A method and apparatus that use complex impedance measurements of tissue in human or animal bodies for the detection and characterization of medical pathologies is disclosed. An analysis of the complex impedance measurements is performed by a trained evaluation system that uses a nonlinear continuum model to analyze the resistive, capacitive, and inductive measurements collected from a plurality of sensing electrodes. The analysis of the impedance measurements results in the construction of a multidimensional space that defines the tissue characteristics, which the trained evaluation system uses to detect and characterize pathologies. The method and apparatus are sufficiently general to be applied to various types of human and animal tissues for the analysis of various types of medical pathologies.