= Atrial conduit function
\b[Atrial conduit function] is the passive passage of returning <blood> through an atrium toward the ventricle, distinguished from temporary storage in <atrial reservoir function> and active pumping in <atrial booster-pump function>. For the <left atrium>, the pathway connects <pulmonary vein> inflow with <mitral valve> outflow during ventricular filling.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§19.1, Left Atrium; §19.3, Cardiac Cycle]{ref}
Two measurement descriptions need to be distinguished. A volumetric account compares chamber-volume changes with total ventricular filling. A parcel-based account asks when particular modeled <blood> enters and leaves the <left atrium>. A primary study defined conduit flow as entry and exit within the same ventricular diastolic phase and compared such components with volumetric indices.<Comprehensive left atrial flow component analysis reveals abnormal flow patterns in paroxysmal atrial fibrillation by Sophia Bäck and others>[Abstract; flow-component definitions; Figure 7]{ref} The operational definition determines what is counted.
An original bookkeeping model illustrates the volumetric approach. Suppose a periodic system has ventricular <stroke volume> $S$, and suppose a reservoir release $R$ and direct onward passage $C$ form a complete, nonoverlapping partition of that delivered volume. Then
$$
S=R+C,\qquad C=S-R.
$$
If a further idealization identifies $R$ with the atrial excursion $V_{\max}-V_{\min}$, values $S=80$ mL and an excursion of 30 mL give a conduit proxy of 50 mL. The arithmetic is exact for the stipulated partition; the correspondence between that partition and real trajectories is an additional assumption.
For example, simultaneous inflow and outflow can exchange <blood> while chamber volume remains constant. In the balance $dV/dt=Q_{\rm in}-Q_{\rm out}$, equal 100 mL/s flows give zero volume change even though 20 mL passes in 0.2 s. Thus a flat volume trace does not demonstrate absent transport. Geometry, timing and modeled parcel histories supply information that volume extrema alone cannot provide.
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