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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Format: | Article |
Language: | English |
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Wiley
2020-10-01
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Series: | ESC Heart Failure |
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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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format | Article |
id | doaj.art-2f8e78f06e1f4588bc04b83fec71c844 |
institution | Directory Open Access Journal |
issn | 2055-5822 |
language | English |
last_indexed | 2024-12-19T21:31:55Z |
publishDate | 2020-10-01 |
publisher | Wiley |
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series | ESC Heart Failure |
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 |