4D flow MRI has been used to quantify normal and deranged left ventricular blood flow characteristics on the basis of functionally distinct flow components [1,2]. However, although several studies have used 4D flow MRI to describe general atrial flow patterns [3-7], the identification of functionally distinct subsets of atrial blood flow is unexplored. Compartmental analysis of left atrial blood flow is challenging as the left atrium lacks a cardiac phase in which it contains all blood involved in a cardiac cycle, as is the case for the left ventricle. This means that the inflowing blood from the pulmonary veins have to be included in the analysis, which has been difficult with particle traces that represent different volumes of blood.

The aim of this study was to develop a novel fixed-volume approach for particle tracing and employ this to develop quantitative analysis of 4D blood flow characteristics in the left atrium (LA).

Fixed volume particle trace emission: Time-resolved 3D particle traces (pathlines) are commonly emitted from a plane grid at fixed time-intervals. With this fixed time-interval approach, each emitted particle represents a different volume and this makes the visual interpretation of the particle traces ambiguous. Here, we propose emission of particles with the same volume. In this fixed volume approach, the emission time step Δt at time t is derived by solving the flux equation Δt = V/(A|v(t)|) where V is the pre-determined fixed volume of blood to be represented by each particle, A is the area of each emitter, and |v(t)| is the instantaneous flow velocity in the plane’s normal direction.

LA flow analysis: Particle traces with fixed volume were emitted from all pulmonary veins throughout one complete cardiac cycle, starting at the time of onset systole. The particles were traced until end diastole, at which time their position was mapped against segmentations of the LA and left ventricle in order to differentiate LA flow into:
* Direct flow = particle traces that enter and leave the atrium in one heart beat
* Retained flow = particle traces that enter the atrium and remains there for one cardiac cycle
* Reversed flow = particle traces that enter the atrium but travel back out into a pulmonary vein. These traces were excluded from further analysis.

Particle traces that at some point during the analysis were outside of the left atrium were considered aberrant traces and were excluded from further analysis. The computation and analysis of particle traces were implemented in Matlab.

MRI data: The proposed LA flow analysis method was applied in three male normal volunteers in which 4D flow and morphological MRI data was acquired at a 1.5T scanner (Philips Achieva, Philips Healthcare, Best, the Netherlands). The 4D flow data were acquired with spatial resolution = 3x3x3 mm³, temporal resolution = 50 ms, and VENC = 100 cm/s [2].

Data analysis: To confirm that particle tracing with the proposed fixed volume approach accurately captures the blood volume of interest, the blood volume captured by the method was compared against the net stroke volume, obtained by 2D phase-contrast MRI in the ascending aorta. The direct and retained flows were visualized in each volunteer and their respective volume and kinetic energy were computed.

A visualization of LA flow components for one representative volunteer is shown in Figure 1, with flow separated into direct (green) and retained (yellow) flow components. Beginning in early ventricular systole (a), flow enters the atrium and engages with residual blood volume (not visualized) to form a vortex (b). In early diastole during early ventricular filling (c), the organized vortical flow is extinguished, followed by formation of a second transient atrial vortex (d). Finally, in late diastole during atrial contraction, a second acceleration of blood into the ventricle is seen (e). The direct and retained flow components were between 44-57% and 43-56% of the stroke volume, respectively (Table 1). The total blood volume sampled by the fixed volume approach compared favorably against through-plane flow measurements in the aorta (Table 1). Inflow volumes and kinetic energy for the direct and retained flow components are shown in Figures 2 and 3.The proposed fixed volume approach for emission of particle traces permits sampling of LA blood volumes and intuitive visualizations where each trace represents the same volume. Using fixed-volume particle traces, LA flow can be separated into different components based on the transit of blood through the LA. Quantitative analysis of functionally distinct subsets of LA flow may provide new perspectives on LA function in health and disease.