MultiFrequency Trans-Admittance Scanner: Mathematical Framework and Feasibility

A trans-admittance scanner (TAS) is a device for breast cancer diagnosis based on numerous experimental findings that complex conductivities of breast tumors significantly differ from those of surrounding normal tissues. In TAS, we apply a sinusoidal voltage between a hand- held electrode and a scanning probe placed on the breast skin to make current travel through the breast. The scanning probe has an array of electrodes at zero voltage. We measure exit currents (Neumann data) through the electrodes that provide a map of trans-admittance data over the breast surface. The inverse problem of TAS is to detect a suspicious abnormality underneath the breast skin from the measured Neumann data. Previous anomaly detection methods used the difference between the measured Neumann data and a reference Neumann data obtained beforehand in the absence of anomaly. However, in practice, the reference data is not available and its computation is not possible since the inhomogeneous complex conductivity of the normal breast is unknown. To deal with this problem, we propose a frequency-difference TAS (fdTAS), in which a weighted frequency difference of the trans-admittance data measured at a certain moment is used for anomaly detection. This paper provides a mathematical framework and the feasibility of fdTAS by showing the relationship between the anomaly information and the weighted frequency difference of the Neumann data.