A Markov chain model of particle deposition in the lung

Particle deposition in the lung during inhalation is of interest to a wide range of biomedical sciences due to the noninvasive therapeutic route to deliver drugs to the lung and other organs via the blood stream. Before reaching the alveoli, particles must transverse the bifurcating network of airways. Computational fluid mechanical studies are often used to estimate high-fidelity flow patterns through the large conducting airways, but there is a need for reduced-dimensional modeling that enables rapid parameter optimization while accommodating the complete airway network. Here, we introduce a Markov chain model with each state corresponding to an airway segment in which a particle may be located. The local flows and transition probabilities of the Markov chain, verified against computational fluid dynamics simulations, indicate that the independent effects of three fundamental forces (gravity, fluid drag, diffusion) provide a sufficient approximation of overall particle behavior. The model enables fast computation of how different inhalation strategies, called flow policies, determine total particle escape rates and local particle deposition. In a 3-dimensional airway tree model, the optimal flow policy minimizing the risk of deposition at each generation, compared to other inlet flow waveforms, predicted significantly higher probability of escape defined as the fraction of particles exiting the tree. The model also predicts a small influence of body orientation with respect to a gravitational field on total escape probability, but a significant effect of airway narrowing on regional deposition. In summary, this model provides insight into inhalation strategies for targeted drug delivery.