## Info

individual airways in the lung, resulting in the need for more than 1012 grid points in total. At each grid point we need to store the air and aerosol conditions, so we will require several terabytes (i.e., several thousand gigabytes) of RAM on any computer on which we hope to solve these equations. This is a major limitation, since only a handful of computers in the world have this kind of memory capacity, and access to these computers is severely restricted, usually to military applications.

Assuming we did manage to find a computer with terabytes of RAM, how long would it take for such a computer to solve the governing equations at our 1012 grid points? A reasonable estimate can be made by assuming 103 floating point operations are needed to solve for the air and aerosol conditions at a grid point, with these operations being needed at each of approximately 100 steps in time throughout a breath (since the lung geometry varies with time as the alveoli fill), yielding a total of 1017 floating point operations. Typical desktop computers can perform less than 109 floating point operations per second (flops), so we would need to wait over 108 seconds, which is more than three years!

Even the latest ASCI (Advanced Strategic Computing Initiative) computer developed by the U.S. Department of Defense, costing \$200 million, occupying 21,000 square feet, and running at 30 X 1012 flops, would take an hour to solve this problem.

From these simple estimates, it is seen that while a three-dimensional full lung simulation (hereafter abbreviated as FLS, with "three-dimensional" always implied) of the air and aerosol flow in the entire respiratory is not beyond the realm of possibility if the detailed geometry of the lung was known, such a large calculation is impractical at present. Assuming that, according to "Moore's law," computers double in speed every 18 months, it will be less than 20 years before FLS takes less than 20 minutes on a good desktop computer, which may make it a more attractive approach at that time. However, deposition of aerosol particles in the respiratory tract is merely the first step in a series of relatively poorly understood steps (at least from a mechanistically predictive point of view) that lead to the onset of action of a drug. Simulation of the subsequent disposition of drug, including its dissolution, pharmacokinetics, and finally pharmacodynamics, requires an understanding at a cellular and molecular level that remains incomplete. As a result, although FLS may be useful in developing and refining simpler deposition models, at present it is not feasible from the perspective of aiding preclinical development. Instead, simplifications are used, to which we now turn.

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