A Bidirectional Coupling Procedure Applied to Multiscale Respiratory Modeling.

In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFD) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the Modified Newton's Method with nonlinear Krylov accelerator developed by Carlson and Miller [1, 2, 3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a "pressure-drop" residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design.