A110-11 A Mathematical Model of the Mosaic Pattern, the Alveolus-Level Heterogeneity in Particle Deposition

Rationale Previous studies have predicted the heterogeneous distribution of inhaled material within the conducting airways (Sonnenberg, SciRep 2020). Recently, our group discovered that the distribution of deposited matter is highly heterogeneous within the deep lung, too (Grifno, bioRxiv 2025). Aerosolized droplets and inhaled particles, like pathogens and nanoparticles, were found to be heterogeneously distributed at lobar, ductal, and alveolar length scales. In fluorescence images, the deposition pattern, termed the mosaic pattern, is characterized by the presence of bright tiles of deposited material, which are separated by dim bands that fail to receive inhaled material. The pattern’s geometry experimentally depends on several factors, including gravity, particle size, and membrane-binding affinity, but the mechanism of its development remains unclear. Although researchers have constructed simplified models of aerosol delivery to the alveoli, none have predicted the highly heterogeneous pattern that we reported (Li, Journal of Aerosol Science 2023). To understand its cause, we built a data-driven, mathematical model of aerosol delivery within the rat’s lung from a high-resolution image volume (Schittny, Histochem Cell Biol 2018). Methods From a 1.4-um synchrotron x-ray tomography volume of a rat, we segment individual pulmonary alveoli and airways. We define the functional diameter (cf. Figure 1(a)(i)) that partitions the lung between wider, functional airways, which are rapidly reachable by inhaled particles, and narrower airways. At the end of this functional region, we simulate the arrival of inhaled particles whose motion obeys the Langevin equation, which includes inertial, gravitational, drag, and Brownian forces (Tsuda, Comprehensive Physiology 2013). Upon first contact with the epithelium, particles deposit, and subsequently spread over the epithelium according to Fick’s law of diffusion. After the simulation, we construct virtual microscopy images of the lung with the deposited solute. We systematically vary the model’s parameters to investigate how the pattern changes in response. Results The pattern’s geometry strongly depends on (i) the functional region’s diameter and (ii) the solute’s post-deposition diffusivity, with uniformity increasing with diffusivity. In contrast, the pattern depends weakly on particle diffusivity within air. This finding disagrees with a previous theoretical hypothesis that chaotic mixing in the alveoli would determine the distribution (Tsuda, PNAS 2002). Conclusions As the first theoretical characterization of the mosaic pattern, the alveolus-level heterogeneity in particle transport in the lung, and its dependence on physical parameters within a physiologically representative geometry, this model may improve our understanding of airborne pulmonary disease development and the design of inhalation-based therapeutics.