Dissecting the Metabolic Costs of Uphill and Downhill Walking

Work- and collision-based models of locomotion relate the body's mechanical work requirements to metabolic energy expenditure at a system level, but do not capture the underlying force and work demands of muscle that drive energy use. Energy is liberated as heat to activate muscle and maintain force production ("force-related costs") and as heat and work to shorten or lengthen active muscle ("work-related costs"). We collected experimental inverse dynamics, electromyography, and ultrasound data from the main power-producing lower-limb muscles during walking at slopes spanning ±15%. These data were used to evaluate a musculoskeletal modeling approach that simulates muscle states, inputs them to a phenomenological energy cost model to estimate metabolic power, and partitions force- and work-related costs. Simulated metabolic power was compared with indirect calorimetry. Summing simulated metabolic power across only the eight muscles evaluated experimentally correlated more strongly with experimental metabolic power than summing across all modeled muscles (adjusted R² = 0.95 vs. 0.86), so analyses focused on this subset. Both approaches differed from experimental metabolic power in absolute terms, so results are interpreted as relative changes across slopes. Simulated force-related costs increased at steeper inclines and declines and were moderately correlated with mean joint moments (adjusted R² = 0.67), with unexplained variance likely reflecting muscle operating lengths. Simulated work-related costs increased as slope became more positive and were strongly correlated with net joint work (adjusted R² = 0.95). Knee joint mechanics seem particularly indicative of these costs. Incorporating a force-related cost term may offer a more explanatory link to muscle mechanical demands than work- and collision-based models alone.