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

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.Comment: To appear in Inverse Problem

Current clinical practice and outcome of neoadjuvant chemotherapy for early breast cancer: analysis of individual data from 94,638 patients treated in 55 breast cancer centers

Neoadjuvant chemotherapy (NACT) is frequently used in patients with early breast cancer. Randomized controlled trials have demonstrated similar survival after NACT or adjuvant chemotherapy (ACT). However, certain subtypes may benefit more when NACT contains regimes leading to high rates of pathologic complete response (pCR) rates. In this study we analyzed data using the OncoBox research from 94,638 patients treated in 55 breast cancer centers to describe the current clinical practice of and outcomes after NACT under routine conditions. These data were compared to patients treated with ACT. 40% of all patients received chemotherapy. The use of NACT increased over time from 5% in 2007 up to 17.3% in 2016. The proportion of patients receiving NACT varied by subtype. It was low in patients with HR-positive/HER2-negative breast cancer (5.8%). However, 31.8% of patients with triple-negative, 31.9% with HR-negative/HER2-positive, and 26.5% with HR-positive/HER2-positive breast cancer received NACT. The rates of pCR were higher in patients with HR-positive/HER2-positive, HR negative/HER2-positive and triple-negative tumors (36, 53 and 38%) compared to HR-positive/HER2-negative tumors (12%). PCR was achieved more often in HER2-positive and triple-negative tumors over time. This is the largest study on use and effects of NACT in German breast cancer centers. It demonstrates the increased use of NACT based on recommendations in current clinical guidelines. An improvement of pCR was shown in particular in HER2-positive and triple-negative breast cancer, which is consistent with data from randomized controlled trails