Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Manipulating Kondo Temperature via Single Molecule Switching

Two conformations of isolated single TBrPP-Co molecules on a Cu(111) surface are switched by applying +2.2 V voltage pulses from a scanning tunneling microscope tip at 4.6 K. The TBrPP-Co has a spin-active cobalt atom caged at its center and the interaction between the spin of this cobalt atom and free electrons from the Cu(111) substrate can cause a Kondo resonance. Tunneling spectroscopy data reveal that switching from the saddle to a planar molecular conformation enhances spin-electron coupling, which increases the associated Kondo temperature from 130 K to 170 K. This result demonstrates that the Kondo temperature can be manipulated just by changing molecular conformation without altering chemical composition of the molecule.Comment: To appear in Nano Lett (2006

Quantitative imaging of 124I and 86Y with PET

The quantitative accuracy and image quality of positron emission tomography (PET) measurements with 124I and 86Y is affected by the prompt emission of gamma radiation and positrons in their decays, as well as the higher energy of the emitted positrons compared to those emitted by 18F. PET scanners cannot distinguish between true coincidences, involving two 511-keV annihilation photons, and coincidences involving one annihilation photon and a prompt gamma, if the energy of this prompt gamma is within the energy window of the scanner. The current review deals with a number of aspects of the challenge this poses for quantitative PET imaging. First, the effect of prompt gamma coincidences on quantitative accuracy of PET images is discussed and a number of suggested corrections are described. Then, the effect of prompt gamma coincidences and the increased singles count rates due to gamma radiation on the count rate performance of PET is addressed, as well as possible improvements based on modification of the scanner’s energy windows. Finally, the effect of positron energy on spatial resolution and recovery is assessed. The methods presented in this overview aim to overcome the challenges associated with the decay characteristics of 124I and 86Y. Careful application of the presented correction methods can allow for quantitatively accurate images with improved image contrast

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE

The future of hybrid imaging—part 2: PET/CT

Since the 1990s, hybrid imaging by means of software and hardware image fusion alike allows the intrinsic combination of functional and anatomical image information. This review summarises the state-of-the-art of dual-modality imaging with a focus on clinical applications. We highlight selected areas for potential improvement of combined imaging technologies and new applications. In the second part, we briefly review the background of dual-modality PET/CT imaging, discuss its main applications and attempt to predict technological and methodological improvements of combined PET/CT imaging. After a decade of clinical evaluation, PET/CT will continue to have a significant impact on patient management, mainly in the area of oncological diseases. By adopting more innovative acquisition schemes and data processing PET/CT will become a fast and dose-efficient imaging method and an integral part of state-of-the-art clinical patient management

Total 18F-dopa PET tumour uptake reflects metabolic endocrine tumour activity in patients with a carcinoid tumour

Positron emission tomography (PET) using 6-[(18)F]fluoro-L-dihydroxyphenylalanine ((18)F-dopa) has an excellent sensitivity to detect carcinoid tumour lesions. (18)F-dopa tumour uptake and the levels of biochemical tumour markers are mediated by tumour endocrine metabolic activity. We evaluated whether total (18)F-dopa tumour uptake on PET, defined as whole-body metabolic tumour burden (WBMTB), reflects tumour load per patient, as measured with tumour markers. Seventy-seven consecutive carcinoid patients who underwent an (18)F-dopa PET scan in two previously published studies were analysed. For all tumour lesions mean standardised uptake values (SUVs) at 40% of the maximal SUV and tumour volume on (18)F-dopa PET were determined and multiplied to calculate a metabolic burden per lesion. WBMTB was the sum of the metabolic burden of all individual lesions per patient. The 24-h urinary serotonin, urine and plasma 5-hydroxindoleacetic acid (5-HIAA), catecholamines (nor)epinephrine, dopamine and their metabolites, measured in urine and plasma, and serum chromogranin A served as tumour markers. All but 1 were evaluable for WBMTB; 74 patients had metastatic disease. (18)F-dopa PET detected 979 lesions. SUV(max) on (18)F-dopa PET varied up to 29-fold between individual lesions within the same patients. WBMTB correlated with urinary serotonin (r = 0.51) and urinary and plasma 5-HIAA (r = 0.78 and 0.66). WBMTB also correlated with urinary norepinephrine, epinephrine, dopamine and plasma dopamine, but not with serum chromogranin A. Tumour load per patient measured with (18)F-dopa PET correlates with tumour markers of the serotonin and catecholamine pathway in urine and plasma in carcinoid patients, reflecting metabolic tumour activity

An international multi-center investigation on the accuracy of radionuclide calibrators in nuclear medicine theragnostics

Background: Personalized molecular radiotherapy based on theragnostics requires accurate quantification of the amount of radiopharmaceutical activity administered to patients both in diagnostic and therapeutic applications. This international multi-center study aims to investigate the clinical measurement accuracy of radionuclide calibrators for 7 radionuclides used in theragnostics: 99mTc, 111In, 123I, 124I, 131I, 177Lu, and 90Y. Methods: In total, 32 radionuclide calibrators from 8 hospitals located in the Netherlands, Belgium, and Germany were tested. For each radio

Southward displacement of the North Atlantic Subtropical Gyre circulation system during North Atlantic cold spells

Key Points: - Rapid subsurface oceanographic change in the tropical W Atlantic reflect shifting Subtropical Gyre - Subsurface warming responds to deglacial AMOC perturbations (Heinrich Stadials 2, 1, and the Younger Dryas) - Southward propagation of Salinity Maximum Water during Northern Hemisphere cold spells shift the mixing zone of tropical and subtropical waters During times of deglacial Atlantic Meridional Overturning Circulation (AMOC) perturbations, the tropical Atlantic experienced considerable warming at subsurface levels. Coupled ocean‐atmosphere simulations corroborate the tight teleconnection between the tropical Atlantic and climate change at high northern latitudes, but still underestimate the relevance of the subsurface N Atlantic Subtropical Gyre (STG) for heat and salt storage and its sensitivity to rapid climatic change. We here reconstruct vertical and lateral temperature and salinity gradients in the tropical W Atlantic and the Caribbean over the last 30 kyrs, based on planktic deep and shallow dwelling foraminiferal Mg/Ca and δ18O‐records. The rapid and large amplitude subsurface changes illustrate a dynamic STG associated with abrupt shifts of North Atlantic hydrographic and atmospheric regimes. During full glacial conditions, the STG has been shifted southward while intensified Ekman‐downwelling associated to strengthened trade winds fostered the formation of warm and saline Salinity Maximum Water (SMW). The southward propagation of SMW was facilitated by the glacially eastward deflected North Brazil Current. During periods of significant AMOC perturbations (Heinrich Stadials 1, and the Younger Dryas), extreme subsurface warming by ~6°C led to diminished lateral subsurface temperature gradients. Coevally, a deep thermocline suggests that SMW fully occupied the subsurface tropical W Atlantic and that the STG reached its southernmost position. During the Holocene, modern‐like conditions gradually developed with the northward retreat of SMW and the development of a strong thermocline ridge between the Subtropical Gyre and the tropical W Atlantic

Lesion segmentation for MR spectroscopic imaging using the convolution difference method

Delineation of lesion boundaries from volumetric MRSI metabolite ratio maps using a method that accounts for the spatial response function of the acquisition and variable spectral quality and is robust to signal heterogeneity within the lesion. A novel method for lesion segmentation, termed convolution difference, has been developed that is robust to signal heterogeneity within the lesion and to differences in the spatial response function. Procedures are described for processing metabolite ratio maps and to exclude regions of inadequate spectral quality. This method was evaluated using computer simulations, and the results were compared with an iterative thresholding technique that determines an optimal amplitude threshold, and with the use of a fixed amplitude threshold. These methods were evaluated for segmentation of volumetric MRSI studies of gliomas using maps of the choline to N-acetylaspartate ratio, and a qualitative comparison of lesion volumes carried out. Simulation studies indicated improved performance for the convolution difference method when applied to ratio maps. Variations in tumor volume were observed for the in vivo studies between the convolution difference and the iterative thresholding methods; however, visual analysis indicates that both showed improved accuracy in comparison to using a fixed amplitude threshold. This study reinforces previous reports indicating that the use of fixed threshold values for segmentation of maps with broad spatial response functions can result in errors in lesion volume definition. A novel segmentation method, termed the convolution difference, has been introduced and demonstrated to be robust for segmentation of volumetric MRSI metabolite data