Abstract. We study a problem set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. The unknown electric potential solves standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by a dielectric surface (the cell membranes), which exhibits both a capacitive and a nonlinear conductive behaviour. Accordingly, dynamical conditions prevail on the membranes, so that the dependence of the solution on the time variable t is not only of parametric character. As the spatial period of the medium goes to zero, the eletric potential approaches a homogenization limit u0, solving div − σ0∇xu0 − A 0 ∫ ∇xu0 −

www.imm.dtu.dk In dynamic positron emission tomography (PET) an artery sampling is needed for assessment and validation of parameters in kinetic models. The sampling can be uncomfortable and painful for the patient and technically demanding for the personnel performing the sampling. Noninvasive estimation of the artery time activity curve (TAC) is thus very useful, since the sampling then can be avoided. Methods are tested on simulated data which is an approximation to PET data. The results from the simulated data are used to quantify how well the different methods perform and to illustrate their limitations. The methods are then used on real PET data, and the estimated TACs are compared to the sampled artery TAC. Non-negative matrix factorization (NMF) and independent component analysis (ICA) show the best results with correlations around 0.95 with the artery