Energy Expenditure of Dynamic Submaximal Human Plantarflexion Movements: Model Prediction and Validation by in-vivo Magnetic Resonance Spectroscopy

Abstract

To understand the organization and efficiency of biological movement, it is important to evaluate the energy requirements on the level of individual muscles. To this end, predicting energy expenditure with musculoskeletal models in forward-dynamic computer simulations is currently the most promising approach. However, it is challenging to validate muscle models in-vivo in humans, because access to the energy expenditure of single muscles is difficult. Previous approaches focused on whole body energy expenditure, e.g., oxygen consumption (VO2), or on thermal measurements of individual muscles by tracking blood flow and heat release (through measurements of the skin temperature). This study proposes to validate models of muscular energy expenditure by using functional phosphorus magnetic resonance spectroscopy (³¹P-MRS). ³¹P-MRS allows to measure phosphocreatine (PCr) concentration which changes in relation to energy expenditure. In the first 25 s of an exercise, PCr breakdown rate reflects ATP hydrolysis, and is therefore a direct measure of muscular enthalpy rate. This method was applied to the gastrocnemius medialis muscle of one healthy subject during repetitive dynamic plantarflexion movements at submaximal contraction, i.e., 20% of the maximum plantarflexion force using a MR compatible ergometer. Furthermore, muscle activity was measured by surface electromyography (EMG). A model (provided as open source) that combines previous models for muscle contraction dynamics and energy expenditure was used to reproduce the experiment in simulation. All parameters (e.g., muscle length and volume, pennation angle) in the model were determined from magnetic resonance imaging or literature (e.g., fiber composition), leaving no free parameters to fit the experimental data. Model prediction and experimental data on the energy supply rates are in good agreement with the validation phase (<25 s) of the dynamic movements. After 25 s, the experimental data differs from the model prediction as the change in PCr does not reflect all metabolic contributions to the energy expenditure anymore and therefore underestimates the energy consumption. This shows that this new approach allows to validate models of muscular energy expenditure in dynamic movements in vivo.

Keywords: 31P-MRS; biomechanical modeling; energy; magnetic resonance imaging (MRI); magnetic resonance spectroscopy; muscle; plantar flexion; validation.

Figure 1

Study design, including three experiments and model based simulation of energy turnover changes in loaded calf muscle. Experiment 1: Structural MRI to determine muscle volume, muscle-tendon-unit length, fiber length, fiber angle, and lever arm in two joint angles (neutral, and extended). Morphological data was used to individualize the leg-foot geometry in the muscle model. Experiments 2 (EMG) and 3 (³¹P-MRS) were performed in a contracting calf muscle at 20% of the single repetition maximum force with 0.8 Hz pedaling cadence. Data from Experiment 2 were used to determine dynamic muscle length (based on recorded joint angle) and myoelectrical stimulations (EMG) during the exercise. The ³¹P-MRS data were used to quantify the ATP turnover and to determine the muscular energy expenditure, which was compared with the output of model based simulations. The model receives input from experiment 1 in terms of muscle parameters and experiment 2 in terms of dynamic muscle length and EMG.

Figure 2

Experiment 1—Determination of muscle morphology: (A–C) Sagittal (magenta boxes), transverse (blue boxes) and coronal (yellow boxes) MRI planes illustrating anatomical landmarks (indicated by line cross-sections), which were identified to determine the tendon (l_SEE) and muscle lengths (l_CE). (D) Manually segmented GM muscle and corresponding GM surface.

Figure 3

Left: Transverse T₁-weighted gradient-echo image (3D T₁-weighted gradient-echo MRI, TR/TE = 10/6.15 ms) with selected ³¹P-MRS slice in M. gastrocnemius medialis (GM, green area) and outer volume suppression bands (OVS, blue areas) selected to suppress signal contributions from adjacent tissue. Right: “Stack plot” of dynamic ³¹P-MR spectra series from GM muscle. The spectra acquired during the 3 min load phase (red graphs in the right chart) show rapid PCr decrease during the validation phase as well as a subsequent, significant resonance frequency shift of inorganic phosphate (Pi) due to a strong, anaerobic glycolysis related pH decrease. Please note that this paper focuses on the first steep decrease of PCr in the validation phase (t < 25 s).

Figure 4

Evolution of PCr concentration ([PCr], A) and pH level (B) extracted from ³¹P-MR spectra, which were acquired in the M. gastrocnemius medialis during dynamic plantarflexion exercise (experiment 3, section 2.3). The time point t = 0 s marks the onset of the exercise. Highlighted is the validation phase (t = 0…25 s) for which we hypothesized agreement between experiment and model. During this phase, the PCr concentration reveals a continuous decrease indicating ATP re-synthesis and, thus, energy consumption in the muscle (see section 2.4). During the validation phase the energy supply is dominated by the PCr depletion. The pH decrease for t > 25 s reflects the H+ accumulation during the anaerobic glycolysis. Subplot (C) shows the raw spectra (red graphs) and corresponding AMARES fits (blue dashed graphs), obtained during the validation phase. The black graph in the sublot (C) shows a spectrum obtained prior to exercise.

Figure 5

Prediction of the energy consumption by the model (mean: blue line, standard deviation: very small light-blue shade around the blue line) compared to the measured energy consumption in the experiments (derived from the PCr decay; green data points) for dynamic plantarflexion. The model predicts the energy rate (${Ė}_{\mathrm{\text{sim}}}=5.081\pm 0.064Jk{g}^{-1}{s}^{-1}$, linear fit, dotted blue line) as the sum of activation-maintenance heat, shortening-lengthening heat, and mechanical work performed by the muscle fibers: Ė = ḣ_AM + ḣ_SL +ẇ_CE. The experimental data shows a similar energy rate (${Ė}_{\mathrm{\text{exp}}}=5.8\pm 1.8Jk{g}^{-1}{s}^{-1}$, linear fit, dotted green line) during the first 25s (validation phase). During this time, the PCr decay dominates the ATP re-synthesis. Afterwards, the aerobic and anaerobic metabolism additionally contributes (see the progressing pH depletion in Figure 4B). Hence, after 25s not the whole energy consumption is reflected by the measured [PCr] reduction. The error margin for the simulation (light blue) was determined by a Monte-Carlo simulation based on the estimated errors of the subject specific parameters determined in Experiment 1. The error for the experimental energy consumption estimates the maximum error of the ³¹P-MRS.