In order to describe the properties of these types of complex porous samples, different virtual systems with pores of flat ellipsoidal shapes in randomly generated positions were generated and analyzed. These pores have a much smaller size on vertical axis than in the perpendicular plan to the field direction (Fig. 4d). By comparisons with the other configurations for which EMA models still could be applied with a certain approximation, this LP533401 hcl complex case describing the realistic microstructures (Fig. 2c and d) cannot be described by analytical formulas and for this reason, 3D Finite Element Method (FEM) has been employed. In the FEM procedures the Laplace equation (∇·(ε∇V)=0∇·(ε∇V)=0, where ? is the local permittivity and V is the local potential) is solved, taking into account the boundary conditions in a parallel-plate capacitor: Dirichlet boundary conditions on the top and bottom surfaces and Neumann boundary conditions at lateral surfaces, as described in detail elsewhere  and . After computing the local potentials and the local electric fields, the average electric displacement and the average electric field were estimated and the effective permittivity was derived from Eq. (2). Using pituitary gland method, different simulations were performed at different porosity levels in the range from 0% to 30% and the dependence of the computed effective permittivity on the porosity for this type of microstructure is represented in Fig. 4. This method succeeds to explain the dielectric properties of the samples with 18% and 29% porosity levels (BST20 and BST35, respectively) in relation with the observed microstructural features: the lower permittivity is related to the narrow pores oriented perpendicular on the applied field direction, similar to the case of the layered structures.