A model-based estimation of critical torques reduces the experimental effort compared to conventional testing

Johannes L Herold,Andreas Sommer

doi:10.1007/s00421-020-04358-w

Abstract

PurposeCritical torque (CT) is an important fatigue threshold in exercise physiology and can be used to analyze, predict, or optimize performance. The objective of this work is to reduce the experimental effort when estimating CTs for sustained and intermittent isometric contractions using a model-based approach.Materials and methodsWe employ a phenomenological model of the time course of maximum voluntary isometric contraction (MVIC) torque and compute the highest sustainable torque output by solving an optimization problem. We then show that our results are consistent with the steady states obtained when simulating periodic maximum loading schemes. These simulations correspond to all-out tests, which are used to estimate CTs in practice. Based on these observations, the estimation of CTs can be formulated mathematically as a parameter estimation problem. To minimize the statistical uncertainty of the parameter estimates and consequently of the estimated CTs, we compute optimized testing sessions. This reduces the experimental effort even further.ResultsWe estimate CTs of the elbow flexors for sustained isometric contractions to be 28% of baseline MVIC torque and for intermittent isometric contractions consisting of a 3 s contraction followed by 2 s rest to be 41% of baseline MVIC torque. We show that a single optimized testing session is sufficient when using our approach.ConclusionsOur approach reduces the experimental effort considerably when estimating CTs for sustained and intermittent isometric contractions.

Highlights

Critical power and critical torqueThe power–endurance relationship of a constant power task can be described (Monod and Scherrer 1965) by Tlim = W P − Pc (1)or equivalently by P W Tlim + Pc, (2)
Previous work (Herold et al 2018) allows us to predict how maximum voluntary isometric contraction (MVIC) torque of a muscle group decreases and recovers under isometric loading (Eq (3)). This enables us to find the maximum contraction intensity for which MVIC torque can reach a steady state during intermittent contractions of any desired duty cycle (Eq (4)), which corresponds to critical torque
To illustrate the benefits of optimum experimental design (OED), we compare the uncertainties of the parameters resulting from an intuitive testing session (Scenario ITS) with those resulting from algorithmically designed optimized testing sessions (Scenarios OTS200 and OTS400)

Summary

Introduction

The power–endurance relationship of a constant power task can be described (Monod and Scherrer 1965) by. We propose a model-based approach to reduce the experimental effort when estimating CTs for sustained or intermittent isometric contractions. We show that our results are consistent with the steady states obtained when simulating periodic maximum loading schemes These simulations correspond to all-out tests, which are used to estimate CTs in practice (Burnley 2009). The estimation of CTs can be formulated mathematically as a parameter estimation problem, for which the necessary measurements can be obtained in a single testing session compared to several testing sessions when using the traditional approach or an individual adjustment when using all-out tests As these measurements are subject to random measurement errors, the resulting parameter estimates are random variables (Bock et al 2013, overview in English; Bock 1987, original work in German).

Materials and methods

Results

Discussion

Limitations and future work

Compliance with ethical standards