Lumped Parameter Modeling of Human Respiratory System

Rachana Visaria,

Rachana Visaria

In Vivo Temperatures, LLC, Burnsville, MN, USA

Search for more papers by this author

Rachana Visaria,

Rachana Visaria

In Vivo Temperatures, LLC, Burnsville, MN, USA

Search for more papers by this author

Book Editor(s):Devashish Shrivastava,

Devashish Shrivastava

US Food and Drug Administration, Silver Spring, NY, 10903 USA

Search for more papers by this author

First published: 27 April 2018

https://doi.org/10.1002/9781119127420.ch7

Citations: 1

Summary

Mathematical models can be lumped or distributed parameter representations of a system. In both the lumped and distributed parameter modeling, the system isdivided into independent compartments or lumps and each individual part of a section of a model is called a component/parameter. This chapter describes the process of lumped parameter modeling by using an example of respiratory system. The developed lumped model is shown to aid in identifying pulmonary abnormalities quickly (within minutes of onset), noninvasively and with a minimum physiological monitoring (only airway pressure and flow) that is readily available in ICUs and ORs. The respiratory system properties are related to the forces (viscous, elastic, and inertial) that develop in the system. To determine which one of the candidate models presented in the chapter is a best approximation of the respiratory system, the chapter explores the distribution of the mechanical properties in 24 generations of the respiratory system.

References

Lorino AM, Lorino H, and Harf A. A synthesis of the Otis, Mead, and Mount mechanical respiratory models, Respir Physiol, vol. 97: 123–133, 1994.
10.1016/0034-5687(94)90020-5
Google Scholar
Eyles JG and Pimmel RL. Estimating respiratory mechanical parameters in parallel compartment models, IEEE Trans Biomed Eng, vol. 28: 313–317, 1981.
10.1109/TBME.1981.324798
CAS PubMed Web of Science® Google Scholar
Kaczka DW, Brown RH, and Mitzner W. Assessment of heterogeneous airway constriction in dogs: A structure-function analysis. J Appl Physiol (1985), vol. 106(2): 520–530, 2009.
Google Scholar
Wegner CD, Jackson AC, and Gillespie JR. Linear-lumped-parameter modeling of pulmonary impedance in monkeys, Ann Biomed Eng, vol. 14: 401–415, 1986.
Google Scholar
Lutchen KR, Costa KD. Physiological interpretations based on lumped element models fit to respiratory impedance data: Use of forward-inverse modeling. IEEE Transactions on Biomedical Engineering 37(11): 1076–1086, 1990.
Google Scholar
Tomalak W, Peslin R, Duvivier C, and Gallina C. Optimal frequency range to analyze respiratory transfer impedance with six-element model. J Appl Physiol, vol. 75: 2656–2664, 1993.
Google Scholar
Liu CH, Niranjan SC, Clark JW Jr, et al. Airway mechanics, gas exchange, and blood flow in a nonlinear model of the normal human lung, J Appl Physiol, vol. 84: 1447–1469, 1998.
10.1152/jappl.1998.84.4.1447
CAS PubMed Web of Science® Google Scholar
Weibel ER. Morphometry of the Human Lung. Academic, New York, 1963.
10.1007/978-3-642-87553-3
Google Scholar
Visaria RK and Westenskow DR. Model-based detection of partially obstructed endotracheal tube. Crit Care Med, 33(1): 149–54; discussion 249–250, 2005.
10.1097/01.CCM.0000150656.01906.9F
Google Scholar
Visaria RK and Westenskow DR. Model-based detection of endobronchial intubation. Anesth Analg, 103(4): 888–893, 2006.
10.1213/01.ane.0000237271.78867.1f
Google Scholar
Winters B, Custer J, Galvagno SM Jr, et al. Diagnostic errors in the intensive care unit: A systematic review of autopsy studies. BMJ Quality & Safety Online First, BMJ Qual Saf, 21(11): 894–902, 2012.
Google Scholar
Grimmett WG and Poh J. Clearance of an obstructed endotracheal tube with an arterial embolectomy catheter with the patient in the prone position. Anaesth Intensive Care, vol. 26: 579–581, 1998.
10.1177/0310057X9802600517
Google Scholar
Redding GJ, Fan L, Cotton EK, and Brooks JG. Partial obstruction of endotracheal tubes in children: Incidence, etiology, significance. Crit Care Med, vol. 7: 227–231, 1979.
10.1097/00003246-197905000-00004
CAS PubMed Web of Science® Google Scholar
Watremez C, Roeseler J, De Kock M, et al. An improved porcine model of stable methacholine-induced bronchospasm, Intensive Care Med, vol. 29: 119–125, 2003.
PubMed Web of Science® Google Scholar
Bardoczky GI, Engelman E, and d'Hollander A. Continuous spirometry: An aid to monitoring ventilation during operation. Br J Anaesth, vol. 71: 747–751, 1993.
10.1093/bja/71.5.747
CAS PubMed Web of Science® Google Scholar
Feied CF. Pulmonary embolism, in Emergency Medicine Principles and Practice , P Rosen and R Barkin (eds), Emergency Medicine: Concepts and Clinical Practice, 4th edn. Philadelphia: Lippincott, Williams & Wilkins, 1998.
Google Scholar
Satz AK, Stoelting RK, and Gibbs PS. Intraoperative pulmonary edema in a patient being treated with amiodarone. Anesth Analg, vol. 73: 821–823, 1991.
Google Scholar
Redding GJ, Fan L, Cotton EK, and Brooks JG. Partial obstruction of endotracheal tubes in children: Incidence, etiology, significance. Crit Care Med, 7(5): 227–231, 1979.
Google Scholar
Bijaoui EL, Champagne V, Baconnier PF, et al. Mechanical properties of the lung and upper airways in patients with sleep-disordered breathing. Am J Respir Crit Care Med, 165(8): 1055–1061, 2002.
Google Scholar
Makinen MT, Yli-Hankala A, and Kansanaho M. Early detection of CO2 pneumothorax with continuous spirometry during laparoscopic fundoplication. Acta Anaesthesiol Scand, 39(3): 411–413, 1995.
10.1111/j.1399-6576.1995.tb04087.x
PubMed Web of Science® Google Scholar
Perko G and Fernandes A. Subcutaneous emphysema and pneumothorax during laparoscopy for ectopic pregnancy removal. Acta Anaesthesiol Scand, 41(6): 792–794, 1997.
10.1111/j.1399-6576.1997.tb04786.x
CAS PubMed Web of Science® Google Scholar
Lee BP, Chiang ST, and Hwang JC. Effects of intrapleural pressure on phrenic nerve activity. Chin J Physiol, 29(2): 79–90, 1986.
Google Scholar
Sobh JF, Lilly CM, Drazen JM, and Jackson AC. Respiratory transfer impedance between 8 and 384 Hz in guinea pigs before and after bronchial challenge. J Appl Physiol, 82(1): 172–181, 1997.
Google Scholar
Hirshman CA and Downes H. Airway responses to methacholine and histamine in basenji greyhounds and other purebred dogs. Respir Physiol, 63(3): 339–346, 1986.
Google Scholar
Breen PH, Becker LJ, Ruygrok P, et al. Canine bronchoconstriction, gas trapping, and hypoxia with methacholine. J Appl Physiol, 63(1): 262–269, 1987.
Google Scholar
Kaczka DW, Ingenito EP, Suki B, and Lutchen KR. Partitioning airway and lung tissue resistances in humans: Effects of bronchoconstriction. J Appl Physio, 82(5): 1531–1541, 1997.
Google Scholar
Woolcock AJ and Macklem PT. Mechanical factors influencing collateral ventilation in human, dog, and pig lungs. J Appl Physiol, 30(1): 99–115, 1971.
Google Scholar
Kelly S, Cohen C, Powell E, et al. Gas mixing in the lungs of dogs and pigs. Respir Physiol, 47(3): 341–349, 1982.
10.1016/0034-5687(82)90062-7
CAS PubMed Web of Science® Google Scholar

Citing Literature

Theory and Applications of Heat Transfer in Humans, Volume 2