Applications of FSI for Cardiovascular Haemodynamics - Computational Hemodynamics: Theory, Modelling and Applications - page 302

Fig. 8.70 Opening angle versus time of simulated and measured mitral leaflets. (Image from Dahl
et al. 2010)
the instant when the displayed image was taken. The inflow region was modelled
as a typical, but fixed, atrium with two inlets in the upper part, each reflecting
an orifice of a pulmonary vein. The leaflets were modelled as two separate rigid
bodies, rotating around their annulus attachment points. The anterior and posterior
valve lengths were taken as l a = 19.9 mm and l p = 6.6 mm, respectively. The choice
of lengths was based on ultrasound recordings. The thickness was set to t = 1.0 mm
uniformly for both leaflets.
A deforming mesh under the Arbitrary-Lagrangian-Eulerian formulation was
used where grid velocities are included in the momentum and continuity equations.
The domain was discretised with triangular cells with increased density around the
leaflets to allow for their large motions. Due to limitations in the dynamic mesh
module, a gap is required between the moving parts to maintain a continuous fluid
domain. A two-cell gap of 0.5 mm between the leaflets and the wall, and a two-cell
gap of 0.6 mm between the two leaflets in their closed position were included in the
model. The blood was modelled as an incompressible, laminar, Newtonian fluid,
with properties representative for healthy human blood, a density of 1056 kg/m 3 and
a dynamic viscosity of 3.5 × 10 −3 kg/ms. The diastole time of 0.43 s was discretised
with 2150 time steps (e.g. time step of 0.2 ms).
Figure 8.70 shows the opening angle of the simulated valve plotted against the
opening of a natural mitral valve measured in the same ultrasound recordings dur-
ing left ventricle wall movement. The three stages of diastole can be identified in
the graph. These are: early diastole, that depicts, the rapid or early filling phase;
mid-diastole or the diastasis, which shows the partial closing; and end-diastole,
which represents the second opening due to atrial contraction. During early diastolic
filling, the simulated anterior leaflet's opening angle coincides relatively well with
the measurements. In mid- and end-diastole, there are some deviations between
the simulation and the measurements. The posterior leaflet, on the other hand, has