Calibration-Free Method for Cardiac Output and Vascular Profiling via Windkessel 𝛂-Parameterization

Abstract

Aims: Conventional pulse-contour analysis estimates cardiac output (𝐶𝑂) from arterial pressure waveforms but relies on empirical or calibrated mappings, reducing waveform morphology to a scalar estimate with limited physiological interpretability. We propose a framework based on a structurally identifiable reformulation of the Windkessel model. Four 𝛼-parameters are derived, each encoding a distinct morphological feature of the radial pressure waveform, enabling calibration-free 𝐶𝑂 estimation and simultaneous vascular parameter quantification. Methods: A four-element Windkessel model of the arterial circulation was reformulated to yield four structurally identifiable parameters: 𝛼𝐶 (compliance pulsatility), 𝛼𝑅 (systolic pressure load), 𝛼𝐿 (early-systolic inertial rise rate), and 𝛼𝜏 (diastolic time constant). These were extracted by fitting preprocessed radial arterial pressure (pABP) waveforms to the reformulated model and, combined with biometric covariates, used as inputs to a generalized linear model (GLM) for 𝐶𝑂 estimation, trained on 3,077 waveforms from 380 patients (VitalDB; EV1000/FloTrac comparator) and validated on 510 Vigileo waveforms without retraining. Results: 𝐶𝑂 estimation yielded 𝑅2 = 0.82, bias = −0.02 L.min−1, and percentage error 𝑃𝐸 = 26%, satisfying the interchangeability criterion (𝑃𝐸 < 30%); external validation on Vigileo without retraining gave 𝑅2 = 0.72 and 𝑃𝐸 = 28%. Arterial compliance (𝐶), impedance (𝑅𝑧), resistance (𝑅𝑑𝑖𝑠), and inertance (𝐿) were simultaneously recovered (𝑅2 = 0.82−0.93). Patient-specific 𝛼-profiles revealed mechanistically distinct phenotypes: stiffness-dominated loading (elevated 𝛼C, 𝛼𝑅) in chronic kidney disease, and a reservoir-driven pattern (prolonged 𝛼τ, reduced 𝛼L) in elderly isolated systolic hypertension. Conclusion: Our method transforms peripheral arterial pressure waveforms into mechanistically interpretable hemodynamic descriptors (𝛼-parameters). Beyond calibration-free 𝐶𝑂 estimation, it simultaneously quantifies 𝐶, 𝑅𝑧, 𝑅𝑑𝑖𝑠, and 𝐿, while patient-specific 𝛼-profiles characterize the vascular mechanisms shaping waveform morphology. This provides a mechanistic complement to scalar 𝐶𝑂 monitoring for hemodynamic assessment in perioperative and critical care settings (Taheri & Haut, Ann. Biomed. Eng., 2026).