  Classical homogenization theory based on the Hashin-Shtrikman coated
ellipsoids is used to model the changes in the complex valued conductivity (or
admittivity) of a lung during tidal breathing. Here, the lung is modeled as a
two-phase composite material where the alveolar air-filling corresponds to the
inclusion phase. The theory predicts a linear relationship between the real and
the imaginary parts of the change in the complex valued conductivity of a lung
during tidal breathing, and where the loss cotangent of the change is
approximately the same as of the effective background conductivity and hence
easy to estimate. The theory is illustrated with numerical examples, as well as
by using reconstructed Electrical Impedance Tomography (EIT) images based on
clinical data from an ongoing study within the EU-funded CRADL project. The
theory may be potentially useful for improving the imaging algorithms and
clinical evaluations in connection with lung EIT for respiratory management and
monitoring in neonatal intensive care units.
