A numerical study of the hemodynamic effect of the aortic valve on coronary flow

Abstract

During diastole, coronary perfusion depends on the pressure drop between the myocardial tissue and the coronary origin located at the aortic root. This pressure difference is influenced by the flow field near the closing valve leaflets. Clinical evidence is conclusive that patients with severe aortic stenosis (AS) suffer from diastolic dysfunction during hyperemia, but show increased coronary blood flow (CBF) during rest. Transcatheter aortic valve implantation (TAVI) was shown to decrease rest CBF along with its main purpose of improving the aortic flow and reducing the risk of heart failure. Physiological or pathological factors do not provide a clear explanation for the increase in rest CBF due to AS and its decrease immediately after TAVI. In this manuscript, we present a numerical study that examines the impact of AS and TAVI on CBF during rest conditions. The study compares the hemodynamics of five different 2D numerical models: a baseline “healthy valve” case, two AS cases and two TAVI cases. The analysis used time-dependent computational fluid–structure interaction simulations of blood flow in the aortic root including the dynamics of the flexible valve leaflets and the varying resistance of the coronary arteries. Despite its simplifications, our 2D model succeeded to capture the major effects that dominate the hemodynamics in the aortic root and to explain the hemodynamic effect that leads to the changes in CBF found in in vitro and clinical studies.

Appendix

1.1 Model validation

1.1.1 Time step independence tests

Fig. 19

velocity magnitude for the different time steps intervals at time 0.42 s

Mesh and time step independence tests were conducted to validate the numerical model. To evaluate the optimal time step size for the transient simulations, simulations of the healthy case with the mesh of 30,000 nodes were performed using 5 different time step intervals of dt = 5, 10, 15, 20 and 25 ms. The resulted velocity magnitude for the different time steps intervals are shown in Fig. 19 corresponding to $t=0.42\,\hbox {s}$.

For all the cases, at $t = 0.5\,\hbox {s}$, the time step is reduced to dt = 1 ms to allow converge at the delicate stage of valve closure. Figure 20 shows a comparison of the average coronary velocity during the cardiac cycle for the five cases of time step resolutions.

Fig. 20

Time-dependent average coronary velocity for the different time steps intervals

To evaluate the discretization error, we calculated the relative difference (ERR) between the average coronary flow of each case and the finest time resolution case, as follows:

$$\begin{aligned} ERR_i \left[ \% \right] =\int _T {\left( {\frac{\left( {V_y } \right) _{finest} -\left( {V_y } \right) _i }{\left( {V_y } \right) _{finest} }} \right) dt*100} \left[ \% \right] \nonumber \\ \end{aligned}$$

(A.1)

Table 5 Details of the time step intervals, calculation time and average relative difference

where $V_{y}$ is the time-dependent average coronary velocity (as described by Eq. 5) and T is the cycle period. Table 5 details the average ERR of the different cases. The results show that the time step of dt = 10 ms is sufficient during systole, with ERR = 1.5%. During diastole (t > 0.5 s), steps of 1 ms were used to allow convergence. Therefore, for the transient analyses in this study, 551 steps were set per cycle.

1.1.2 Mesh independence tests

To evaluate the optimal mesh resolution, five models of the healthy base case with different mesh resolutions were built (with 20,000–60,000 nodes). The models were simulated during a period of one cardiac cycle. Figure 21 shows a comparison of the average coronary velocity during the cardiac cycle for the five mesh resolutions and Table 6 details the average relative differences of the different cases. Based on these results, mesh resolutions of 30,000 nodes were found suitable for our model with ERR = 4% of the finest mesh.

Fig. 21

Time-dependent average coronary velocity for the different mesh models (number of nodes)

Table 6 Details of mesh models, calculation time and average relative difference

Fig. 22

Experimental models, a healthy/AS; b TAVI

1.1.3 Comparison with in vitro results

The numerical study was conducted in parallel to an experimental study that was performed by another member in our group (to be published in a future publication). The study included a healthy, AS and TAVI in vitro models with similar characteristics as the numerical model described here (Fig. 22). The flow was driven by a pulsatile piston pump which was synchronized with a controlled coronary arteries resistance. Similar working conditions (HR and CO) were used. Measurement of coronary flow rates are shown as red columns in Fig. 23. Although only one AS model (severe AS) and one TAVI model (the long TAVI) were modeled in the in vitro study, the experimental results agree with the numerical results. AS case showed higher coronary flow than healthy case, and TAVI leads to normalization of the coronary flow.

Fig. 23

Coronary flow rate for the different cases in the numerical (blue) and experimental (red) models