Old and new equations for maximal heart rate prediction in patients with heart failure and reduced ejection fraction on beta-blockers treatment: results from the MECKI score data set

Predicting maximal heart rate (MHR) in heart failure with reduced ejection fraction (HFrEF) still remains a major concern. In such a context, the Keteyian equation is the only one derived in a HFrEF cohort on optimized β-blockers treatment. Therefore, using the Metabolic Exercise combined with Cardiac and Kidney Indexes (MECKI) data set, we looked for a possible MHR equation, for an external validation of Keteyien formula and, contextually, for accuracy of the historical MHR formulas and their relationship with the HR measured at the anaerobic threshold (AT).

Data from 3487 HFrEF outpatients on optimized β-blockers treatment from the MECKI data set were analyzed. Besides excluding all possible confounders, the new equation was derived by using HR data coming from maximal cardiopulmonary exercise test. The simplified derived equation was [109–(0.5*age) + (0.5*HR rest) + (0.2*LVEF)–(5 if haemoglobin <11 g/dL)]. The R² and the standard error of the estimate were 0.24 and 17.5 beats min⁻¹ with a mean absolute percentage error (MAPE) = 11.9%. The Keteyian equation had a slightly higher MAPE = 12.3%. Conversely, the Fox and Tanaka equations showed extremely higher MAPE values. The range 75–80% of MHR according to the new and the Keteyian equations was the most accurate in identifying the HR at the AT (MAPEs = 11.3–11.6%).

The derived equation to estimate the MHR in HFrEF patients, by accounting also for the systolic dysfunction degree and anaemia, improved slightly the Keteyian formula. Both formulas might be helpful in identifying the true maximal effort during an exercise test and the intensity domain during a rehabilitation programme.