The D-bar method for electrical impedance tomography-demystified.

Electrical impedance tomography (EIT) is an imaging modality where a patient or object is probed using harmless electric currents. The currents are fed through electrodes placed on the surface of the target, and the data consists of voltages measured at the electrodes resulting from a linearly independent set of current injection patterns. EIT aims to recover the internal distribution of electrical conductivity inside the target. The inverse problem underlying the EIT image formation task is nonlinear and severely ill-posed, and hence sensitive to modeling errors and measurement noise. Therefore, the inversion process needs to be regularized. However, traditional variational regularization methods, based on optimization, often suffer from local minima because of nonlinearity. This is what makes regularized direct (non-iterative) methods attractive for EIT. The most developed direct EIT algorithm is the D-bar method, based on Complex Geometric Optics solutions and a nonlinear Fourier transform. Variants and recent developments of D-bar methods are reviewed, and their practical numerical implementation is explained.

Bayesian multiresolution method for local tomography in dental x-ray imaging.

Dental tomographic cone-beam x-ray imaging devices record truncated projections and reconstruct a region of interest (ROI) inside the head. Image reconstruction from the resulting local tomography data is an ill-posed inverse problem. A new Bayesian multiresolution method is proposed for local tomography reconstruction. The inverse problem is formulated in a well-posed statistical form where a prior model of the target tissues compensates for the incomplete x-ray projection data. Tissues are represented in a wavelet basis, and prior information is modeled in terms of a Besov norm penalty. The number of unknowns in the reconstruction problem is reduced by abandoning fine-scale wavelets outside the ROI. Compared to traditional voxel-based models, this multiresolution approach allows significant reduction of degrees of freedom without loss of accuracy inside the ROI, as shown by 2D examples using simulated and in vitro local tomography data.

Multiresolution local tomography in dental radiology using wavelets.

A Bayesian multiresolution model for local tomography in dental radiology is proposed. In this model a wavelet basis is used to present dental structures and the prior information is modeled in terms of Besov norm penalty. The proposed wavelet-based multiresolution method is used to reduce the number of unknowns in the reconstruction problem by abandoning fine-scale wavelets outside the region of interest (ROI). This multiresolution model allows significant reduction in the number of unknowns without the loss of reconstruction accuracy inside the ROI. The feasibility of the proposed method is tested with two-dimensional (2D) examples using simulated and experimental projection data from dental specimens.

Imaging cardiac activity by the D-bar method for electrical impedance tomography.

A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to reconstruct a 2D cross-section of the torso. The images show changes in conductivity during a cardiac cycle.

Statistical inversion for medical x-ray tomography with few radiographs: I. General theory.

In x-ray tomography, the structure of a three-dimensional body is reconstructed from a collection of projection images of the body. Medical CT imaging does this using an extensive set of projections from all around the body. However, in many practical imaging situations only a small number of truncated projections are available from a limited angle of view. Three-dimensional imaging using such data is complicated for two reasons: (i) typically, sparse projection data do not contain sufficient information to completely describe the 3D body, and (ii) traditional CT reconstruction algorithms, such as filtered backprojection, do not work well when applied to few irregularly spaced projections. Concerning (i), existing results about the information content of sparse projection data are reviewed and discussed. Concerning (ii), it is shown how Bayesian inversion methods can be used to incorporate a priori information into the reconstruction method, leading to improved image quality over traditional methods. Based on the discussion, a low-dose three-dimensional x-ray imaging modality is described.

Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology.

Diagnostic and operational tasks in dental radiology often require three-dimensional information that is difficult or impossible to see in a projection image. A CT-scan provides the dentist with comprehensive three-dimensional data. However, often CT-scan is impractical and, instead, only a few projection radiographs with sparsely distributed projection directions are available. Statistical (Bayesian) inversion is well-suited approach for reconstruction from such incomplete data. In statistical inversion, a priori information is used to compensate for the incomplete information of the data. The inverse problem is recast in the form of statistical inference from the posterior probability distribution that is based on statistical models of the projection data and the a priori information of the tissue. In this paper, a statistical model for three-dimensional imaging of dentomaxillofacial structures is proposed. Optimization and MCMC algorithms are implemented for the computation of posterior statistics. Results are given with in vitro projection data that were taken with a commercial intraoral x-ray sensor. Examples include limited-angle tomography and full-angle tomography with sparse projection data. Reconstructions with traditional tomographic reconstruction methods are given as reference for the assessment of the estimates that are based on the statistical model.

Adrenocortical tumorigenesis in transgenic mice: the role of luteinizing hormone receptor and transcription factors GATA-4 and GATA-61.

Transgenic (TG) mice, bearing the Simian Virus 40 T-antigen (Tag) under a 6-kb fragment of the murine inhibin alpha-subunit promoter (inhalpha), develop gonadal tumors of granulosa or Leydig cell origin with 100% penetrance by the age of 5-7 months. When these TG mice were gonadectomized prepubertally, between 21-25 days of life, adrenal gland tumors were observed in each mouse by the age of 5-7 months. No adrenal tumors were detected in any intact TG, gonadectomized or intact or control non-TG littermates. The adrenocortical tumors appeared to originate from the X-zone of the adrenal cortex. If functional gonadectomy was induced by GnRH antagonist treatment or by cross-breeding of the TG mice into hypogonadotropic hpg genetic background, neither gonadal nor adrenal tumorigenesis appeared. This prompted a hypothesis that adrenal tumor development in inhalpha/Tag TG mice is related to elevated gonadotropin secretion, which is the most obvious difference between the surgical and functional gonadectomy models. The adrenal tumors and a cell line (Calpha1) derived from them, was found to express luteinizing hormone receptor (LHR), but no FSHR, and hCG treatment stimulated their proliferation. No FSHR was found in the adrenal glands. On the basis of this it was suggested that expression of the potent oncogene T-antigen, allow LH in adrenocortical cells to function as a tumor promoter, and induction of high level functional LHR expression in adrenal tumors. Given the induction of expression and regulation of the GATA-4 and GATA-6 zinc finger family of transcription factors in the gonads by gonadotropins, it was in our interest to explore their expression in the adrenals. We utilized the inalpha/Tag TG mouse model and pathological human adrenal samples to explore the role of GATA-4 and GATA-6 in adrenocortical tumorigenesis. Abundant GATA-6 mRNA expression was found in normal control adrenal cortex during mouse development, whereas GATA-4 mRNA was undetectable. In striking contrast to this, GATA-6 was absent from murine adrenocortical tumors, while GATA-4 mRNA expression was dramatically upregulated in the murine adrenal tumors as well as in human adrenocortical carcinomas. Taken together, these results suggest different roles for GATA-4 and GATA-6 in the adrenal gland, and implicate GATA-4 in adrenal LHR expression and tumorigenesis. Immunohistochemical detection of GATA-4 may serve as a useful marker in differential diagnosis of human adrenal tumors. In addition, the inhalpha/Tag TG model will be helpful for exploring the molecular mechanisms underlying adrenocortical tumorigenesis, ectopic LHR expression in adrenals and the GATA-4/LHR interaction that is related to adrenal tumorigenesis in TG mice.

Transcription factor GATA-4 is expressed in pediatric yolk sac tumors.

Yolk sac tumors (YSTs) are malignant tumors that occur in the gonads of children and young adults, and at extragonadal sites in young children. The histological features of YSTs are variable and can be superimposed on other germ cell tumor histologies. Malignant endodermal cells within YSTs express alpha-fetoprotein, which can be detected in tumor tissue or serum. However, additional markers of endoderm differentiation would be beneficial for the classification of these tumors. Transcription factor GATA-4 regulates the differentiation and function of murine yolk sac endoderm, and its expression correlates with proliferation and cell survival in certain tissues. To see whether GATA-4 plays a role in human YSTs, we surveyed its expression in human germ cell tumors and cell lines. Northern analysis demonstrated expression of GATA-4 mRNA in four human germ cell tumor lines exhibiting yolk sac endoderm differentiation. GATA-4 protein was detected in eight of nine pediatric YSTs by immunohistochemistry. Three of five immature teratomas exhibited GATA-4 in neural blastematous cells and in cylindrical epithelium, whereas all 16 mature teratomas were devoid of GATA-4. We conclude that GATA-4 is a clinically useful marker of human YSTs and speculate that it may play a role in the maintenance of the malignant phenotype.

Reciprocal changes in the expression of transcription factors GATA-4 and GATA-6 accompany adrenocortical tumorigenesis in mice and humans.

While certain genetic changes are frequently found in adrenocortical carcinoma cells, the molecular basis of adrenocortical tumorigenesis remains poorly understood. Given that the transcription factors GATA-4 and GATA-6 have been implicated in gene expression and cellular differentiation in a variety of tissues, including endocrine organs such as testis, we have now examined their expression in the developing adrenal gland, as well as in adrenocortical cell lines and tumors from mice and humans. Northern blot analysis and in situ hybridization revealed abundant GATA-6 mRNA in the fetal and postnatal adrenal cortex of the mouse. In contrast, little or no GATA-4 expression was detected in adrenal tissue during normal development. In vivo stimulation with ACTH or suppression with dexamethasone did not affect the expression of GATA-4 or GATA-6 in the murine adrenal gland. To assess whether changes in the expression of GATA-4 or GATA-6 accompany adrenocortical tumorigenesis, we employed an established mouse model. When gonadectomized, inhibin alpha/SV40 T-antigen transgenic mice develop adrenocortical tumors in a gonadotropin-dependent fashion. In striking contrast to the normal adrenal glands, GATA-6 mRNA was absent from adrenocortical tumors or tumor-derived cell lines, while GATA-4 mRNA and protein were abundantly expressed in the tumors and tumor cell lines. Analogous results were obtained with human tissue samples; GATA-4 expression was detected in human adrenocortical carcinomas but not in normal tissue, adenomas, or pheochromocytomas. Taken together these results suggest different roles for GATA-4 and GATA-6 in the adrenal gland, and implicate GATA-4 in adrenal tumorigenesis. Immunohistochemical detection of GATA-4 may serve as a useful marker in the differential diagnosis of human adrenal tumors.