Collaborative Research: A Molecular-to-Continuum, Data-Driven Strategy for Mucus Transport Modeling

University Of South Carolina At Columbia, Columbia SC

Investigators

Abstract

The project develops predictive mathematical theory and computational tools for both the flow of lung airway liquids and the diffusion of inhaled particles (pathogens, particulates, drug carrier particles) that are deposited in human airways. The predictive mathematical modeling and computational tools are developed on the basis of experimental data. The experimental data on particle diffusion in mucus and the physical properties that govern mucus flow transport are collected on human bronchial epithelial mucus from lung cultures and clinical patients. This experimental-theoretical-computational strategy has the promise for direct applications in clinical treatment of humans with diverse lung diseases and disorders, both for assessment of disease and for design of physical therapy and drug treatment strategies. Mathematically, these models and simulation tools promise to provide insight into mean mucus flow properties from physiological forcing (cilia and air drag from breathing and cough) and also to resolve microstructural changes in the mucus molecular network. These tools can offer insight into the biophysical differences in mucus during disease and disease progression, which are keys to a predictive design of physical and drug therapies. When integrated with clinical knowledge, this modeling will provide the capability to infer flow and diffusive transport properties of mucus samples and healthy and disease conditions, and the capability to test therapies to reinstate mucus clearance on an individualized patient basis. This project develops a data-driven strategy for the modeling of lung mucus transport, linking stochastic molecular kinetic processes, evolution equations for microstructure-based stresses, and momentum equations for flow. The experimental data consists of stochastic (entropic fluctuations) and deterministic (controlled forcing) probes of mucus microstructure, together with high-resolution microscopy of mucus transport in cell cultures derived from human lung tissue. These rich data sets provide unprecedented probes of the broad mucus relaxation spectrum arising from single mucin molecules, their entanglement network in mucus gels, transient mucin crosslinking, and chain scission kinetics. Cell cultures afford insights into cilia-driven flow transport of mucus, and provide a laboratory setting to explore molecular-to-macroscopic consequences of imposed physical stresses and chemical dosing. To translate this remarkable data into a predictive understanding of mucus transport, a modeling platform is studied that resolves molecular-to-continuum processes of mucus, both near and far from equilibrium. Our strategy begins with stochastic time series of passive microbead probes in mucus gels of various concentrations, to solve the inverse and direct problems for linear (near equilibrium) viscoelastic characterization. Next, active microbead data for the same set of concentrations is used over a range of controlled magnetic forces to determine nonlinear thresholds and the signatures of non-equilibrium behavior at the microscale. These data directly feed into the main objective of this project, which is the formulation of a new microscopic-macroscopic constitutive law for mucus. This formulation is proposed to interpret the linear and nonlinear data, and to integrate molecular-to-continuum processes into a new mucus transport model. A numerical strategy is under study for direct numerical simulations and comparison with data from each type of experiment.