Physicomathematical modeling of human breathing in situations of various pulmonary diseases

Three-dimensional numerical simulations of the air flow in the full human bronchial tree in situations of obstructive and chronical pulmonary diseases are performed. Based on the previously developed three-dimensional analytical model of the lower respiratory airways, the air distributions in the lungs (from the trachea to alveoli) in situations with lung injuries and bronchial asthma are calculated. Breathing modeling is based on a numerical technique of stage-by-stage computations, which allows one to avoid the loss of solution accuracy caused by the difference in the bronchus scales; moreover, the time needed to calculate the air flow in the lungs can be reduced by several times by using this technique.