Mathematical Modeling of Airflow on Respiratory Narrowing Due to Mumps Using Finite Element Method

Abstract

Mumps can cause narrowing of the airway respiratory when the swelling occurs toward the chest because it can suppress the airways (trachea). This research will be constructed a mathematical model airway on respiratory narrowing due to mumps and solve it by using finite element method. The main problem in this research, how the results of simulation analysis airflow velocity airway on respiratory narrowing due to mumps are influenced by the size of radius of respiratory tract and the initial velocity. After the simulated, will be searched a relative error to be compared with the value of tolerance. Based on the simulation result using MATLAB found that the first simulation influence the size of radius with an initial velocity 0.4 m/s during normal condition (r=0.025 m) velocity in the narrowing airway 0.4010 m/s. If r=0.020 m and r=0.015 m the velocity will be increased being 1.0060 m/s and 3.2199 m/s with relative error value 0.005964. The second simulation an initial velocity and r=0.01631 m and velocity are 0.2 m/s, 0.4 m/s and 0.6 m/s found that the velocity in the narrowing airways increase being 1.0024 m/s, 2.2982 m/s and 4.0929 m/s with relative error value 0.002394.