Effect of the Mitral Valve on the Intra Ventricular Hemodynamics

Figures

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  FIGURE 1. Computational Domain: The 4 pulmonary veins are highlighted in red, the Left Atrium (LA) in orange, the LV in green, and the Aorta in purple. The black lines indicate the positions of the slices used to display the flow, as detailed in Section 3. Specifically, the vertical line represents slice #1, while the nearly horizontal line corresponds to slice #2. (a) Domain at t/T=0.01 (start systole), (b) Domain at t/T=0.38 (end systole).

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  FIGURE 2. Modeling of the MV (a) Typical geometry as provided by the formulation of Pedrizzetti and Domenichini [74] ε=0.35;k=0.6. (b) Positioning of the valve in the whole computational domain. (c) Temporal evolution of the function Γ(t). (d–h) Snapshots of the synthetic MV illustrating the transition from the open to the closed configuration at times t/T=0.95, t/T=0.00, t/T=0.01, t/T=0.03, and t/T=0.06, respectively.

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  FIGURE 3. Different MV geometries shown at time of maximum opening. For all cases, ε=0.35, k=0.6, and R=17.5 mm. For each case, the top image shows the 3D view of the valve within the heart, while the bottom image displays the 2D projection of the valve on slice 1 (visible in Figure 1). The red line represents the MV‐apex line, while the green line indicates the geometrical axis of the valve, which connects the centers of the top and bottom cross section area.

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  FIGURE 4. Details of the flow domain over which the kinetic energy budget is established. The inlet (Mitral Plane (ΓMP)) is above the MV and the outlet (Aortic Plane (ΓAP)) under the AV. The outward normals are represented as arrows. D(t) is the ventricular domain at time t and Ωt represents the fixed domain which is such that Ωt=D(t) at time t.

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  FIGURE 5. Curves of P0 over the cardiac cycle and the PV loop. These evolutions were obtained from Equation (19) and the elastance model provided by Reymond et al. [83]

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  FIGURE 6. Volume rendering of non‐dimensional vorticity magnitude (non‐dimensionalised by the period T) at different times (t/T) in a cardiac cycle. Each row corresponds to a specific time instant. Top: t/T=0.47 (early‐diastole). Middle: t/T=0.57 (mid‐diastole). Bottom: t/T=0.83 (end‐diastole). Below each set of images, the curves represent the flow at the entrance (the 4 pulmonary veins), exit (the aorta), and the ventricular volume over time, with the red line indicating the current time in the cardiac cycle. For the vorticity color scale, black represents ω=0, red indicates ω=500, yellow corresponds to ω=800, and white is for ω=1000.

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  FIGURE 7. Phase‐averaged velocity field at t/T=0.57 (beginning‐mid diastole) in the plane slice #1 defined in Figure 1. The labels represent the vortices mentioned in the main text. See Figure 6 for the curves at the bottom of the Figure.

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  FIGURE 8. Phase‐averaged velocity field at t/T=0.7 (mid‐diastole) in the plane slice #1 defined in Figure 1. Green regions denote the different vortices within the ventricle, while red markers indicate their respective center. See Figure 6 for the curves at the bottom of the Figure.

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  FIGURE 9. (a) Kinetic energy balance for case C01 (see Table 2) during a cycle (averaged over 10 cycles). See Equation (23) for the definition of the different terms. “Error” is the difference between the left and the right‐hand side of Equation (23), which should be zero in the absence of any numerical approximation. Note that the “Error” is plotted on a different scale (right axis) compared to the other terms. (b) Intraventricular viscous dissipation (ψ) during a cardiac cycle (averaged over 10 cycles) for the four cases considered. (c) Kinetic energy of the phase‐averaged velocity field. (d) Kinetic energy of the fluctuating velocity field.