Instantaneous Metabolic Cost of Walking: Joint-Space Dynamic Model with Subject-Specific Heat Rate

Abstract

A subject-specific model of instantaneous cost of transport (ICOT) is introduced from the joint-space formulation of metabolic energy expenditure using the laws of thermodynamics and the principles of multibody system dynamics. Work and heat are formulated in generalized coordinates as functions of joint kinematic and dynamic variables. Generalized heat rates mapped from muscle energetics are estimated from experimental walking metabolic data for the whole body, including upper-body and bilateral data synchronization. Identified subject-specific energetic parameters—mass, height, (estimated) maximum oxygen uptake, and (estimated) maximum joint torques—are incorporated into the heat rate, as opposed to the traditional in vitro and subject-invariant muscle parameters. The total model metabolic energy expenditure values are within 5.7 ± 4.6% error of the measured values with strong (R2 > 0.90) inter- and intra-subject correlations. The model reliably predicts the characteristic convexity and magnitudes (0.326–0.348) of the experimental total COT (0.311–0.358) across different subjects and speeds. The ICOT as a function of time provides insights into gait energetic causes and effects (e.g., normalized comparison and sensitivity with respect to walking speed) and phase-specific COT, which are unavailable from conventional metabolic measurements or muscle models. Using the joint-space variables from commonly measured or simulated data, the models enable real-time and phase-specific evaluations of transient or non-periodic general tasks that use a range of (aerobic) energy pathway similar to that of steady-state walking.

A simple model of mechanical effects to estimate metabolic cost of human walking

“…by 63% 16 ), and Roberts et al . 33 , who included measured kinematics and kinetics, had a 12% error.…”

Differences between joint-space and musculoskeletal estimations of metabolic rate time profiles

“…Using the resulting muscle behaviors, Umberger [ 20 ] obtained the first detailed estimation of the time profile of metabolic rate during the walking stride cycle. Kim et al, [ 22 ] and Roberts et al, [ 23 ] argue that there are specific challenges associated with muscle models because they simulate only a subset of muscles and because complicated interactions between muscles and other tissues are difficult to simulate. They developed equations to estimate the time profile of metabolic rate as a function of joint parameters of a 3D full-body model [ 22 , 23 ].…”

“…Kim et al, [ 22 ] and Roberts et al, [ 23 ] argue that there are specific challenges associated with muscle models because they simulate only a subset of muscles and because complicated interactions between muscles and other tissues are difficult to simulate. They developed equations to estimate the time profile of metabolic rate as a function of joint parameters of a 3D full-body model [ 22 , 23 ]. Their equations also divide metabolic rate into subcomponents due to activation-maintenance, shortening-lengthening, and mechanical work.…”

“…Estimations of the total cost of both double support phases (approximately 45%) from experiments with added mass and body weight support [ 26 ] are higher than those from certain simulation studies (27% [ 19 , 20 ]). The forward simulation from Umberger [ 20 ] predicts a higher cost for the weight-acceptance phase and a lower cost for the push-off phase compared to the joint-space estimation method from Roberts et al, [ 23 ]. These inconsistencies could be due to differences in the estimation methods [ 12 , 14 , 30 ] or differences in measurement data due to participant selection, walking conditions (e.g., speed, shoes), measurement errors (e.g., soft tissue artifacts, [ 31 ]), and marker placement artifacts [ 32 ].…”

“…In the present study, we compared the following two methods for estimating the time profile of metabolic cost: an EMG-driven musculoskeletal simulation with muscle metabolic rate equations from Umberger et al, [ 17 ], and a joint-space method [ 23 ] ( Fig 1 ). We applied both methods to the same experimental data to exclude the possibility that differences in metabolic rate estimations are due to differences in underlying measurement data.…”