Assessing spatial distribution of sites with a risk of developing bronchopulmonary pathology based on mathematical modeling of air-dust flows in the human airways and lungs

Abstract

The article continues the series of studies that describe a mathematical model of the respiratory system developed by the authors and dwell on its use in practice to assess and predict risks for human health caused by negative effects of airborne environmental factors. The mathematical model includes several submodels that describe how an air mixture flows in the air-conducting zone (it includes the nasal cavity, pharynx, larynx, trachea and five generations of bronchi) and the lungs approximated with a continuous two-phase elastically deformed porous medium. The mathematical model is described by using continuum mechanics relationships. It is realized numerically by using engineering software (to investigate processes in the airways) and a self-developed set of programs (to simulate processes in the lungs). Numeric modeling of a non-stationary flow of an air-dust mixture is performed for a personalized three-dimensional geometry of the human respiratory system based on CT-scans. The study provides calculated lines of velocity for a flow of particles in inhaled air in the airways. We have quantified shares of deposited articles with their diameters being 10 µm, 2.5 µm, and 1 µm (РМ10, РМ2,5, РМ1) in the airways; the study also provides trajectories of particulate matter. As particles become smaller and lighter, the share of deposited ones goes down in the airways and grows in the lungs. According to numeric modeling, most (more than 95 %) large particles (PM10) are deposited in the nasal cavity, pharynx and larynx; small particles are able to reach the lower airways and bronchi (most particles that reach the lungs penetrate lobar bronchi predominantly in the right lung). Sites with maximum health risks in the human lungs have been identified relying on assessing changes in an air phase mass within the respiration cycle; they are located in lower lobes of the lungs. When contacting airway walls, particles are able to be deposited and accumulate over time producing irritating, toxic and fibrogenic effects; they can thus cause and / or exacerbate pathological states.

Keywords

• mathematical model
• respiratory system
• air-dust mixture
• particle sedimentation
• risk sites
• human health
• numeric modeling
• personalized model