Analytical Expression for the Dependence of Ejection Fraction on End-systolic or End-diastolic Volume

Cardiac compartmental shape and volume estimation has fascinated investigators, beginning with Serveto and Berengar around the year 1500. The pulsatile nature of cardiac pumping implies sequences of minimum and maximum volumes, known as end-systolic volume (ESV) and end-diastolic volume (EDV), respectively. This data pair is identified as the "working point", which forms the cornerstone of cardiac performance determination. Each point can be presented in the volume domain by relating ESV to EDV, yielding the Volume Regulation Graph (VRG). Due to adaptation, the working point follows a specific trajectory in the VRG during exercise, after medical intervention, or due to a cardiac disease process.A ratio-based metric, termed ejection fraction (EF), became popular. As EF depends on both ESV and EDV, it was often thought that the single value of EF can replace the data pair {EDV, ESV}. Two cohorts (420 heart failure (HF) patients, and 96 with acute heart disease) are analyzed using the VRG. Our study formulates a robust analytical expression for the dependence of EF on either ESV or EDV, while comparing the results with those obtained by alternative published approximations.It is concluded that EF is inferior to ESV as estimator of cardiac compartmental performance. In addition, EF is not suitable as a criterion for HF phenotyping.Clinical Relevance- Cardiac contraction performance is best analyzed by considering ESV combined with EDV. The VRG allows derivation of a mathematical formalism to express EF as a function of ESV or EDV, documenting shortcomings of EF. Also, EF is inappropriate for HF phenotyping.