Structural identifiability of single-beat estimation of the ventricular end-systolic pressure–volume relationship

Single-beat (SB) approaches for estimating the end-systolic pressure-volume relationship (ESPVR) from a single pressure-volume (P-V) loop are widely used in experimental and clinical research, yet their structural foundations remain insufficiently formalized. ESPVR is a phenomenological construct defined from multi-beat (MB) measurements across varying loading conditions, and its SB estimation therefore constitutes an inverse problem. We show that SB estimation of the ESPVR slope (Ees) is intrinsically underdetermined, as a single P-V loop provides fewer independent constraints than unknown parameters. Consequently, any SB method requires auxiliary information to achieve mathematical closure. Using nine high-fidelity P-V loops obtained during vena cava occlusion in a porcine model as a demonstrator dataset, we quantify (i) the sensitivity of the MB-derived Ees,MB to the selection of the P-V loop subset, and (ii) the sensitivity of Ees to representative classes of auxiliary information. The analysis reveals that auxiliary information based solely on population-averaged normalized elastance curves is structurally inconsistent with the MB reference definition. Among the examined candidates, the normalized elastance at the onset of ejection (EN,dia) exhibits the most favorable structural properties, combining low sensitivity of Ees to estimation errors with a strong empirical association captured by regression modeling. By reframing SB estimation of ESPVR as a structural identifiability problem rather than a purely numerical task, this study establishes criteria for physiologically consistent auxiliary relations and highlights the necessity of large, standardized MB databases for future data-driven SB methodologies. .