Title: Mathematical Framework in Frequency Difference Electrical Impedance Tomography 

Speaker: Jin Keun Seo (Computaional Science & Engineering, Yonsei University, Korea) 


Although time-difference EIT(tdEIT) has shown promise as a medical EIT imaging technique such as monitoring lung function, static EIT has suffered from forward computational model errors including boundary geometry and electrode positions uncertainty combined with the ill-posed and highly nonlinear nature of the corresponding inverse problem. Since 1980s, there has been great endeavor to create forward computational models with the necessary accuracy required for EIT reconstruction, but these efforts were not successful in clinical environment. 

Lately, frequency-difference electrical impedance tomography (fdEIT) was proposed to image a frequency-dependent change of a complex conductivity distribution inside the human body. The motivation was to overcome technical difficulties related with modeling errors in static EIT imaging. Compared with time-difference EIT, it has unique potential applications such as tumor and stroke imaging since it does not require a time-reference data. A new method of frequency-difference electrical impedance tomography (fdEIT) has been lately suggested to produce frequency-difference images of a complex conductivity distribution inside an imaging object. The most distinct feature was the use of weighted voltage differences at two different frequencies. In this talk, we explain why the weighted difference is essential in fdEIT. Based on a relationship between a sequence of injection currents at two different frequencies and corresponding weighted differences of complex voltages, we establish an fdEIT image reconstruction algorithm. To deal with more realistic cases, we elaborate the algorithm using the concept of an equivalent homogeneous complex conductivity. To validate the algorithm, we performed numerical simulations and phantom imaging experiments using a 16-channel multi-frequency EIT (mfEIT) system KHU Mark1. Reconstructed real- and imaginary-part images show changes of complex conductivity distributions with respect to frequency. Results indicate that reconstructed frequency-difference images using weighted voltage differences are comparable with time-difference EIT (tdEIT) images in terms of the image quality. This means that numerous common errors are effectively canceled out in the new fdEIT method. 

In this this talk, we review recent progress in fdEIT.