Efficient computations of gas transport in the respiratory tree

The equation governing the transport of an inert gas in the respiratory tree is a linear PDE. There are several clinical situations where the PDE must be solved on a large number of consecutive breaths and, on each breath, a very small number of linear functionals of this solution evaluated. In this study we show how the solution of a relatively small number of adjoint problems may be used to calculate these linear functionals, thus reducing the volume of computation significantly. This technique may be used with other physical problems.