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

References

• Barbini , P . 1982 . Nonlinear Models of the Mechanics of Breathing Applied to the Use and Design of Ventilators . Journal of Biomedical Engineering , 4 : 294 – 304 .
   PubMedGoogle Scholar
• Campbell , D and Brown , J . 1963 . The Electrical Analog of the Lung . British Journal of Anaesthesia , 35 : 684 – 693 .
   Google Scholar
• Crooke , PS , Head , JD and Marini , JJ . 1996 . A General Two-compartment Model for Mechanical Ventilation . Mathematical and Computer Modeling , 24 : 1 – 18 .
   Google Scholar
• Epstein , MA and Epstein , RA . 1979 . Airway Flow Patterns During Mechanical Ventilation of Infants: A Mathematical Model . IEEE Transactions on Biomedical Engineering , 26 : 299 – 306 .
   PubMed Web of Science ®Google Scholar
• Haddad , WM and Chellaboina , V . 2008 . Nonlinear Dynamical Systems and Control: A Lyapunov-based Approach , Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Haddad , WM , Chellabonia , V and Hui , Q . 2010 . Nonnegative and Compartmental Dynamical Systems. , Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Haddad , WM , Chellabonia , V and Nersesov , SG . 2006 . Impulsive and Hybrid Dynamical Systems , Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Hofman , WF and Meyer , DC . 1999 . “ Respiratory Physiology ” . In in Essentials of Human Physiology , 2nd , Edited by: Nosek , TM . Florida : Gold Standard Media, Inc . http://www.lib.mcg.edu/edu/eshuphysio/program/section4/4outline.htm
   Google Scholar
• Horsfield , K . 1990 . Diameters, Generations, and Orders of Branches in the Bronchial Tree . Journal of Applied Physiology , 68 : 457 – 461 .
   PubMed Web of Science ®Google Scholar
• Horsfield , K and Cumming , G . 1975 . Morphology of the Bronchial Tree in Man . Journal of Applied Physiology , 38 : 990 – 1975 .
   PubMedGoogle Scholar
• Hotchkiss , JR , Crooke , PS , Adams , AB and Marini , JJ . 1994 . Implications of a Biphasic Two-compartment Model of Constant Flow Ventilation for the Clinical Setting . Journal of Critical Care , 9 : 114 – 123 .
   PubMed Web of Science ®Google Scholar
• Kallet , RH , Dicker , RA , Katz , JA and Mackersie , RC . 2006 . Effects of Tidal Volume on Work of Breathing During Lung-protective Ventilation in Patients with Acute Lung Injury and Acute Respiratory Distress Syndrome . Critical Care Medicine , 34 : 8 – 14 .
   PubMed Web of Science ®Google Scholar
• Kitaoka , H and Suki , B . 1997 . Branching Design of the Bronchial Tree Based on a Diameter-flow Relationship . Journal of Applied Physiology , 82 : 968 – 976 .
   PubMed Web of Science ®Google Scholar
• Marini , JJ and Crooke , PS . 1993 . A General Mathematical Model for Respiratory Dynamics Relevant to the Clinical Setting . American Review of Respiratory Disease , 147 : 14 – 24 .
   PubMedGoogle Scholar
• Martinez , S , Michon , G and Martin , JS . 1994 . Inverse of Strictly Ultrametric Matrices are of Stieltjes Type . SIAM Journal on Matrix Analysis and Applications , 15 : 98 – 106 .
   Web of Science ®Google Scholar
• Narendra , KS and Annaswamy , AM . 1989 . Stable Adaptive Systems , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Nilsestuen , JO and Hargett , KD . 2005 . Using Ventilator Graphics to Identify Patient–ventilator Asynchrony . Respiratory Care , 50 : 202 – 234 .
   PubMedGoogle Scholar
• Similowski , T and Bates , JH . 1991 . Two-compartment Modeling of Respiratory System Mechanics at Low Frequencies: Gas Redistribution or Tissue Rheology . European Respiratory Journal , 4 : 353 – 358 .
   PubMed Web of Science ®Google Scholar
• Thulasiraman , K and Swamy , MNS . 1992 . Graphs: Theory and Algorithms , New York : Wiley-Interscience .
   Google Scholar
• Wald , AA , Murphy , TW and Mazzia , VD . 1968 . A Theoretical Study of Controlled Ventilation . IEEE Transactions on Biomedical Engineering , 15 : 237 – 248 .
   PubMedGoogle Scholar
• Weibel , ER . 1963 . Morphometry of the Human Lung , New York : Academic Publishers .
   Google Scholar
• Wiggins , S . 2003 . Introduction to Applied Nonlinear Dynamical Systems and Chaos , 2nd , New York : Springer .
   Google Scholar