Computational tools for clinical support: a multi-scale compliant model for haemodynamic simulations in an aortic dissection based on multi-modal imaging data

Figures

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  Figure 1.. (a) Rendering of the CT data showing the dissected aorta. (b) Three-dimensional model extracted from CT data representing the dissected aorta from the ascending aorta (inlet) to the abdominal aorta (AbAo). The supra-aortic branches (left and right subclavian arteries (LSA, RSA), left and right common carotid arteries (LCC, RCC)) and the main visceral branches (coeliac trunk (CT), superior mesenteric artery (SMA), left and right renal arteries (LRA, RRA)) are included. (c) Flow-rate curves at different locations extracted from 2D PC-MRI data: (A) ascending aorta; (B) RCC and LCC; (C) aortic arch, distal to the LSA; (D,E) flow rate in the TL of the dissected aorta at two sections along the descending aorta, above and below the diaphragm, respectively; (F) AbAo, proximal to the iliac bifurcation.

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  Figure 2.. (a) Schematic of the multi-scale model domain and its BCs. WK3 indicates the Windkessel models coupled at the outlets (see inset). The colour map shows the area compliance of the aorta (CA = ΔA/ΔP), estimated with patient-specific 2D cine-MRI data. The inset shows a cross-section of the ascending aorta and a schematic depicting how the displacement of a node n on the vessel wall is related to the pressure pn calculated in the fluid domain according to the MB method. (b) Schematic of the 0D model (lumped-parameters model) used during the tuning procedure. LR indicates the elementary building block, composed by an inertance (L) and a resistance (R) (see inset), representing a vessel segment: LR1: ascending aorta and arch, LR2: brachiocephalic trunk, LR3: right subclavian artery, LR4: right common carotid, LR5: left common carotid, LR6: left subclavian artery, LR7: descending aorta, LR8: coeliac trunk, LR9: superior mesenteric artery, LR10: right renal artery, LR11: left renal artery, LR12: abdominal aorta. (c) Flowchart of the procedure adopted to tune the parameters of the multi-scale model. Steps 1–4 are described in more detail in the text.

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  Figure 3.. (a,b,d,e) Flow (Q) and pressure (P) waves obtained with CFD simulation at the inlet and selected outlets (c) of the compliant model. P is calculated as the average pressure over the boundary area. (f) Comparison between the flow and pressure target values used for the tuning procedure of the Windkessel parameters and CFD results. The relative percentage difference between CFD results and target values are reported in the figure, showing a good agreement. (Online version in colour.)

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  Figure 4.. (a) Velocity magnitude at peak systole (t = 0.12 s). Inset: streamlines passing through the entry tear at peak systole showing the blood flowing into the FL. (b) Colour map of the pressure at peak systole in the ascending aorta and aortic arch. An area of increased pressure can be noted in the proximal FL where the blood flow impinges on the vessel wall. (c) Colour map of the TAWSS. (d) Colour map of the OSI.

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  Figure 5.. Comparison between computed and measured flow rates at different locations along the dissected aorta, as indicated in (a). (b) CFD results are presented with the solid lines, while 2D PC-MRI data are shown by the dashed lines. (Online version in colour.)

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  Figure 6.. (a) Displacement of the vessel wall obtained with the computational model at peak systole (t = 0.12 s), systolic deceleration phase (t = 0.23 s) and end-diastole (t = 0.78 s). (b) Percentage cross-sectional area variation (ΔA%) during a cardiac cycle at the level of the ascending and abdominal aorta: comparison between CFD results and 2D cine-MRI measurements. ΔA% = (A – A0)/A0, where A is the cross-sectional area of the vessel lumen and A0 is the lowest cross-sectional area of the vessel lumen throughout a cardiac cycle.

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  Figure 7.. (a) Pressure colour map at peak systole (t = 0.12 s). (b) Comparison between the TMP across the IF obtained with the CFD compliant model during a cardiac cycle and the displacement of the IF observed from 2D cine-MRI data at different time instances (TMP = PTL − PFL, where PTL and PFL are the pressures in the TL and FL averaged over a cross-section—indicated by an asterisk in the figure—located at the same level of the respective 2D cine-MRI slice). It can be noted that the direction of the IF displacement agrees well with the sign of the TMP: a positive TMP corresponds with the motion of the IF through the FL, whereas a negative TMP relates to the motion of the IF through the TL.

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  Figure 8.. (a,b) Comparison between CFD results obtained with compliant and rigid models. TL results are presented with solid blue lines, whereas FL results are shown by dashed red lines. The pressure results are presented as the averaged values calculated over the cross-sections shown in the schematic in (a), whereas the flow results are calculated as the integral of the velocity over the same sections (a positive flow corresponds to fluid moving towards the abdominal aorta). , and are the mean flow rates calculated over the entire cardiac cycle, the systole and diastole phase, respectively. (Online version in colour.)

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  Figure 9.. Haemodynamic indices in the ascending aorta and aortic arch obtained with the rigid CFD model, and comparison with compliant model results. (a) TAWSS obtained with the rigid model and percentage difference relative to the compliant model results, calculated as: %diff = (TAWSSR − TAWSSC)/(5 (Pa)). (b) OSI obtained with the rigid model and percentage difference relative to the compliant model results, calculated as: %diff = (OSIR − OSIC)/0.5 (where OSIR and OSIC are the OSI values for rigid and compliant, respectively). The percentage difference figures were normalized by values representing the range of the respective parameter distributions for better visualization.