Mathematical Modeling of Mucus Transport in the Bronchial Tree with Ventilation Effects
Résumé
Mucociliary clearance plays a central role in respiratory defense by transporting mucus along the bronchial tree through the combined action of cilia, mucus secretion, and airflow. We propose a multiscale mathematical model of this process that explicitly couples ciliary-driven transport, mucus production, and ventilation effects. The model combines a one-dimensional variational formulation for mucus velocity within individual airways with a system of ordinary differential equations describing the evolution of mucus thickness across bronchial generations. Realistic airway geometry and breathing scenarios are incorporated. The analysis reveals stable equilibrium mucus distributions in the absence of ventilation and periodic regimes under physiological breathing. Numerical results quantify the impact of secretion, ciliary activity, and airflow, and highlight nonlinear feedbacks between mucus accumulation and airway resistance, with potential relevance for pathological conditions.
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