Quantitative Photo-acoustic Tomography with Partial Data

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and improve an earlier result of Bal and Uhlmann to the partial date case. We show that the reconstruction can be uniquely determined by the knowledge of 4 internal data based on well-chosen partial boundary conditions. Stability of this reconstruction is ensured if a convexity condition is satisfied. Similar stability result is obtained without this geometric constraint if 4n well-chosen partial boundary conditions are available, where $n$ is the spatial dimension. The set of well-chosen boundary measurements is characterized by some complex geometric optics (CGO) solutions vanishing on a part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250

Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double layer potentials for the wave equation, for the domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure

The SOD2 C47T polymorphism influences NAFLD fibrosis severity: evidence from case-control and intra-familial allele association studies.

AIMS: Non-alcoholic fatty liver disease (NAFLD) is a complex disease trait where genetic variations and environment interact to determine disease progression. The association of PNPLA3 with advanced disease has been consistently demonstrated but many other modifier genes remain unidentified. In NAFLD, increased fatty acid oxidation produces high levels of reactive oxygen species. Manganese-dependent superoxide dismutase (MnSOD), encoded by the SOD2 gene, plays an important role in protecting cells from oxidative stress. A common non-synonymous polymorphism in SOD2 (C47T; rs4880) is associated with decreased MnSOD mitochondrial targeting and activity making it a good candidate modifier of NAFLD severity. METHODS: The relevance of the SOD2 C47T polymorphism to fibrotic NAFLD was assessed by two complementary approaches: we sought preferential transmission of alleles from parents to affected children in 71 family trios and adopted a case-control approach to compare genotype frequencies in a cohort of 502 European NAFLD patients. RESULTS: In the family study, 55 families were informative. The T allele was transmitted on 47/76 (62%) possible occasions whereas the C allele was transmitted on only 29/76 (38%) occasions, p=0.038. In the case control study, the presence of advanced fibrosis (stage>1) increased with the number of T alleles, p=0.008 for trend. Multivariate analysis showed susceptibility to advanced fibrotic disease was determined by SOD2 genotype (OR 1.56 (95% CI 1.09-2.25), p=0.014), PNPLA3 genotype (p=0.041), type 2 diabetes mellitus (p=0.009) and histological severity of NASH (p=2.0×10(-16)). CONCLUSIONS: Carriage of the SOD2 C47T polymorphism is associated with more advanced fibrosis in NASH

Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography

The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A uniqueness of reconstruction result is also obtained

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page

Thermoacoustic tomography arising in brain imaging

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary

Liver collagen proportionate area predicts decompensation in patients with recurrent hepatitis C virus cirrhosis after liver transplantation

Background and Aims: Current histological scoring systems do not subclassify cirrhosis. Computer-assisted digital image analysis (DIA) of Sirius Red-stained sections measures fibrosis morphologically producing a fibrosis ratio (collagen proportionate area [CPA]). CPA could have prognostic value within a disease stage, such as cirrhosis. The aim of the present study was to evaluate CPA in patients with recurrent hepatitis C virus (HCV) allograft cirrhosis and assess its relationship with hepatic venous pressure gradient (HVPG). Methods: In 121 consecutively-transplanted HCV patients with HVPG, measured contemporaneously with transjugular liver biopsies, 65 had Ishak stage 5 or 6 disease (43 with HVPG measurement). Biopsies were stained with Sirius Red for DIA, and the collagen content was expressed as a CPA. In three cases, a tissue for Sirius Red staining was not obtained, and the patients were excluded. Results: Sixty-two patients were analyzed. The median HVPG was 8mmHg (interquartile range [IQR]: 5-10). Portal hypertension (HVPG ≥6<10mmHg) was present in 30 (69.8%), and HVPG ≥10mmHg in 13 (30.2%). The median CPA was 16% (IQR 10.75-23.25). Median Child-Pugh score and HVPG were not significantly different between Ishak fibrosis stage 5 or 6, whereas CPA was statistically different: 13% in stage 5 (IQR 8.3-12.4) versus 23% in stage 6 (IQR 17-33.7, P<0.001). In the multivariate analysis, CPA was the only variable significantly associated with clinically-significant portal hypertension (HVPG ≥10mmHg, odds ratio: 1.085, confidence interval: 1.004-1.172, P=0.040). A CPA of 14% was the best cut-off value for clinically-significant portal hypertension (CSPH) and liver decompensation, which occurred in 24 patients. Event-free survival was significantly shorter in patients with CSPH or with a CPA value ≥14%, or with a combination of both. Conclusion: In Ishak stages 5 and 6, CPA correlated with HVPG, but had a wider range of values, suggesting a greater sensitivity for distinguishing "early" from "late" severe fibrosis/cirrhosis. CPA was a unique, independent predictor of HVPG ≥10mmHg. CPA can be used to subclassify cirrhosis and for prognostic stratification. © 2012 Journal of Gastroenterology and Hepatology Foundation and Blackwell Publishing Asia Pty Ltd

A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data