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

Abstract

Motion capture laboratories can measure multiple variables at high frame rates, but we can only measure the average metabolic rate of a stride using respiratory measurements. Biomechanical simulations with equations for calculating metabolic rate can estimate the time profile of metabolic rate within the stride cycle. A variety of methods and metabolic equations have been proposed, including metabolic time profile estimations based on joint parameters. It is unclear whether differences in estimations are due to differences in experimental data or due to methodological differences. This study aimed to compare two methods for estimating the time profile of metabolic rate, within a single dataset. Knowledge about the consistency of different methods could be useful for applications such as detecting which part of the gait cycle causes increased metabolic cost in patients. Here we compare estimations of metabolic rate time profiles using a musculoskeletal and a joint-space method. The musculoskeletal method was driven by kinematics and electromyography data and used muscle metabolic rate equations, whereas the joint-space method used metabolic rate equations based on joint parameters. Both estimations of changes in stride average metabolic rate correlated significantly with large changes in indirect calorimetry from walking on different grades showing that both methods accurately track changes. However, estimations of changes in stride average metabolic rate did not correlate significantly with more subtle changes in indirect calorimetry due to walking with different shoe inclinations, and both the musculoskeletal and joint-space time profile estimations did not correlate significantly with each other except in the most downward shoe inclination. Estimations of the relative cost of stance and swing matched well with previous simulations with similar methods and estimations from experimental perturbations. Rich experimental datasets could further advance time profile estimations. This knowledge could be useful to develop therapies and assistive devices that target the least metabolically economic part of the gait cycle.

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. Experimental procedures.

(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. Processing methods.

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.

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. R_rm-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. R_rm-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. R_rm-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. R_rm-values indicate mean ± s.e.m. of the repeated measures correlations of the different walking conditions.