Validated Predictions of Metabolic Energy Consumption for Submaximal Effort Movement

Abstract

Physical performance emerges from complex interactions among many physiological systems that are largely driven by the metabolic energy demanded. Quantifying metabolic demand is an essential step for revealing the many mechanisms of physical performance decrement, but accurate predictive models do not exist. The goal of this study was to investigate if a recently developed model of muscle energetics and force could be extended to reproduce the kinematics, kinetics, and metabolic demand of submaximal effort movement. Upright dynamic knee extension against various levels of ergometer load was simulated. Task energetics were estimated by combining the model of muscle contraction with validated models of lower limb musculotendon paths and segment dynamics. A genetic algorithm was used to compute the muscle excitations that reproduced the movement with the lowest energetic cost, which was determined to be an appropriate criterion for this task. Model predictions of oxygen uptake rate (VO2) were well within experimental variability for the range over which the model parameters were confidently known. The model's accurate estimates of metabolic demand make it useful for assessing the likelihood and severity of physical performance decrement for a given task as well as investigating underlying physiologic mechanisms.

Fig 1. Schematic of dynamic knee extension model.

In the experiment modeled [21, 22], subjects performed periodic knee extensions against different loads exerted by a cycle ergometer (see Figure 1 in [21]). A musculoskeletal model of the knee was constructed to model the motion actuated by the muscles crossing the knee as well as the corresponding energy consumed. A model of the cycle ergometer was also included (see text for details). Graphic of musculoskeletal model is a screenshot of the model we constructed in open-source software named MusculoSkeletal Modeling Software (MSMS; [27]).

Fig 2. Quantitative definition of the task.

The task was defined as minimizing a combination of kinematic error and energetic cost. Kinematic error was a function of the deviation of knee angle from an idealized trajectory (θ_desired) derived from Andersen et al. [21]. Energetic cost was the rate of metabolic energy consumption of all muscles, averaged over the duration of the exercise. The relative weight of the kinematic and energetic terms (E_w) was determined such that the optimization algorithm converged reliably to solutions with kinematics within experimental variability at the lowest possible metabolic energy consumption. Graphic of musculoskeletal model is a screenshot of the model we constructed in open-source software named MusculoSkeletal Modeling Software (MSMS; [27]).

Fig 3. Optimization algorithm.

A genetic algorithm was used to compute the muscle excitation parameters that satisfied the performance criteria. See S2 Appendix for a detailed description of each step.

Fig 4. Exemplary optimization trial.

The population of solutions discovered by the genetic algorithm is shown for the initial, intermediate, and final generations. Each point in this plot corresponds to one solution, or alternatively, one set of parameters that define the muscle excitation signals. Solutions are plotted in terms of their associated movement error and energy consumption. Solutions within the shaded region exhibited acceptable kinematics. The minimum energy solution that satisfied the kinematic criteria is shown on the bottom left. Experimental muscle activity is shown in gray [21] and is overlaid on model predictions to highlight similarities in timing. An exemplary solution with non-physiological kinematics is shown at the bottom right and non-physiological energetics is at the top right. Graphic of musculoskeletal model is a screenshot of the model we constructed in open-source software named MusculoSkeletal Modeling Software (MSMS; [27]).

Fig 5. Validation of model predictions.

A. Model predictions of energy consumption across dynamic knee extension loads is compared against the rise of pulmonary VO₂ measured experimentally for eighteen subjects [21]. Δ Pulmonary VO₂ refers to the increase in steady state rate of oxygen uptake rate by the lungs from rest to exercise. This quantity corresponds to oxygen uptake due to exercise alone (i.e., it does not include the oxygen uptake due to physiological processes contributing to basal oxygen uptake). The model predicts metabolic energy consumption of leg muscles due to exercise (in watts) so to compare it with the Δ Pulmonary VO₂ data reported, the model output of energy consumption of the leg in watts was converted to liters of oxygen uptake per minute [36] and then added to the oxygen uptake due to exercise from energy sources other than the leg (Δ pulm VO₂ - Δ leg VO₂; derived from Krustrup et al. [24]). B. Model predictions are compared against oxygen uptake of the knee extensors measured for five subjects [22]. Knee extensor VO₂ refers to the steady state rate of oxygen uptake by the knee extensor muscles during exercise. This quantity includes oxygen uptake due to exercise as well as the basal oxygen uptake that is measured at rest. The model predicts metabolic energy consumption due to exercise in watts so to compare it with the knee extensor VO₂ data reported, the model output of energy consumption of the knee extensors in watts was converted to liters of oxygen uptake per minute [36] and then added to the resting level of knee extensor oxygen uptake obtained from Krustrup et al. [24].

Fig 6. Sensitivity analysis.

A. Effect of upper limit of knee extension range on pulmonary VO₂ predictions. B. Energetic predictions using nominal, least and most economical musculoskeletal configurations. Mean experimental VO₂ plus/minus one standard deviation is plotted for comparison.

Fig 7. Least and most economical musculoskeletal configurations.

A. Musculoskeletal parameter changes that resulted in the least and most economical musculoskeletal configurations. Changes are shown as percentages of the difference between nominal values and one standard deviation above and below the subject mean. B. Maximum moment generating capacity and metabolic economy for maximum muscle excitation is shown for each musculoskeletal configuration. The moment required to perform dynamic knee extension at a 60W ergometer load (i.e. near maximum intensity) is also shown for reference. See S3 Appendix for more a more detailed description of these musculoskeletal configurations.