Oxygen Uptake Estimation in Humans During Exercise Using a Hammerstein Model

Abstract

Abstract-This paper aims to establish a block-structured model to predict oxygen uptake in humans during moderate treadmill exercises. To model the steady state relationship between oxygen uptake (oxygen consumption) and walking speed, six healthy male subjects walked on a motor driven treadmill with constant speed from 2 to 7 km/h. The averaged oxygen uptake at steady state (VO 2 ) was measured by a mixing chamber based gas analysis and ventilation measurement system (AEI Moxus Metabolic Cart). Based on these reliable date, a nonlinear steady state relationship was successfully established using Support Vector Regression methods. In order to capture the dynamics of oxygen uptake, the treadmill velocity was modulated using a Pseudo Random Binary Signal (PRBS) input. Breath by breath analysis of all subjects was performed. An ARX model was developed to accurately reproduce the measured oxygen uptake dynamics within the aerobic range. Finally, a Hammerstein model was developed, which may be useful for implementing a control system for the regulation of oxygen uptake during treadmill exercises.

Nonparametric modelling of VO<inf>2</inf> response to exercise

“…Although minimising the cost function (3) can be solved by least square (LS) estimation or maximum likelihood (ML) estimation directly, it is not appropriate for modelling the Oxygen uptake, as the measurements are normally extremely noisy [8]. Hence, to guarantee the validity of the obtained model and avoid any ill-conditioned solution, a regularisation term is crucial to weight the variation of the estimated parameters in the objective function.…”

“…For example, [6], [7] developed a first order system to approximate the process based on step response. Later, [8] developed a nonlinear dynamic model for Oxygen uptake modelling during running exercise with pseudo random binary signal (PRBS) as the input. However, broadly speaking, it is relatively difficult for the exercisers to follow the PRBS signal as the treadmill speed.…”

Optimizing Heart Rate Regulation for Safe Exercise

“…Brief introduction of SVR regression can be found in papers. 29,28 Details about SVR, such as the selection of radius of the tube, kernel function, and the regularization constant C, can be found in references. 18 It should be emphasized that, as we need to model the inverse of the nonlinear function f(u), the measured steady state output y (heart rate) will be used as the input data, and the input u (treadmill speed) as the output data.…”

Transient and steady state estimation of human oxygen uptake based on noninvasive portable sensor measurements

“…Article [19] presented a novel single input single output (SISO) Hammerstein modeling (a static nonlinear block followed by a dynamic linear system) method to depict both steady state and transient of oxygen uptake. However, the estimation of oxygen uptake in article [19] is based on the information of walking speed which is obtained from the motor speed of treadmill machine and is not applicable for free-living conditions. In this study, TA combined with a wireless HR sensor are used to dynamically estimate VO 2 as the replacement of the recording of walking speed.…”