= Atrial residual-volume component
The \b[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.<Comprehensive left atrial flow component analysis reveals abnormal flow patterns in paroxysmal atrial fibrillation by Sophia Bäck and others>[Methods, Flow Component Analysis; Figure 1]{ref}
The observation window is essential. Write $\Omega(t)$ for the moving atrial cavity and $\boldsymbol x_i(t)$ for a represented parcel's <pathline>. A mathematical statement of uninterrupted retention over $I$ is
$$
\boldsymbol x_i(t)\in\Omega(t)\quad\text{for every }t\in I.
$$
If each qualifying marker represents volume $w_i$, the component volume is $V_{\rm res}=\sum_{i\in R}w_i$. 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.
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