Translational Research: Multi-Scale Models of the Pulmonary Circulation in Health and Disease
Abstract
The pulmonary circulation is a unique low resistance system that carries almost the entire cardiac output, and is responsible for the essential role of providing oxygenated blood to the body. As the pulmonary circulation differs from the systemic circulation in its development, structure, and function, it is often most appropriate to study the mechanisms that contribute toward pulmonary vascular disease separately from those of systemic vascular disease at the genetic, cellular, tissue and organ level. Here we review the development of multi-scale, anatomically based models of the pulmonary circulation. These models aim to describe the interaction of structural and functional aspects of the pulmonary circulation that are the most important in determining the effective uptake of oxygen to the blood. We describe how these models have been used to understand normal lung physiology and to explain outcomes in pulmonary disease. Finally, we consider the future of multi-scale modeling in the pulmonary circulation and discuss what can be learned from well-developed multi-scale models of the pulmonary airspaces that interact closely with the lung’s circulatory system.
Keywords
Right Ventricle Pulmonary Vascular Resistance Pulmonary Arterial Pressure Pulmonary Circulation Pulmonary Blood FlowReferences
- 1.Weibel, E.R.: Morphometry of the Human Lung. Springer, Berlin (1963)Google Scholar
- 2.Levitzky, M.G.: Pulmonary Physiology, 7th edn. The McGraw-Hill Companies, Inc., New York (2007)Google Scholar
- 3.Grassino, A.E., Anthonisen, N.R.: Chest wall distortion and regional lung volume distribution in erect humans. J. Appl. Physiol. 39(6), 1004–1007 (1975)Google Scholar
- 4.Whitfield, A., Waterhouse, J., Arnott, W.M.: The total lung volume and its subdivisions. II. The effect of posture. Brit J Soc Med 4, 86–97 (1950)Google Scholar
- 5.Hoffman, E.A., Sinak, L.J., Riman, E.L.: Effect of body position on regional lung expansion: A computer tomographic approach. Physiologist 26(4), A-69 (1983)Google Scholar
- 6.Amis, T., Jones, H., Hughes, J.: Effect of posture on inter-regional distribution of pulmonary perfusion and VA/Q ratios in man. Respir. Physiol. 56, 169–182 (1984)CrossRefGoogle Scholar
- 7.West, J.B.: Regional differences in gas exchange in the lung of erect man. J. Appl. Physiol. 17(6), 893–898 (1962)Google Scholar
- 8.Hopkins, S.R., Henderson, A.C., Levin, D.L., Yamada, K., Arai, T., Buxton, R.B., Prisk, G.K.: Vertical gradients in regional lung density and perfusion in the supine human lung: the slinky effect. J. Appl. Physiol. 103(1), 240–248 (2007)CrossRefGoogle Scholar
- 9.Prisk, G.K., Yamada, K., Henderson, A.C., Arai, T.J., Levin, D.L., Buxton, R.B., Hopkins, S.R.: Pulmonary perfusion in the prone and supine postures in the normal human lung. J. Appl. Physiol. 103, 883–894 (2007)CrossRefGoogle Scholar
- 10.Albert, M.S., Cates, G.D., Driehuys, B., Happer, W., Saam, B., Springer Jr., C.S., Wishnia, A.: Biological magnetic resonance imaging using laser-polarized 129Xe. Nature 370(6486), 199–201 (1994)CrossRefGoogle Scholar
- 11.West, J.B., Dollery, C.T., Naimark, A.: Distribution of blood flow in isolated lung; relation to vascular and alveolar pressures. J. Appl. Physiol. 19, 713–724 (1964)Google Scholar
- 12.Hughes, M., West, J.B.: Point: Gravity is the major factor determining the distribution of blood flow in the human lung. J. Appl. Physiol. 104(5), 1531–1533 (2008)CrossRefGoogle Scholar
- 13.West, J.: Importance of gravity in determining the distribution of pulmonary blood flow. J. Appl. Physiol. 93(5), 1888–1889 (2002)Google Scholar
- 14.Glenny, R.W.: Counterpoint: gavity is not the major factor determining the distribution of blood flow in the healthy human lung. J. Appl. Physiol. 104(5), 1533–1535 (2008)CrossRefGoogle Scholar
- 15.Glenny, R.W., Bernard, S., Robertson, H.T., Hlastala, M.P.: Gravity is an important but secondary determinant of regional pulmonary blood flow in upright primates. J. Appl. Physiol. 86(2), 623–632 (1999)Google Scholar
- 16.Glenny, R.W., Lamm, W.J.E., Albert, R.K., Robertson, H.T.: Gravity is a minor determinant of pulmonary blood flow distribution. J. Appl. Physiol. 71, 620–629 (1991)Google Scholar
- 17.Clark, A.R., Tawhai, M.H., Burrowes, K.S.: The interdependent contributions of gravitational and structural features to the distribution of pulmonary perfusion in a multi-scale model of the pulmonary circulation. J. Appl. Physiol. 110, 943–945 (2011)CrossRefGoogle Scholar
- 18.Rideout, V., Katra, J.: Computer simulation of the pulmonary circulation. Simulation 12, 239–245 (1969)Google Scholar
- 19.Parker, J.C., Cave, C.B., Ardell, J.L., Hamm, C.R., Williams, S.G.: Vascular tree structure affects lung blood flow heterogeneity simulated in three dimensions. J. Appl. Physiol. 83(4), 1370–1382 (1997)Google Scholar
- 20.Glenny, R.W., Robertson, H.T.: Fractal modeling of pulmonary blood flow heterogeneity. J. Appl. Physiol. 70(3), 1024–1030 (1991)Google Scholar
- 21.Bshouty, Z., Younes, M.: Distensibility and pressure-flow relationship of the pulmonary circulation. II. Multibranched model. J. Appl. Physiol. 68(4), 1514–1527 (1990)Google Scholar
- 22.Burrowes, K.S., Hunter, P.J., Tawhai, M.H.: Anatomically-based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels. J. Appl. Physiol. 99, 731–738 (2005)CrossRefGoogle Scholar
- 23.Marshall, B., Marshall, C.: A model for hypoxic constriction of the pulmonary circulation. J. Appl. Physiol. 64(1), 68–77 (1988)CrossRefGoogle Scholar
- 24.Nelin, L.D., Krenz, G.S., Rickaby, D.A., Linehan, J.H., Dawson, C.A.: A distensible vessel model applied to hypoxic pulmonary vasoconstriction in the neonatal pig. J. Appl. Physiol. 74(5), 2049–2056 (1993)Google Scholar
- 25.Burrowes, K.S., Hoffman, E.A., Tawhai, M.H.: Species-specific pulmonary arterial asymmetry determines species differences in regional pulmonary perfusion. Ann. Biomed. Eng. 37(12), 2497–2509 (2009)CrossRefGoogle Scholar
- 26.Burrowes, K.S., Hunter, P.J., Tawhai, M.H.: Investigation of the relative effects of vascular branching structure and gravity on pulmonary arterial blood flow heterogeneity via an image-based computational model. Acad. Radiol. 12(11), 1464–1474 (2005)CrossRefGoogle Scholar
- 27.Burrowes, K.S., Swan, A.J., Warren, N.J., Tawhai, M.H.: Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system. Philos. Trans. R. Soc. A 366(1879), 3247–3263 (2008)CrossRefGoogle Scholar
- 28.Burrowes, K.S., Tawhai, M.H.: Computational predictions of pulmonary blood flow gradients: gravity versus structure. Respir. Physiol. Neurobiol. 154(3), 515–523 (2006)CrossRefGoogle Scholar
- 29.Burrowes, K.S., Tawhai, M.H.: Coupling of lung tissue tethering force to fluid dynamics in the pulmonary circulation. Int. J. Numer. Methods. Biomed. Eng. 26, 862–875 (2010)MATHGoogle Scholar
- 30.Burrowes, K.S., Tawhai, M.H., Hunter, P.J.: Modeling RBC and neutrophil distribution through an anatomically based pulmonary capillary network. Ann. Biomed. Eng. 32(4), 585–595 (2004)CrossRefGoogle Scholar
- 31.Clark, A.R., Burrowes, K.S., Tawhai, M.H.: Contribution of serial and parallel micro-perfusion to spatial variability in pulmonary inter- and intra-acinar blood flow. J. Appl. Physiol. 108(5), 1116–1126 (2010)CrossRefGoogle Scholar
- 32.Clark, A.R., Burrowes, K.S., Tawhai, M.H.: The impact of micro-embolism size on haemodynamic changes in the pulmonary micro-circulation. Respir. Physiol. Neurobiol. 175, 365–374 (2011)CrossRefGoogle Scholar
- 33.Burrowes, K.S., Clark, A.R., Marcinkowski, A., Wilsher, M.L., Milne, D.G., Tawhai, M.H.: Pulmonary embolism: predicting disease severity. Philos. Trans. R. Soc. A 369(1954), 4145–4148 (2011)MathSciNetCrossRefGoogle Scholar
- 34.Burrowes, K.S., Clark, A.R., Tawhai, M.H.: Blood flow redistribution and ventilation–perfusion mismatch during embolic pulmonary occlusion. Pulm. Circ. 1(3), 365–376 (2011)CrossRefGoogle Scholar
- 35.MacLean, M., Herve, P., Eddahibi, S., Adnot, S.: 5-hydroxytryptamine and the pulmonary circulation: receptors, transporters and relevance to pulmonary arterial hypertension. Br. J. Pharmacol. 131(2), 161–168 (2000)CrossRefGoogle Scholar
- 36.Howell, J.B.L., Permutt, S., Proctor, D.F., Riley, R.L.: Effect of inflation of the lung on different parts of pulmonary vascular bed. J. Appl. Physiol. 16(1), 71–76 (1961)Google Scholar
- 37.Horsfield, K.: Morphometry of the small pulmonary arteries in man. Circ. Res. 42, 537–593 (1978)CrossRefGoogle Scholar
- 38.Pump, K.K.: The circulation in the peripheral parts of the human lung. Chest 49(2), 119–129Google Scholar
- 39.Clough, A.V., Audi, S.H., Molthen, R.C., Krenz, G.S.: Lung circulation modeling: status and prospects. Proc. IEEE 94(4), 753–768 (2006)CrossRefGoogle Scholar
- 40.Hillier, S.C., Graham, J.A., Hanger, C.C., Godbey, P.S., Glenny, R.W., Wagner Jr., W.W.: Hypoxic vasoconstriction in pulmonary arterioles and venules. J. Appl. Physiol. 82(4), 1084–1090 (1997)Google Scholar
- 41.Marshall, B.E., Marshall, C.: Continuity of response to hypoxic pulmonary vasoconstriction. J. Appl. Physiol. Respir. Environ. Exerc. Physiol. 49, 189–196 (1980)Google Scholar
- 42.Elliot, F.M., Reid L.: Some new facts about the pulmonary artery and its branching pattern. Clin Radiol 16, 193–198 (1965)Google Scholar
- 43.Huang, W., Yen, R.T., McLaurine, M., Bledsoe, G.: Morphometry of the human pulmonary vasculature. J. Appl. Physiol. 81(5), 2123–2133 (1996)Google Scholar
- 44.Horsfield, K., Gordon, W.I.: Morphometry of pulmonary veins in man. Lung 159, 211–218 (1981)CrossRefGoogle Scholar
- 45.Singhal, S., Henderson, R., Horsfield, K., Harding, K., Cumming, G.: Morphometry of the human pulmonary arterial tree. Circ. Res. 33(2), 190–197 (1973)CrossRefGoogle Scholar
- 46.Glenny, R.W., Robertson, T.J.: Fractal properties of pulmonary blood flow: charaterization of spatial heterogeneity. J. Appl. Physiol. 69(2), 532–545 (1990)Google Scholar
- 47.Tawhai, M.H., Hunter, P.J., Tschirren, J., Reinhardt, J.M., McLennan, G., Hoffman, E.A.: CT-based geometry analysis and finite element models of the human and ovine bronchial tree. J. Appl. Physiol. 97(6), 2310–2321 (2004)CrossRefGoogle Scholar
- 48.Tawhai, M.H., Pullan, A.J., Hunter, P.J.: Generation of an anatomically based three-dimensional model of the conducting airways. Ann. Biomed. Eng. 28(7), 793–802 (2000)CrossRefGoogle Scholar
- 49.West, J.B.: Respiratory Physiology—The Essentials. Williams and Wilkins, Baltimore (1995)Google Scholar
- 50.Yen, M.: Elastic properties of pulmonary blood vessels. In: Respiratory Physiology: An Analytical Approach, pp. 553–560. Marcel Dekker, Inc. (1989)Google Scholar
- 51.Krenz, G.S., Dawson, C.A.: Flow and pressure distributions in vascular networks consisting of distensible vessels. Am. J. Physiol. Heart Circ Physiol 284(6), H2192–H2203 (2003)Google Scholar
- 52.Glenny, R.W., Lamm, W.J.E., Bernard, S.L., An, D., Chornuk, M., Pool, S., Wagner Jr., W.W., Hlastala, M.P., Rovertson, H.T.: Physiology of a microgravity environment, selected contribution: redistribution of pulmonary perfusion during weightlessness and increased gravity. J. Appl. Physiol. 89(3), 1239–1248 (2000)Google Scholar
- 53.Fernandez, J.W., Mithraratne, P., Thrupp, S.F., Tawhai, M.H., Hunter, P.J.: Anatomically based geometric modelling of the musculo-skeletal system and other organs. Biomech. Model. Mechanobiol. 2(3), 139–155 (2004)CrossRefGoogle Scholar
- 54.Tawhai, M., Nash, N., Lin, C., Hoffman, E.: Supine and prone differences in regional lung density and pleural pressure gradients in the human lung with constant shape. J. Appl. Physiol. 107(3), 912–920 (2009)CrossRefGoogle Scholar
- 55.Swan, A.J., Clark, A.R., Tawhai, M.H.: A computational model of the topographic distribution of ventilation in healthy human lungs. J. Theor. Biol. 300, 222–231 (2012)MathSciNetCrossRefGoogle Scholar
- 56.Hopkins, S.R., Henderson, A.C., Levin, D.L., Yamada, K., Arai, T., Buxton, R.B., Prisk, G.K.: Vertical gradients in regional lung density and perfusion in the supine human lung: the Slinky effect. J. Appl. Physiol. 103(1), 240–248 (2007)CrossRefGoogle Scholar
- 57.Spilker, R.L., Feinstein, J.A., Parker, D.W., Reddy, V.M., Taylor, C.A.: Morphometry-based impedance boundary conditions for patient-specific modeling of blood flow in pulmonary arteries. Ann. Biomed. Eng. 35(4), 546–559 (2007)CrossRefGoogle Scholar
- 58.Clipp, R., Steele, B.N.: Impedance boundary conditions for the pulmonary vasculature including the effects of geometry, compliance, and respiration. IEEE Trans. Biomed. Eng. 56(3), 862–870 (2009)CrossRefGoogle Scholar
- 59.Ochs, M., Nyengaard, J.R., Jung, A., Knudsen, L., Voigt, M., Wahlers, T., Richter, J., Gundersen, H.J.: The number of alveoli in the human lung. Am. J. Respir. Crit. Care Med. 169(1), 120–124 (2004)CrossRefGoogle Scholar
- 60.Fung, Y.C., Sobin, S.S.: Theory of sheet flow in lung alveoli. J. Appl. Physiol. 26, 472–488 (1969)Google Scholar
- 61.Guntheroth, W.G., Luchtel, D.L., Kawabori, I.: Pulmonary microcirculation: tubules rather than sheet or post. J. Appl. Physiol. 53(2), 510–515 (1982)Google Scholar
- 62.Maina, J.N., West, J.B.: Thin and strong! The bioengineering dilema in the structural and functional design of the blood gas barrier. Physiol. Rev. 85, 811–844 (2005)CrossRefGoogle Scholar
- 63.Fahraeus, R., Lindqvist T.: The viscosity of the blood in narrow capillary tubes. J. Appl. Physiol. 96, 562–568 (1931)Google Scholar
- 64.Hogg, J.: Neutrophil kinetics and lung injury. Physiol. Rev. 67(4), 1249–1295 (1987)MathSciNetGoogle Scholar
- 65.Doerschuk, C.: Neutrophil rheology and transit through capillaries and sinusoids. Am. J. Respir. Crit. Care Med. 159, 1693–1999 (1999)CrossRefGoogle Scholar
- 66.Fung, Y.C., Sobin, S.S.: Elasticity of the pulmonary alveolar sheet. Circ. Res. 30(4), 451–469 (1972)CrossRefGoogle Scholar
- 67.Pries, A.R., Secomb, T.W.: Microcirculatory network structures and models. Ann. Biomed. Eng. 28, 916–921 (2000)CrossRefGoogle Scholar
- 68.Pries, A.R., Secomb, T.W., Gaehtgens, P., Gross, J.F.: Blood flow in microvascular networks. Experiments and simulation. Circ. Res. 67(4), 826–834 (1990)CrossRefGoogle Scholar
- 69.Fenton, B., Wilson, D., Cokelet, G.: Analysis of the effect of measured white blood cell entrance time on hemodynamics in a computer model of a mircovascular bed. Pflugers Arch. 403, 396–401 (1985)CrossRefGoogle Scholar
- 70.Dhadwal, A., Wiggs, B., Doerschuk, C., Kamm, R.: Effects of anatomic variability on blood flow and pressure gradients in the pulmonary circulation. J. Appl. Physiol. 83(5), 1711–1720 (1997)Google Scholar
- 71.Huang, Y., Doerschuk, C.M., Kamm, R.D.: Computational modeling of RBC and neutrophil transit through the pulmonary capillaries. J. Appl. Physiol. 90(2), 545–564 (2001)CrossRefGoogle Scholar
- 72.Fung, Y.C., Sobin, S.S.: Pulmonary alveolar blood flow. Circ. Res. 30(4), 470–490 (1972)CrossRefGoogle Scholar
- 73.Fung, Y.C., Yen, R.T.: A new theory of pulmonary blood flow in zone 2 condition. J. Appl. Physiol. 60(5), 1638–1650 (1986)Google Scholar
- 74.Sobin, S.S., Fung, Y.C., Tremer, H.M., Rosenquist, T.H.: Elasticity of the pulmonary microvascular sheet in the cat. Circ. Res. 30(4), 440–450 (1972)CrossRefGoogle Scholar
- 75.Sobin, S.S., Tremer, H.M., Fung, Y.C.: Morphometric basis of the sheet-flow concenpt of the alveolar microcirculation in the cat. Circ. Res. 26(3), 397–414 (1970)CrossRefGoogle Scholar
- 76.Sobin, S.S., Tremer, H.M., Lindal, R.G., Fung, Y.C.: Distensibility of human pulmonary capillary blood vessels in the interalveolar septa. Fed. Proc. 38, 990 (1979)Google Scholar
- 77.Read, J.: Redistribution of stratified pulmonary blood flow during exercise. J. Appl. Physiol. 27(3), 374–377 (1969)Google Scholar
- 78.Read, J.: Stratified pulmonary blood flow: some consequences in emphysema and pulmonary embolism. Br. Med. J. 2, 44–46 (1969)CrossRefGoogle Scholar
- 79.Wagner, P., McRae, J., Read, J.: Stratified distribution of blood flow in secondary lobule of the rat lung. J. Appl. Physiol. 22(6), 1115–1123 (1967)Google Scholar
- 80.West, J.B., Maloney, J.E., Castle, B.L.: Effect of stratified inequality of blood flow on gas exchange in liquid-filled lungs. J. Appl. Physiol. 32(3), 357–361 (1972)Google Scholar
- 81.Hughes, J.M., Glazier, J.B., Maloney, J.E., West, J.B.: Effect of lung volume on the distribution of pulmonary blood flow in man. Respir. Physiol. 4(1), 58–72 (1968)CrossRefGoogle Scholar
- 82.Hopkins, S.R., Arai, T.J., Henderson, A.C., Levin, D.L., Buxton, R.B., Prisk, G.K.: Lung volume does not alter the distribution of pulmonary perfusion in dependent lung in supine humans. J. Physiol. 588(Pt 23), 4759–4768 (2010)CrossRefGoogle Scholar
- 83.Tawhai, M.H., Clark, A.R., Burrowes, K.S.: Computational models of the pulmonary circulation: insights and the move towards clinically directed studies. Pulm. Circu. 1(2), 224–238 (2011)CrossRefGoogle Scholar
- 84.Ben-Tal, A.: Simplified models for gas exchange in the human lungs. J. Theor. Biol. 238, 474–495 (2006)CrossRefGoogle Scholar
- 85.Kapitan, K., Hempleman, S.: Computer simulation of mammalian gas exchange. Comput. Methods Biol. Med. 16(2), 91–101 (1986)CrossRefGoogle Scholar
- 86.Monod, J., Wyman, J., Changeaux, J.: On the nature of allosteric transitions: a plausible model. J. Mol. Biol. 12, 88–112 (1965)CrossRefGoogle Scholar
- 87.Tawhai, M., Clark, A., Wilsher, M., Millne, D., Subramaniam, K., Burrowes, K.: Spatial redistribution of perfusion and gas exchange in patient specific models of pulmonary embolism. In: 2012 IEEE International Symposium on Biomedical Imaging. Barcelona, SpainGoogle Scholar
- 88.Wagner, P.D.: The multiple inert gas elimination technique (MIGET). Intensive Care Med. 34(6), 994–1001 (2008)CrossRefGoogle Scholar
- 89.McIntyre, K., Sasahara, A.: Hemodynamic alterations related to extent of lung scan perfusion defect in pulmonary embolism. J. Nucl. Med. 4, 166–170 (1971)Google Scholar
- 90.McIntyre, K., Sasahara, A.: The hemodynamic response to pulmonary embolism in patients without prior cardiopulmonary disease. Am. J. Cardiol. 28(3), 288–294 (1971)CrossRefGoogle Scholar
- 91.Ghaye, B., Ghuysen, A., Bruyere, P.J., D’Orio, V., Dondelinger, R.F.: Can CT pulmonary angiography allow assessment of severity and prognosis in patients presenting with pulmonary embolism? What the radiologist needs to know. Radiographics 26(1), 23–39; discussion 39–40 (2006) (discussion 39–40)Google Scholar
- 92.Malik, A.: Pulmonary microembolism. Physiol. Rev. 63, 1115–1207 (1983)MathSciNetGoogle Scholar
- 93.Tawhai, M.H., Hunter, P.J.: Characterising respiratory airway gas mixing using a lumped parameter model of the pulmonary acinus. Respir. Physiol. 127, 241–248 (2001)CrossRefGoogle Scholar
- 94.Haefeli-Bleuer, B., Weibel, E.R.: Morphometry of the human pulmonary acinus. Anat. Rec. 220, 401–414 (1988)CrossRefGoogle Scholar
- 95.Delcroix, M., Mélot, C., Lejeune, P., Leeman, M., Naeije, R.: Effects of vasodilators on gas exchange in acute canine embolic pulmonary hypertension. Anesthesiology 72, 77–84 (1990)Google Scholar
- 96.Delcroix, M., Mélot, C., Vachiery, J.-L., Lejeune, P., Leeman, M., Vanderhoeft, P., Naeije, R.: Effects of embolus size on hemodynamics and gas exchange in canine embolic pulmonary hypertension. J. Appl. Physiol. 69(6), 2254–2261 (1990)Google Scholar
- 97.Hasinoff, I., Ducas, J., Schick, U., Prewitt, R.: Pulmonary vascular pressure-flow characteristics in canine pulmonary embolism. J. Appl. Physiol. 68(2), 462–467 (1990)Google Scholar
- 98.Mélot, C., Delcroix, M., Closset, J., Vanderhoeft, P., Lejeune, P., Leeman, M., Naeije, R.: Starling resistor vs. distensible vessel models for embolic pulmonary hypertension. Am. J. Physiol. Heart Circ. Physiol. 268(2), H817–H827 (1995)Google Scholar
- 99.Levine, J.A., Schleusner, S.J., Jensen, M.D.: Energy expenditure of nonexercise activity. Am. J. Clin. Nutr. 72, 1451–1454 (2000)Google Scholar
- 100.Nishimura, M., Kiyamoto, K., Suzuki, A., Yamamoto, H., Tsuji, M., Kishi, F., Kawakami, Y.: Ventilatory and heart rate responses to hypoxia and hypercapnia in patients with diabetes mellitus. Thorax 44, 215–257 (1989)CrossRefGoogle Scholar
- 101.Politi, A.Z., Donovan, G.M., Tawhai, M.H., Sanderson, M.J., Lauzon, A., Bates, J.H.T., Sneyd, J.: A multiscale, spatially distributed model of asthmatic airway hyper-responsiveness. J. Theor. Biol. 266, 614–624 (2010)CrossRefGoogle Scholar
- 102.Wang, I., Politi, A.Z., Tania, N., Bai, Y., Sanderson, M.J., Sneyd, J.: A mathematical model of airway and pulmonary arteriole smooth muscle. Biophys. J. 94(6), 2053–2064 (2008)CrossRefGoogle Scholar
- 103.Hai, C., Murphy, R.: Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am. J. Physiol. 254, C99–C106 (1988)Google Scholar
- 104.Lai-Fook, S.J., Hyatt, R.E.: Effect of parenchyma and length changes on vessel pressure-diameter behavior in pig lungs. J. Appl. Physiol. 47(4), 666–669 (1979)Google Scholar
- 105.Donovan, G., Bullimore, S., Elvin, A., Tawhai, M., Bates, J., Lauzon, A., Sneyd, J.: A continuous-binding cross-linker model for passive airway smooth muscle. Biophys. J. 99(10), 3164–3171 (2010)CrossRefGoogle Scholar