Combining 4D Flow MRI and Complex Networks Theory to Characterize the Hemodynamic Heterogeneity in Dilated and Non-dilated Human Ascending Aortas

Figure 1. Schematic diagram of the methodology used to apply the Complex Networks theory to in vivo velocity data. a: Image acquisition and anatomic landmarks identification from 4D flow MRI: STJ: sinotubular junction; BCA brachiocephalic artery; LSA left subclavian artery. b: Lumen 3D geometry reconstruction. C: Definition of hemodynamic descriptors and complex networks analysis. Hemodynamic descriptors panel: Vx, Vy and Vz: cartesian components of the velocity vector V; C(S): vessel centerline; C’: vector tangent to the centerline; R: vector orthogonal to C’ directed from the centerline to a generic voxel; S: vector orthogonal to vectors R and C’. The investigated clinical and geometric parameters are also listed, with a schematic representation of flow jet angle (FJA), flow displacement (FD), the AAo maximum diameter Dmax and the aortic root maximum diameter Droot, the latter used to compute Dratio. Complex Networks panel: N: number of voxels in the aortic domain; lij: Euclidean distance between voxels i and j; NLC: number of nodes of the network’s largest connected component, i.e., the maximal set of nodes such that each pair of nodes is connected by a path. An explanatory example of a…

Figure 2. Visualizations of instantaneous streamlines at peak systole in patients with (bottom row) and without (top row) ascending aortic dilation. Colors represent velocity magnitude.

Figure 3. Volumetric maps of hDC for |V| (top row), Vax (middle row) and Vsc (bottom row) CNs.

Figure 4. Volumetric maps of hAED for |V| (top row), Vax (middle row) and Vsc (bottom row) CNs.

Figure 5. Effect of AAo dilation on the distributions of hAED values for |V|, Vax and Vsc CNs. The median is indicated by the red line, the box indicates the interquartile range and the whiskers indicate the extreme values of the distribution.

Figure 6. Associations between the geometric clinical indicator Dratio and CNs metrics hDC (left column), hAED (middle column), and ASPL (right column) for |V| (top row), Vax (middle row) and Vsc (bottom row) CNs. For each CN, hDC and hAED are expressed as the median value of all voxels. R: Pearson’s correlation coefficient (*p < 0.05, †p < 0.01).

Figure 7. Associations of blood flow kinetic energy at the systolic peak (KEpeak) with hDC (top) and ASPL (bottom) for |V| CNs. Here hDC is expressed as the median value of all voxels. R Pearson’s correlation coefficient (*p < 0.05, †p < 0.01).

Figure 8. Explanatory example of differently correlated pairs of Vax time-histories in a representative case. Regions of flow reversal, like the inner AAo, are characterized by Vax waveforms with negative values (Vax,j in the Figure), which are anti-correlated (negative Rax values) with Vax,j waveforms mainly aligned with the forward flow direction (Vax,i, Vax,m and Vax,n in the Figure). Vax waveforms shown in the Figure were interpolated using a higher number of time points for visualization purposes.