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The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
(2018)
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
The hybrid K+/Ca2+ sensor based on laser scanned silicon transducer for multi-component analysis
(2002)
The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
Humic substances originating from various organic matters can ameliorate soil properties, stimulate plant growth, and improve nutrient uptake. Due to the low calorific heating value, leonardite is rather unsuitable as fuel. However, it may serve as a potential source of humic substances. This study was aimed at characterizing the leonardite-based soil amendments and examining the effect of their application on the soil microbial community, as well as on potato growth and tuber yield. A high yield (71.1%) of humic acid (LHA) from leonardite has been demonstrated. Parental leonardite (PL) and LHA were applied to soil prior to potato cultivation. The 16S rRNA sequencing of soil samples revealed distinct relationships between microbial community composition and the application of leonardite-based soil amendments. Potato tubers were planted in pots in greenhouse conditions. The tubers were harvested at the mature stage for the determination of growth and yield parameters. The results demonstrated that the LHA treatments had a significant effect on increasing potato growth (54.9%) and tuber yield (66.4%) when compared to the control. The findings highlight the importance of amending leonardite-based humic products for maintaining the biogeochemical stability of soils, for keeping their healthy microbial community structure, and for increasing the agronomic productivity of potato plants.
The Crystal Clear Collaboration has developed a modular system for a small animal PET scanner (ClearPET). The modularity allows the assembly of scanners of different sizes and characteristics in order to satisfy the specific needs of the individual member institutions. The system performs depth of interaction detection by using a phoswich arrangement combining LSO and LuYAP scintillators which are coupled to Multichannel Photomultipliers (PMTs). For each PMT a free running 40 MHz ADC digitizes the signal and the complete scintillation pulse is sampled by an FPGA and sent with 20 MB/s to a PC for preprocessing. The pulse provides information about the gamma energy and the scintillator material which identifies the interaction layer. Furthermore, the exact pulse starting time is obtained from the sampled data. This is important as no hardware coincidence detection is implemented. All single events are recorded and coincidences are identified by software. The system in Jülich (ClearPET Neuro) is equipped with 10240 crystals on 80 PMTs. The paper will present an overview of the data acquisition system.
Following the success of PET/CT during the last decade and the recent increasing proliferation of SPECT/CT, another hybrid imaging instrument has been gaining more and more interest: MR-PET. First combined, simultaneous PET and MR studies carried out in small animals demonstrated the feasibility of the new approach. Concurrently, some prototypes of an MR-PET scanner for simultaneous human brain studies have been built, their performance is being tested and preliminary applications have already been shown. Through this pioneering work, it has become clear that advances in the detector design are necessary for further optimization.
Recently, the different issues related to the present state and future prospects of MR-PET were presented and discussed during an international 2-day workshop at the Forschungszentrum Jülich, Germany, held after, and in conjunction with, the 2008 IEEE Nuclear Science Symposium and Medical Imaging Conference in Dresden, Germany on October 27–28, 2008. The topics ranged from small animal MR-PET imaging to human MR-BrainPET imaging, new detector developments, challenges/opportunities for ultra-high field MR-PET imaging and considerations of possible future research and clinical applications. This report presents a critical summary of the contributions made to the workshop.
The ClearPET™ project: Development of a 2nd generation high-performance small animal PET scanner
(2005)
Second generation high-performance PET scanners, called ClearPET™1, have been developed by working groups of the Crystal Clear Collaboration (CCC). High sensitivity and high spatial resolution for the ClearPET camera is achieved by using a phoswich arrangement combining two different types of lutetium-based scintillator materials: LSO from CTI and LuYAP:Ce from the CCC (ISTC project). In a first ClearPET prototype, phoswich arrangements of 8×8 crystals of 2×2×10 mm3 are coupled to multi-channel photomultiplier tubes (Hamamatsu R7600). A unit of four PMTs arranged in-line represents one of 20 sectors of the ring design. The opening diameter of the ring is 120 mm, the axial detector length is 110 mm.The PMT pulses are digitized by free-running ADCs and digital data processing determines the gamma energy, the phoswich layer and even the exact pulse starting time, which is subsequently used for coincidence detection. The gantry allows rotation of the detector modules around the field of view.
Preliminary data shows a correct identification of the crystal layer about (98±1)%. Typically the energy resolution is (23.3±0.5)% for the luyap layer and (15.4±0.4)% for the lso layer. early studies showed the timing resolution of 2 ns FWHM and 4.8 ns FWTM. the intrinsic spatial resolution ranges from 1.37 mm to 1.61 mm full-width of half-maximum (FWHM) with a mean of 1.48 mm FWHM. further improvements in image and energy resolution are expected when the system geometry is fully modeled.
A 2nd generation high performance small animal PET scanner, called ClearPET™, has been designed and a first prototype is built by working groups of the Crystal Clear Collaboration (CCC). In order to achieve high sensitivity and maintain good uniform spatial resolution over the field of view in high resolution PET systems, it is necessary to extract the depth of interaction (DOI) information and correct for spatial degradation. The design of the first ClearPET™ Demonstrator based on the use of the multi-anode photomultiplier tube (Hamamatsu R7600-M64) and a LSO/LuYAP phoswich matrix. The two crystal layers of 8*8 crystals (2*2*10 mm3) are stacked on each other and mounted without light guide as one to one on the PMT. A unit of four PMTs arranged in-line represents one of 20 sectors of the ring design. The opening diameter of the crystal ring is 137 mm, the axial detector length is 110 mm. The PMT pulses are digitized by free-running ADCs and digital data processing determines the gamma energy, the phoswich layer and even the pulse arrival time. Single gamma interactions are recorded and coincidences are found by software. The gantry allows rotation of the detector modules around the field of view. The measurements have been done using the first LSO/LuYAP detector cassettes.
The ClearPET project
(2004)
The Crystal Clear Collaboration has designed and is building a high-resolution small animal PET scanner. The design is based on the use of the Hamamatsu R7600-M64 multi-anode photomultiplier tube and a LSO/LuYAP phoswich matrix with one to one coupling between the crystals and the photo-detector. The complete system will have 80 PM tubes in four rings with an inner diameter of 137 mm and an axial field of view of 110 mm. The PM pulses are digitized by free-running ADCs and digital data processing determines the gamma energy, the phoswich layer and even the pulse arrival time. Single gamma interactions are recorded and coincidences are found by software. The gantry allows rotation of the detector modules around the field of view. Simulations, and measurements a 2×4 module test set-up predict a spatial resolution of 1.5 mm in the centre of the field of view and a sensitivity of 5.9% for a point source in the centre of the field of view.
Within the Crystal Clear Collaboration a modular system for a small animal PET scanner (ClearPET™) has been developed. The modularity allows the assembly of scanners of different sizes and characteristics in order to fit the specific needs of the individual member institutions. Now a first demonstrator is being completed in Julich. The system performs depth of interaction detection by using a phoswich arrangement combining LSO and LuYAP scintillators which are coupled to multi-channel photomultipliers (PMTs). A free-running ADC digitizes the signal from the PMT and the complete scintillation pulses are sampled by an FPGA and sent with 20 MB/S to a PC for preprocessing. The pulse provides information about the gamma energy and the scintillator material which identifies the interaction layer. Furthermore, the exact pulse starting time is obtained from the sampled data. This is important as no hardware coincidence detection is implemented. All single events are recorded and coincidences are identified by software. An advantage of that is that the coincidence window and the dimensions of the field of view can be adjusted easily. The ClearPET™ demonstrator is equipped with 10240 crystals on 80 PMTs. This paper presents an overview of the data acquisition system.