Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Simultaneous multi-slice readout-segmented echo planar imaging for accelerated diffusion-weighted imaging of the breast

OBJECTIVES Readout-segmented echo planar imaging (rs-EPI) significantly reduces susceptibility artifacts in diffusion-weighted imaging (DWI) of the breast compared to single-shot EPI but is limited by longer scan times. To compensate for this, we tested a new simultaneous multi-slice (SMS) acquisition for accelerated rs-EPI. MATERIALS AND METHODS After approval by the local ethics committee, eight healthy female volunteers (age, 38.9±13.1 years) underwent breast MRI at 3T. Conventional as well as two-fold (2× SMS) and three-fold (3× SMS) slice-accelerated rs-EPI sequences were acquired at b-values of 50 and 800s/mm(2). Two independent readers analyzed the apparent diffusion coefficient (ADC) in fibroglandular breast parenchyma. The signal-to-noise ratio (SNR) was estimated based on the subtraction method. ADC and SNR were compared between sequences by using the Friedman test. RESULTS The acquisition time was 4:21min for conventional rs-EPI, 2:35min for 2× SMS rs-EPI and 1:44min for 3× SMS rs-EPI. ADC values were similar in all sequences (mean values 1.62×10(-3)mm(2)/s, p=0.99). Mean SNR was 27.7-29.6, and no significant differences were found among the sequences (p=0.83). CONCLUSION SMS rs-EPI yields similar ADC values and SNR compared to conventional rs-EPI at markedly reduced scan time. Thus, SMS excitation increases the clinical applicability of rs-EPI for DWI of the breast.

Optimized on-line enantioselective capillary electrophoretic method for kinetic and inhibition studies of drug metabolism mediated by cytochrome P450 enzymes.

Pharmacokinetic and pharmacodynamic properties of a chiral drug can significantly differ between application of the racemate and single enantiomers. During drug development, the characteristics of candidate compounds have to be assessed prior to clinical testing. Since biotransformation significantly influences drug actions in an organism, metabolism studies represent a crucial part of such tests. Hence, an optimized and economical capillary electrophoretic method for on-line studies of the enantioselective drug metabolism mediated by cytochrome P450 enzymes was developed. It comprises a diffusion-based procedure, which enables mixing of the enzyme with virtually any compound inside the nanoliter-scale capillary reactor and without the need of additional optimization of mixing conditions. For CYP3A4, ketamine as probe substrate and highly sulfated γ-cyclodextrin as chiral selector, improved separation conditions for ketamine and norketamine enantiomers compared to a previously published electrophoretically mediated microanalysis method were elucidated. The new approach was thoroughly validated for the CYP3A4-mediated N-demethylation pathway of ketamine and applied to the determination of its kinetic parameters and the inhibition characteristics in presence of ketoconazole and dexmedetomidine. The determined parameters were found to be comparable to literature data obtained with different techniques. The presented method constitutes a miniaturized and cost-effective tool, which should be suitable for the assessment of the stereoselective aspects of kinetic and inhibition studies of cytochrome P450-mediated metabolic steps within early stages of the development of a new drug.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.