Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls

Figures

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  Figure A1. Mesh sensitivity analyses of five meshes (3, 2, 1, 0.5, and 0.25 mm) conducted on relative area change (a) and maximum flow rate (b) measured at a specific model’s cross-section.

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  Figure 1. CT imaging processing: sagittal (a), axial (b), and coronal (c) planes of CT dataset, raw segmentation result (d), and refined model of the aorta (e).

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  Figure 2. Evenly spaced subsample of PCMRI frames, with aortic lumen countered with ROI (magenta) in both magnitude (a) and phase images (b); (c) flow velocity (magenta boxes) obtained from PCMRI segmentation of the lumen of the aorta.

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  Figure 3. Fluid domain mesh (a) and plane cut showing internal elements (b) with grid details at wall surface (c) and at plane cut (d).

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  Figure 4. Location of the cross-sections extracted from the FSI simulations, perpendicular to the model centerline: CS1 (green) proximal to inlet valve; CS2 (blue) at the ascending aorta; CS3 (yellow) after supra-aortic branches; and CS4 (pink) and CS5 (orange) at the descending aorta, with this latter closer to the outlet section.

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  Figure 5. (a) Flow and area variations along the cardiac cycle obtained from the segmentation of the patient’s PCMRI data; (b) QA loop (white circles) with indication of the points belonging to the early systole period (black circles) used for the linear interpolation (black line) to compute the PWV.

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  Figure 6. Localizer image (a) used to define the acquisition plane ΣPCMRI of the PCMRI at the descending aorta (b) and equivalent plane ΣFSI in the FSI domain (c); (d) comparison between flow curves as extracted from PCMRI data of the patient (black line with diamond markers) and FSI simulation (blue line with circle markers) at the same plane of the descending aorta.

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  Figure 7. Mean and standard deviation computed along the selected cross-sections of the coefficient ratio ar/a0 of the gPC polynomial expansion for the performed stochastic analyses.

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  Figure 8. PDF (color scale), mean (straight line), and standard deviation (dashed line) plots of flow variations along the cardiac cycle at cross-sections CS1 (a), CS2 (b), CS3 (c), CS4 (d), and CS5 (e), respectively identified by the green, blue, yellow, pink, and orange slices in the aortic model (f).

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  Figure 9. PDF (color scale), mean (straight line), and standard deviation (dashed line) plots of area variations along the cardiac cycle at cross-sections CS1 (a), CS2 (b), CS3 (c), CS4 (d), and CS5 (e), respectively identified by the green, blue, yellow, pink, and orange slices in the aortic model (f).

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  Figure 10. PDFs of area variation at the five cross-sections, i.e., CS1 (a,b), CS2 (c,d), CS3 (e,f), CS4 (g,h), and CS5 (i,j) along the entire cardiac cycle (a,c,e,g,i) and at the time instances t1, t2, and t3 of the cardiac cycle (b,d,f,h,j).