Rotation sets of billiards with one obstacle

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets

Coherent States Measurement Entropy

Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the unpredictability induced by the process of a quantum approximate measurement. We study the CS--measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the time limit $n \to \infty$. In particular we propose an effective technique of computing the entropy by iterated function systems. The dependence of CS--measurement entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail: [email protected]). Submitted to J.Phys.

Physiologically Based Pharmacokinetic Modeling of TransporterMediated Hepatic Disposition of Imaging Biomarker Gadoxetate in Rats

[Image: see text] Physiologically based pharmacokinetic (PBPK) models are increasingly used in drug development to simulate changes in both systemic and tissue exposures that arise as a result of changes in enzyme and/or transporter activity. Verification of these model-based simulations of tissue exposure is challenging in the case of transporter-mediated drug–drug interactions (tDDI), in particular as these may lead to differential effects on substrate exposure in plasma and tissues/organs of interest. Gadoxetate, a promising magnetic resonance imaging (MRI) contrast agent, is a substrate of organic-anion-transporting polypeptide 1B1 (OATP1B1) and multidrug resistance-associated protein 2 (MRP2). In this study, we developed a gadoxetate PBPK model and explored the use of liver-imaging data to achieve and refine in vitro–in vivo extrapolation (IVIVE) of gadoxetate hepatic transporter kinetic data. In addition, PBPK modeling was used to investigate gadoxetate hepatic tDDI with rifampicin i.v. 10 mg/kg. In vivo dynamic contrast-enhanced (DCE) MRI data of gadoxetate in rat blood, spleen, and liver were used in this analysis. Gadoxetate in vitro uptake kinetic data were generated in plated rat hepatocytes. Mean (%CV) in vitro hepatocyte uptake unbound Michaelis–Menten constant (K(m,u)) of gadoxetate was 106 μM (17%) (n = 4 rats), and active saturable uptake accounted for 94% of total uptake into hepatocytes. PBPK–IVIVE of these data (bottom-up approach) captured reasonably systemic exposure, but underestimated the in vivo gadoxetate DCE–MRI profiles and elimination from the liver. Therefore, in vivo rat DCE–MRI liver data were subsequently used to refine gadoxetate transporter kinetic parameters in the PBPK model (top-down approach). Active uptake into the hepatocytes refined by the liver-imaging data was one order of magnitude higher than the one predicted by the IVIVE approach. Finally, the PBPK model was fitted to the gadoxetate DCE–MRI data (blood, spleen, and liver) obtained with and without coadministered rifampicin. Rifampicin was estimated to inhibit active uptake transport of gadoxetate into the liver by 96%. The current analysis highlighted the importance of gadoxetate liver data for PBPK model refinement, which was not feasible when using the blood data alone, as is common in PBPK modeling applications. The results of our study demonstrate the utility of organ-imaging data in evaluating and refining PBPK transporter IVIVE to support the subsequent model use for quantitative evaluation of hepatic tDDI