Corrector theory for MsFEM and HMM in random media

We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential equations with highly heterogeneous coefficients. Such multi-scale algorithms are often shown to correctly capture the homogenization limit when the highly oscillatory random medium is stationary and ergodic. This paper is concerned with the random fluctuations of the solution about the deterministic homogenization limit. We consider the simplified setting of the one dimensional elliptic equation, where the theory of random fluctuations is well understood. We develop a fluctuation theory for the multi-scale algorithms in the presence of random environments with short-range and long-range correlations. What we find is that the computationally more expensive method MsFEM captures the random fluctuations both for short-range and long-range oscillations in the medium. The less expensive method HMM correctly captures the fluctuations for long-range oscillations and strongly amplifies their size in media with short-range oscillations. We present a modified scheme with an intermediate computational cost that captures the random fluctuations in all cases.Comment: 41 page

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

Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem

The first patient treatment of computed tomography ventilation functional image-guided radiotherapy for lung cancer.

BACKGROUND AND PURPOSE: Radiotherapy that selectively avoids irradiating highly-functional lung regions may reduce pulmonary toxicity. We report on the first clinical implementation and patient treatment of lung functional image-guided radiotherapy using an emerging technology, computed tomography (CT) ventilation imaging. MATERIAL AND METHODS: A protocol was developed to investigate the safety and feasibility of CT ventilation functional image-guided radiotherapy. CT ventilation imaging is based on (1) deformable image registration of four-dimensional (4D) CT images, and (2) quantitative image analysis for regional volume change, a surrogate for ventilation. CT ventilation functional image-guided radiotherapy plans were designed to minimize specific lung dose-function metrics, including functional V20 (fV20), while maintaining target coverage and meeting standard constraints to other critical organs. RESULTS: CT ventilation functional image-guided treatment planning reduced the lung fV20 by 5% compared to an anatomic image-guided plan for an enrolled patient with stage IIIB non-small cell lung cancer. Although the doses to several other critical organs increased, the necessary constraints were all met. CONCLUSIONS: An emerging technology, CT ventilation imaging has been translated into the clinic and used in functional image-guided radiotherapy for the first time. This milestone represents an important first step toward hypothetically reduced pulmonary toxicity in lung cancer radiotherapy

Primary signet ring carcinoma of the rectum: a rare entity

Signet ring cell carcinoma constitute an uncommon histological type of rectal cancer with less than 1% of all rectal neoplasms. It usually behaves aggressively and has an inferior prognosis. Herein, we present a rare case in young male diagnosed by trucut biopsy

Corticothalamic projections control synchronization in locally coupled bistable thalamic oscillators

Thalamic circuits are able to generate state-dependent oscillations of different frequencies and degrees of synchronization. However, only little is known how synchronous oscillations, like spindle oscillations in the thalamus, are organized in the intact brain. Experimental findings suggest that the simultaneous occurrence of spindle oscillations over widespread territories of the thalamus is due to the corticothalamic projections, as the synchrony is lost in the decorticated thalamus. Here we study the influence of corticothalamic projections on the synchrony in a thalamic network, and uncover the underlying control mechanism, leading to a control method which is applicable in wide range of stochastic driven excitable units.Comment: 4 pages with 4 figures (Color online on p.3-4) include

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