Mathematical Biology Seminar E. Kyriakou School of Physics, University of Sydney, Sydney, NSW, Australia "Breathing as a low frequency wave propagation in a non linear elastic permeable medium" Lung tissue consists of a porous permeable medium with non linear elastic properties. Breathing can be regarded a type of low frequency wave propagation in this medium. Unlike sound propagation, in breathing, the air compressibility is not as important as the flow of air. The permeability and non linearity are important in describing the motion of the lung during the breathing cycle. We relate this type of wave propagation to previous work on wave propagation in the lung which has focused on the propagation of high frequency compressional waves in response to intense sudden pressure on the exterior of the thorax arising from the blast wave from an explosion. We have developed a numerical model to predict non-rigid motion of the lung that incorporates the mechanics of actual patient anatomy, including the mechanical properties of the tissues. This model, matched only to the exterior boundaries of the thorax during the breathing cycle, can be used to predict the non-rigid body motion of any structure in the thorax at any time. This enables medical images blurred by respiration to be corrected to give high quality images of superior diagnostic value. The accuracy of the model is demonstrated by predicting the motion of a lung tumor displacement during the breathing cycle.