Lagrangian Dynamical Models Ldms

To overcome some of the limitations just mentioned that are associated with purely empirical models, simulations that include various aspects of the inhaled aerosol dynamics have been developed. The simplest of these belong to a class of models we refer to as Lagrangian dynamical models (LDMs), meaning that the model simulates some of the dynamical behavior of the aerosol in a frame of reference that travels with the aerosol (i.e., a "Lagrangian viewpoint").

A complete Lagrangian dynamical model would be ridiculously difficult, since it would follow all individual particles and air parcels as they travel through the entire lung and would require computation times of the same order as FLS mentioned earlier. Instead, existing one-dimensional LDMs make the major simplifying assumption that the aerosol and air travel together at the same velocity, and this velocity is obtained by treating the lung as a sequence of branching circular pipes whose diameter is given by some idealized lung geometry. For example, if the inhalation flow rate is Q, then the flow rate in each airway in the 10th lung generation is Q/210 and the average velocity in these airways is

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