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 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 À 1) is reducible to a fundamental property of Phi: 1/Φ = (Φ À 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.

Clinical implication of intraoperative ventricular‐arterial coupling in pediatric patients undergoing ventricular septal defects repair: A retrospective cohort study

“…24 The recent studies also showed that the oversimplified metric such as ESP/ESV-based methods could not substitute the modified single-beat method for the assessment of VAC in critically ill patients, and the simplified Ea formula is another caveat in understanding VAC as the relationship between heart and periphery. 25,26 Therefore, potential inaccuracies may exist. Nonetheless, our results clearly showed that a large population of pediatric patients undergoing VSDs repair has disproportionately elevated Ea to Ees after CPB and that the increase in simplified VAC is associated significantly with poor postoperative outcomes.…”

Overcoming the Limits of Ejection Fraction and Ventricular-Arterial Coupling in Heart Failure

“…However, its significance is controversial, as Vo is only a virtual theoretical value, extrapolated from research invasive studies. Meanwhile, available Vo formulas derived from single-beat determinations non-invasive data have wide, uncertain margins (24).…”

“…However, VAC has a more dynamic behavior than LVEF being a valuable tool in heart failure with reduced ejection fraction (HFrEF) and/or unstable hemodynamic situations. LVEF and VAC have a well-proven negative correlation but are not reducible to a simple formula (24). Less frequently, the VAC is calculated by the inverse ratio (Ees/Ea), the relation between the two ratios being like comparing x to 1/x.…”

La serendipia en torno la fracción de eyección: una revisión de la historia, la casualidad y la cuasi-funcionalidad de una métrica aplaudida

“…Claramente, la inclusión de cualquier variable clínicamente relevante, compensa la pérdida inherente al uso focalizado de la FE. Algunos ejemplos, se refieren al uso del acoplamiento ventrículo-arterial 7 , el VFS 27 , o la masa miocárdica 28 . Incluso, cuando se estudia pacientes con insuficiencia cardíaca con FE de rango medio, entre 40-50% (ver triángulo de color púrpura en la Figura 4), se ha documentado una enorme heterogeneidad, lo que desvía la atención a otros factores, más allá del uso de la Figura 6.…”

“…Algunas discusiones críticas sobre la FE, se han publicado recientemente en la literatura 6,7 , y es de esperar que tales advertencias se mantengan, hasta que el defecto fundamental de la FE sea reconocido. En el presente artículo, se analiza la estructura matemática de la relación FE y se discuten sus implicancias.…”