was drawn randomly according to the probability function p(v) derived from the measured velocity distribution S(v). Streamlines were generated in time-reverse direction to avoid split pathways in bifurcating vessels. The final streamline was chosen as the mean of all realizations. For comparison conventional 4-point phasedifference (PC) data were computed from the Fourier velocity encoded data by selecting the encoding velocity venc closest to the maximal measured velocity.