Models for Computing Effect of Pollutants on the Lower Respiratory Tract

Oyelami Benjamin Oyediran^{1, 2,}

¹National Mathematical Centre Abuja, Nigeria

²Plateau State University Bokkos, Nigeria

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

Abstract

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.

Keywords:
models pollutants airflow lower respiratory tracks and fractals

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