American Journal of Modeling and Optimization
ISSN (Print): 2333-1143 ISSN (Online): 2333-1267 Website: Editor-in-chief: Dr Anil Kumar Gupta
Open Access
Journal Browser
American Journal of Modeling and Optimization. 2016, 4(2), 40-50
DOI: 10.12691/ajmo-4-2-2
Open AccessArticle

Models for Computing Effect of Pollutants on the Lower Respiratory Tract

Oyelami Benjamin Oyediran1, 2,

1National Mathematical Centre Abuja, Nigeria

2Plateau State University Bokkos, Nigeria

Pub. Date: July 01, 2016

Cite this paper:
Oyelami Benjamin Oyediran. Models for Computing Effect of Pollutants on the Lower Respiratory Tract. American Journal of Modeling and Optimization. 2016; 4(2):40-50. doi: 10.12691/ajmo-4-2-2


In this paper, a model for aerodynamic behaviour of particulates (pollutants) that diffuses into the airway in the human lower respiratory track (LRT) containing mixture of pollutants, water droplets and mucus is considered. The velocity of the airflow is computed using the Nervier Stokes equation with fractal morphologic boundaries and the population of bacteria in the mixture studied using the Lauffeger-Aris-Keller model. The series solutions to the models are obtained using eigenvalue and eigenfunction techniques. The concentration of the pollutants in the LRT and the airflow velocity profile are obtained. It is found that as the thickness of the irreversible structures formed on the walls of LRT increases then the airflow into the airway decreases. The population of bacteria is found to be stable if the if sustenance function is very small compared to the death rate of the bacteria. Therefore, for good throughput of airflow, the muscles of the walls of breathing ducts need to be dilated with drugs or through surgery by constructing Nano pipes to allow passages of air into the air sacs by bypassing the pulmonary obstacles to enhance free flow of air into the lungs.

models pollutants airflow lower respiratory tracks and fractals

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


Figure of 14


[1]  Andreas Ratz, Axel Voigt, Edge diffusion in phase-field models for epitaxial growth. Multiscale modelling in epitaxial growth Vol.149, of Series ISNM International Series of Numerical Mathematics pp115-125, 2005.
[2]  Anoop J Chauhan and Sebastian L Johnston. Air pollution and infection in respiratory illness. British Medical Bulletin (2003) 68 (1): 95-112.
[3]  Barrett KE, Barman SM, Boitano S, et al. Pulmonary function. Ganong's Review of Medical Physiology. 23E. New York: McGraw-Hill; 2009. Chapter 35.
[4]  D’Amato G Cecchi, Bonini L., Numes S, Annesi C., Maesano, Behrendt I., Liccandi H., Popov G., and Van Cauwenber P. Allergic Pollen and Pollen allergy in Europe, Allergy 62, 976-990, 2007.
[5]  Frederica P. Perera, Shuang Wang, Virginia Rauh, Hui Zhou, Laura Stigter, David Camann, Wieslaw Jedrychowski, Elzbieta Mroz, and Renata Majewska. PrenatalExposure to Air Pollution, Maternal Psychological Distress, and Child Behavior. Pediatrics, October 2013.
[6]  Jay B Brodsky, Alex Macario and James B.D.Mark, M Tracheal Diameter Predicts Double-Lumen Tube Sizea Method for selecting left Double-LumenTubes .Anesth. Analog 1996, 82; 861-864.
[7]  Joachim Heyder, Deposition of inhaled Particles in the Human Respiratory Track and Consequences for Regional Targeting in Respiratory Drug Delivery. Proceedings American Thoracic Society, Vol.1, Nineteenth Transatlantic Airways Conference (2004), and pp.315-320.
[8]  Markov I V,Crystal growth for Beginners: Fundamentals of Nucleation, Chrystal growth and Epitary. World scientific, 1995.
[9]  Mridul K. Thomas, Colin T. Kremer, Christopher A. Klausmeier, and Elena Litchman. A Global Pattern of Thermal Adaptation in Marine Phytoplankton. Science, 2012.
[10]  Nathan R. Meltzer E., Selner J. and Storms W. Prevalence of allergenic-rhinitis in the United State. J. Allergy clin.Imm, 99, 808-814, 1997.
[11]  Pimpernel A. Villian J, Physics of crystal growth Cambridge University press 1988.
[12]  Oyelami Benjamin Oyelami, Buba M. Wufem Models for computing emission of carbon dioxide from liquid fuel in Nigeria. American Statistical Review (To appear).
[13]  Schulze, Weinan E.T.P, Journal of Chrystal growth 222 (2001), 414-425.
[14]  Shouliang Qi, Zhengzhou Li, Yong Yue, Han JW van Triest, and Yan Kang Computational fluid dynamics simulation of airflow in the trachea and main bronchi for the subjects with left pulmonary artery sling.Biomed Eng. Online. 2014; 13: 85. Published online 2014 Jun 24.
[15]  Ted B. Martonen,Zongqin Zhang, Genqian Yu, Cynthia J. Musante. Three dimensional Computer modelling of the human upper respiratory tract.Cell Biochemistry and Biophysics.Vol.35, (3), 2001, pp255-261.
[16]  Byron Bird Warren E Stewart, Edwin N. Lightfoot, Transport Phenomena. Second edition Wiley International Press.2012, Singapore.
[17]  Byun D. and Schere K. Review of the governing equation, computational algorithms, and other components of the models-3 community multiscale air quality (CMAQ) modelling system, Appl.Mech Rev. 59,51-57, 2006.
[18]  Laufenberg D., Airs R., and Keller K. H. Effects of random mobility on growth of bacteria population. Microb Ecol.7, 207-227.
[19]  Zhang K., Duhl T., Salam M.T., House J.M., Flagan R.C., Avol F. D., Gilliland, Guenther A., Chung S.H., Lamb B. K. and VanRekan T.M. Development of a regional –scale pollen emission and transport modelling framework for investigating the impact of climate change on allergic airway disease .Biogescience 11, 1461-1478, 2014.