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Updated: Oct 15, 2025

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
Comparison of the FRIEND and Wasserman-Hansen Equations in Predicting Outcomes in Heart Failure
Jonathan Myers1,2,3, Christina G de Souza E Silva4,5, Ross Arena3,6
1Cardiology Division Veterans Affairs Palo Alto Health Care System Palo Alto CA.
Abstract:
Background Percentage of age-predicted peak oxygen uptake (VO2) achieved (ppVO2) has been widely used to stratify risk in patients with heart failure. However, there are limitations to traditional normal standards. We compared the recently derived FRIEND (Fitness Registry and the Importance of Exercise: A National Data Base) equation to the widely used Wasserman-Hansen (WH) ppVO2 equation to predict outcomes in patients with heart failure. Methods and Results A subgroup of 4055 heart failure patients from the FRIEND registry (mean age 53±15 years) was followed for a mean of 28±16 months. The FRIEND and WH equations along with measured peak VO2 expressed in mL/kg-1 per min-1 were compared for mortality and composite cardiovascular events. ppVO2 was higher for the FRIEND versus the WH equation (66±30% versus 58±25%; P<0.001). The areas under the receiver operating characteristic curves were slightly but significantly higher for the FRIEND equation for mortality (0.74 versus 0.72; P=0.03) and cardiac events (0.70 versus 0.68; P=0.008). Area under the receiver operating characteristic curve for measured peak VO2 was 0.70 (P<0.001) for mortality and 0.73 (P<0.001) for cardiovascular events. For each 1-SD higher ppVO2 for the FRIEND equation, mortality was reduced by 18% (hazard ratio, 0.82; 95% CI, 0.69-0.97; P<0.02); for each 1-SD higher ppVO2 for the WH equation, the mortality was reduced by 17% (hazard ratio, 0.83; 95% CI, 0.71-0.97; P=0.02). The corresponding reductions in risk per 1 SD for cardiovascular events for the FRIEND and WH equations were 23 and 21%, respectively (both P<0.001). Conclusions Peak VO2 expressed as percentage of an age-predicted standard strongly predicts mortality and major cardiovascular events in patients with heart failure. The FRIEND registry equation exhibited test characteristics slightly superior to the commonly used WH equation.
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