Mathematical Problems of Thermoacoustic and Compton Camera Imaging

The results presented in this dissertation concern two different types of tomographic imaging. The first part of the dissertation is devoted to the time reversal method for approximate reconstruction of images in thermoacoustic tomography. A thorough numerical study of the method is presented. Error estimates of the time reversal approximation are provided. In the second part of the dissertation a type of emission tomography, called Compton camera imaging is considered. The mathematical problem arising in Compton camera imaging is the inversion of the cone transform. We present three methods for inversion of this transform in two dimensions. Numerical examples of reconstructions by these methods are also provided. Lastly, we turn to a problem of significance in homeland security, namely the detection of geometrically small, low emission sources in the presence of a large background radiation. We consider the use of Compton type detectors for this purpose and describe an efficient method for detection of such sources. Numerical examples demonstrating this method are also provided

Movement of cadmium and lead in anthropogenically formed trophic chains of a pasture type

ABSTRACT: An investigation on the movement of Lead (Pb) and cadmium (Cd) in a trophic chain in 2 villages (industrial polluted and non polluted) has been conducted. The contents of the 2 heavy metals in the soil, food and in different organs of young kids, so as their transfer in the 3 trophic levels (using different static and dynamic methods of recalculation) have been established. The authors show, that it is expedient to determine quantitatively the chemical heterogeneity at the heterotrophic levels applying two criteria: along with the dynamic criterion “Clarc of concentration”(Cc), used up to know, to include also “Factor of bioaccumulation” (FB), which shows the real value of accumulation or dispersal of the chemical element according to its content in soil or at the trophic level of the autotrophic organisms. The increased Cc of lead /4,72/ and cadmium /49,14/ in soil is not the reason for the concentration in the nutrition chain at the level of the autotrophic organisms and at the level of the organisms phytophages /kids/. The studies of the FB show that the technogenically high Clarc of lead and cadmium in the ecotope is the reason for some changes in the metabolism, enabling the dispersal of lead along the trophic chain, the values falling down to 0,05 – 0,02 compared to its content in the ecotope, and, of cadmium – down to 0,03 – 0,15 in the tested organs and tissues. РЕЗЮМЕ: Проведено е изследване за движението на олово (Pb) и кадмий (Cd) в трофична верига в две села(промишлено замърсено и незамърсено). Установено е съдържанието на двата тежки метала в почвата, храната и различните органи на млади ярета и трансферът им в трите трофични нива, използвайки различни статични и динамични методи на изчисление. Авторите доказват, че е възможно количественото определяне на химичната хетерогенност на хетеротрофните нива, използвайки два критерия: наред с динамичния критерий “Кларк на концентрация” (Сс), използван досега, се включва и “Фактор на биоакумулация” (FB), който показва реалната стойност на натрупване или разсейване на химичния елемент според съдържанието му в почвата или на трофично ниво в автотрофния организъм. Повишеният Сс на олово /4,72/ и кадмий /49,14/ в почвата не е причина за концентрацията им в хранителната верига на нивото на автотрофните организми и на нивото на организмите-фитофаги /ярета/. Изследванията на FB показват, че техногенно високият кларк на олово и кадмий в екотопа е причина за някои промени в метаболизма, способстващи за разпръскване на оловото по трофичната верига и спада на стойностите до 0,05 – 0,02 в сравнение със съдържанието му в екотопа, и на кадмия – до 0,03 – 0,15 в изследваните органи и тъкани