Mathematical Analysis of Ultrafast Ultrasound Imaging

This paper provides a mathematical analysis of ultrafast ultrasound imaging. This newly emerging modality for biomedical imaging uses plane waves instead of focused waves in order to achieve very high frame rates. We derive the point spread function of the system in the Born approximation for wave propagation and study its properties. We consider dynamic data for blood flow imaging, and introduce a suitable random model for blood cells. We show that a singular value decomposition method can successfully remove the clutter signal by using the different spatial coherence of tissue and blood signals, thereby providing high-resolution images of blood vessels, even in cases when the clutter and blood speeds are comparable in magnitude. Several numerical simulations are presented to illustrate and validate the approach.Comment: 25 pages, 13 figure

Infection of Chilli (Capsicum Annuum L.) Seeds by Colletotrichum Gloeosporioides (Penz.) Sacc. and its Transmission

This study aimed to detect the external and internal seed - borne infection of C. gloeosporioides in chilli seeds and to determine its site of infection in the seeds. The study also proposed to investigate the mechanism of seed infection and its role in t he development of anthracnose fruit rot in the field

Invagination colo-colique sur des adénomes

L’invagination intestinale chez l’adulte est rare, et l’invagination colo-colique est encore plus rare. Contrairement à l’enfant où l’invagination intestinale est idiopathique, chez l’adulte elle survient presque toujours sur une lésion organique notamment sur des lésions malignes.Notre objectif est de rapporter deux nouveaux cas d’invaginations colo-coliques chez l’adulte les différentes étiologies, et leurs circonstances de découverte.Nos deux patients ont consulté en urgence pour un tableau d’occlusion intestinale aigue. Le diagnostic a été posé en préopératoire sur le scanner qui a révélé l’existence d’une invagination intestinale sur des lésions tumorales. Nos deux patient ont été opérés en urgence par laparotomie médiane à cheval sur l’ombilic. L’exploration peropératoire a confirmé le diagnostic d’invagination colo-colique sur une lésion tumorale. Ne disposant pas d’examen extemporané en urgence, et n’ayant pas ainsi, de certitude sur bénignité ou la malignité de ces lésions organiques, nous avons opté pour des colectomies carcinologiques pour pallier à toutes surprise sur lors de l’étude anatomopathologique de la pièce opératoire. L’absence de souffrance intestinale et l’absence de distension colique importante, nous a motivé à rétablir immédiatement la continuité digestive a été faite immédiatement.L’étude anatomopathologique est revenue en faveur d’un polype adénomateux inflammatoire pour le premier patient et d’une adénome villeux pour le 2ème patient.Conclusion :L’invagination intestinale colo-colique est rare chez l’adulte, elle survient presque toujours sur une lésion organique. Les tumeurs malignes sont la principale cause d’invagination intestinale chez l’adulte. Le traitement reste chirurgical la seule arme thérapeutique

Stabilization of the wave equation on 1-D networks

In this paper we study the stabilization of the wa ve equation on general 1-d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. Zuazua, Wave Propagation, Observation, and Control in 1-d Flexible Multi-structures, Math. Appl. 50, Springer-Verlag, Berlin, 2006]) into a weighted observability estimate for dissipative systems. Then we use an interpolation inequality similar to the one proved in [P. Bégout and F. Soria, J. Differential Equations, 240 (2007), pp. 324-356] to obtain the explicit decay estimates of the energy for smooth initial data. The obtained decay rate depends on the geometric and topological properties of the network. We also give some examples of particular networks in which our results apply, yielding different decay rates. © 2009 Society for Industrial and Applied Mathematics

The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles, and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary, and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.Comment: 25 pp, 11 figure