Three-Dimensional Model of the Human Bronchial Tree - Modeling of the Air Flow in Normal and Pathological Cases
A. E. Medvedev1,2, V. M. Fomin1,2, P. S. Gafurova1,2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: бронхиальное дерево человека, бифуркация, математическая модель, ламинарное течение, сечение бронха, human bronchial tree, bifurcation, mathematical model, laminar flow, bronchus cross section
Abstract
The air flow in the human bronchial tree is simulated in the normal and pathological cases. Analytical formulas are derived to design the full bronchial tree. All surfaces of the bronchial tree are matched with the second order of smoothness (there are no acute angles or ribs). The geometric characteristics of the human bronchial tree in the pathological case are modeled by a “starry” shape of the inner structure of the bronchus; the pathology degree is defined by two parameters: bronchus constriction level and degree of distortion of the cylindrical shape of the bronchus. A numerical technique is proposed for stage-by-stage computing of the air motion in the human bronchial tree. A laminar air flow in the human bronchial tree is computed from the input bronchus to alveoli). It is demonstrated that the pressure decrease in the case of a laminar air flow in the bronchial tree is twice smaller than that in the turbulent case. Distortions of the cylindrical shape of the bronchi in the pathological case lead to a more significant pressure decrease in the bronchial tree.
|
