The Point of Maximum Curvature as a Marker for Physiological Time Series

References

• Astrand , P O , Rodahl , K , Dahl , H A and Stromme , S B . 2003 . Textbook of Work Physiology: Physiological of Bases of Exercise . Human Kinetics ,
   Google Scholar
• Barstow , T J and Mole , P A . 1991 . Linear and nonlinear characteristics of oxygen uptake kinetics during heavy exercise . J. Appl. Physiol. , 71 ( 6 ) : 2099 – 2106 .
   PubMed Web of Science ®Google Scholar
• Billat , V L . 2000 . V˙O2 slow component and performance in endurance sports . Brit. J. Sports Med. , 34 ( 2 ) : 83 – 85 .
   PubMed Web of Science ®Google Scholar
• Broman , S and Wigertz , O . 1971 . Transient dynamics of ventilation and heart rate with step changes in work load from different load levels . Acta Physiol Scand. , 81 ( 1 ) : 54 – 74 .
   PubMedGoogle Scholar
• Brooks , G A , Fahey , T D , White , T P and Baldwin , K M . 1999 . Exercise Physiology, human bioenergetics and its applications, 3rd McGraw-Hill
   Google Scholar
• Cerretelli , P , Sikand , R and Farhi , L E . 1966 . Readjustments in cardiac output and gas exchange during onset of exercise and recovery . J Appl Physiol. , 21 ( 4 ) : 1345 – 1350 .
   PubMedGoogle Scholar
• Davies , C T , Di Prampero , P E and Cerretelli , P . 1972 . Kinetics of the cardiac output and respiratory gas exchange during exercise and recovery . J. Appl. Physiol. , 32 : 618 – 625 .
   PubMed Web of Science ®Google Scholar
• Engelen , M , Porszasz , J , Riley , M , Wasserman , K , Maehar , K and Barstow , T J . 1996 . Effects of hypoxic hypoxia on O2 uptake and heart rate kinetics during server exercise . J. Appl. Physiol. , 81 ( 6 ) : 2500 – 2508 .
   PubMed Web of Science ®Google Scholar
• Hill , A V and Lupton , L . 1923 . Muscular Exercise, Lactic Acid And The Supply and utilization of oxygen . Q. J. Med. , 16 : 135 – 171 .
   Google Scholar
• Jones , A N and Poole , D C . 2005 . Oxygen uptake kintetics in sport and exercise . Routledge ,
   Google Scholar
• Linnarsson , D . 1974 . Dynamics of pulmonary gas exchange and heart rate changes at start and end of exercise . Acta Physiol. Scand. Suppl. , 415 : 1 – 68 .
   PubMedGoogle Scholar
• Martin , D E and Coe , P N . 1991 . Better training for distance runners , 2nd , Human Kinetics .
   Google Scholar
• Ozyener , F , Rossiter , H B , Ward , S A and Whipp , B J . 2001 . Influence of exercise intensity on the on-and off-transient kinetics of pulmonary oxygen uptake in humans . J. Physiol. , 53 ( 3 ) : 891 – 902 .
   Google Scholar
• Stirling , J R , Zakynthinaki , M S , Sampedro , J and Refoyo , I . 2007 . A model of heart rate klrietlcs in response to exercise . J. Nonlinear Math. Phys. , 15 ( 3 ) : 416 – 426 .
   Google Scholar
• Stirling , J R , Zakynthinaki , M S and Billat , V L . 2008 . Modelling and analysis of the effect of training on V˙O 2 kinetics and anaerobic capacity . Bul. Math. Biol. , 70 ( 5 ) : 1348 – 1370 .
   PubMedGoogle Scholar
• Stirling , J R , Bang , O , Christiansen , P L , Zakynthinaki , M S and Johansen , S K . 2008 . Geometry and transport in a model of two coupled quadratic nonlinear waveguides . Chaos , 18 : 013116
   Google Scholar
• Stirling , J R , Zakynthinaki , M S and Saltin , B . 2005 . A model of oxygen uptake kinetics in response to exercise: Including a method for calculating oxygen demand, deficit and debt . Bul. Math. Biol. , 67 ( 5 ) : 989 – 1015 .
   PubMedGoogle Scholar
• Stirling , J R and Zakynthinaki , M S . 2004 . Stability and the maintenance of balance following a perturbation from quiet stance . Chaos , 14 ( 1 ) : 96 – 105 .
   PubMedGoogle Scholar
• Stirling , J R and Zakynthinaki , M S . 2003 . Mathematical modelling in sport . Matematiques del segle XXI: dels fonaments a la tecnologia, III Cicle Ferran Sunyer i Balaguer, Manuel Castellet ed., Fundacio Caixa de Sabadell , : 73 – 97 .
   Google Scholar
• Stirling , J R . 2003 . Nonlinear dynamics, transport and the patchiness of clouds of pollution in an estuarine fluid flow . Discr Cont. Dyn. Sys. Series B. , 3 ( 2 ) : 263 – 284 .
   Google Scholar
• Stirling , J R . 2000 . Transport and bifurcation in a non area preserving 2 dimensional map with applications to the discharge of pollution in an estuarine flow . Physica D , 144 : 169 – 193 .
   Google Scholar
• Whipp , B J and Wasserman , K . 1972 . Oxygen uptake kinetics for various intensities of constant load work . J. Appl. Physiol. , 33 : 351 – 356 .
   PubMed Web of Science ®Google Scholar
• Zakynthinaki , M S and Stirling , J R . 2003 . Stochastic optimization for the calculation of the time dependency of the physiological demand during exercise and recovery . Comp. Phys. Commun. , doi:10.1016/j.cpc.2008.07.012
   Google Scholar
• Zakynthinaki , M S , Stirling , J R , Sillero , M , Sampedro , J and Refoyo , I . 2007 . Obtaining the basic response pattern of physiological time series data: a comparison of methods . Materials Matematics, UAB ,
   Google Scholar
• Zakynthinaki , M S and Stirling , J R . 2007 . Stochastic optimization for modelling physiological time series: application to the heart rate response to exercise . Comp. Phys. Commun. , 176 ( 2 ) : 981 – 908 .
   Google Scholar
• Zakynthinaki , M S and Saridakis , Y G . 2003 . Stochastic optimization for atip-tilt adaptive correcting system . Comp. Phys. Commun. , 150 ( 3 ) : 274 – 292 .
   Google Scholar