Purpose Conventional pulse-contour analysis estimates cardiac output (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation>) 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation> and vascular parameters from peripheral arterial pressure waveforms. Methods The proposed framework is based on a four-element Windkessel model reformulated through <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-parameters (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">${\alpha }_{C},{\alpha }_{R},{\alpha }_{L}, {\alpha }_{\tau }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>α</mi> <mi>C</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mi>L</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mi>τ</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>) that encapsulate arterial compliance, resistive and inertial loads, and pressure decay dynamics. Radial peripheral arterial pressure (pABP) waveforms are preprocessed, smoothed, converted into a periodic representation, and fitted to the Windkessel model to extract <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-parameters. Combined with biometric covariates, these parameters serve as inputs to a generalized linear model (Gamma distribution, identity link) trained to estimate <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation>. The estimated <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation> is subsequently reinjected into the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-parameter expressions to derive arterial compliance (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$C$</EquationSource> <EquationSource Format="MATHML"><math> <mi>C</mi> </math></EquationSource> </InlineEquation>), characteristic impedance (<InlineEquation ID="IEq11"> <EquationSource Format="TEX">${R}_{z}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>z</mi> </msub> </math></EquationSource> </InlineEquation>), distal resistance (<InlineEquation ID="IEq12"> <EquationSource Format="TEX">${R}_{dis}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">dis</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>), and inertance (<InlineEquation ID="IEq13"> <EquationSource Format="TEX">$L$</EquationSource> <EquationSource Format="MATHML"><math> <mi>L</mi> </math></EquationSource> </InlineEquation>). Results Internal validation against the EV1000 pulse-contour reference yields an <InlineEquation ID="IEq14"> <EquationSource Format="TEX">${R}^{2}=0.82$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>0.82</mn> </mrow> </math></EquationSource> </InlineEquation>, negligible bias (− 0.02 <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$\text{L}.{\text{min}}^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>L</mtext> <mo>.</mo> <msup> <mrow> <mtext>min</mtext> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>), and a percentage error (<InlineEquation ID="IEq16"> <EquationSource Format="TEX">$PE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">PE</mi> </mrow> </math></EquationSource> </InlineEquation>) of 26.17%, meeting the clinical interchangeability criterion (<InlineEquation ID="IEq17"> <EquationSource Format="TEX">$PE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">PE</mi> </mrow> </math></EquationSource> </InlineEquation> < 30%). External evaluation on an independent Vigileo dataset achieves <InlineEquation ID="IEq18"> <EquationSource Format="TEX">${R}^{2}=0.72$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>0.72</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$PE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">PE</mi> </mrow> </math></EquationSource> </InlineEquation> = 28.41% without retraining, confirming robustness across platforms. Conclusion The <InlineEquation ID="IEq20"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-parameterized Windkessel framework provides a physiologically interpretable, data-efficient, and calibration-free alternative for <InlineEquation ID="IEq21"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation> estimation. Beyond <InlineEquation ID="IEq22"> <EquationSource Format="TEX">$CO$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CO</mi> </mrow> </math></EquationSource> </InlineEquation>, it simultaneously quantifies <InlineEquation ID="IEq23"> <EquationSource Format="TEX">$C$</EquationSource> <EquationSource Format="MATHML"><math> <mi>C</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq24"> <EquationSource Format="TEX">${R}_{z}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>z</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq25"> <EquationSource Format="TEX">${R}_{dis}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">dis</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq26"> <EquationSource Format="TEX">$L$</EquationSource> <EquationSource Format="MATHML"><math> <mi>L</mi> </math></EquationSource> </InlineEquation>, 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.

A Novel Method for Cardiac Output and Vascular Parameters Estimation Using Peripheral Arterial Waveforms: Integrating Windkessel Model via $\boldsymbol{\alpha }$-parameter identification

期刊论文
发表日期：

2026年2月23日

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Rami Taheri,
Benoit Haut

摘要

Purpose

Conventional pulse-contour analysis estimates cardiac output ( $CO$ $CO$ ) 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 $CO$ $CO$ and vascular parameters from peripheral arterial pressure waveforms.

Methods

The proposed framework is based on a four-element Windkessel model reformulated through $\alpha $ $α$ -parameters ( ${\alpha }_{C},{\alpha }_{R},{\alpha }_{L}, {\alpha }_{\tau }$ $α_{C}, α_{R}, α_{L}, α_{τ}$ ) 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 $\alpha $ $α$ -parameters. Combined with biometric covariates, these parameters serve as inputs to a generalized linear model (Gamma distribution, identity link) trained to estimate $CO$ $CO$ . The estimated $CO$ $CO$ is subsequently reinjected into the $\alpha $ $α$ -parameter expressions to derive arterial compliance ( $C$ $C$ ), characteristic impedance ( ${R}_{z}$ $R_{z}$ ), distal resistance ( ${R}_{dis}$ $R_{dis}$ ), and inertance ( $L$ $L$ ).

Results

Internal validation against the EV1000 pulse-contour reference yields an ${R}^{2}=0.82$ $R^{2} = 0.82$ , negligible bias (− 0.02 $\text{L}.{\text{min}}^{-1}$ $L . {min}^{- 1}$ ), and a percentage error ( $PE$ $PE$ ) of 26.17%, meeting the clinical interchangeability criterion ( $PE$ $PE$ < 30%). External evaluation on an independent Vigileo dataset achieves ${R}^{2}=0.72$ $R^{2} = 0.72$ and $PE$ $PE$ = 28.41% without retraining, confirming robustness across platforms.

Conclusion

The $\alpha $ $α$ -parameterized Windkessel framework provides a physiologically interpretable, data-efficient, and calibration-free alternative for $CO$ $CO$ estimation. Beyond $CO$ $CO$ , it simultaneously quantifies $C$ $C$ , ${R}_{z}$ $R_{z}$ , ${R}_{dis}$ $R_{dis}$ , and $L$ $L$ , 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.

A Novel Method for Cardiac Output and Vascular Parameters Estimation Using Peripheral Arterial Waveforms: Integrating Windkessel Model via \(\boldsymbol{\alpha }\)-parameter identification

摘要