Fig 1.
Flow chart of both metabolic rate time profile estimation methods.
The musculoskeletal estimation method uses a musculoskeletal model driven by joint kinematics and EMG signals in conjunction with the muscle metabolic cost equations [17]. This method also used joint moment data for optimizing the participant-specific muscle parameters but not for the metabolic rate estimation. The joint-space estimation method uses only the joint kinematics and joint moments as inputs [23].
Fig 2.
(a) Conditions. We analyzed previously collected data from walking with level shoes at downhill, level and uphill treadmill grades (-6, 0 and +6°), and walking on a level treadmill with shoes with different outsole inclinations (from -7 to +7°) [36]. The red lines indicate the treadmill grades and shoe inclinations. (b) Measurements. We measured metabolic rate using indirect calorimetry, 3D kinematics using motion capture, ground reaction forces using a force treadmill, and muscle activation using surface EMG sensors.
Fig 3.
Models for musculoskeletal and joint-space methods.
Kinematic, kinetic, and musculoskeletal analyses were performed in OpenSim using a model based on Rajagopal et al., [48]. (a) Musculoskeletal method. Schematic of the model that was used to estimate muscle-tendon paths and calculate the muscle metabolic rate, and the degrees of freedom that were used for each joint. The muscles shown were simulated based on EMG recordings. (b) Joint-space method. Schematic of the joints that were used to estimate the metabolic rate time profile using the method from Roberts et al., [23] and the sign conventions for joint angular velocity and joint moment.
Fig 4.
Flowchart describing the steps that were used to process the recorded data for the inverse kinematics, inverse dynamics, and forward dynamics muscle state estimation. The default muscle parameters from the scaling step (tendon slack length and optimal fiber length) were optimized with a generalized pattern search algorithm to maximize the agreement with the moments from the inverse dynamics. The optimized muscle parameters were used as inputs for the musculoskeletal simulation that was used for the estimation of metabolic rate with muscle metabolic rate equations. The data from the kinematic and inverse dynamic analyses were used as inputs for the joint-space metabolic rate estimation.
Table 1.
Muscle parameters in musculoskeletal simulation and muscle metabolic rate estimation.
Table 2.
Optimal fiber lengths and tendon slack lengths that minimize the cost function and were used for calibrating the muscle parameters (mean ± inter-participant s.e.m.).
Table 3.
Estimated metabolic rate (% mean ± s.e.m.) of different phases of the gait cycle during level walking from the current work and other studies.
We segmented the strides into double support phases, single support phase, and swing phase based on our ground reaction force data from both legs. Strides are segmented from the ipsilateral heel strike to the next ipsilateral heel strike such that the first double support phase starts with an ipsilateral heel strike and ends with contralateral toe-off, and the second double support phase starts with contralateral heel strike and ends with ipsilateral toe-off. The metabolic rate time profile in the normal walking condition from the Jackson et al., [18] study was obtained by applying the modified Umberger [20] estimation code from [68]. The data from Roberts et al., [23] were obtained from their supplementary data file for walking at 70% of the preferred walking speed. We selected this trial from their supplementary data because the walking speed is most similar to the walking speed from our study (1 m∙s-1). We obtained the unilateral metabolic rate from the right ankle knee and hip joints by entering the data from the right ankle knee and hip as inputs to their MATLAB code and entering signals with zeros for all non-lower limb joints and all joints on the left side of the body.
Fig 5.
Musculoskeletal method validation.
(a) Hip moments, (b) Knee moments, (c) Ankle moments. Red lines represent the net joint moments from the simulated muscles in the normal walking condition. The shaded area is s.e.m. The black line represents the net joint moments from inverse dynamic analyses. Dashed lines represent the mean inverse dynamics joint moments ± two times the standard deviation, which is suggested as a validation threshold [38]. Values in the plots represent mean ± inter-subject s.e.m. of root mean square errors of the difference between muscle-generated and inverse dynamics moments. The muscle-generated hip moments followed the inverse dynamics moments in the extension direction but not in the flexion direction since the optimization algorithm was programmed only to minimize the error during hip extension moment generation.
Fig 6.
Estimations of the stride average metabolic rate and the time profile of metabolic rate during downhill, level, and uphill walking with level shoes.
(a) Stride average metabolic rate. Red triangles, blue circles, and black diamonds indicate the results from the musculoskeletal estimation, the joint-space estimation method, and indirect calorimetry, respectively. Error bars indicate s.e.m. The average trends across conditions from the same method are shown as a solid line from a second-order polynomial curve fit. (b) Individual stride averages. Symbols are individual trials. Lines are individual fits from the repeated measures correlation test. Slopes that are less or more steep than a slope of 1/1 indicate overestimation or underestimation, respectively. Rrm-values indicate the repeated measures correlation. ** indicate that the P-value of the repeated measures correlation is ≤ 0.01. (c) Time profiles under different treadmill conditions. Red and blue lines indicate the results from the musculoskeletal estimation and joint-space estimation methods, respectively. Strides are segmented from the ipsilateral heel strike to the next ipsilateral heel strike. The shaded area indicates s.e.m. (d) Individual phase averages. Symbols are averages of the phases during the level walking condition separated by vertical lines: first double support (from ipsilateral heel strike to contralateral toe-off), single support, second double support (from contralateral heel strike to ipsilateral toe-off), and swing phase. Rrm-values indicate mean ± s.e.m. of the repeated measures correlations of the different walking conditions.
Fig 7.
Estimations of the stride average metabolic rate and the time profile of metabolic rate during walking on a level grade with different shoe inclinations.
(a) Stride average metabolic rate. Red triangles, blue circles, and black diamonds indicate the results from the musculoskeletal estimation method, the joint-space estimation method, and indirect calorimetry, respectively. Error bars indicate s.e.m. The average trends across conditions from the same method are shown as a solid line from a second-order polynomial curve fit. (b) Individual stride averages. Symbols are individual trials. Lines are individual fits from the repeated measures correlation test. Slopes that are less or more steep than a slope of 1/1 indicate overestimation or underestimation, respectively. Rrm-values indicate the repeated measures correlation. (c) Time profiles under different shoe inclination conditions. Red and blue lines indicate the results from the musculoskeletal estimation and joint-space estimation methods, respectively. Strides are segmented from the ipsilateral heel strike to the next ipsilateral heel strike. The shaded area indicates s.e.m. (d) Individual phase averages. Symbols are averages of the phases during the level walking condition separated by vertical lines: first double support (from ipsilateral heel strike to contralateral toe-off), single support, second double support (from contralateral heel strike to ipsilateral toe-off), and swing phase. Rrm-values indicate mean ± s.e.m. of the repeated measures correlations of the different walking conditions.
Table 4.
Estimated metabolic rate (% mean ± s.e.m.) of different muscle groups during level walking in our own analyses and other studies.
For the musculoskeletal estimation method, we grouped the metabolic costs of different functions similar to [20] as follows: soleus, gastrocnemius medialis and gastrocnemius lateralis for the plantarflexors, vastus medialis for the knee extensors, gluteus maximus for the hip extensors, tibialis anterior for the dorsiflexors, and biceps femoris for the knee flexors. For the joint-space estimation method, we partitioned the metabolic costs for the ankle plantar flexors/dorsiflexors, knee extensors/flexors, and hip extensors/flexors based on when the joint moments were in the corresponding direction. The metabolic rate of muscle groups in the normal walking condition from the study by Jackson et al., [18] was obtained by applying the modified Umberger [20] estimation code from [68]. The data from Roberts et al., [23] were obtained from their supplementary data file for walking at 70% of the preferred walking speed. We selected this trial from their supplementary data because the walking speed is most similar to the walking speed from our study (1 m∙s-1. We obtained the unilateral metabolic rate from the right ankle knee and hip joints by entering the data from the right ankle knee and hip as inputs to their MATLAB code and entering signals with zeros for all non-lower limb joints and all joints on the left side of the body.