Estimating human metabolic energy expenditure using a bootstrap particle filter

Metabolic energy expenditure is a physiological measure of importance to multiple scientific fields including nutrition, athletic performance, and thermoregulatory modeling. However, measuring metabolic rate in non-laboratory settings is difficult due to the restrictions imposed by laboratory grade measurement methods. The use of probabilistic graphical models, a type of machine learning model, may provide a means to estimate hidden variables such as metabolic rate from more easily observed variables such as heart rate and core body temperature. Using a probabilistic graphical model approach, a particle filter was applied to estimate metabolic rate from continuous heart rate and core body temperature observations. This paper examines which set of observations allows the particle filter to make more accurate estimations of metabolic rate and whether or not the addition of change in metabolic rate as a state variable improves accuracy. Observation and state parameters were learned by linear regression from continuous heart rate, core temperature, and metabolic rate collected from 15 volunteers (age: 23 ± 3 yr, ± SD) over N = 24, 3-hour periods during which 1 hour was spent running up to 8 km distance. State segmentations were learned using k-means clustering with up to 10 states. Observations of heart rate alone and with core temperature were used to predict metabolic rate with a root mean square error ± standard deviation of 166 ± 27 W and 133 ± 26 W.