Simulation studies of statistical distributions of cell membrane capacities and an ellipse model to assess the frequency behaviour of biological tissues

The frequency behaviour of biological tissues is commonly described by a Cole model reflecting a single-cell bio-impedance model extended with an exponent α. However, for this parameter α there is no physical or biological substrate, which impedes an interpretation. The present study confirms by computer simulations of tissue models that the factual frequency behaviour can be explained by assuming a distribution of the electrical impedance properties of cells and of the capacitive coupling between cells. This behaviour is modelled mathematically by an ellipse. A mathematical procedure is presented to estimate this ellipse from experimental data by a least square method. A model parameter β is introduced, representing the ratio of the axes of the ellipse. A higher value of β means a larger variation in cell properties, which makes a patho-physiological interpretation of changes possible.