Metabolic cost calculations of gait using musculoskeletal energy models, a comparison study

Abstract

13This paper compares predictions of metabolic energy expenditure in gait using 14 seven metabolic energy expenditure models to assess their correlation with 15 experimental data. Ground reaction forces, marker data, and pulmonary gas 16 exchange data were recorded for six walking trials at combinations of two speeds, 17 0.8 m/s and 1.3 m/s, and three inclines, -8% (downhill), level, and 8% (uphill). 18 The metabolic cost, calculated with the metabolic energy models was compared to 19 the metabolic cost from the pulmonary gas exchange rates. A repeated measures 20 correlation showed that the model by Bhargava et al. [7] and the model by 21 Lichtwark and Wilson [21] correlated best with the experimental data. It was 22 found that for all metabolic energy models, the subject's weight affected the 23 calculated metabolic cost. 24 Introduction 25 Humans prefer to walk in energetically optimal ways. Walking speed [1], the ratio 26 between step length and frequency [2], step width [3] and vertical movement of the 27 March 25, 2019 1/25 center of mass [4, 5] are chosen to minimize energy expenditure. Whole-body energy 28 expenditure can be measured using direct calorimetry, by measuring the heat 29 production in the body, or indirect calorimetry, by measuring the volume of oxygen 30 inspired and carbon dioxide expired [6]. However, these measurements are not always 31 available, but an accurate prediction of energy expenditure is often desired. 32 Instead, musculoskeletal modeling can be used to simulate human gait and to 33 calculate the energy expenditure based on a metabolic energy expenditure model (e.g., 34 [7-10]). These calculations are based on variables that are studied in gait analysis, such 35 as joint moments, joint power, or muscle forces, lengths and activations [11]. With a 36 metabolic energy expenditure model, the energy expenditure can be calculated for gait 37 experiments that did not take metabolic energy expenditure measurements, or for 38 predictive gait simulations, where no experimental data is available. Recently, these 39 simulations have been used to analyze 'what-if scenarios' such as the effect of an 40 intervention such as a prosthesis [12], an exoskeleton [13], ankle foot orthosis [14], 41 additional weight [15], loaded and inclined walking [16], or changing the gait pattern to 42 minimize knee reaction force [17] on gait. Energy cost is an important variable in gait, 43 and should be considered whenever a clinical intervention is studied or designed. 44 In literature several energy models were suggested. The Huxley crossbridge 45 model [18] finds both the muscle force and the energy expenditure of a muscle, but 46 requires up to 18 states [19]. Instead, Hill-type muscle models [20] are typically used to 47 simulate muscles, but these do not output metabolic energy expenditure. Therefore, 48 several metabolic energy expenditure models have been proposed that calculate the 49 energy expenditure during walking based on Hill-type muscles [7-10, 21, 22], based on 50 muscle effici...

Achilles tendon stiffness minimizes the energy cost in simulations of walking in older but not in young adults

“…The methods to calculate the energy cost of walking were equally accurate in describing the relationship between whole-body energy consumption and walking speed. This is in agreement with a previous study that also reported small differences in accuracy between different methods to calculate the energy cost of walking only in young adults (Koelewijn et al, 2019). Moreover, in our study, the accuracy of these methods differed greatly between different subjects.…”

“…Such experimental validation, comparing measured and calculated energy cost of walking using different methods, can only be performed at the level of the whole-body energy cost of walking that can be measured using indirect calorimetry (Wert et al, 2015) because it is infeasible to measure the triceps surae energy cost of walking (Marsh and Ellerby, 2006). A previous validation study showed that these methods better predict within-subject differences than between-subject differences, however only two-dimensional musculoskeletal models with a very limited amount of muscle actuators were used (Koelewijn et al, 2019).…”

Muscle metabolic energy costs while modifying propulsive force generation during walking

“…In 2019) found very strong positive correlations between the output from both these models and measured net metabolic power during walking (r 2 = 0.92 and 0.86, respectively) (Koelewijn et al 2019). In this study, our model predictions explained approximately one-third of the variance in empirical measurements across a relatively broad combination of walking conditions.…”

OpenSim Moco: Musculoskeletal optimal control

“…Metabolic energy consumption is a commonly used cost term, but direct collocation struggles with the nonconvexity of many energy consumption models. Koelewijn et al recently published a smoothed energy consumption model for use in direct collocation [39]; we hope Moco will include this model in the future. Implementing a cost term that minimizes the error between measured and simulated contact forces would improve the accuracy of simulated ground reaction forces in tracking problems.…”

“…The advantages of direct collocation have led biomechanists to use the method for tracking motions [16,23], predicting motions [24][25][26][27][28][29][30][31][32][33], fitting muscle properties [34], and optimizing design parameters [35]. Researchers have made key methodological advances, including efficiently handling multibody and muscle dynamics via implicit formulations [36,37], minimizing energy consumption [38,39], and employing algorithmic differentiation to simulate complex models more rapidly compared to using finite differences [40]. Along with these methodological advances, researchers have discovered that minimizing an energy-related cost produces non-physiological motions during walking [24], skipping is the most efficient gait on our moon [41], and unilateral amputees can improve gait symmetry with only a minor increase in effort [42].…”