Estimating instantaneous energetic cost during non-steady-state gait

Respiratory measures of oxygen and carbon dioxide are routinely used to estimate the body's steady-state metabolic energy use. However, slow mitochondrial dynamics, long transit times, complex respiratory control mechanisms, and high breath-by-breath variability obscure the relationship between the body's instantaneous energy demands (instantaneous energetic cost) and that measured from respiratory gases (measured energetic cost). The purpose of this study was to expand on traditional methods of assessing metabolic cost by estimating instantaneous energetic cost during non-steady-state conditions. To accomplish this goal, we first imposed known changes in energy use (input), while measuring the breath-by-breath response (output). We used these input/output relationships to model the body as a dynamic system that maps instantaneous to measured energetic cost. We found that a first-order linear differential equation well approximates transient energetic cost responses during gait. Across all subjects, model fits were parameterized by an average time constant (τ) of 42 ± 12 s with an average R(2) of 0.94 ± 0.05 (mean ± SD). Armed with this input/output model, we next tested whether we could use it to reliably estimate instantaneous energetic cost from breath-by-breath measures under conditions that simulated dynamically changing gait. A comparison of the imposed energetic cost profiles and our estimated instantaneous cost demonstrated a close correspondence, supporting the use of our methodology to study the role of energetics during locomotor adaptation and learning.