Fig 1.
Workflow of creating the digital input model (shown inside the dashed panel) for the patient-specific blood flow simulations.
Geometric Model Reconstruction: this block (on the left) shows how CT angiogram data (in DICOM format) are segmented in 3D slicer software (where the region of interest is marked up) and then converted in to a 3D volumetric model of the aorta. Velocity Support: the velocity waveform is extracted from echocardiography data and is used directly at aortic inflow boundary. It is then converted, using a reference cardiac output, to a flow-rate waveform which is required for construction of a pressure waveform. Pressure Support: the numerical solver is capable of assimilation of in vivo pressure data, if available, into the solution (this is done rigorously by modifying the Poisson equation for pressure). In absence of this data, a surrogate model of the outflow pressure is constructed based on the Windkessel model (WKM). In this study, a pure velocity waveform is used at the inlet, a pure pressure waveform (based a two-element WKM) is used at the descending aorta outlet, and adaptive zero-stress boundary conditions are applied in the neck artery outflows.
Fig 2.
Simulation domain Ωsim and the embedded subset of interest ΩCT.
The ΩCT includes the segmented model geometry, all velocity and pressure support data are applied over fringe zones outside of ΩCT, as volumetric patches attached to the inlet and outlets of the model. The flow equations are then solved for the whole Ωsim. The blue window which is magnified on to the right side of the simulation domain shows the spatial resolution represented by thin mesh lines on the surface.
Table 1.
Physical dimensions of the geometric and waveform input models.
The “TAVI0 Restored” and “TAVI0-Restored+S” (which is the stressed version of restored case) cases are based on the geometry of TAVI0 case. The sizes of inflow and outflow boundaries (which roughly take the shape of an ovoid) are given in a a × b format where a is the major axis and b is the minor axis of the ovoid.
Fig 3.
Geometric models for patients “TAVI0”, “TAVI1” and “TAVI2”, as well as the Idealized model “Idealized”.
Fig 4.
Wall shear stress magnitude maps for instances MA, 3QA, PF, QD, MD and ES are shown for patient-specific cases TAVI0, TAVI1 and TAVI2 as well as the Idealized case.
A persistent focal area of elevated and oscillatory wall shear stress is observed on the outer curvature of the ascending aorta for TAVI0 and the Idealized cases, whereas elevated values of WSS are more dispersed in space for cases TAVI1 and TAVI2. This could be due to more downstream branching location of the Brachiocephalic artery for the TAVI0 and Idealized cases, compared to TAVI1 and TAVI2. The former cases allow jet impingement on the vessel wall without further disturbance due to cross-flow caused by this neck artery, while the latter cases include further disturbing of this zone by this cross-flow effect (which acts as a source of blowing/suction of fluid).
Fig 5.
Time instance references used in the paper for the in-beat snapshot presentations: Peak flow (PF) denotes when flow rate reaches its maximum.
End systole (ES), denotes the state of flow at the end of systolic deceleration. Other instances are then defined accordingly as follows: mid-acceleration (MA) is temporally halfway between the start of the pulse (t = 0) and PF, three-quarters acceleration (3QA) is halfway between MA and PF, mid-deceleration (MD) is halfway between PF and ES, quarter-deceleration (QD) is halfway between PF and MD.
Fig 6.
Volume rendering of the undisturbed (left, TAVI0 case) and disturbed (right, TAVI2) aortic jet impingement on the aortic wall at time QD.
The undisturbed impingement case shows that the aortic jet changes direction without breakdown while the disturbed impingement case shows the jet undergoing large disturbances while impinging (the destabilizing effect of blowing/suction by Brachiocephalic artery).
Fig 7.
Evolution of wall shear stress values over time (top panels) for a band (solid black line shown on the bottom panels) in the ascending aortic region.
For each point on the band, the angle θ is defined with respect to an origin on the surface enclosed within the band, and is taken to be the mean value of x, y and z coordinates of the surface. Red bullet mark shows θ = 0 and the positive azimuthal direction is shown by arrows. Wall shear stress data on the band are then collected in time and plotted over a period from the start of the pulse t = 0 until t = 0.225s, which is slightly past the peak flow. It can be seen that wall shear stress peaks cover the entire band for cases TAVI1 and TAVI2, but are concentrated on one side of the band for cases TAVI0 and Idealized. The white dashed lines show approximately the boundary of high wall shear stress zones and the quiet zone on for the cases TAVI0 and Idealized.
Fig 8.
Realization of the jet impingement process through velocity magnitude (top panels) and pressure (middle panels) visualizations in the Idealized case. From left to right, time instances PF, QD and MD are shown. The bottom plot shows the time history of pressure values taken on four probes A, B, C and D (see the middle left panel) around the impingement zone. It is shown that probe A which is located roughly close to the centre of impingement zone, consistently marks a higher pressure (of 1000Pa approximately) than other neighbouring probes.
Fig 9.
Wall pressure maps for instances 3QA, PF, QD, MD are shown for patient-specific cases TAVI0, TAVI1 and TAVI2 as well as the Idealized case Idealized.
A persistent zone of high pressure, which corresponds to a high wall shear stress zone (cf. Fig 4), is observed on the ascending aorta for cases TAVI0 and Idealized, but not for the cases TAVI1 and TAVI2.
Fig 10.
Pressure signal taken as a time series of pressure at a probe located on the aortic wall slightly upstream of neck arteries (the probe is marked in magenta on the left column of Fig 9, and is located at centre of the HWSS zone) for TAVI0, TAVI 1, TAVI 2, and Idealized cases. Cases TAVI 0 and Idealized show distinct pressure build up.
Cases TAVI 1 and TAVI 2 lack a pressure build up, but show strong oscillations near peak flow which is shown by the dimenstionless parameter |δp|max/pi, where δp denotes twice the maximum amplitude of the oscillations, and pi is the initial pressure value taken at 3QA instance.
Fig 11.
Wall shear stress maps for the virtually restored case of TAVI0 at times 3QA, PF and QD.
Top row corresponds to restored flow with the same cardiac output (no stress scenario) as the stenosis case, and the bottom row corresponds to a stressed scenario where cardiac output is doubled. It is seen that both scenarios do not mark a high wall shear stress zone on the ascending aorta as opposed to the stenosis case. However, new zones of high wall shear stress have emerged downstream of the aortic arch bend towards the descending aorta. Signs of helical wall-shear stress waves can be also observed on the ascending aorta for the stressed scenario (see bottom right panel).
Fig 12.
Wall pressure maps for the virtually restored case of TAVI0 at times 3QA, PF and QD.
Top row corresponds to restored flow with the same cardiac output (unstressed scenario) as the stenosis case, and the bottom row corresponds to a stressed scenario where cardiac output is doubled. It is seen that the regional zone of high wall pressure on the ascending aorta which was observed in the stenosis case is no longer present. The unstressed scenario shows an almost uniformly decaying pressure from ascending towards the descending aorta, but the stressed scenario shows an oscillatory behaviour, which is likely to be related to the helical wave footprints on wall shear stress maps for this case (see Fig 11).
Fig 13.
Peak flow velocity magnitude (left) and z−component of the velocity field (right) for the TAVI0 case at stenosis (bottom), restored and unstressed (middle) and restored and stressed (top) cases.
Even though the flow is less chaotic after restoration in the ascending aorta, the descending aortic flow marks a major instability (a separation bubble) which is linked to elevated wall shear stress in that location (see Fig 11). This bubble could be due to the major out-of-plane bending of the aorta.