so as to have a smooth enclosure for the LV geometry. A bivariate strategy is employed for closing the LV geometry with the valves. The bivariate strategy is such that the interpolation is performed in $\eta$ direction, and the smoothing is performed in $\xi$ direction (Fig. \[lid\]) using following steps: 1) a section of the valve bases are connected to the LV base using cubic spline interpolation method 2) the remaining space is covered with linearly interpolated data so as to have a closed geometry 3) smoothing is performed in the orthogonal direction to have a smooth geometry and to incorporate information from both the directions. Steps of this process can be seen in Fig. \[lid\].

Hybrid echo-CFD framework {#Hybrid echo-CFD framework}
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To handle the complex shape and motion of LV, a curvilinear immersed boundary (CURVIB) method [@gilmanov2005hybrid; @ge2007numerical; @borazjani2008curvilinear] is used which has been extensively validated for a variety of complex flow problems [@borazjani2013parallel; @asgharzadeh2017newton] and implemented in various applications such as cardiovascular flows [@Asgharzadeh2019; @hedayat2019comparison; @hedayat2017platelet], aquatic motions and vortex dynamics [@asadi2018scaling; @daghooghi2016self] and rheology of suspensions [@daghooghi2015influence; @daghooghi2018effects]. The 3D reconstructed surfaces of LV from 2D-echo which are meshed using triangular elements are given to the 