Assessment of mucus transport rate in the human lung airways using mathematical model
In this study, a planar two layer mathematical model is presented to study the mucus transport in the human lung airways under steady state condition due to cilia beating and certain immotile cilia forming porous matrix bed in serous sub-layer in contact with the epithelium and air-motion by considering mucus as a visco-elastic fluid. The effect of air-motion due to external forces and other processes is considered by prescribing shear stress at mucus air interface. It is seen that the mucus transport rate increases as the pressure drop, shear stress due to air-motion, the velocity generated by cilia tips and porosity parameter increase. It is noted that the effect of gravity is similar to that of the pressure drop. It is also observed that transport rate of mucus decreases as the viscosity of serous layer fluid or mucus increases, but any increase in mucus viscosity at its higher values does not seem to affect the mucus transport rate. It is also seen that for given total depth of serous sub-layer and mucus layer, there exists a serous fluid layer thickness for which mucus transport is maximum. It is also seen that mucus transport rate increases as its shear modulus of elasticity decreases i.e. mucus transport increases as the relaxation time increases.
Agarwal M, King M, Shukla JB (1989) Mucus transport in a miniaturized simulated cough machine: Effect of construction and serous layer simulant. Biorheology 26:997-988
Agarwal M, Shukla JB (1988) Mucus transport in the lung. Mathl Comput Modelling 11:797-800
Agarwal M, Verma VS (1997) A planar model for mucociliary transport: Effects of air motion and porosity. Proc Acad Sci India 67(A) II:193-204
Agarwal M, Verma VS (1998) A visco-Elastic two layer planar unsteady state model for mucus transport due to coughing. Ganita 49 (I):7-18
Barton C, Raynor S (1967) Analytic investigation of cilia induced mucus flow. Bull Math Biophys 29:419-428
Beavers GS, Joseph DD (1967) Boundary conditions at a naturally permeable wall. J Fluid Mech 30(1):197-207
Benjamin M, Christian F, Dominique P, Jacques M, Patrice F (2011) Towards the modeling of mucus draining from the human lung: role of the geometry of the airway tree. Phys Biol 8:056006(12pp)
Blake JR (1971a) Spherical envelope approach to ciliary propulsion. J Fluid Mechan 46:209-222
Blake JR (1971b) Infinite models for ciliary propulsion, J Fluid Mechan 49:199-208
Blake JR (1973) Mucus Flow. Math Biosci 17:301-313
Blake JR, Sleigh MA (1974) Mechanics of ciliary locomotion. Biological Reviews of the Cambridge Philosophical Society 49(1):85-125
Blake JR (1975) On movement of mucus in lung. J Biomechan 8(3-4):179-190
Blake JR, Winet H (1980) On the Mechanics of muco-ciliary transport. Biorheology 17(1-2):125-134
Blake JR, Fulford GR (1984) Mechanics of Muco-ciliary Transport. Physicochemical Hydrodynamics 5(5-6):401-411
Clarke SW, Jones JG, Oliver DR (1970) Resistance two-phase gas-liquid flow in airways. J Appl Physiol 29:464-471
Clarke SW (1973) The role of two phase flow in bronchial clearance. Bull Eur Physiopath Respir 9:359-372
Lucas AM, Douglas LC (1934) Principles underlying ciliary activity in the respiratory tract. Arch Otolaryngol 20(4):518-541
Mow VC (1967) Effects of viscoelastic lubricant on squeeze film lubrication between impinging spheres. J Lub Tech 24:1-4
Pedley TJ, Schroter RC, Sudlow MF (1970) The prediction of pressure drop and variation of resistance within the human bronchialairways. Res Physiol 9:387-405
Polak AG (2008) A model-based method for flow limitation analysis in the heterogeneous human lung. Computer methods and program in Biomedicine 89:123-131
Puchelle E, Zahm JM, Duvivier C (1983) Spinnability of bronchial mucus: Relationship with viscoelasticity and mucus transport properties. Biorheology 20:265-272
Ross SM, Corrsin S (1974) Results of an analytical model of mucociliary pumping. J Appl Physiol 37:333-340
Sathpathi DK, Ramu A (2013a) Circular model for mucus transport in the airways due to air motion. International J Emerg Technol Computat App Sci 5(5):513-517
Sathpathi DK, Ramu A (2013b) A laminar flow model for mucous gel transport in a cough machine simulated trachea: Effect of surfactant as a sol phase layer. Open J Appl Sci 3:312-317
Schroter RC, Sudlow MF (1969) Flow patterns in models of human bronchial airways. J Biomech 11:183-187
Sleigh MA (1977) The nature and action of respiratory tract cilia. Respir. Def Mech 5:247-288
Sleigh MA, Blake JR, Liron N (1988) The propulsion of mucus by cilia. Am Rev Respir Dis 137:726-741
Smith DJ, Gaffney EA, Blake JR (2008) Modeling on muco-ciliary clearance. Respir Physio 163:178-188
Tomkiewicz RP, Biviji A, King M (1994) Effects of oscillating air flow on the theoretical properties and clearability of mucus gel simulants. Biorheology 31(5):511-520
Tripathee SM, Verma VS (2016) Mucus flow in human lung airways: Effects of Air velocity cilia tip velocity and porosity parameter. International J Sci nad Res 632-636
Verma VS (2007) A mathematical study on mucus transport in the lung. J Nat Acad Math 21:107-117
Verma VS (2008) A planar two layer unsteady state for mucociliary transport. JTS India 2:115-127
Verma VS (2009) Mucus transport: A fluid mechanical Steady state model. J Rajasthan Acad Phy Sci 8(3):371-384
Verma VS (2010) A planar model for mucus transport in human respiratory tract: Effect of air-flow, porosity and and mucus viscoelasticity. J Nat Acad Math 24:53-60
Verma VS, Tripathee SM (2011) A study on mucus flow in human lung airways. JPS 2(1):113-120
Verma VS (2012) Mucus flow in lung airways: A planar two layer steady state mathematical model. JTS India 6(1):69-77
Verma VS, Tripathee SM (2013) A planar model for muco-ciliary transport in the human lung: Effects of mucus viscoelasticity, cilia beating and porosity. IJMRS’s International J Mathemat Model Phy Sci 1(1):19-25
Verma VS, Tripathee SM (2013) A planar model for muco-ciliary transport in the human lung: Effects of Vicoelasticity, cilia baeating and porosity. International J Mathemat Model Phy Sci 19-25
Wanner A (1981) Alteration of tracheal mucociliary transport in airway disease: The effect of pharmacologic agents. Chest 80:867-870
Weibel ER (1963) Morphometry of human lung. Academic Press Inc., New York.
Yeates DB, Spektor DM, Leikauf GD, Pitt BR (1981) Effects of drugs on muco-ciliary transport in the trachea and bronchial airways. Chest 80:870-873
Zahm JM, King M, Duvivier C, Pierot D, Girod S, Puchelle E (1991) Role of simulated repetitive coughing in mucus clearance. Eur. Respir. J. 4:311-315
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