Method of Constructing an Asymmetric Human Bronchial Tree in Normal and Pathological Cases

Abstract

The goal of the study is the analytical design of the full asymmetric human bronchial tree (irregular dichotomy) for healthy patients and patients with obstructive pulmonary diseases. For this purpose, the author has derived the special analytical formulas. All surfaces of the bronchial tree are matched with the second-order 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; a level of the pathology is defined by two parameters: bronchus constriction level and level of distortion of the cylindrical shape of the bronchus. Closed analytical formulas allow a researcher to construct the human bronchial tree of an arbitrary complexity (up to alveoli); moreover, the parametric dependences make it possible to specify any desirable level of airway obstruction.