Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling

Abstract The aim of this article was to analyse in‐depth the relationship between left ventricular (LV) ejection fraction (EF) (LVEF) and the most commonly used formulas for the calculation of LV elastance (Ees), volume intercept at 0 mmHg pressure (V0), effective arterial elastance (Ea), and ventri...

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Main Authors: Serban Mihaileanu, Elena‐Laura Antohi
Format: Article
Language:English
Published: Wiley 2020-10-01
Series:ESC Heart Failure
Subjects:
Online Access:https://doi.org/10.1002/ehf2.12880
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author Serban Mihaileanu
Elena‐Laura Antohi
author_facet Serban Mihaileanu
Elena‐Laura Antohi
author_sort Serban Mihaileanu
collection DOAJ
description Abstract The aim of this article was to analyse in‐depth the relationship between left ventricular (LV) ejection fraction (EF) (LVEF) and the most commonly used formulas for the calculation of LV elastance (Ees), volume intercept at 0 mmHg pressure (V0), effective arterial elastance (Ea), and ventricular–arterial coupling (VAC) as are validated today. We analyse the mathematical resulting consequences, raising the question on the physiological validity. To our knowledge, some of the following mathematical consequences have never been published. On the basis of studies demonstrating that normal LV dimensions and LVEF have a Gaussian unimodal distribution, we considered that the normal modal LVEF is 62% or very close to it. Expressed as a fraction, it is 0.62, that is, the reciprocal of the Phi number (namely, 1/Φ ~ 0.618). Applying Euclid's mathematical law on the extreme and mean ratio (the golden ratio), we studied the LVEF–VAC relationship in normal hearts. The simplification of the VAC formula (with V0 = 0) leads to false physiological results; V0 extraction from single‐beat Chen's formula leads to high negative results in normal subjects; based on the Euclid law, LVEF and Ea/Ees will be equal for a ratio value of 0.618 (62%) where V0 cannot be different from 0 mL; LVEF and VAC inverse relationship formula (Ea/Ees = 1/LVEF − 1) is reducible to a fundamental property of Phi: 1/Φ = (Φ − 1), being valid only if LVEF = VAC at a 0.618 value; according to this restriction, Vo can only be 0 mL, thus describing a very limited range. The Ea/Ees ratio, owing to its mathematical more dynamic behaviour, can be more sensitive than LVEF, being a valuable clinical tool in patients with heart failure (HF) with reduced EF, acute unstable haemodynamic situations, where Ees and Ea variations are disproportionate. However, the application is doubtful in HF with preserved EF where Ees and Ea may have same‐direction augmentation. The modified VAC formula suffers from oversimplification, reducing it to a dimensionless ratio, which is supposed to approximate non‐linear time‐varying functions. Thus, we advocate for caution and in‐depth understanding when using simplified formulas in clinical practice.
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spelling doaj.art-2f8e78f06e1f4588bc04b83fec71c8442022-12-21T20:04:53ZengWileyESC Heart Failure2055-58222020-10-01752214222210.1002/ehf2.12880Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial couplingSerban Mihaileanu0Elena‐Laura Antohi1Institut Mutualiste Montsouris Paris FranceEmergency Institute for Cardiovascular Diseases ‘C.C. Iliescu’ Bucharest RomaniaAbstract The aim of this article was to analyse in‐depth the relationship between left ventricular (LV) ejection fraction (EF) (LVEF) and the most commonly used formulas for the calculation of LV elastance (Ees), volume intercept at 0 mmHg pressure (V0), effective arterial elastance (Ea), and ventricular–arterial coupling (VAC) as are validated today. We analyse the mathematical resulting consequences, raising the question on the physiological validity. To our knowledge, some of the following mathematical consequences have never been published. On the basis of studies demonstrating that normal LV dimensions and LVEF have a Gaussian unimodal distribution, we considered that the normal modal LVEF is 62% or very close to it. Expressed as a fraction, it is 0.62, that is, the reciprocal of the Phi number (namely, 1/Φ ~ 0.618). Applying Euclid's mathematical law on the extreme and mean ratio (the golden ratio), we studied the LVEF–VAC relationship in normal hearts. The simplification of the VAC formula (with V0 = 0) leads to false physiological results; V0 extraction from single‐beat Chen's formula leads to high negative results in normal subjects; based on the Euclid law, LVEF and Ea/Ees will be equal for a ratio value of 0.618 (62%) where V0 cannot be different from 0 mL; LVEF and VAC inverse relationship formula (Ea/Ees = 1/LVEF − 1) is reducible to a fundamental property of Phi: 1/Φ = (Φ − 1), being valid only if LVEF = VAC at a 0.618 value; according to this restriction, Vo can only be 0 mL, thus describing a very limited range. The Ea/Ees ratio, owing to its mathematical more dynamic behaviour, can be more sensitive than LVEF, being a valuable clinical tool in patients with heart failure (HF) with reduced EF, acute unstable haemodynamic situations, where Ees and Ea variations are disproportionate. However, the application is doubtful in HF with preserved EF where Ees and Ea may have same‐direction augmentation. The modified VAC formula suffers from oversimplification, reducing it to a dimensionless ratio, which is supposed to approximate non‐linear time‐varying functions. Thus, we advocate for caution and in‐depth understanding when using simplified formulas in clinical practice.https://doi.org/10.1002/ehf2.12880Left ventricular ejection fractionVentricular–arterial couplingLeft ventricle elastanceEffective arterial elastancePhi number
spellingShingle Serban Mihaileanu
Elena‐Laura Antohi
Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
ESC Heart Failure
Left ventricular ejection fraction
Ventricular–arterial coupling
Left ventricle elastance
Effective arterial elastance
Phi number
title Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
title_full Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
title_fullStr Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
title_full_unstemmed Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
title_short Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
title_sort revisiting the relationship between left ventricular ejection fraction and ventricular arterial coupling
topic Left ventricular ejection fraction
Ventricular–arterial coupling
Left ventricle elastance
Effective arterial elastance
Phi number
url https://doi.org/10.1002/ehf2.12880
work_keys_str_mv AT serbanmihaileanu revisitingtherelationshipbetweenleftventricularejectionfractionandventriculararterialcoupling
AT elenalauraantohi revisitingtherelationshipbetweenleftventricularejectionfractionandventriculararterialcoupling