5D Flow Tensor MRI to Efficiently Map Reynolds Stresses of Aortic Blood Flow In-Vivo

Abstract

Diseased heart valves perturb normal blood flow with a range of hemodynamic and pathologic consequences. In order to better stratify patients with heart valve disease, a comprehensive characterization of blood flow including turbulent contributions is desired. In this work we present a framework to efficiently quantify velocities and Reynolds stresses in the aorta in-vivo. Using a highly undersampled 5D Flow MRI acquisition scheme with locally low-rank image reconstruction, multipoint flow tensor encoding in short and predictable scan times becomes feasible (here, 10 minutes), enabling incorporation of the protocol into clinical workflows. Based on computer simulations, a 19-point 5D Flow Tensor MRI encoding approach is proposed. It is demonstrated that, for in-vivo resolution and signal-to-noise ratios, sufficient accuracy and precision of velocity and turbulent shear stress quantification is achievable. In-vivo proof of concept is demonstrated on patients with a bio-prosthetic heart valve and healthy controls. Results demonstrate that aortic turbulent shear stresses and turbulent kinetic energy are elevated in the patients compared to the healthy subjects. Based on these data, it is concluded that 5D Flow Tensor MRI holds promise to provide comprehensive flow assessment in patients with heart valve diseases.

Figure 1

Illustration of in-vivo 5D Flow Tensor MRI: (a) K-space data are continuously acquired on a Cartesian golden angle trajectory during free breathing of the subject. (b) Velocities are encoded along six non-collinear directions with different velocity encodings VENC for improved accuracy of ISVD quantification over the desired range. (c) Each readout is assigned to a discrete respiratory motion state and cardiac phase, leading to undersampling patterns as required by compressed sensing reconstructions. (d) Images for each velocity encoding are reconstructed separately by exploiting correlations over cardiac and respiratory dimensions using a locally low-rank reconstruction. (e) For each direction, the measurements with different VENCs are combined using a Bayesian approach which selects the most likely values $\overline{\mathit{v}}$ and $\mathit{\sigma }$ given the signal model ${\mathit{S}}_{kv}$ and the measured data ${\mathit{d}}_{kv}$.

Figure 2

Exemplary distributions of IVSD in healthy and pathological aortae and illustration of IVSD encoding accuracy. (a) For healthy volunteers, IVSD is distributed mainly between 0 m/s and 0.3 m/s. For patients, a wider distribution can be observed with values of IVSD up to 0.8 m/s. (b) Examples of the region of interest for healthy controls and patients with aortic stenosis. (c) IVSD leads to a reduction in signal magnitude which depends on the encoding velocity VENC. The signal shows a high sensitivity to changes in IVSD within a limited range. For low values, the magnitude changes little, whereas for high values the signal vanishes completely. (d) Uncertainty of IVSD considering noisy data with an SNR of 30 dB. If ISVD is too high or too low, the IVSD estimates decrease in accuracy. Moreover, IVSDs for which the signal magnitude vanishes cannot be discerned and lead to a plateau in the plot.

Figure 3

Impact of SNR and image resolution on quantification of TKE and MPTSS. (a) Decreasing SNR leads to an overestimation of TKE and MPTSS. At an SNR of 30 dB, as estimated for in-vivo experiments, this overestimation is relatively low. (b) Increasing voxel sizes lead to a skewed distribution of TKE and MPTSS. At a resolution of 2.5 mm, as used for in-vivo experiments, TKE is overestimated by 3.1% and MPTSS is overestimated by 15.9% on average.

Figure 4

In-vivo assessment of turbulent flow through healthy and a bio-prosthetic heart valves. (a) Shows exemplary slices of a healthy and a bioprosthetic heart valve. The flow field shows uniform distribution of velocity magnitudes throughout the proximal aorta for the healthy valve whereas a jet with high velocities can be observed for the bio-prosthetic valve. MPTSS and TKE are elevated downstream of the bio-prosthetic valve. Visual assessment shows highest MPTSS and TKE near the vessel wall for the healthy valve and elevated values throughout the proximal aorta for the bio-prosthetic valve. (b) Shows value distributions for the different metrics, with healthy 1 and bioprosthetic 1 corresponding to the examples from (a). MPTSS and TKE are elevated for the bio-prosthetic heart valves. Velocities are on average lower for the bio-prosthetic heart valve but are distributed over a larger value range.