Estimating energy expenditure from heart rate in older adults: a case for calibration

Abstract

Background: Accurate measurement of free-living energy expenditure is vital to understanding changes in energy metabolism with aging. The efficacy of heart rate as a surrogate for energy expenditure is rooted in the assumption of a linear function between heart rate and energy expenditure, but its validity and reliability in older adults remains unclear.

Objective: To assess the validity and reliability of the linear function between heart rate and energy expenditure in older adults using different levels of calibration.

Design: Heart rate and energy expenditure were assessed across five levels of exertion in 290 adults participating in the Baltimore Longitudinal Study of Aging. Correlation and random effects regression analyses assessed the linearity of the relationship between heart rate and energy expenditure and cross-validation models assessed predictive performance.

Results: Heart rate and energy expenditure were highly correlated (r=0.98) and linear regardless of age or sex. Intra-person variability was low but inter-person variability was high, with substantial heterogeneity of the random intercept (s.d. =0.372) despite similar slopes. Cross-validation models indicated individual calibration data substantially improves accuracy predictions of energy expenditure from heart rate, reducing the potential for considerable measurement bias. Although using five calibration measures provided the greatest reduction in the standard deviation of prediction errors (1.08 kcals/min), substantial improvement was also noted with two (0.75 kcals/min).

Conclusion: These findings indicate standard regression equations may be used to make population-level inferences when estimating energy expenditure from heart rate in older adults but caution should be exercised when making inferences at the individual level without proper calibration.

Figure 1

a shows a spaghetti plot (N = 290) of the relationship between heart rate (bpm) and energy expenditure (ml/kg/min). b shows an age and sex stratified LOWESS of the relationship between heart rate (bpm) and energy expenditure (ml/kg/min).

Figure 2. Figure 2 shows Kernel density estimates for the distribution of prediction errors for the four calibration data scenarios considered: (1) no calibration data, (2) resting heart rate and energy expenditure, (3) resting and peak heart rates and energy expenditures, and (4) all five levels of heart rate and energy expenditure.

The left panel shows prediction errors computed under model (1), which uses four age/gender categories to predict energy expenditure, and the right panel prediction errors computed under model (2), which uses gender and age as continuous variables, and their interaction to predict energy expenditure.

Figure 3. Figure 3 shows an Illustration of the difference between population-level and individual-level relationships between heart rate and energy expenditure.

The solid black is the population equation, estimated from the subject's age and sex, omitting subject-specific random effects; the solid red line is the subject equation including the subject-level random-effects; and the vertical dashed red line shows the difference between the population-level and subject-level equations at the slow walking heart rate.