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This paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography. Our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on finding a proper way to cope with the ill-posed nature of the problem, mainly caused by strong attenuation phenomena; this is done by devising regularization techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regularization matrix is determined by space-uniformization of the variance of the reconstructed condictivities. Both methods are nonsupervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography. Index Terms - Electrical impedance tomography, ill-posed inverse problem, reconstruction, regularization.

The decomposition of the time reversal operator (DORT) is a detection and focusing technique using an array of transmit-receive transducers. In the absence of noise and under certain conditions, the eigenvectors of the time reversal operator contain the focal laws to focus ideally on well-resolved scatterers even in the presence of strong aberration. This paper describes a new algorithm, FDORT, which uses focused transmission schemes to acquire the operator. It can be performed from medical scanner data. A mathematical derivation of this algorithm is given and it is compared with the conventional algorithm, both theoretically and with numerical experiments. In the presence of strong speckle signals, the DORT method usually fails. The influence of the speckle noise is explained and a solution based on FDORT is presented, that enables detection of targets in complex media. Finally, an algorithm for microcalcification detection is proposed. In-vivo results show the potential of these techniques. [ABSTRACT FROM AUTHOR]

Objective: The objective of our study was to compare quantitative maximum breast mass stiffness on shear-wave elastography (SWE) with histopathologic outcome., Subjects and Methods: From September 2008 through September 2010, at 16 centers in the United States and Europe, 1647 women with a sonographically visible breast mass consented to undergo quantitative SWE in this prospective protocol; 1562 masses in 1562 women had an acceptable reference standard. The quantitative maximum stiffness (termed "Emax") on three acquisitions was recorded for each mass with the range set from 0 (very soft) to 180 kPa (very stiff). The median Emax and interquartile ranges (IQRs) were determined as a function of histopathologic diagnosis and were compared using the Mann-Whitney U test. We considered the impact of mass size on maximum stiffness by performing the same comparisons for masses 9 mm or smaller and those larger than 9 mm in diameter., Results: The median patient age was 50 years (mean, 51.8 years; SD, 14.5 years; range, 21-94 years), and the median lesion diameter was 12 mm (mean, 14 mm; SD, 7.9 mm; range, 1-53 mm). The median Emax of the 1562 masses (32.1% malignant) was 71 kPa (mean, 90 kPa; SD, 65 kPa; IQR, 31-170 kPa). Of 502 malignancies, 23 (4.6%) ductal carcinoma in situ (DCIS) masses had a median Emax of 126 kPa (IQR, 71-180 kPa) and were less stiff than 468 invasive carcinomas (median Emax, 180 kPa [IQR, 138-180 kPa]; p = 0.002). Benign lesions were much softer than malignancies (median Emax, 43 kPa [IQR, 24-83 kPa] vs 180 kPa [IQR, 129-180 kPa]; p < 0.0001). Usual benign lesions were soft, including 62 cases of fibrocystic change (median Emax, 32 kPa; IQR, 24-94 kPa), 51 cases of fibrosis (median Emax, 36 kPa; IQR, 22-102 kPa), and 301 fibroadenomas (median Emax, 45 kPa; IQR, 30-79 kPa). Eight lipomas (median Emax, 14 kPa; IQR, 8-15 kPa), 154 cysts (median Emax, 29 kPa; IQR, 10-58 kPa), and seven lymph nodes (median Emax, 17 kPa; IQR, 9-40 kPa) were softer than usual benign lesions (p < 0.0001 for lipomas and cysts; p = 0.007 for lymph nodes). Risk lesions were slightly stiffer than usual benign lesions (p = 0.002) but tended to be softer than DCIS (p = 0.14). Fat necrosis and abscesses were relatively stiff. Conclusions were similar for both small and large masses., Conclusion: Despite overlap in Emax values, maximum stiffness measured by SWE is a highly effective predictor of the histopathologic severity of sonographically depicted breast masses.

Purpose: To determine whether adding shear-wave (SW) elastographic features could improve accuracy of ultrasonographic (US) assessment of breast masses., Materials and Methods: From September 2008 to September 2010, 958 women consented to repeat standard breast US supplemented by quantitative SW elastographic examination in this prospective multicenter institutional review board-approved, HIPAA-compliant protocol. B-mode Breast Imaging Reporting and Data System (BI-RADS) features and assessments were recorded. SW elastographic evaluation (mean, maximum, and minimum elasticity of stiffest portion of mass and surrounding tissue; lesion-to-fat elasticity ratio; ratio of SW elastographic-to-B-mode lesion diameter or area; SW elastographic lesion shape and homogeneity) was performed. Qualitative color SW elastographic stiffness was assessed independently. Nine hundred thirty-nine masses were analyzable; 102 BI-RADS category 2 masses were assumed to be benign; reference standard was available for 837 category 3 or higher lesions. Considering BI-RADS category 4a or higher as test positive for malignancy, effect of SW elastographic features on area under the receiver operating characteristic curve (AUC), sensitivity, and specificity after reclassifying category 3 and 4a masses was determined., Results: Median participant age was 50 years; 289 of 939 (30.8%) masses were malignant (median mass size, 12 mm). B-mode BI-RADS AUC was 0.950; eight of 303 (2.6%) BI-RADS category 3 masses, 18 of 193 (9.3%) category 4a lesions, 41 of 97 (42%) category 4b lesions, 42 of 57 (74%) category 4c lesions, and 180 of 187 (96.3%) category 5 lesions were malignant. By using visual color stiffness to selectively upgrade category 3 and lack of stiffness to downgrade category 4a masses, specificity improved from 61.1% (397 of 650) to 78.5% (510 of 650) (P<.001); AUC increased to 0.962 (P=.005). Oval shape on SW elastographic images and quantitative maximum elasticity of 80 kPa (5.2 m/sec) or less improved specificity (69.4% [451 of 650] and 77.4% [503 of 650], P<.001 for both), without significant improvement in sensitivity or AUC., Conclusion: Adding SW elastographic features to BI-RADS feature analysis improved specificity of breast US mass assessment without loss of sensitivity., (© RSNA, 2012)