Background: Electrical impedance tomography (EIT) is a noninvasive, radiation-free, and low-cost imaging modality for monitoring the conductivity distribution inside a patient. Nowadays, time-difference EIT (tdEIT) is used extensively as it has fast imaging speed and can reflect the dynamic changes of diseases, which make it attractive for a number of medical applications. Moreover, modeling errors are compensated to some extent by subtraction of voltage measurements collected before and after the change. However, tissue conductivity varies with frequency and tdEIT does not efficiently exploit multi-frequency information as it only uses measurements associated with a single frequency.
Methods: This paper proposes a tdEIT algorithm that imposes spectral constraints on the framework of the linear least squares problem. Simulation and phantom experiments are conducted to compare the proposed spectral constraints algorithm (SC) with the damped least squares algorithm (DLS), which is a stable tdEIT algorithm used in clinical practice. The condition number and rank of the matrices needing inverses are analyzed, and image quality is evaluated using four indexes. The possibility of multi-tissue imaging and the influence of spectral errors are also explored.
Results: Significant performance improvement is achieved by combining multi-frequency and time-difference information. The simulation results show that, in one-step iteration, both algorithms have the same condition number and rank, but SC effectively reduces image noise by 20.25% compared to DLS. In addition, deformation error and position error are reduced by 8.37% and 7.86%, respectively. In two-step iteration, the rank of SC is greatly increased, which suggests that more information is employed in image reconstruction. Image noise is further reduced by an average of 32.58%, and deformation error and position error are also reduced by 20.20% and 31.36%, respectively. The phantom results also indicate that SC has stronger noise suppression and target identification abilities, and this advantage is more obvious with iteration. The results of multi-tissue imaging show that SC has the unique advantage of automatically extracting a single tissue to image.
Conclusions: SC enables tdEIT to utilize multi-frequency information in cases where the spectral constraints are known and then provides higher quality images for applications.
Keywords: Electrical impedance tomography (EIT); Fraction model; Image reconstruction algorithm; Inverse problem.