Vector flow mapping is a novel technology that enables the evaluation of intracardiac flow and calculation of energy loss and kinetic energy [3]. This technology uses both color Doppler and speckle tracking images applied to continuity equation from the left and right boundaries. The calculated velocity vectors are integrated according to a weight function [4, 5]. Intracardiac energy loss can be calculated using the following equation [5]:
$$ \boldsymbol{Energy}\boldsymbol{Loss}=\int \mu \left\{2{\left(\frac{\partial u}{\partial x}\right)}^2+2{\left(\frac{\partial v}{\partial y}\right)}^2+{\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\right)}^2\right\} dA, $$
where μ is the viscosity of blood, u and v are velocity components along the Cartesian axes (x and y), and A is the area of the unit of the grid.
As the equation indicates, energy loss is the total of squared differences between neighboring velocity vectors which were calculated by vector flow mapping method. It increases with a change in the size and direction of the velocity vectors. For example, energy loss is likely to increase due to turbulent flow caused by factors such as aortic stenosis or an unnatural intracardiac vortex due to surgery [6,7,8].
The kinetic energy of the left ventricular outflow tract can be calculated from the following equation:
$$ \boldsymbol{KE}=\int \frac{1}{2}\rho {v}^2\times vdL, $$
where ρ is the density of blood (1060 kg/m3), v is the velocity vector of the blood flow, and dL is an increment of the cross-sectional line.
Energy loss is considered to be related to prognosis [9]. It is important to take into account the changes in energy loss and kinetic energy postoperatively because both these parameters show an increase in the hyperdynamic state [6].
Staged palliative surgery markedly shifts the balance of volume load on a single ventricle and pulmonary vascular bed. After BTS, a single ventricle serves an important role in both systemic and pulmonary circulations; this ventricle becomes hyperdynamic and the volume load increases as the hemodynamic parameters indicate in Table 1. Energy loss and kinetic energy increase due to the hyperdynamic state. Conversely, after BCPS, the single ventricle is not involved in pulmonary circulation; it becomes hypodynamic and the volume load decreases as the hemodynamic parameters indicate in Table 1. Energy loss and kinetic energy decrease due to the hypodynamic state [10, 11]. These volume loads are difficult to detect using classic hemodynamic parameters. However, we could detect these volume loads using vector flow mapping in terms of energetic performance. After BTS, the increase in kinetic energy (35.6 mW/m to 83.8 mW/m) exceeded the increase in energy loss (29.4 mW/m to 41.9 mW/m) because the single ventricle was additionally involved in pulmonary circulation. Conversely, after BCPS, the single ventricle became hypodynamic, which decreased both energy loss and kinetic energy. The decrease in kinetic energy (127.4 mW/m to 62.0 mW/m) exceeded the decrease in energy loss (38.3 mW/m to 30.7 mW/m) due to the release from pulmonary circulation. Although energy loss is wasted energy, volume loading condition could be estimated by energy loss combined with kinetic energy.
