Oxygen Uptake Estimation in Humans During Exercise Using a Hammerstein Model

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 (VO2) 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.

[1]  K. U. Leuven.  A COMPARATIVE STUDY OF LS-SVM’S APPLIED TO THE SILVER BOX IDENTIFICATION PROBLEM , 2004 .

[2]  D. Abe,et al.  Effects of load carriage, load position, and walking speed on energy cost of walking. , 2004, Applied ergonomics.

[3]  P E Di Prampero,et al.  An analysis of O2 debt contracted in submaximal exercise. , 1970, Journal of applied physiology.

[4]  Laura Giarré,et al.  Approximation of the Feasible Parameter Set in worst-case identification of Hammerstein models , 2005, Autom..

[5]  J. Holloszy,et al.  Faster adjustment to and recovery from submaximal exercise in the trained state. , 1980, Journal of applied physiology: respiratory, environmental and exercise physiology.

[6]  C. H. Wyndham,et al.  An equation for prediction of energy expenditure of walking and running. , 1973, Journal of applied physiology.

[7]  E. Bai.  An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[8]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[9]  M. Korenberg.  Identification of Nonlinear Systems , 1994 .

[10]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[11]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: Wiener and Hammerstein cascade models , 1986, Biological Cybernetics.

[12]  M. Pawlak.  On the series expansion approach to the identification of Hammerstein systems , 1991 .

[13]  Er-Wei Bai,et al.  Identification of linear systems with hard input nonlinearities of known structure , 2002, Autom..

[14]  R. Kearney,et al.  Nonparametric Block-Structured Modeling of Lung Tissue Strip Mechanics , 1998, Annals of Biomedical Engineering.

[15]  Christian Kleinewächter,et al.  On identification , 2005, Electron. Notes Discret. Math..

[16]  Peter L. Lee,et al.  Control of Multivariable Hammerstein Systems by Using Feedforward Passivation , 2005 .

[17]  M. Munih,et al.  Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle , 1998, IEEE Transactions on Biomedical Engineering.

[18]  Er-Wei Bai,et al.  Decoupling the linear and nonlinear parts in Hammerstein model identification , 2004, Autom..

[19]  R. Luus,et al.  A noniterative method for identification using Hammerstein model , 1971 .

[20]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machines , 2002 .

[21]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[22]  Stanley H. Johnson,et al.  Use of Hammerstein Models in Identification of Nonlinear Systems , 1991 .

[23]  B. Ninness,et al.  Quantifying the accuracy of Hammerstein model estimation , 2000, Autom..

[24]  P. Thompson,et al.  ACSM's Guidelines for Exercise Testing and Prescription , 1995 .

[25]  S. Ward,et al.  Parameters of ventilatory and gas exchange dynamics during exercise. , 1982, Journal of applied physiology: respiratory, environmental and exercise physiology.

[26]  S.W. Su,et al.  Modeling of a Gas Concentration Measurement System , 2005, 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference.

[27]  J. Suykens,et al.  A comparative study of ls-svm’s applied to the silver box identification problem , 2004 .

[28]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[29]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[30]  Julian J. Bussgang,et al.  Crosscorrelation functions of amplitude-distorted gaussian signals , 1952 .

[31]  Jozef Vörös,et al.  Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities , 1999, IEEE Trans. Autom. Control..

[32]  G. Inbar,et al.  FNS Parameter Selection and Upper Limb Characterzation , 1986, IEEE Transactions on Biomedical Engineering.

[33]  L. A. Bernotas,et al.  A Discrete-Time Model of Electrcally Stimulated Muscle , 1986, IEEE Transactions on Biomedical Engineering.

[34]  D. B. Dill.  OXYGEN USED IN HORIZONTAL AND GRADE WALKING AND RUNNING ON THE TREADMILL. , 1965, Journal of applied physiology.

[35]  David T. Westwick,et al.  Identification of Hammerstein models with cubic spline nonlinearities , 2004, IEEE Transactions on Biomedical Engineering.

[36]  Uwe Hoffmann,et al.  Dynamic linearity ofVO2 responses during aerobic exercise , 2004, European Journal of Applied Physiology and Occupational Physiology.

[37]  Stephen A. Billings,et al.  Identi cation of a class of nonlinear systems using correlation analysis , 1978 .

[38]  Er-Wei Bai,et al.  A blind approach to the Hammerstein-Wiener model identification , 2002, Autom..

[39]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[40]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[41]  Johan A. K. Suykens,et al.  Identification of MIMO Hammerstein models using least squares support vector machines , 2005, Autom..

[42]  H T Milhorn,et al.  Dynamic and steady-state respiratory responses to bicycle exercise. , 1977, Journal of applied physiology: respiratory, environmental and exercise physiology.

[43]  Uwe Hoffmann,et al.  VO2 kinetics in subjects differing in aerobic capacity: investigation by spectral analysis , 2004, European Journal of Applied Physiology and Occupational Physiology.

[44]  A.V. Savkin,et al.  Modelling and Control for Heart Rate Regulation during Treadmill Exercise , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[45]  V. Vapnik.  Pattern recognition using generalized portrait method , 1963 .

[46]  Ivan Kneppo,et al.  An iterative method for the identification of nonlinear systems , 1969, Kybernetika.

[47]  Johan A. K. Suykens,et al.  Weighted least squares support vector machines: robustness and sparse approximation , 2002, Neurocomputing.

[48]  John Shawe-Taylor,et al.  Covering numbers for support vector machines , 1999, COLT '99.

[49]  Vladimir Vapnik,et al.  The Nature of Statistical Learning , 1995 .

[50]  A. Hill,et al.  Muscular Exercise, Lactic Acid, and the Supply and Utilization of Oxygen , .

[51]  Lu Wang,et al.  Identification and Control for Heart Rate Regulation During Treadmill Exercise , 2007, IEEE Transactions on Biomedical Engineering.