Exploratory Comparative Analysis of Gellish and Fox Equations in Determining Maximal Heart Rate and Target Heart Rate for Critically Ill Patients

Abstract

Background: Target heart rate (THR) monitoring is central to safe physiotherapy intervention in critically ill patients. In settings where direct cardiopulmonary testing is contraindicated, age-predicted equations such as the Fox and Gellish formulas are commonly used to estimate maximal heart rate (HRmax) and guide submaximal exercise prescription. However, their comparative implications in critically ill populations remain unclear.

Methods: An exploratory comparative cross-sectional study was conducted among 61 critically ill patients admitted to medical wards. HRmax, THR (60% HRmax), and estimated VO₂max were derived using the Fox and Gellish equations. Descriptive statistics summarized participant characteristics, while paired samples t-tests were used to compare parameters generated by the two equations. Statistical significance was set at p < 0.05.

Results: Participants had a mean age of 48.6 ± 16.3 years, with females comprising 59% of the sample. There was no statistically significant difference in predicted HRmax between the Fox and Gellish equations (p = 0.59). However, significant differences were observed in THR and estimated VO₂max, with higher values produced by the Gellish equation (p < 0.001).

Conclusion: Although both equations yielded comparable HRmax estimates, they generated significantly different THR and VO₂max values. These differences may influence the prescription of submaximal exercise in critically ill patients, highlighting the need for cautious and context-specific application of HR prediction equations in clinical practice.