Ejection fraction as related to basic components in the left and right ventricular volume domains

Kerkhof, Peter L. M.; Ven, Peter M. van de; Yoo, Byung Won; Peace, Richard; Heyndrickx, Guy R.; Handly, Neal

doi:10.1016/j.ijcard.2017.09.019

Cited by 36 publications

(48 citation statements)

References 22 publications

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“…Figure 8 presents FFR against mean pressure as measured distal from the coronary stenosis, using adenosine induced hyperemia. The blue curve refers to the best fitting regression (yielding R 2 = 0.581), calculated on the basis of the theoretically derived formula FFR = P D /(c 1 +c * 2 P D ) described elsewhere (11). This approach ensures that the theoretical point where the value for FFR 8(triangles).…”

Section: Patient Studymentioning

confidence: 99%

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

Faes

Meer

Heyndrickx³

et al. 2020

Front. Cardiovasc. Med.

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Introduction: Coronary arterial stenosis may impair myocardial perfusion with myocardial ischemia and associated morbidity and mortality as result. The myocardial fractional flow reserve (FFR) is clinically used as a stenosis-specific index. Aim: This study aims to identify the relation between the FFR and the degree of coronary arterial stenosis using a simple mathematical model of the coronary circulation. Methods: A mathematical model of the coronary circulation, including an arterial stenosis of variable degree, was developed. The relation between the FFR and the degree of stenosis (defined as the fractional cross sectional area narrowing) was investigated, including the influence of the aortic and venous pressures and the capillary resistance. An additional study concerning 22 patients with coronary artery disease permits comparison of clinical data and in silico findings. Results: The FFR shows an S-shaped relationship with the stenosis index. We found a marked influence of venous and aortic pressure and capillary resistance. The FFR is accompanied by a clinically relevant co-metric (FFR C), defined by the Pythagorean sum of the two pressures in the definition formula for FFR. In the patient group the FFR C is strongly related to the post-stenotic pressure (R = 0.91). The FFR C requires establishment of a validated cutoff point using future trials. Conclusion: The S-shaped dependence of FFR on the severity of the stenosis makes the FFR a measure of the ordinal scale. The marked influences of the aortic and venous pressures and the capillary resistance on the FFR will be interpreted as significant variations in intra-and inter-individual clinical findings. These fluctuations are partly connected to the neglect of considering the FFR C. At otherwise identical conditions the FFR as measured at baseline differs from the value obtained during hyperemic conditions. This expected observation requires further investigation, as the current hyperemia based evaluation fails to take advantage of available baseline data.

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Section: Patient Studymentioning

confidence: 99%

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

Faes

Meer

Heyndrickx³

et al. 2020

Front. Cardiovasc. Med.

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“…The EF is a dimensionless ratio. This fact implies that the number (often displayed as a percentage) attached to EF per se cannot tell us anything about the order of magnitude of ESV and EDV, being the two constituting components [2]. However, as a ratio the EF can help to reduce non-random (systematic) measurement errors of volume inherent in the imaging technique [14].…”

Section: What Is Ejection Fraction?mentioning

confidence: 99%

“…The quantification of ventricular performance in research and clinical practice has steadily relied on ejection fraction (EF), with few alternative candidates [1]. A recent study explored the relative contribution of the constituent components in various patient populations, and unequivocally established that end-systolic volume (ESV) is the primary determinant of EF [2]. The other component, being end-diastolic volume (EDV), exhibits significantly (P b 0•0001) less association with EF.…”

Section: Introductionmentioning

confidence: 99%

“…Our starting point is the VRG where each combination of coordinates denoted as {EDV, ESV} refers to the individual working point for the subject studied ( Fig. 1) [1][2][3][4]. Volume data may be indexed (i) for body surface area (BSA), yielding {EDVi, ESVi}.…”

Section: Introductionmentioning

confidence: 99%

“…The interpretation of EF can best be realized in the VRG domain, where the connection between a collection of ESV(i) and EDV(i) data points is expressed as a linear relationship ESV(i) = α + β EDV(i), with intercept α and slope β [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

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The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

Kerkhof¹,

Merillon

Yoo

et al. 2018

International Journal of Cardiology

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

Mihǎileanu

Antohi

2020

ESC Heart Failure

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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.

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Ejection fraction as related to basic components in the left and right ventricular volume domains

Cited by 36 publications

References 22 publications

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

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

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