On the other hand, the high-frequency relaxation of the cluster shows the relaxation of a suspension of spheroids with the same volume as the volume of a single cell. Therefore the dielectric spectrum for a suspension of clusters is the same as the spectrum of a two species suspension made of thin cylinders and spheroids. We present a theoretical framework based on a spectral representation of BIE and able to calculate the dielectric behavior of linear clusters with a wide range of shapes and dielectric structures. The theory agrees with the results of Pauly and Schwan for a sphere covered with a shell [1, 8]. In fact, for spheroids, our theory is the same as the analytical results of Asami et al. [2]. We present extensive calculations of clusters with shapes resembling MDCK cells. A practical numerical recipe to compute the effective permittivity of linear clusters with arbitrary number of cells is provided. Examples are given for cluster with shapes described as r ( θ ) in spherical coordinates or using ( z , ϕ ) parameters as { x = g ( z ) cos ϕ, y = g ( z ) sin ϕ, z } . Other studies in the literature used only spherical coordinates representation [25, 27, 35]. A direct relation between the geometry and dielectric parameters of the cells and their dielectric behavior described by a Debye representation has been formulated for the first time. Other work [22], which is based on a closely related spectral method [18–21], found a direct relation linking the geometry and electric parameters to the dielectric behavior only for homogenous particles. Moreover, the method used in [22] treats only particles with spheroidal geometry. We show that the spectral representation provides a straightforward evaluation of the characteristic time constants and dielectric decrements of the relaxations induced by cell membrane. We prove that the effective permittivity is sensitive to the shape of the embed- ded particles, specially when the linear response operator has strong dipole active modes (with large weights p$_{k}$ ). A low-frequency and distinct relaxation occurs when the largest dipole-active eigenvalue is very close to 1 / 2. Clusters of living cells connected by tight junctions or very long cells have such an eigenvalue. Our results also shed a new light on the understanding of recent numerical calculations [38] performed with a boundary element method on clustered cells where the low-frequency relaxation is attributed to the tight (gap) junctions connecting the cells. The method used in [38] does not use the confocal geometry IV. CONCLUSIONS 24