The Need For Simplification

Most readers would probably intuitively agree that simulating the behavior of an aerosol as it is inhaled and dispersed throughout the entire respiratory tract is a difficult task. In fact, at the present time it is impossible to precisely simulate this behavior because the geometry of the lung, including the time-dependent shape of all several hundred million alveoli, is not known. However, let us say that some dramatic breakthrough in imaging technology allowed us to determine the detailed three-dimensional geometry of all airspaces in the lung throughout an entire breath. Would it then be feasible to precisely simulate what happens to an inhaled aerosol in the respiratory tract?

To answer this question, let us take the simplest case of a dilute aerosol consisting of spherical, stable (i.e., nonevaporating, noncondensing) particles. To determine the fate of this aerosol, we must solve the governing equations, which are based simply on mass conservation and Newton's second law, both for the air that carries the aerosol and the aerosol itself. It is not possible to solve these equations at the infinite number of spatial locations in the respiratory tract, so instead we solve these equations on a computer at a finite number of "grid points" and interpolate the solution at all other points. To achieve reasonable accuracy, each individual airway (with associated alveoli) in each generation in the lung needs to be divided into approximately 105 grid points. With 23 lung generations, there are

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