On the Visualization of Patient Specific Arterial Geometries Using the Virtual Histology

The simulation of a balloon–angioplasty (clinical treatment of atherosclerotically degenerated arteries) requires information of the anatomical and physiological composition of the arterial wall. The intravascular ultrasound and the interpretation by a virtual histology provide cross–sectional images of the diseased arterial walls where the different components are characterized by color–coding. Using these information and the reconstruction of the vessel path from biplane angiography the patient specific data are visualized and discretized. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

CO2 and SnII Adducts of N‐Heterocyclic Carbenes as Delayed‐Action Catalysts for Polyurethane Synthesis

Catalytic rivals : Both CO₂‐protected tetrahydropyrimidin‐2‐ylidene‐based N‐heterocyclic carbenes (NHCs) and Sn^II‐1,3‐dimesitylimidazol‐2‐ylidene, as well as Sn^II‐1,3‐dimesitylimidazolin‐2‐ylidene complexes (example displayed), have been identified as truly latent catalysts for polyurethane (PUR) synthesis rivaling all existing systems both in activity and latency.

     

Validated quantitation method for a peptide in rat serum using liquid chromatography/high‐field asymmetric waveform ion mobility spectrometry

The analysis of peptides presents serious challenges for bioanalytical scientists including low total ion current and non‐selective fragmentation during tandem mass spectrometry (MS/MS). During method validation of a peptide in rat serum matrix some interferences could not be easily removed and thus prevented accurate and precise measurement. These problems associated with peptide quantitation were resolved by using FAIMS (high‐Field Asymmetric waveform Ion Mobility Spectrometry). This selectivity‐enhancing technique filters out matrix interferences, and the resulting pseudo‐selected reaction monitoring (pseudo‐SRM) chromatograms were nearly free from interferences. Control blank matrix samples contained an acceptable level of interference (only 7% signal as compared to the lower level of quantitation). Chromatographic peaks were easily, accurately and precisely integrated resulting in a validated liquid chromatography (LC)/FAIMS‐MS/MS method for the analysis of a peptide drug in rat serum according to United States Food and Drug Administration (US FDA) bioanalytical guidelines. These results confirm that new selectivity‐enhancing technologies aid the pharmaceutical industry in reliably producing acceptable pharmacokinetic data. Copyright © 2009 John Wiley & Sons, Ltd.     

On Kalai’s Conjectures Concerning Centrally Symmetric Polytopes

In 1989, Kalai stated three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture, A, became known as the “3 ^d -conjecture.” It is well known that the three conjectures hold in dimensions d≤3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conjectures B and C fail in all dimensions d≥5.     

Traveling Wave Solutions of Nonlinear Scalar Integral Differential Equations Arising from Synaptically Coupled Neuronal Networks

Consider the following nonlinear scalar integral differential equations arising from synaptically coupled neuronal networks. These model equations generalize many important nonlinear scalar integral differential equations aris ing from synaptically coupled neuronal networks. The kernel functions K and W represent synaptic couplings between neurons in synaptically coupled neuronal networks. The synaptic couplings can be very general, including not only pure excitations (modeled with nonnegative kernel functions), lateral inhibitions (modeled with Mexican hat kernel functions), lateral excitations (modeled with upside down Mexican hat kernel functions), but also synaptic couplings which may change sign for finitely many times or even infinitely many times. The function H = H(u − ) represents the Heaviside step function, which is defined by H(u − ) = 0 for all u < , H(0) = 1 2 and H(u − ) = 1 for all u > . The functions and represent probability density functions defined on (0,1). The parameter c > 0 represents the speed of an action potential and the parameter > 0 represents a constant delay. In these equations, u = u(x, t) stands for the membrane potential of a neuron at position x and time t. The positive constants > 0 and > 0 represent synaptic rates. The positive constants > 0 and > 0 represent thresholds for excitation of neurons. The function f = f(u) represents the sodium currents in neuronal networks. The positive constant w 0 > 0 is to be given. The authors will establish the existence and stability of traveling wave solutions of these nonlinear scalar integral differential equations by coupling together speed index functions, stability index func tions (often called Evans functions, that is, complex analytic functions), implicit function theorem, intermediate value theorem, mean value theorem, global strong maximum principle for Evans func tions, linearized stability criterion and many other important techniques in dynamical systems. They will find sufficient conditions satisfied by the synaptic couplings, by the probability density functions, by the synaptic rate constants and by the thresholds so that the traveling wave solutions and their wave speeds exist, and the stability of the traveling wave solutions is true. The main results obtained in this paper greatly improve many previous results.