What should a metabolic energy model look like? Sensitivity of metabolic energy model parameters during gait

Gambietz M, Nitschke M, Miehling J, Koelewijn A (2022)

Publication Language: English

Publication Status: Accepted

Publication Type: Conference contribution, Abstract of a poster

Future Publication Type: Conference contribution

Publication year: 2022

Event location: Taipei

Abstract

Introduction
Many experimental [1] and simulation [2] studies have shown that metabolic energy is minimized in human movement. This makes metabolic energy an important variable in movement studies, e.g. to assess the quality of a prosthesis. The measurement of metabolic energy consumption is time-consuming and associated with methodological limitations, while metabolic energy models could estimate it from kinematic and kinetic variables of a single gait cycle [3]. However, there is currently only limited validation of the empirically chosen model parameters. Different metabolic energy models with different levels of complexity exist, while it is unclear whether increased complexity, i.e. more input parameters, are beneficial. Here, we compared different levels of complexity using pseudo-optimized models based on Monte-Carlo (MC) simulation investigate the benefit of the additional complexity.

Methods
We performed a MC simulation on the empirical parameters of seven metabolic energy models (see [4]). We used a gait dataset with optical motion capturing and indirect calorimetry recordings from 12 participants at three inclines and two speeds [5]. We ranked the parameters according to their resulting sensitivity indices. Further, optimized metabolic models were obtained.

Results
The original metabolic models resulted in a root mean square error (RMSE) of 1.00 to 2.45 J/(kg*m) for the data set. In the MC simulation, the RMSE was reduced to 0.75 J/(kg*m) for the best performing model (Bhargava, 2004 [6]), while the differences between the models were small. Among all pseudo-optimized metabolic models, negative metabolic rates of muscles were observed for the best fits, although this would not be biologically possible [7].
We investigated the necessity of several relationships that were common between the different metabolic models, namely muscle-length dependencies, fiber-type differentiation and activation-time thresholding. Muscle-length dependencies and activation heat rate fiber-type distinction mostly showed high sensitivity indices. On the other hand, fiber-type distinction in the maintenance heat rate as well as the muscle activation-time dependencies turned out to be mostly non-significant (p>0.05) in this dataset.

Discussion
We showed that highly complex metabolic energy expenditure models only provide little advantage over simpler metabolic energy expenditure models using MC simulation. Specifically, we found that activation-time dependency was ranked low in terms of sensitivity, which could therefore be omitted in metabolic energy models. We also found that negative metabolic rates yielded more accurate results. These results could be explained by the shortcomings of the Hill model, which, for example, overlooks the role of titin [8,9]. In the future, assuming more data and better personalized musculoskeletal models exist, a deep-learning based metabolic model could be an alternative to the current metabolic models.

Acknowledgements
This work was funded by the DFG: SFB 1483 – Project-ID 442419336.

References
[1] Hatze, Buys (1977). Biological Cybernetics, (27):9–20.
[2] Srinivasan, Ruina (2006). Nature, 439(7072), 72-75.
[3] Miller (2014). J. Biomech., 47(6):1373-81.
[4] Koelewijn et al. (2019). PLOS ONE 14(9):e0222037.
[5] Koelewijn et al. (2018). Zenodo: 10.5281/zenodo.1973799.
[6] Bhargava et al. (2004). J. Biomech., 37(1):81–88.
[7] Woledge et al. (2003). Adv. Exp. Med. Biol., 538:627–34.
[8] Kiisa et al. (2012). Proceedings. Biological sciences, 279(1730):981–990.
[9] Winter (2009). Wiley, Hoboken, N.J, 4th ed.

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How to cite

APA:

Gambietz, M., Nitschke, M., Miehling, J., & Koelewijn, A. (2022). What should a metabolic energy model look like? Sensitivity of metabolic energy model parameters during gait. Poster presentation at 9th World Congress of Biomechanics 2022 Taipei, Taipei, TW.

MLA:

Gambietz, Markus, et al. "What should a metabolic energy model look like? Sensitivity of metabolic energy model parameters during gait." Presented at 9th World Congress of Biomechanics 2022 Taipei, Taipei 2022.

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