sections for the mitral reconstruction $$\vec{c}_r(SA_i,LA_j)=~\vec{r}(SA_i,LA_j) \times \frac{\vec{r_p(LA_j)}}{\vec{r_{int}(LA_j)}}
\label{pred-corr}$$ where $\vec{c}_r(SA_i,LA_j)$ is the corrected radial dimension, $\vec{r}(SA_i,LA_j)$ is the original dimension, $\vec{r}_p(LA_j)$ is the mitral orifice data, and $\vec{r_{int}(LA_j)}$ is the interpolated data in the mitral orifice section, or the predicted data. The results of this procedure can be found in Fig. \[MV\_rec\]. Considering two directions, $\xi$ and $\eta$, shown in Fig. \[MV\_rec\], the interpolation is performed in one of the directions (e.g. $\xi$), and the correction to the interpolation is done in the other direction (e.g. $\eta$) using a bi-variate interpolation. However, there is only one cross-section (Apical three-chambered view) of echo images in which AV is clearly visible. Therefore, the AV is reconstructed using only this view assuming that AV has a circular cross-section which is shown to be a reasonable assumption for AV reconstruction [@labrosse2006geometric]. The final reconstruction of the MV and AV during a cardiac cycle is shown in Fig. \[valve\_motion\] which shows the valve motion is well synchronized with the phases of LV.

Superior wall reconstruction {#Superior wall reconstruction}
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Closed geometry is essential to perform CFD simulation in the LV. Hence, the superior wall is modeled to connect the valves and the Endocardium wall 