The models used for modeling the airflow in the human airways are either 0-dimensional compartmental or full 3-dimensional (3D) computational fluid dynamics (CFD) models. In the former, airways are treated as compartments, and the computations are performed with several assumptions, thereby generating a low-fidelity solution. The CFD method displays extremely high fidelity since the solution is obtained by solving the conservation equations in a physiologically consistent geometry. However, CFD models (1) require millions of degrees of freedom to accurately describe the geometry and to reduce the discretization errors, (2) have convergence problems, and (3) require several days to simulate a few breathing cycles. In this paper, we present a novel, fast-running, and robust quasi-3D wire model for modeling the airflow in the human lung airway. The wire mesh is obtained by contracting the high-fidelity lung airway surface mesh to a system of connected wires, with well-defined radii. The conservation equations are then solved in each wire. These wire meshes have around O(1000) degrees of freedom and hence are 3000 to 25 000 times faster than their CFD counterparts. The 3D spatial nature is also preserved since these wires are contracted out of the actual lung STL surface. The pressure readings between the 2 approaches showed minor difference (maximum error = 15%). In general, this formulation is fast and robust, allows geometric changes, and delivers high-fidelity solutions. Hence, this approach has great potential for more complicated problems including modeling of constricted/diseased lung sections and for calibrating the lung flow resistances through parameter inversion.
Most current models used for modeling the pulmonary drug absorption, transport, and retention are 0D compartmental models where the airways are generally split into the airways and alveolar sections. Such block models deliver low fidelity solutions and the spatial lung drug concentrations cannot be obtained. Other approaches use high fidelity CFD models with limited capabilities due to their exorbitant computational cost. Recently, we presented a novel, fast-running and robust quasi-3D (Q3D) model for modeling the pulmonary airflow. This Q3D method preserved the 3D lung geometry, delivered extremely accurate solutions, and was 25 000 times faster in comparison to the CFD methods. In this paper, we present a Q3D-compartment multiscale combination to model the pulmonary drug absorption, transport, and retention. The initial deposition is obtained from CFD simulations. The lung absorption compartment model of Yu and Rosania is adapted to this multiscale format. The lung is modeled in the Q3D format till the eighth airway generation. The remainder of the lung along with the systemic circulation and elimination processes was modeled using compartments. The Q3D model is further adapted, by allowing for various heterogeneous annular lung layers. This allows us to model the drug transport across the layers and along the lung. Using this multiscale model, the spatiotemporal drug concentrations in the different lung layers and the temporal concentration in the plasma are obtained. The concentration profile in the plasma was found to be better aligned with the experimental findings in comparison with compartmental model for the standard test cases. Thus, this multiscale model can be used to optimize the target-specific drug delivery and increase the localized bioavailability, thereby facilitating applications from the bench to bedside for various patient/lung-disease variations.
This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational finite volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's finite volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted Eulerian-Lagrangian formulation to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a finite number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd.
SUMMARYA high-order spectral volume (SV) method was implemented for solving the steady-state moment models, such as the hydrodynamic (HD) models and the energy transport (ET) models for semiconductor device simulations (in 1D). The first derivative inviscid/convective fluxes are handled using an approximate Riemann flux and the second derivative diffusive fluxes are discretized using the local discontinuous Galerkin formulation (LDG). The LDG method is also used for discretizing the potential equation. An implicit pre-conditioned LU-SGS p-multigrid method developed for the SV Navier-Stokes (NS) solver by Kannan and Wang is adopted here for time marching. The entire formulation is compact and hence can be easily parallelized. A n + -n-n + diode was assumed for simulation purposes and the results are compared with the existing discontinuous Galerkin simulation results. In general, the numerical results are very promising and indicate that the approach has a great potential for higher-dimensional device problems.
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