In electrical resistance tomography (ERT) technology for human lung, under the same experimental conditions, the width of the sensitive field boundary electrode has a significant impact on the calculation accuracy of the inverse problem besides the finite element model (FEM) topology. Aiming to improve the quality of reconstructed images, the FEM for human lung was set up based on prior knowledge. On this basis, the electrode width of the FEM was optimised by comparing the morbidity degrees of the sensitivity matrix and Hessian matrix, the uniformity of sensitivity distribution, and the quality of reconstructed images, which can improve the accuracy of solving the inverse problem significantly.
In recent years, critical respiratory diseases have become a hot area of critical care medicine and one of the primary directions of disease prevention and control in China with features of high complexity, morbidity, mortality, and risk of great harm. Respiratory diseases have become one of the diseases that seriously threaten the health of Chinese residents, according to the statistical results of Vols. 2013–2017 of China Health and Family Planning Statistical Yearbook and Vols. 2018 and 2019 of China Health Statistics Yearbook [
Due to the complexity of critical respiratory diseases, the current clinical treatment plan depends on the individual patient. Therefore, timely assessing the effectiveness of medical measures and accurately grasping the changes in the progress of lung diseases is an essential basis for successful treatment of critical respiratory diseases. However, currently, there is a lack of clinically effective means for real-time monitoring and quantitative evaluation of critical respiratory diseases.
Electrical tomography (ET) technology consists of 4 different branches, namely, electrical impedance tomography (EIT) [
Human lung ERT technology is based on the characteristics that different human tissues and organs have different conductivities/resistivities. Various physiological and pathological conditions often correspond to conductivity/resistivity changes of certain tissues and organs. Firstly, a safe excitation current signal is applied on the electrode array on the body surface to establish a sensitive field in the lungs. Secondly, the effective boundary voltage of the sensitive field is obtained through the data acquisition circuit. Finally, according to the effective boundary voltage of the sensitive field, the image reconstruction algorithm is employed to solve the inverse problem of the human lung ERT to obtain the conductivity/resistivity image distribution of tissues and organs (including lungs, heart, and spine) in the sensitive field.
The current density
The calculation of forward problem for human lung ERT is to calculate the potential distribution of the sensitive field generated by the given boundary stimulating electrical signal to obtain the effective boundary voltage value for solving the inverse problem, based on the known or given conductivity/resistivity distributions of tissues and organs (including the lungs, heart, and spine) within the sensitive field region. Due to the irregular geometry of the measured field, it is a challenge to use analytical methods to obtain analytical solutions to the positive problem through theoretical derivation. The numerical calculation method of FEM, which is more adaptable to the geometric shape of the measured field, is usually used to calculate the forward problem.
In the FEM-based calculation process of the forward problem of the human lung ERT, the current density
The so-called image reconstruction is to solve the conductivity/resistance image distribution of tissues and organs in the sensitive field based on the given boundary excitation electrical signal and the corresponding effective boundary voltage, which is essential to the human lung ERT. In the two types of different image reconstruction methods for the human lung ERT, although dynamic imaging can achieve real-time imaging, static imaging has a wider application range and higher clinical value because the latter can present the absolute value of the conductivity of tissues and organs. People can diagnose different tissues and organs (including lungs, heart, and spine) as normal tissues or diseased ones according to their conductivity/resistivity values.
When the boundary curve equationuation of lungs is determined, the width of the sensitive field boundary electrode only depends on the electrode angle. Although the optimisation of electrode width of the ERT system is realized in [
Now, the FEM for ERT is chosen and shown in Figure
Schematic diagram of the FEM for ERT.
Schematic diagram of the internal tissue and organ distribution based on prior knowledge.
The internal tissue and organ distribution in the FEM for human lung ERT is shown in Figure
The electrodes are evenly distributed and numbered anticlockwise. The electrode pair N-M means that the electrodes N and M are used as excitation electrodes or measurement electrodes. When the electrode pair 1–2 is the excitation electrode, parts of the sensitivity distribution corresponding to the FEM are shown in Figure
Schematic diagram of sensitivity distribution.
Comparison of different parameters of the corresponding sensitivity matrices.
Parameters | 1.8750 degrees | 3.7500 degrees | 5.6250 degrees | 7.5000 degrees | 9.3750 degrees | 11.2500 degrees | 13.1250 degrees |
---|---|---|---|---|---|---|---|
Maximum | 0.0186 | 0.0192 | 0.0187 | 0.0192 | 0.0188 | 0.0189 | 0.0186 |
Minimum | −0.0035 | −0.0029 | −0.0026 | −0.0025 | −0.0025 | −0.0025 | −0.0025 |
6.3435 | 6.3314 | 6.3183 | 6.3003 | 6.2789 | 6.2507 | 6.2195 |
It can be seen from Table
Based on prior knowledge, 6 distributions of internal tissues and organs in the FEM for human lung ERT are shown in Figure Step 1: set the algorithm parameters, including the maximum iteration number and the regularization factor, which have an important influence on the results of image reconstruction. Step 2: calculate the sensitivity matrix Step 3: randomly generate the diagonal matrix where Step 4: Ttke the reconstruction result of the linear backprojection algorithm as the initial estimated value where Step 5: the termination of the algorithm is based on the criteria of the number of iterations and the allowable error of the algorithm. If it is satisfied, the algorithm returns the optimal value Step 6: calculate Step 7: correct the resistivity distribution
Configurations of the internal tissue and organ distribution of the FEM of the human lung.
Using the abovementioned modified Newton–Raphson image reconstruction algorithm, the reconstructed images are shown in Figure
Reconstructed images. (a) The electrode angle
And, the image correlation coefficient, image relative error
Comparison of image correlation coefficients.
Distribution configuration | 1.8750 degrees | 3.7500 degrees | 5.6250 degrees | 7.5000 degrees | 9.3750 degrees | 11.2500 degrees | 13.1250 degrees |
---|---|---|---|---|---|---|---|
1 | 0.8672 | 0.8374 | 0.8481 | 0.8450 | 0.8531 | 0.8260 | 0.7763 |
2 | 0.8677 | 0.8531 | 0.8724 | 0.8604 | 0.8874 | 0.8250 | 0.8009 |
3 | 0.8248 | 0.8253 | 0.8034 | 0.7468 | 0.7615 | 0.7523 | 0.6922 |
4 | 0.8544 | 0.8396 | 0.8481 | 0.8103 | 0.8102 | 0.7658 | 0.7421 |
5 | 0.9115 | 0.8804 | 0.8928 | 0.8491 | 0.8557 | 0.8736 | 0.8180 |
6 | 0.8890 | 0.8444 | 0.8754 | 0.8439 | 0.8646 | 0.8545 | 0.8168 |
Average value | 0.8691 | 0.8467 | 0.8567 | 0.8259 | 0.8388 | 0.8162 | 0.7744 |
Comparison of image relative error (%).
Distribution configuration | 1.8750 degrees | 3.7500 degrees | 5.6250 degrees | 7.5000 degrees | 9.3750 degrees | 11.2500 degrees | 13.1250 degrees |
---|---|---|---|---|---|---|---|
1 | 42.3959 | 44.9342 | 44.2451 | 41.9743 | 40.5445 | 44.6119 | 49.8141 |
2 | 40.9719 | 42.8324 | 39.3069 | 39.6172 | 35.6991 | 44.3858 | 47.6893 |
3 | 46.4351 | 47.8764 | 48.9121 | 51.8914 | 50.8653 | 51.0591 | 56.3174 |
4 | 42.5821 | 45.7429 | 43.8716 | 46.1569 | 46.4721 | 50.4642 | 52.6781 |
5 | 34.8015 | 39.3734 | 38.2171 | 43.1964 | 41.9310 | 37.2090 | 45.0135 |
6 | 37.9780 | 43.8795 | 40.8065 | 42.5448 | 39.7991 | 40.0577 | 45.1568 |
Average value | 40.8608 | 44.1065 | 42.5599 | 44.2302 | 42.5519 | 44.6313 | 49.4449 |
Comparison of absolute errors.
Distribution configuration | 1.8750 degrees | 3.7500 degrees | 5.6250 degrees | 7.5000 degrees | 9.3750 degrees | 11.2500 degrees | 13.1250 degrees |
---|---|---|---|---|---|---|---|
1 | 0.1129 | 0.0719 | 0.0591 | 0.1259 | 0.1398 | 0.1573 | 0.1545 |
2 | 0.0901 | 0.1018 | 0.0809 | 0.1386 | 0.1228 | 0.1185 | 0.1636 |
3 | 0.1558 | 0.1783 | 0.1739 | 0.2023 | 0.1897 | 0.1562 | 0.1650 |
4 | 0.0809 | 0.1142 | 0.0860 | 0.1256 | 0.1065 | 0.1467 | 0.1619 |
5 | 0.1219 | 0.1641 | 0.1214 | 0.2009 | 0.1582 | 0.1905 | 0.1370 |
6 | 0.1053 | 0.0776 | 0.0970 | 0.1070 | 0.1145 | 0.1413 | 0.1484 |
Average value | 0.1112 | 0.1180 | 0.1030 | 0.1500 | 0.1386 | 0.1518 | 0.1551 |
It can be seen from Tables
Base on the comprehensive comparison in the aspect of the morbidity degrees of the sensitivity matrix and Hessian matrix, the uniformity of sensitivity distribution, and the quality of reconstructed images at electrode angles of 1.8750 degrees, 3.7500 degrees, 5.6250 degrees, 7.5000 degrees, 9.3750 degrees, 11.2500 degrees, and 13.1250 degrees, the optimised result of the electrode angle is 1.8750 degrees.
To improve the accuracy of solving the inverse problem for human lung ERT, first, the FEM for human lung ERT was set up based on prior knowledge. On this basis, the results were compared and analysed in the aspects of the morbidity degrees of sensitivity matrix and Hessian matrix, the uniformity of sensitivity distribution, and the quality of reconstructed images at electrode angles of 1.8750 degrees, 3.7500 degrees, 5.6250 degrees, 7.5000 degrees, 9.3750 degrees, 11.2500 degrees, and 13.1250 degrees, respectively, and the optimisation of electrode width was obtained. In the future, by adjusting the position of the outermost triangular finite element node, the number of array electrode widths can be increased. On this basis, the number of array electrodes, array electrode widths, and data acquisition mode can be comprehensively optimised.
The data used to support the findings of the study can be obtained from the author upon request.
The author declares no conflicts of interest.
This work was supported by the Huainan Normal University Research and Innovation Team: Intelligent Detection Technology Research and Innovation Team (XJTD202009) and Key Project of Excellent Young Talents Supporting Program of Colleges and Universities in Anhui Province in 2019 under Grant gxyqZD2019065.