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Blood flow characteristics in the normal left ventricle are studied by using the magnetic resonance imaging, the Navier-Stokes equations, and the work-energy equation. Vortices produced during the mitral valve opening and closing are modeled in a two-dimensional analysis and correlated with temporal variations of the Reynolds number and pressure drop. Low shear stress and net pressures on the mitral valve are obtained for flow acceleration and deceleration. Bernoulli energy flux delivered to blood from ventricular dilation is practically balanced by the energy influx and the rate change of kinetic energy in the ventricle. The rates of work done by shear and energy dissipation are small. The dynamic and energy characteristics of the 2D results are comparable to those of a 3D model.

Analysis of blood flow in the left ventricle is of fundamental interest in studying cardiac function and dysfunction. Using magnetic resonance velocity mapping, Kim et al. [

Numerical modeling of flow in LV was classified into three types [

Using 2D velocities obtained from phase-contrast MR imaging, Thompson and McVeigh [

The present study is to relate kinematic, dynamic, and energy characteristics of inflow to a normal left ventricle. Because of rapid flow acceleration and deceleration with mitral valve motion, the 3D effect is relatively small in comparison with the longitudinal flow. The main feature of inflow can be captured and learned by using 2D finite volumes and MRI data of cardiac contraction and dilation. The effect of mitral valve motion on pressure drop is studied by comparing cases with and without modeling mitral leaflet motions. The detailed flow patterns indicate momentum transfer in the rapid curvilinear flow produced by ventricular dilation and reveal alteration in boundary layer, vortices, shear stress, pressure variations, and net pressure on valve leaflets. The flow process is continued by the ventricular contraction and the results are reported by Hung et al. [

MRI scanning was performed for a healthy adult on a 1.5T Siemens scanner (Avanto, Siemens Medical Solutions, Erlangen) using the steady-state-free precession cine gradient echo sequences. The data were acquired from 2-chamber, 4-chamber, and short-axis planes of the left ventricle using 12–14 equidistant slices. They were utilized for 3D reconstruction of movements of the left ventricle and atrium. The end-systolic and end-diastolic volumes are, respectively, 48.8 and 162.5 mL, producing a stroke volume of 113.7 mL and an ejection fraction of 70%. To simulate blood flow, 25 frames of LV endocardial walls were obtained from the MRI during one cardiac cycle. The temporal variation of ventricle volume,

(a) Temporal variation of the left ventricle volume,

Blood flow in large arteries can be treated as homogeneous Newtonian fluid of density 1050 kg/m^{3} and dynamic viscosity of 0.00316 Pa·sec. An arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations can be expressed as [

The computation was initiated at the onset diastole and periodic solutions were obtained after 4 cycles of diastolic and systolic flow simulation. Figure

Time variations of inlet velocity

Streamlines at (a)

The color scale 66 in Figure

Streamlines at (a)

Streamlines at (a)

Streamlines at (a)

Streamlines at (a)

Dynamic characteristics are demonstrated by pressure contours in Figure ^{−1}) of the Poiseuille flow for the median Reynolds number of 2842.

Pressure contours and net pressure on the mitral valve leaflets for (a) rapid filling, (b) for peak of inlet velocity, and (c) during closing of mitral valve.

Vorticity and shear stress distribution of the flow past the mitral valve for (a) rapid filling, (b) for peak of inlet velocity, and (c) during closing of mitral valve.

Figure

Time variation of inflow Reynolds number

Rate of energy transfer of 2D model of diastolic flow in the left ventricle: curve A: kinetic energy flux on the wall,

The fluid dynamics of cardiac pumping can be further studied by using an integral form of the work-energy equation [

The kinetic energy influx at the mitral section is indicated by the difference between curves D and E. It is about 13 times higher than that of kinetic energy flux from the ventricular wall (see curve A in Figure

Comparison of the rate of energy dissipation between the 2D model (curve 1) and the 3D model (cure 2); curve 3 is the 2D results multiplied by the ratio between 3D and 2D flow rates.

Fluid dynamic characteristics of blood flow in the left ventricle are obtained by using 2D CFD with MRI data of a normal adult. The flow patterns are dominated by ventricular dilation and flow induced mitral valve movements. Generation and growth of vortices correlate well with flow acceleration and deceleration and mitral valve motion. They are solely for momentum balance and energy transfer from ventricle dilation to the curvilinear inflow of blood. Boundary layer and high shear stress do not develop on moving leaflets and ventricle. The work done by viscous stresses and dissipation of energy are small for normal diastolic flow. The energy loss is about 2% of the kinetic energy influx to the ventricle and is almost balanced with work done by viscous stresses. The Bernoulli energy flux from the ventricle dilatation to blood flow is practically balanced by the energy flux across the mitral annulus and the rate change of kinetic energy in the ventricle. In other words, the Bernoulli energy is conservative, indicating an optimal transport of blood from the left atrium to the ventricle. The dynamic and energy transfer characteristics obtained in the 2D model are in agreement with those of the 3D model. Similar dynamic and energy transfer characteristics were identified for the ejection phase of cardiac pumping of the left ventricle [

The authors declare that there is no conflict of interests regarding the publication of this paper.

The study was supported by the Nanyang Technological University, the University of Pittsburgh, the Singapore International Graduate Award to Seyed Saeid Khalafvand, and the research grant from Singapore Ministry of Health National Medical Research Council (NMRC/EDG/1037/2011) to Liang Zhong.