The study is aimed at the analytical design of the full human bronchial tree for healthy patients and patients with obstructive pulmonary diseases. Analytical formulas for design of the full bronchial tree are derived. 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; the pathology degree is defined by two parameters: bronchus constriction level and degree of distortion of the cylindrical shape of the bronchus. Closed analytical formulas allow the human bronchial tree of an arbitrary complexity (up to alveoli) to be designed; moreover, the parametric dependences make it possible to specify any desirable degree of airway obstruction.

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The work is devoted to the mathematical construction of the human bronchial tree, calculating the flow of gas in the lungs and modelling the deposition of drops of medicinal aerosols in the human bronchial tree. Analytically built a symmetrical human bronchial tree. To calculate the flow of gas in the lungs and the deposition of aerosols, the method of phasing out the flow in one branch of the bronchial tree is used. Three-dimensional numerical calculations of air flow and aerosol droplets in human lungs were carried out. It is shown that the number of past drops depends (except for the flow, size of drops) on the duration of inhalation.

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