The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction.

BACKGROUND: Quantification of ventricular performance requires a comprehensive metric which is manageable for patient care and clinical trials. Ejection fraction (EF) has been embraced as an attractive candidate. However, being a dimensionless ratio, EF has serious limitations. METHODS: We aim to identify what information is not recognized when limiting the volume-related analysis by exclusively relying on EF. This investigation applies the volume domain concept, relating end-systolic volume (ESV) to end-diastolic volume (EDV). This approach allows graphical identification of the information not covered by EF. Implications for atria, left ventricle (LV) and right ventricle (RV) are investigated in healthy individuals, and cardiac patient groups using various imaging modalities. RESULTS: The Pythagorean theorem indicates that the hypotenuse which relates any {EDV, ESV} combination to EF corresponds with the information not covered by the single metric EF. The impact of the recovered EF companion (EFC) is illustrated in healthy adults (N = 410, LV 2D echocardiography), heart transplant patients (N = 101, LV CT), individuals with heart failure (N = 197, biplane angiocardiography), for the RV with corrected Fallot (N = 124, MRI), diameters for left atrium (N = 49, MRI) and area for right atrium (N = 51, MRI). For any limited EF range we find a spectrum of EFC values, showing that the two metrics contain (partly) independent information, and emphasizing that the sole use of EF only partially conveys the full information available. CONCLUSIONS: The EFC is a neglected companion, containing information which is additive to EF. Analysis based on ESV and EDV is preferred over the use of EF.

Monte Carlo method applied to the evaluation of the relationship between ejection fraction and its constituent components.

Ventricular function is routinely assessed by applying the clinically accepted metric ejection fraction (EF). The numerical value of EF depends on the interplay between end-systolic volume (ESV) and end-diastolic volume (EDV). The relative impact of the two constitutive components has received little attention. Pediatric cardiologists are interested in EF vs ESV when evaluating various congenital abnormalities. Following successful surgical intervention of Fallot tetralogy, many of these patients receive follow-up, not only during childhood, but also when being adults. Cardiologists diagnosing and treating elderly patients often analyze EF vs EDV, notably for phenotyping heart failure patients. Therefore, we study EF vs ESV as well as EF vs EDV in more detail. We explore the fundamentals of EF while analyzing a Fallot patient group. Three routes were followed, namely nonlinear regression, by implementing a Monte Carlo approach to generate EDV on the basis of known ESV values, and by using a theoretical graphical derivation. Our MRI-based post Fallot repair study includes left (LV) and right ventricular (RV) data (N=124). Using a robust approach we employed nonlinear regression with ESV as an independent variable. EDV was also assessed by Monte Carlo generated values for stroke volume within a physiological range. In all cases ESV emerges as the dominant component of EF, with less (P<;0.0001) impact of EDV. Using three independent routes we demonstrate that values for EF primarily depend on the corresponding ESV. This relationship is nonlinear, and correlation is always better with ESV compared to EDV in these patients, and confirmed in random number modeling studies.

Left ventricular performance is closely related to the physical properties of the arterial system: Landmark clinical investigations in the 1970s and 1980s.

Left ejection fraction (LVEF)--resulting from the difference between end-diastolic volume (EDV) and end-systolic volume (ESV), divided by EDV--is a poor index of left ventricular (LV) systolic performance due to its dependency on load conditions, inotropic state and LV remodelling. The characteristic impedance of the ascending aorta (Zc) integrates factors opposing LV ejection during the early ejection period when arterial wave reflection can be neglected. Zc is related to the pressure wave velocity (C) and the cross-sectional area of the aorta. The aim is to demonstrate that LV performance and geometry are closely related to the physical properties of the arterial system. LV pressure-volume loops were obtained from simultaneous measurements of LV (or aortic) pressure and LV volume. The slope Ees (also called LV end-systolic elastance) of the ESP-ESV relationship was assessed. Aortic diameters, pressure and flow measurements were synchronized to evaluate C, aortic forward and backward pressure waves, the elasticity of the aorta (Ep) and thereby Zc. In contrast to LVEF, LV end-systolic elastance (Ees), which reflects the stiffness of the chamber at maximal myofilament activation, is relatively insensitive to load conditions and may be considered as an index of ventricular chamber contractility. For a given Ees value, the end-systolic pressure (ESP) determines the LV end-systolic volume. Ees is determined by cardiac myocytes contractility and density, and thereby concentric remodelling. A tight correlation between Zc and the degree of LV concentric remodelling was found in hypertensive and in normal subjects. Zc was found to increase throughout the full lifespan and also with hypertension. Both Zc and wave reflections determine aortic input impedance estimated from the aortic pressure-flow relationship. Increased arterial stiffness resulted in increasing C and overlap of forward and backward waves and thereby in greater pulse pressure and ESP and a greater difference between ESP and diastolic pressure. Ees is an accurate index of LV systolic performance. Besides the inotropic state of myofibers, Ees depends on the concentric remodelling and thereby on the characteristic impedance of the aorta.