A Novel Method for Cardiac Output and Vascular Parameters Estimation Using Peripheral Arterial Waveforms: Integrating Windkessel Model via <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>α</mi></mrow> </math> -parameter identification.

Abstract

Conventional pulse-contour analysis estimates cardiac output ( <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> ) from arterial pressure waveforms but often relies on demographic calibration or black-box modeling, which limits physiological interpretability and generalizability. This study aims to develop and validate a structurally identifiable model that simultaneously estimates <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> and vascular parameters from peripheral arterial pressure waveforms. The proposed framework is based on a four-element Windkessel model reformulated through <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> -parameters ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>α</mi> <mi>C</mi></msub> <mo>,</mo> <msub><mi>α</mi> <mi>R</mi></msub> <mo>,</mo> <msub><mi>α</mi> <mi>L</mi></msub> <mo>,</mo> <msub><mi>α</mi> <mi>τ</mi></msub> </mrow> </math> ) that encapsulate arterial compliance, resistive and inertial loads, and pressure decay dynamics. Radial peripheral arterial pressure (pABP) waveforms are preprocessed, smoothed, converted into a periodic representation, and fitted to the Windkessel model to extract <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> -parameters. Combined with biometric covariates, these parameters serve as inputs to a generalized linear model (Gamma distribution, identity link) trained to estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> . The estimated <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> is subsequently reinjected into the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> -parameter expressions to derive arterial compliance ( <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> ), characteristic impedance ( <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi> <mi>z</mi></msub> </math> ), distal resistance ( <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi> <mrow><mi>dis</mi></mrow> </msub> </math> ), and inertance ( <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> ). Internal validation against the EV1000 pulse-contour reference yields an <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msup><mrow><mi>R</mi></mrow> <mn>2</mn></msup> <mo>=</mo> <mn>0.82</mn></mrow> </math> , negligible bias (- 0.02 <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>L</mtext> <mo>.</mo> <msup><mrow><mtext>min</mtext></mrow> <mrow><mo>-</mo> <mn>1</mn></mrow> </msup> </mrow> </math> ), and a percentage error ( <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>PE</mi></mrow> </math> ) of 26.17%, meeting the clinical interchangeability criterion ( <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>PE</mi></mrow> </math> < 30%). External evaluation on an independent Vigileo dataset achieves <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msup><mrow><mi>R</mi></mrow> <mn>2</mn></msup> <mo>=</mo> <mn>0.72</mn></mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>PE</mi></mrow> </math> = 28.41% without retraining, confirming robustness across platforms. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> -parameterized Windkessel framework provides a physiologically interpretable, data-efficient, and calibration-free alternative for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> estimation. Beyond <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>CO</mi></mrow> </math> , it simultaneously quantifies <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi> <mi>z</mi></msub> </math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi> <mrow><mi>dis</mi></mrow> </msub> </math> , and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> , offering a comprehensive and mechanistically grounded hemodynamic profile from a single peripheral arterial pressure signal, suitable for real-time integration into perioperative and critical care monitoring.