Department of Biomedical Engineering, Air Force Medical University (Fourth Military Medical University), Xi'an, 710032, People's Republic of China.
Biomed Eng Online. 2019 Jul 29;18(1):84. doi: 10.1186/s12938-019-0703-9.
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.
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.
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.
SC enables tdEIT to utilize multi-frequency information in cases where the spectral constraints are known and then provides higher quality images for applications.
电阻抗断层成像（EIT）是一种非侵入性、无辐射且低成本的成像方式，可用于监测患者内部的电导率分布。如今，时差分 EIT（tdEIT）被广泛应用，因为它具有快速成像速度，并能反映疾病的动态变化，这使其成为许多医学应用的理想选择。此外，通过减去变化前后采集的电压测量值，可以在一定程度上补偿建模误差。然而，组织电导率随频率而变化，tdEIT 并没有有效地利用多频信息，因为它只使用与单个频率相关的测量值。
本文提出了一种在线性最小二乘问题框架上施加谱约束的 tdEIT 算法。通过仿真和体模实验，将所提出的谱约束算法（SC）与在临床实践中使用的稳定 tdEIT 算法——阻尼最小二乘法（DLS）进行比较。分析了需要求逆的矩阵的条件数和秩，并使用四个指标评估图像质量。还探讨了多组织成像的可能性和谱误差的影响。
结合多频和时差分信息可显著提高性能。仿真结果表明，在一步迭代中，两种算法的条件数和秩相同，但与 DLS 相比，SC 可有效将图像噪声降低 20.25%。此外，变形误差和位置误差分别降低了 8.37%和 7.86%。在两步迭代中，SC 的秩大大增加，这表明在图像重建中使用了更多的信息。图像噪声进一步降低了平均 32.58%，变形误差和位置误差也分别降低了 20.20%和 31.36%。体模结果也表明，SC 具有更强的噪声抑制和目标识别能力，并且随着迭代的进行，这一优势更加明显。多组织成像的结果表明，SC 具有自动提取单个组织进行成像的独特优势。
SC 使 tdEIT 能够在已知谱约束的情况下利用多频信息，从而为应用提供更高质量的图像。
