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The atrial delayed-ejection flow component comprises blood leaving the left atrium during ventricular diastole after entering during the preceding diastole or earlier. The Bäck study calls this delayed outflow. In contrast, the atrial reservoir flow component enters during the intervening ventricular systole.^[ref]

This is a transport-history definition, not a statement that ventricular electrical activation was delayed. A constructed timeline illustrates it. Number successive one-second cardiac cycles so the current ventricular systole occupies $0\le t<0.4$ s and its following diastole occupies $0.4\le t<1$ s. Suppose a parcel entered in the previous diastole at $t=-0.2$ s and crosses the mitral valve at $t=0.6$ s. Its 0.8 s passage spans a ventricular systole. A second parcel entering at $t=0.5$ s and leaving at $t=0.8$ s instead belongs to the atrial conduit flow component.

For represented parcels with exit times $t_i^{\mathrm{out}}$, entry times $t_i^{\mathrm{in}}$ and volume weights $w_i$, a volume-weighted transit time within a selected exiting category isTwo hypothetical parcels representing 1 and 3 mL and taking 0.8 and 1.2 s give $\overline{\tau }=1.1$ s, rather than the unweighted mean of 1 s. If an entry occurred before the available record, the exact transit time is unknown: an observed exit can establish a category without recovering an exact entry date.

The atrial delayed-ejection flow component thus complements the atrial retained-inflow component: one identifies an observed exit of older atrial blood, while the other identifies entered blood still present at the specified endpoint.

Atrial flow component analysis classifies blood transport through an atrium by the entry, exit and retention histories of represented fluid parcels. It asks a different question from measuring only maximum and minimum left atrium volumes: which blood passed onward, remained within the chamber, or crossed a boundary in another direction?

A primary study used time-resolved computed tomography to reconstruct moving atrial anatomy, computational fluid dynamics to estimate the flow field, and modeled particle trajectories to classify six components. It distinguished atrial conduit flow component, atrial reservoir flow component, atrial delayed-ejection flow component, atrial retained-inflow component, atrial residual-volume component and pulmonary-vein backflow component.^[ref] These are model-derived transport categories, not six separate anatomical chambers.

A typical trajectory calculation followswhere $\mathbf{u}$ is the modeled fluid velocity. Boundary crossings and their timing within a defined cardiac cycle determine the category. For example, the study's conduit definition requires entry and exit within the same ventricular diastolic phase.^[ref] Changing the time window or category definition changes what is counted.

An original weighting example shows why counting markers alone can be misleading. Suppose three modeled markers represent 1, 1 and 8 mL, with the first two assigned to one component. That component contains 2 of 10 mL, or $20\%$, although it contains two-thirds of the markers. The relevant fraction iswith $w_i$ the represented volumes for the chosen analysis. The denominator must be stated; an analysis that includes entering flow is not automatically a partition of one instantaneous chamber volume.

The results depend on reconstructed boundaries, flow assumptions, numerical tracking and phase definitions. Atrial reservoir function and atrial conduit function can be investigated with these categories, but a volumetric proxy and a parcel-based component need not be identical observations.

The atrial residual-volume component is the represented blood remaining within the left atrium throughout the two tracked cardiac cycles in the Bäck atrial flow component analysis. It differs from the atrial retained-inflow component, for which an entry during the tracked history is identified.^[ref]

The observation window is essential. Write $\Omega (t)$ for the moving atrial cavity and ${\mathbf{x}}_i(t)$ for a represented parcel's pathline. A mathematical statement of uninterrupted retention over $I$ isIf each qualifying marker represents volume $w_i$, the component volume is $V_{\mathrm{res}}={\sum }_{i\in R}{w}_i$. In a constructed example, 250 qualifying markers representing $0.008$ mL each give 2 mL. This is a weighted volume, not a count of anatomical pockets.

The classification supplies a lower bound on observed uninterrupted residence time, rather than an exact entry date. For a hypothetical two-cycle window lasting 1.6 s, a parcel present throughout has spent at least 1.6 s continuously inside by the window's end; it might have entered much earlier. Extending the window can reveal an entry or exit that a shorter window missed. In an ideal trajectory record, the set remaining throughout a longer interval is a subset of the set remaining throughout any contained shorter interval.

Retention also does not require zero velocity. A circulating parcel can remain inside the cavity while moving rapidly around a closed region. Conversely, briefly slow blood can later leave. The atrial residual-volume component, local velocity and residence time are therefore related transport descriptors with different definitions.

The atrial retained-inflow component is blood that entered the left atrium during the previous cardiac cycle but has not left by the specified endpoint of the Bäck tracking scheme. Its documented entry distinguishes it from the atrial residual-volume component, whose blood remains throughout both tracked cycles.^[ref]

A simple parcel ledger makes the distinction concrete. In a constructed one-second cardiac cycle, let a tracked parcel enter through a pulmonary vein at $t=0.4$ s during the first of two cycles and remain inside until observation ends at $t=2$ s. Its observed residence time at that endpoint is 1.6 s. If that parcel crosses the mitral valve at $t=2.2$ s, a later observation reveals an exit; the earlier record was still correctly classified for its own endpoint.

Different amounts of retention need not produce different instantaneous chamber volumes. Consider two ideal histories, each with 40 mL inside the left atrium at the endpoint. In the first, 10 mL has an observed entry during the designated earlier cycle and remains, while 30 mL was present throughout the entire tracking window. In the second, the corresponding volumes are 25 and 15 mL. Both chamber totals are 40 mL, but their atrial retained-inflow component and atrial residual-volume component differ. A chamber outline alone cannot distinguish these histories.

The component is consequently useful for asking about replacement of atrial blood, alongside atrial delayed-ejection flow component and atrial conduit flow component. Its measured or modeled fraction must identify both the tracking interval and denominator. Dividing 10 mL by a 40 mL chamber volume gives $25\%$; dividing it by a stipulated 80 mL cycle throughput gives $12.5\%$. Those percentages express different comparisons.