Abstract
We present a computational model to predict maximal expiration through a morphometry-based asymmetrical bronchial tree. A computational model with the Horsfield-like geometry of the airway structure, including wave-speed flow limitation and taking into consideration separate airflows from several independent alveolar compartments has been derived. The airflow values are calculated for quasistatic conditions by solving a system of nonlinear differential equations describing static pressure losses along the airway branches. Calculations done for succeeding lung volumes result in the semidynamic maximal expiratory flow–volume (MEFV) curve. Simulations performed show that the model captures the main phenomena observed in vivo during forced expiration: effort independence of the flow–volume curve for the most of vital capacity, independence of limited flow on the properties of airways downstream to the choke points, characteristic differences of lung regional pressures and volumes, and a shape of their variability during exhalation. Some new insights into the flow limitation mechanism were achieved. First, flow limitation begins at slightly different time instants in individual branches of the bronchial tree, however after a short period of time, all regional flows are limited in a parallel fashion. Hence, total flow at the mouth is limited for most of the expired lung volume. Second, each of the airway branches contribute their own flow–volume shape and just these individual flows constitute the measured MEFV curve. Third, central airway heterogeneity can play a crucial role in modification of the entire flow. Fourth, the bronchial tree asymmetry is responsible for a nongravitational component of regional volume variability. Finally, increased inhomogeneity yields results that cannot be explained nor re-created with the use of a symmetrical structure of the bronchial tree.© 2003 Biomedical Engineering Society.
PAC2003: 8719Uv, 8710+e, 8718Bb
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References
Agostoni, E., and W. O. Fenn. Velocity of muscle shortening as a limiting factor in respiratory air flow. J. Appl. Physiol.15:349–353, 1960.
Anafi, R. C., and T. A. Wilson. Airway stability and heterogeneity in the constricted lung. J. Appl. Physiol.91:1185–1192, 2001.
Barnea, O., S. Abbould, A. Guber, and I. Bruderman. New model-based indices for maximum expiratory flow–volume curve in patients with chronic obstructive pulmonary disease. Comput. Biol. Med.26:123–131, 1996.
Bloch, K. E., C. L. Georgescu, E. W. Russi, and W. Weder. Gain and subsequent loss of lung function after lung volume reduction surgery in cases of severe emphysema with different morphologic patterns. J. Thorac. Cardiovasc. Surg.123:845–854, 2002.
Bogaard, J. M., S. E. Overbeek, A. F. M. Verbraak, C. Vons, H. T. M. Folgering, Th. W. van der Mark, C. M. Roos, P. J. Sterk, and the Dutch CNSLD study group. Pressure–volume analysis of the lung with an exponential and linear-exponential model in asthma and COPD. Eur. Respir. J.8:1525–1531, 1995.
Cederlund, K., U. Tylen, L. Jorfeldt, and P. Aspelin. Classification of emphysema in candidates for lung volume reduction surgery (): A new objective and surgically oriented model for describing CT severity and heterogeneity. Chest122:590–596, 2002.
Colebatch, H. J. H., C. K. Y. Ng, and N. Nikov. Use of an exponential function for elastic recoil. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.46:387–393, 1979.
Collins, J. M., A. H. Shapiro, E. Kimmel, and R. D. Kamm. The steady expiratory pressure–flow relation in a model pulmonary bifurcation. J. Biomech. Eng.115:299–305, 1993.
Dawson, S. D., and E. A. Elliott. Wave-speed limitation on expiratory flow—A unifying concept. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.43:498–515, 1977.
Elad, D., and R. D. Kamm. Parametric evaluation of forced expiration using a numerical model. J. Biomech. Eng.111:192–199, 1989.
Elad, D., R. D. Kamm, and A. H. Shapiro. Tube law for the intrapulmonary airway. J. Appl. Physiol.65:7–13, 1988.
Elad, D., R. D. Kamm, and A. H. Shapiro. Mathematical simulation of forced expiration. J. Appl. Physiol.65:14–25, 1988.
Fredberg, J. J., and D. Stamenovic. On the imperfect elasticity of lung tissue. J. Appl. Physiol.67:2408–2419, 1989.
Fry, D. L.A preliminary lung model for simulating the aerodynamics of the bronchial tree. Comput. Biomed. Res.2:111–134, 1968.
Fry, D. L., R. V. Ebert, W. W. Stead, and C. C. Brown. The mechanics of pulmonary ventilation in normal subjects and in patients with emphysema. Am. J. Med.16:80–97, 1954.
Georgopoulos, D., A. Gomez, and S. N. Mink. Factors determining lobar emptying during maximal and partial forced deflations in nonhomogeneous airway obstruction in dogs. Am. J. Respir. Crit. Care Med.149:1241–1247, 1994.
Georgopoulos, D., S. N. Mink, L. Oppenheimer, and N. R. Anthonisen. How is maximal expiratory flow reduced in canine postpneumonectomy lung growth?J. Appl. Physiol.71:834–840, 1991.
Gillis, H. L., and K. R. Lutchen. How heterogeneous bronchoconstriction affects ventilation distribution in human lungs: a morphometric model. Ann. Biomed. Eng.27:14–22, 1999.
Gillis, H. L., and K. R. Lutchen. Airway remodeling in asthma amplifies heterogeneities in smooth muscle shortening causing hyperresponsiveness. J. Appl. Physiol.86:2001–2012, 1999.
Hammersley, J. R., and D. E. Olson. Physical model of the smaller pulmonary airways. J. Appl. Physiol.72:2402–2414, 1992.
Horsfield, K., G. Dart, D. E. Olson, and G. Cumming. Models of the human bronchial tree. J. Appl. Physiol.31:207–217, 1971.
Hughes, J. M. B., F. G. Hoppin, Jr., and J. Mead. Effect of lung inflation on bronchial length and diameter in excised lungs. J. Appl. Physiol.32:25–35, 1972.
Hyatt, R. E.Expiratory flow limitation. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.55:1–8, 1983.
Hyatt, R. E., D. P. Schilder, and D. L. Fry. Relationship between maximum expiratory flow and degree of lung inflation. J. Appl. Physiol.13:331–336, 1958.
Jaeger, M. J., and H. Matthys. The pattern of flow in the upper human airways. Respir. Physiol.6:113–127, 1969.
Lambert, R. K.A new computational model for expiratory flow from nonhomogeneous human lungs. J. Biomech. Eng.111:200–205, 1989.
Lambert, R. K.Sensitivity and specificity of the computational model for maximal expiratory flow. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.57:958–970, 1984.
Lambert, R. K., T. A. Wilson, R. E. Hyatt, and J. R. Rodarte. A computational model for expiratory flow. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.52:44–56, 1982.
Landau, L. I., L. M. Taussig, P. T. Macklem, and P. H. Beaudry. Contribution of inhomogeneity of lung units to the maximal expiratory flow–volume curve in children with asthma and cystic fibrosis. Am. Rev. Respir. Dis.111:725–731, 1975.
Lutchen, K. R., J. L. Greenstein, and B. Suki. How inhomogeneities and airway walls affect frequency dependence and separation of airway and tissue properties. J. Appl. Physiol.80:1696–1707, 1996.
Lutchen, K. R., A. Jensen, H. Atileh, D. W. Kaczka, E. Israel, B. Suki, and E. P. Ingenito. Airway constriction pattern is a central component of asthma severity. Am. J. Respir. Crit. Care Med.164:207–215, 2001.
McNamara, J. J., R. G. Castile, G. M. Glass, and J. J. Fredberg. Heterogeneous lung emptying during forced expiration. J. Appl. Physiol.63:1648–1657, 1987.
McNamara, J. J., R. G. Castile, M. S. Ludwig, G. M. Glass, R. H. Ingram, Jr., and J. J. Fredberg. Heterogeneous regional behavior during forced expiration before and after histamine inhalation in dogs. J. Appl. Physiol.76:356–360, 1994.
Mead, J.Analysis of the configuration of maximum expiratory flow–volume curves. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.44:156–165, 1978.
Mead, J., J. M. Turner, P. T. Macklem, and J. B. Little. Significance of the relationship between lung recoil pressure and maximum expiratory flow. J. Appl. Physiol.22:95–108, 1967.
Melissinos, C. G., P. Webster, Y. K. Tien, and J. Mead. Time dependence of maximum flow as an index of nonuniform emptying. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.47:1043–1050, 1979.
Milic-Emili, J. J., A. M. Henderson, M. B. Dolovich, D. Trop, and K. Kaneko. Regional distribution of inspired gas in the lung. J. Appl. Physiol.21:749–759, 1966.
Mink, S. N.Mechanism of lobar alveolar pressure decline during forced deflation in canine regional emphysema. J. Appl. Physiol.82:632–643, 1997.
Mroczka, J., and A. G. Polak. Noninvasive method for measurement of respiratory system parameters. Proceedings of the XIII IMEKO World Congress, Torino, 5–9 September 1994, Vol. 2, pp. 1561–1565.
Pardaens, J., K. P. van de Woestijne, and J. Clément. A physical model for expiration. J. Appl. Physiol.33:479–490, 1972.
Pardaens, J., K. P. van de Woestijne, and J. Clément. Simulation of regional lung emptying during slow and forced expirations. J. Appl. Physiol.39:191–198, 1975.
Polak, A. G.A forward model for maximum expiration. Comput. Biol. Med.28:613–625, 1998.
Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes: The Art of Scientific Computing. Cambridge, MA: Cambridge University Press, 1986.
Pride, N. B., S. Permutt, R. L. Riley, and B. Bromberger-Barnea. Determinants of maximal expiratory flow from the lungs. J. Appl. Physiol.23:646–662, 1967.
Renotte, C., M. Remy, and Ph. Saucez. Dynamic model of airway pressure drop. Med. Biol. Eng. Comput.36:101–106, 1998.
Reynolds, D. B.Steady expiratory flow-pressure relationship of a model of the human bronchial tree. J. Biomech. Eng.104:153–158, 1982.
Reynolds, D. B., and J.-S. Lee. Steady pressure-flow relationship of a model of the canine bronchial tree. J. Appl. Physiol.: Respir., Environ. Exercise Physiol.51:1072–1079, 1981.
Robatto, F. M., S. Simard, and M. S. Ludwig. How changes in the serial distribution of bronchoconstriction affect lung mechanics. J. Appl. Physiol.74:2838–2847, 1993.
Salazar, E., and J. H. Knowles. An analysis of pressure-volume characteristics of the lungs. J. Appl. Physiol.19:97–104, 1964.
Shapiro, A. H.Steady flow in collapsible tubes. J. Biomech. Eng.99:126–147, 1977.
Shin, J. J., D. Elad, and R. D. Kamm. Simulation of forced breathing maneuvers. In: Biological Flow, edited by M. Y. Jaffrin and C. Caro. New York: Plenum, 1995.
Solway, J., J. J. Fredberg, R. H. Ingram, Jr., O. F. Pedersen, and J. M. Drazen. Interdependent regional lung emptying during forced expiration: a transistor model. J. Appl. Physiol.62:2013–1025, 1987.
Sud, V. K., R. Srinivasan, J. B. Charles, and M. W. Bungo. Effect of lover-body negative pressure on blood flow with applications to the human cardiovascular system. Med. Biol. Eng. Comput.31:569–575, 1993.
Thorpe, C. W., and J. H. T. Bates. Effect of stochastic heterogenity on lung impedance during acute bronchoconstriction: a model analysis. J. Appl. Physiol.82:1616–1625, 1997.
Thurnheer, R., H. Engel, W. Weder, U. Stammberger, I. Laube, E. W. Russi, and K. E. Bloch. Role of lung perfusion scintigraphy in relation to chest computed tomography and pulmonary function in the evaluation of candidates for lung volume reduction surgery. Am. J. Respir. Crit. Care Med.159:301–310, 1999.
Topulos, G. P., G. Nielan, G. Glass, and J. J. Fredberg. Interdependence of regional expiratory flows limits alveolar pressure differences. J. Appl. Physiol.69:1413–1418, 1990.
Verbanck, S., D. Schuermans, A. Van Muylem, M. Noppen, and W. Vincken. Ventilation distribution during histamine provocation. J. Appl. Physiol.83:1907–1916, 1997.
Verbanck, S., D. Schuermans, M. Noppen, W. Vincken, and M. Paiva. Methacholine versus histamine: paradoxical response of spirometry and ventilation distribution. J. Appl. Physiol.91:2587–2594, 2001.
Warner, D. O., R. E. Hyatt, and K. Rehder. Inhomogeneity during deflation of excised canine lungs. I. Alveolar pressures. J. Appl. Physiol.65:1757–1765, 1988.
Warner, D. O., R. E. Hyatt, and K. Rehder. Inhomogeneity during deflation of excised canine lungs. II. Alveolar volumes. J. Appl. Physiol.65:1766–1774, 1988.
Weibel, E. R. Morphometry of the Human Lung. New York: Academic, 1963.
Wheatley, J. R., T. C. Amis, and L. A. Engel. Nasal and oral airway pressure–flow relationships. J. Appl. Physiol.71:2317–2324, 1991.
Wiggs, B. R., R. Moreno, J. C. Hogg, C. Hilliam, and P. D. Paré. A model of the mechanics of airway narrowing. J. Appl. Physiol.69:849–860, 1990.
Wilson, T. A., J. J. Fredberg, J. R. Rodarte, and R. E. Hyatt. Interdependence of regional expiratory flow. J. Appl. Physiol.59:1924–1928, 1985.
Wilson, T. A., M. J. Hill, and R. D. Hubmayr. Regional lung volume trajectories during expiratory flow in dogs. J. Appl. Physiol.80:1144–1148, 1996.
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Polak, A.G., Lutchen, K.R. Computational Model for Forced Expiration from Asymmetric Normal Lungs. Annals of Biomedical Engineering 31, 891–907 (2003). https://doi.org/10.1114/1.1588651
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DOI: https://doi.org/10.1114/1.1588651