Table 1 Main properties of intracardiac vortex, energy and hemodynamic forces

Vortex area (VA, cm²) and VA index (VAi, dimensionless)

It can be measured at specific point in time or throughout the cardiac cycle (total vortex area). The VAi is the ratio between the total vortex area and the LV area.

VAi = total VA/LV area.

Vortex length index (VLi, dimensionless)

It can be measured at specific point in time or throughout the cardiac cycle (total vortex length). The VLi is the ratio between the total vortex length and the LV length.

VLi = total vortex length/LV length.

Vortex depth index (VDi, dimensionless)

It is the vertical position of the center of the vortex (the distance of its center from the mitral annular plane) relative to the LV long-axis.

VDi = distance of vortex center from LV base/LV long-axis

Vortex circulation (cm²/s). If normalized with the LV total vorticity, it is dimensionless.

It is the integral of the vorticity inside the vortex. It may refer to the clockwise (CW) or counterclockwise (CCW) vortex.

Circulation = vortex vorticity/LV total vorticity.

Vortex strength (VS) or intensity (VI, cm²/s)

It is the total amount of vortex vorticity. It refers to the sum of the CW and CCW vortex circulation.

VS = CW circulation + CCW circulation.

Vortex formation time (VFT, dimensionless)

It is a measure of fluid propagation efficiency through the LV and therefore an indicator of overall cardiac health. It quantifies the process of vortex ring formation in the LV.

VFT = 4 × (1 - β) / π x α³ x LV-EF

Kinetic energy (KE, mJ) and KE index (KEi, mJ/ml)

It is the KE contained in the LV cavity area (in two-dimensional images) or volume (in three‐dimensional images). It can be normalized with the LV area/volume, to give average KE and remove dependence from the LV size. The KE of the intraventricular flow depends on blood flow velocity and density.

KE = integral over the LV cavity of 1/2ρ (vx² + vy² + vz²), where vz is present only in three-dimensional analysis; ρ is the blood density (ρ = 1050 Kg/m³).

Viscous KE dissipation (kED) or loss (kEL, mW/m or J/m·s) or kED index (kEDi, dimensionless).

It is the amount of KE, ΔKE, dissipated into the heart (by viscous friction) during the cardiac cycle. The total KE dissipation is the value integrated over the entire LV; it can be normalized with the average KE (kEDi) to avoid direct dependence from the LV size.

kEDi = integral over the LV cavity and over the heartbeat of the rate of KE dissipation (double scalar product of deformation and stress tensors).

Flow force angle φ or flow momentum angle (degrees)

Quantitative parameter describing the orientation of the LV hemodynamic forces, that is, the dominant direction of flow momentum identified by an average angle, that lies between 0° (corresponding to longitudinal forces) and 90° (when forces are transverse). Longitudinally oriented hemodynamic forces (directed along the “base-to‐apex” axis) dominate in the normal LV during both systole and diastole, concordant with the predominant directions of acceleration/ deceleration of the LV inflow through the mitral valve and outflow through the aortic valve. In a pathologically asynchronous condition, the hemodynamic forces develop transverse components (generally from the infero-posterior to the antero-septal wall of the LV) and the flow force angle increases.

The angle φ is obtained by sin²φ by the integral during the heartbeat of F x sin²θ, normalized by the integral of F, where F(t) and θ(t) are the magnitude and orientation respect to the LV axis, of the force at every instant during the heartbeat.