= Atrial flow component analysis
\b[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>.<Comprehensive left atrial flow component analysis reveals abnormal flow patterns in paroxysmal atrial fibrillation by Sophia Bäck and others>[Abstract; Methods, flow-component definitions]{ref} These are model-derived transport categories, not six separate anatomical chambers.
A typical trajectory calculation follows
$$
\frac{d\boldsymbol x}{dt}=\boldsymbol u(\boldsymbol x,t),
$$
where $\boldsymbol u$ 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.<Comprehensive left atrial flow component analysis reveals abnormal flow patterns in paroxysmal atrial fibrillation by Sophia Bäck and others>[Abstract and component definitions]{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 is
$$
f_k=\frac{\sum_{i\in k}w_i}{\sum_iw_i},
$$
with $w_i$ 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.
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