Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling
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–art...
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| Published in | ESC Heart Failure Vol. 7; no. 5; pp. 2214 - 2222 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
England
John Wiley & Sons, Inc
01.10.2020
John Wiley and Sons Inc Wiley |
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| 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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| AbstractList | 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. 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. 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. 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. 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. 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. |
| Author | Mihaileanu, Serban Antohi, Elena‐Laura |
| AuthorAffiliation | 3 University for Medicine and Pharmacy ‘Carol Davila’ Bucharest Romania 2 Emergency Institute for Cardiovascular Diseases ‘C.C. Iliescu’ Bucharest Romania 1 Institut Mutualiste Montsouris Paris France |
| AuthorAffiliation_xml | – name: 1 Institut Mutualiste Montsouris Paris France – name: 2 Emergency Institute for Cardiovascular Diseases ‘C.C. Iliescu’ Bucharest Romania – name: 3 University for Medicine and Pharmacy ‘Carol Davila’ Bucharest Romania |
| Author_xml | – sequence: 1 givenname: Serban surname: Mihaileanu fullname: Mihaileanu, Serban organization: Institut Mutualiste Montsouris – sequence: 2 givenname: Elena‐Laura surname: Antohi fullname: Antohi, Elena‐Laura email: laura.antohi@gmail.com organization: University for Medicine and Pharmacy ‘Carol Davila’ |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/32686316$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1111_pan_14277 crossref_primary_10_1186_s40635_024_00642_7 crossref_primary_10_1016_j_atherosclerosis_2023_04_010 crossref_primary_10_3389_fcvm_2022_948231 crossref_primary_10_1002_jum_16285 crossref_primary_10_1016_j_hlc_2023_12_014 crossref_primary_10_1016_j_ejphar_2022_175014 crossref_primary_10_1142_S2810958923300032 crossref_primary_10_1177_10781552221118530 crossref_primary_10_1016_j_jacadv_2023_100431 crossref_primary_10_3389_fcvm_2021_750965 crossref_primary_10_1186_s40560_024_00730_6 crossref_primary_10_47803_rjc_2021_31_2_351 |
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| Copyright | 2020 The Authors. ESC Heart Failure published by John Wiley & Sons Ltd on behalf of the European Society of Cardiology 2020 The Authors. ESC Heart Failure published by John Wiley & Sons Ltd on behalf of the European Society of Cardiology. 2020. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Keywords | Effective arterial elastance Left ventricle elastance Phi number Ventricular-arterial coupling Left ventricular ejection fraction |
| Language | English |
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| Snippet | 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... 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... 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... 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... |
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| SubjectTerms | Effective arterial elastance Ejection fraction Heart failure Left ventricle elastance Left ventricular ejection fraction Phi number Review Reviews Sepsis Ventricular–arterial coupling |
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| Title | Revisiting the relationship between left ventricular ejection fraction and ventricular–arterial coupling |
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