Pulmonary Fluid Flow Challenges for Experimental and Mathematical Modeling

Abstract

Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make.

Simulating surfactant spreading: Influence of a physically motivated equation of state

“…applications as stabilizers and dispersants [25]. In human lungs, issues such as airway closure and reopening [31] and the dynamics of mucus in the airway system [10,20,6,27] are known to be tied to the presence of surfactants. In particular, biomedical engineers and applied mathematicians studying the liquid lining of the lungs of premature infants proposed a compelling model starting with a well-known thin film equation and coupling the film to the surfactant through surface stress [18,19].…”

Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures – Part I: Idealized Axisymmetric Swirling Flow

“…In general, one can divide the modeling of MCC into three major components: formulation of a constitutive model for mucus based on rheological data, understanding the mechanism (forcing condition) for mucus propulsion either by an individual cilium or carpets of cilia, and development of numerical methods to solve the resulting system of equations [ 2 , 3 ]. Validation of each component in airway simulations is essentially impossible due to the lack of in vivo experimental data and resolution of airway mucus transport.…”

Coming to terms with tissue engineering and regenerative medicine in the lung

“…Added to these passive forces are the active mechanical forces imposed on both airways and vasculature by luminal contraction and relaxation in response to changing demands, and by endogenous and exogenous factors such as local and circulating agonists and antagonists. Although in silico models (79,83,99,132,148,196), in vitro and ex vivo systems (59,92,103,108,118,176,193,202,203), and whole-organ approaches (94,143,205,206) have been developed to explore the importance of such mechanical forces, further advances in airway, lung parenchyma, and vascular mechanobiology will be critical for bioengineering a lung capable of withstanding the internal and external forces exerted on the transplanted lung within the chest cavity and will be critical to ensuring that lung function occurs without airway collapse, injury, or failure of gas exchange. The challenges to our current understanding of lung mechanobiology and their implications for a bioengineered lung are discussed in Materials, Matrix, and Mechanobiology.…”