Electrical impedance spectroscopy (EIS) has been investigated and emerged as a potential non-invasive, low cost, and convenient tool for prescreening and detecting breast abnormalities that could lead to developing breast cancers. However, the performance of conventional EIS is unacceptable in clinical practice. In our laboratory, we developed a new EIS approach based on resonance frequency measurements. This system relies on parameters generated by resonating breast capacitance with a fixed inductor in six different directions using the nipple as a reference electrode. The system detects breast tissue abnormalities due to capacitance changes caused by angiogenesis. Although preliminary testing results from a prospective clinical study were encouraging, we found that detection results were not robust. One of the primary reasons is that the measured EIS signals, in particular, resonance frequencies vary with lesion-depth. Using circuit theory we investigated and derived analytical expressions between the sensitivity of capacitance changes and parallel resistances to pathologies with respect to distances of the lesions from the nipple electrode. The resistance shorts the measured EIS signal thereby decreasing amplitudes of waveforms at resonance frequency. The theoretical analysis is consistent with our experimental observation, which provides valuable data and guidelines for us to develop and construct a new resonance-frequency based EIS system using a lumped parameter (resistance and multi-layer capacitance) based breast model, resulting in an optimal electrical circuit for future studies.