Limit cycle stability analysis of a multi-compartment model for a pressure-limited respirator and lung mechanics system

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 2024-2029

  Chellaboina, VijaySekhar ^a   Haddad, Wassim M ^b   Baileyi, James M ^c   Hancao, Li ^a  

^a University of Tennessee   (United States)

^b Georgia Institute of Technology   (United States)

^c Northeast Georgia Medical Center   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLIED (CO); COMMON PROBLEMS; COMPARTMENT MODELS; DYNAMIC BEHAVIORS; DYNAMICAL SYSTEM THEORY; GENERAL (CO); GLOBALLY ASYMPTOTICALLY STABLE (GAS); INDIVIDUAL (PSS 544-7); INTENSIVE CARE; LIMIT CYCLING; LUNG MECHANICS; LUNG VOLUME; MECHANICAL VENTILATION; PERIODIC ORBITS; RESPIRATORY FAILURES;

BIOLOGICAL ORGANS; DYNAMIC MODELS; DYNAMIC RESPONSE; DYNAMICAL SYSTEMS; INTENSIVE CARE UNITS; MATHEMATICAL MODELS; MECHANICS; MODAL ANALYSIS; OPTICAL BISTABILITY; PRESSURE; RESPIRATORS; RESPIRATORY SYSTEM; RESPIRATORY THERAPY; SCHRODINGER EQUATION; SURGERY;

SYSTEM STABILITY;

EID: 46449123479     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282672     Document Type: Conference Paper

References (16)

1. D. Campbell and J. Brown, "The electrical analog of the lung," Brit. J. Anaesth., vol. 35, pp. 684-693, 1963.
2. A. A. Wald, T. W. Murphy, and V. D. Mazzia, "A theoretical study of controlled ventilation," IEEE Trans. Biomed. Eng., vol. 15, pp. 237-248, 1968.
3. M. A. Epstein and R. A. Epstein, "Airway flow patterns during mechanical ventilation of infants: A mathematical model," IEEE Trans. Biomed. Eng., vol. 26, pp. 299-306, 1979.
4. P. Barbini, "Nonlinear models of the mechanics of breathing applied to the use and design of ventilators," J. Biomed. Eng., vol. 4, pp. 294-304, 1982.
5. J. J. Marini and P. S. Crooke, "A general mathematical model for respiratory dynamics relevant to the clinical setting," American Review of Respiratory Disease, vol. 147, pp. 14-24, 1993.
6. J. R. Hotchkiss, P. S. Crooke, A. B. Adams, and J. J. Marini, "Implications of a biphasic two-compartment model of constant flow ventilation for the clinical setting," Journal of Critical Care, vol. 9, pp. 114-123, 1994.
7. T. Similowski and J. H. Bates, "Two-compartment modeling of respiratory system mechanics at low frequencies: Gas redistribution or tissue rheology," European Respiratory Journal, vol. 4, pp. 353-358, 1991.
8. P. S. Crooke, J. D. Head, and J. J. Marini, "A general two-compartment model for mechanical ventilation," Mathematical and Computer Modeling, vol. 24, pp. 1-18, 1996.
9. W. M. Haddad and V. Chellaboina, "Stability and dissipativity theory for nonnegative and dynamical systems: A unified analysis framework for biological and physiological systems," Nonlinear Analysis: Real World Applications, vol. 6, pp. 35-65, 2005.
10. D. S. Bernstein and D. C. Hyland, "Compartmental modeling and second-moment analysis of state space systems," SIAM J. Matrix Anal. Appl., vol. 14, pp. 880-901, 1993.
11. S. Martinez, G. Michon, and J. S. Martin, "Inverse of strictly ultrametric matrices are of Stieltjes type," SIAM J. Matrix Anal. Appl., vol. 15, pp. 98-106, 1994.
12. K. Thulasiraman and M. N. S. Swamy, Graphs: Theory and Algorithms. Wiley-Interscience, 1992.
13. E. R. Weibel, Morphometry of the Human Lung. New York: Academic Publishers, 1963.
14. K. Horsfield, "Diameters, generations, and orders of branches in the bronchial tree," Journal of Applied Physiology, vol. 68, pp. 457-461, 1990.
15. K. Horsfield and G. Cumming, "Morphology of the bronchial tree in man," Journal of Applied Physiology, vol. 38, pp. 990-1975, 1975.
16. H. Kitaoka and B. Suki, "Branching design of the bronchial tree based on a diameter-flow relationship," Journal of Applied Physiology, vol. 82, pp. 968-976, 1997.