This paper aims at solving an optimal control problem for determining the response of hypoxia to heart rate and alveolar ventilation that are cardiovascular and respiratory control respectively during a physical activity. A twononlinear coupled ordinary differential equations is presented. The cost function of optimal control problem is discretized using the linear B-splines functions defined on a regular grid. The results show the determinant parameters stabilized at normal value.
Cite this paper
J. Ntaganda and B. Mampassi, "An Optimal Control Problem for Hypoxemic Hypoxia Tissue-Blood Carbon Dioxide Exchange during Physical Activity," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 56-61. doi: 10.4236/ojapps.2013.31009.
 A. Cymerman and P. B. Rock, “Medical Problems in High Mountain Environments,” A Handbook for Medical Officers, USARIEM-TN94-2, US Army Research Institute of Environmental Medicine Thermal and Mountain Medicine Division Technical Report, 2009.
 G. Gutierrez, “A Mathematical Model of Tissue-Blood Carbon Dioxide Exchange during Hypoxia,” American Journal of Respiratory Critical Care Medecine, Vol. 169. No. 4, 2004, pp. 525-533.
 J. J. Tyson and B. Novak, “Regulation of the Eukariotic Cell-Cycle: Molecular Antagonism, Hysteresis, and Irreversible Transitions,” Journal of Theoretical Biology, Vol. 210, No. 2, 2001, pp. 249-263.
 D. Gammack, H. M. Byrne and C. E. Lewis, “Estimating the Selective Advantage of Mutant p53 Tumour Cells to Repeated Rounds of Hypoxia,” Bulletin of Mathematical Biology, Vol. 63, No. 1, 2001, pp. 135-166.
 J. A. Dempsey, H. V. Forster and D. M. Ainsworth, “Regulation of Hyperpnea, Hyperventilation, and Respiratory Muscle Recruitment during Exercise,” In: J. A. Dempsey and A. I. Pack, Eds., Regulation of Breathing, Marcel Dekker, New York, 1995, pp. 1065-1133.
 S. Timischl, “A Global Model for the Cardiovascular and Respiratory System,” PhD Thesis, Karl Franzens Univer sit of Graz, 1998.
 S. Timischl, J. J. Batzel and F. Kappel, “Modeling the Human Cardiovascular Respiratory Control System: An Optimal Control Application to the Transition to Non REM Sleep,” Spezialforschungsbereich F-003 Technical Report 190, Karl Franzens Universitat, 2000.
 D. Curran-Everett, “A Classic Learning Opportunity from Fenn, Rahn, and Otis (1946): The Alveolar Gas Equation,” Advances in Physiology Education, Vol. 30, No. 2, 2006, pp. 58-62. doi:10.1152/advan.00076.2005
 I. Giovannini, C. Chiarla, G. Boldrini and M. Castagneto, “Calculation of Venoarterial CO2 Concentration Difference,” Journal of Applied Physiology, Vol. 74, No. 2, 1993, pp. 959-964.
 A. R. Douglas, N. L Jones and J. W. Reed, “Calculation of Whole Blood CO2 Content,” Journal of Applied Physiology, Vol. 65, No. 1, 1988, pp. 473-477.