For image reconstruction in electrical capacitance tomography (ECT) various implementations of the linear backprojection (LBP) algorithm and iterative reconstruction techniques have become the standard in most applications. Most implementations suffer from a smoothing effect and lack of accuracy due to their smooth sensitivity maps and the so-called 'soft' field problem in ECT, respectively. Therefore it is usually difficult in capacitance tomography to reconstruct objects with sharp contours. In the present paper a novel reconstruction model based on a finite-element-method (FEM) calculation is introduced. The model is derived directly from linear (x-ray) tomography, wherein weighting matrices along the rays are calculated. By analogy, weighting matrices in ECT are calculated numerically along the paths of the electrical field lines, which are influenced by the distribution of the various permittivities in the measurement plane. Finally the image reconstruction is done by implementing these new weighting matrices within standard iteration techniques (ART and LBP). With the new algorithm even objects with sharp contours can be reconstructed. The results are more detailed and accurate tomograms.
The diagnosis of lung cancer and early knowledge of its histological type are very important; however, this is still a difficult subject for the physician. The aim of this study was to improve the diagnostic efficiency of tumour markers in the diagnosis of bronchial carcinoma by mathematical evaluation of a tumour marker profile employing fuzzy logic modeling. A panel of five tumour markers, including CYFRA 21-1, CEA, NSE, and five additional parameters was determined in 281 patients with confirmed primary diagnosis of bronchial carcinoma of different histology and stage. A further 131 persons, who had acute and chronic benign lung diseases, served as a control group. A classificator was developed using a fuzzy-logic rule-based system. The diagnostic value of the combined tumour markers was significantly better than that of the individual markers and of a combination of CYFRA 21-1, CEA, and NSE. The discrimination of malignant vs benign diseases was realized with a sensitivity of 87.5% and specificity of 85.5%. The rate of correct classification of small-cell vs non-small-cell lung carcinoma was 90.6% and 91.1%, respectively; for squamous cell carcinoma vs adenocarcinoma it was 76.8% and 78.8%, respectively. Our detailed analysis has shown that the fuzzy logic system improves diagnostic accuracy up to a rate of 20%, especially in early stages and in patients with all marker levels in the grey area. Our concept proved to be more powerful than measurement of single markers or the combination of CEA, CYFRA 21-1, and NSE. Its use may help in distinguishing between malignant and benign disease and make it possible to define different subgroups of patients earlier in the course of their disease.
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