## Threedimensional Partial Lung Simulation

Some of the major limitations of existing one-dimensional LDMs and EDMs are caused by their use of only one dimension in space. By removing this one-dimensional restriction, these limitations can be removed. This is normally done by simulating the airways instead in three spatial dimensions and performing numerical simulation of the fluid and aerosol equations on a three-dimensional grid placed in each lung airway. Since, as discussed earlier, simulation of the whole respiratory tract in this manner (i.e., FLS) is prohibitively demanding of computational resources, work to date in this direction has limited itself to simulations of small parts of the respiratory tract, which we refer to as three-dimensional partial lung simulations (abbreviated as PLS, with "three-dimensional" implied). Since it is easier to solve the fluid flow equations in a Eulerian framework [using standard computational fluid dynamics (CFD) methods] while particle deposition is more naturally dealt with in a Lagrangian framework, most PLS researchers have used a mixed approach, with Eulerian equations for the fluid and Lagrangian equations for the aerosol.

A host of authors since the early 1990s (e.g., Refs. 24,42-47, 52, see Ref. 3 for more of these many references) have performed PLS in various idealized replicas of single-, double-, and triple-bifurcation segments of the lung as well as parts of simplified alveolar ducts. Deposition in the particular respiratory tract segment being simulated can be predicted more accurately with this approach than with the simplified, one-dimensional LDMs or EDMs.

However, PLS is not without its drawbacks, some of which are discussed in Finlay et al. [48]. Perhaps the largest drawback is the inability of such an approach to correctly predict mouth-throat deposition with inhaled pharmaceutical aerosols [49] when a standard semiempirical treatment of turbulence and its effect on particles is used (to avoid having to do direct numerical simulation to resolve all the turbulent motion in this region). A second drawback is the demand on computing time. Although not nearly as demanding as an FLS of the entire respiratory tract, PLS of even just a few lung generations can require many hours on the fastest desktop computers, so patching together simulations done in small parts of the lung in order to make up an entire lung remains impractical for preclinical design purposes.

A major limiting factor with PLS is our lack of knowledge of the three-dimensional geometry of the respiratory tract airways, particularly distal to the first few lung generations. Current imaging technology has been used to give this information only for the mouth-throat and proximal tracheobronchial airways (e.g., Refs. 50,51), so at present PLS in regions distal to the first few airway generations requires speculation as to the actual geometry of these airspaces. This is unfortunate, since the alveolar region has become increasingly important because of its ability to give systemic delivery. Imaging of the alveolar airspaces requires improvement in spatial resolution by at least a factor of 10 over present medical imaging technology. Since the alveoli change shape significantly during inhalation, temporal resolution well below one second is also required in these images. Such imaging demands are likely to remain beyond our technological capabilities for some time to come, so PLS is not yet ready to supplant one-dimensional LDMs and EDMs in inhaled pharmaceutical aerosol design. Its main use at present is to allow research aimed at improving one-dimensional LDMs and EDMs.

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