The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

Peter L. M. Kerkhof, Jean Paul Mérillon, Byung Won Yoo, Richard A. Peace, Gareth Parry, Guy R. Heyndrickx, Tatiana Kuznetsova, Lilian J. Meijboom, Ralf W. Sprengers, Han Ki Park, Neal Handly

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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.
Original languageEnglish
Pages (from-to)237-243
Number of pages7
JournalInternational journal of cardiology
Publication statusPublished - 2018


  • Ejection fraction
  • Left ventricle
  • Right ventricle
  • Sex-specific analysis
  • Systolic function
  • Ventricular volume regulation

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