# Exergy Analysis of the Musculoskeletal System Efficiency during Aerobic and Anaerobic Activities

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## Abstract

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## 1. Introduction

## 2. Thermodynamic Model

**B**is the exergy of the control volume obtained in Joules (J), whereas $\dot{B}=\dot{{m}_{i}}{b}_{i}$ is the exergy associated with the mass flow rate in Watts (W).

## 3. Experimental Procedure

- 1
- Weight lifting (biceps curl): a continuous series of lifting (76 repetitions) was performed and with one arm (the forearm is considered to elevate the mass to 0.26 m) and a mass of 4 kg until the exhaustion of the subject. This was an experimental protocol aiming at the proposition of the most suitable exercise to apply the exergy analysis.
- 2
- Stationary bicycle, where there was an incremental cadence of the bicycle (Wattbike, Model Pro/Trainer) every 4 min. When the subject was exhausted, the level of activity decreased, and the exercise continued only for recovery purposes, which was around 17 min of activity. This protocol was based on the one proposed in [29]. The performed power was obtained directly from the bicycle, taking into account the thermodynamic definition.

## 4. Results and Discussion

- The first column (1) indicates the maximum work that the body could extract from nutrients; therefore, the metabolic exergy (in blue). In order to obtain these values, the exergy metabolism was integrated over the period of time of the test. The value obtained in Figure 9a was 730 kJ. For Figure 9b, it was 18 kJ.
- Because the body only consumes ATP as a nutrient to perform any physical activity, there must be some irreversibilities in this step, as indicated in Column (2), using an integration of Equation (21). This result is in accordance with [5]. Nevertheless, there is a destroyed exergy in the process, in red (${B}_{{d}_{ATP}}$), and an exergy loss associated with heat, in green (${B}_{{Q}_{ATP}}$).

## 5. Concluding Remarks

- The bicycle test is more efficient than weight lifting, from the second law perspective. Nevertheless, this result must be understood with some care, since larger muscular groups are used, although the nature of metabolism is different.
- The metabolic path, from nutrients’ consumption (obtained by indirect calorimetry) to performed power, was first analyzed from the exergy analysis point of view.
- The exergy efficiency achieved values around 40% if the exergy input considered was the ATP and values around 30% if the complete cycle was evaluated (${B}_{M}$ as exergy input).
- The exergy efficiency was no larger than 10% for the weight lifting.
- If all of the metabolism was anaerobic, both cases would violate the second law of thermodynamics. This last result demonstrates the characteristic of this kind of nutrient degradation: fast energy conversion, although with low efficiency (use less exergy from the nutrient).
- The most important conclusion is that for future tests involving the application of the first and second laws of thermodynamics, the stationary bicycle test is adequate. It is more precise in the definition of performed power, even when compared with the treadmill, as indicated [29,36]. In future experiments, the group will focus on the referred exercise.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Human body proposed by [5], dividing it into two control volumes: human thermal model (CV1) and cellular metabolism (CV2). Inside the cellular metabolism, there is a reaction of adenosine triphosphate (ATP) formation and hydrolysis. Note that the body is considered as CV1 + CV2, and the surface of the skin is the control volume named the human body.

**Figure 2.**(

**a**) Exergy conversion process in the cellular metabolism. From nutrient oxidation, ATP formation and the use of ATP. (

**b**) Energy analysis of the conversion of the chemical energy of substrates into work and heat. Obtained and modified from [36].

**Figure 3.**(

**a**) Respiratory quotient and tympanic temperature of a subject under a bicycle test, (

**b**) respiratory quotient of a subject performing a continuous biceps series with 4 kg (the internal temperature was considered constant, equal to 36.5 ${}^{\circ}$C.

**Figure 4.**Physiological data collected during tests: oxygen consumption and carbon dioxide production of a subject under: (

**a**) bicycle test; (

**b**) biceps series.

**Figure 7.**Ratio of ${M}_{exp}$ to ${M}_{calc}$, ${B}_{{M}_{calc}}$ to ${M}_{calc}$ and ${B}_{{M}_{calc}}$ to ${M}_{exp}$, for: (

**a**) bicycle test; (

**b**) weight lifting.

**Figure 8.**Exergy terms indicating the metabolic efficiency, from the transformations of ${B}_{M}$ (Equation (18)) into ATP (ratio of ${W}_{MAX}$ to ${B}_{M}$) and ATP into $Wreal$ (ratio of ${W}_{real}$ to ${W}_{MAX}$) for the two studied cases: (

**a**) bicycle test; (

**b**) weight lifting.

**Figure 9.**Global efficiency (ratio of W to ${B}_{M}$) and the efficiency of the conversion of ATP into ${W}_{real}$ (ratio of ${W}_{real}$ to ${W}_{MAX}$), for two cases (ratio of ${W}_{MAX}$ to W): (

**a**) bicycle test; (

**b**) weight lifting.

**Figure 10.**Exergy conversion process in cellular metabolism. From nutrient oxidation, ATP formation and the use of ATP. Based on the figures proposed in [36]. (

**a**) Bicycle test; (

**b**) weight lifting.

**Figure 11.**Exergy analysis of the conversion of the chemical exergy of substrates into work and heat. Several metabolic efficiencies were evaluated, from 100 % of aerobic to 100 % of anaerobic oxidation. (

**a**) Bicycle test; (

**b**) weight lifting.

**Figure 12.**Extreme case where all of metabolism is considered as anaerobic. The first group of columns is the exergy conversion process in the cellular metabolism. From nutrient oxidation, ATP formation and the use of ATP. Based on the figures proposed in [36]. (

**a**) Bicycle test; (

**b**) weight lifting.

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**MDPI and ACS Style**

Spanghero, G.M.; Albuquerque, C.; Lazzaretti Fernandes, T.; Hernandez, A.J.; Keutenedjian Mady, C.E.
Exergy Analysis of the Musculoskeletal System Efficiency during Aerobic and Anaerobic Activities. *Entropy* **2018**, *20*, 119.
https://doi.org/10.3390/e20020119

**AMA Style**

Spanghero GM, Albuquerque C, Lazzaretti Fernandes T, Hernandez AJ, Keutenedjian Mady CE.
Exergy Analysis of the Musculoskeletal System Efficiency during Aerobic and Anaerobic Activities. *Entropy*. 2018; 20(2):119.
https://doi.org/10.3390/e20020119

**Chicago/Turabian Style**

Spanghero, Gabriel Marques, Cyro Albuquerque, Tiago Lazzaretti Fernandes, Arnaldo José Hernandez, and Carlos Eduardo Keutenedjian Mady.
2018. "Exergy Analysis of the Musculoskeletal System Efficiency during Aerobic and Anaerobic Activities" *Entropy* 20, no. 2: 119.
https://doi.org/10.3390/e20020119