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 (E_es) is intrinsically underdetermined, as a singleP-Vloop provides fewer independent constraints than unknown parameters. Consequently, any SB method requires auxiliary information to achieve mathematical closure. Using nine high-fidelityP-Vloops obtained during vena cava occlusion in a porcine model as a demonstrator dataset, we quantify (i) the sensitivity of the MB-derivedE_es,MBto the selection of theP-Vloop subset, and (ii) the sensitivity ofE_esto 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 (E_N,dia) exhibits the most favorable structural properties, combining low sensitivity ofE_esto 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.