A geometric theory for scroll wave filaments in anisotropic excitable media

Scroll waves are an important example of self-organisation in excitable media. In cardiac tissue, scroll waves of electrical activity underlie lethal ventricular arrhythmias and fibrillation. They rotate around a topological line defect which has been termed the filament. Numerical investigation has shown that anisotropy can substantially affect the dynamics of scroll waves. It has recently been hypothesised that stationary scroll wave filaments in cardiac tissue describe geodesics in a space whose metric is the inverse diffusion tensor. Several computational studies have validated this hypothesis, but until now no quantitative theory has been provided to study the effects of anisotropy on scroll wave filaments. Here, we review in detail the recently developed covariant formalism for scroll wave dynamics in general anisotropy and derive the equations of motion of filaments. These equations are fully covariant under general spatial coordinate transformations and describe the motion of filaments in a curved space whose metric tensor is the inverse diffusion tensor. Our dynamic equations are valid for thin filaments and for general anisotropy and we show that stationary filaments obey the geodesic equation. We extend previous work by allowing spatial variations in the determinant of the diffusion tensor and the reaction parameters, leading to drift of the filament.     

Extrinsic multiecho phase-contrast SSFP: evaluation on cardiac output measurements

Multiecho phase-contrast steady-state free precession (PC-SSFP) is a recently introduced sequence for flow quantification. In this multiecho approach, a phase reference and a velocity-encoded readout were acquired at different echo times after a single excitation. In this study, the sequence is validated in vitro for stationary flow. Subsequently, the sequence was evaluated on cardiac output measurements in vivo for through-plane flow in comparison to regular single gradient echo velocity quantification [phase-contrast spoiled gradient echo (PC-GE)]. In vitro results agreed with regular flow meters (RMS 0.1 cm/s). Cardiac output measurements with multiecho PC-SSFP on 10 healthy subjects gave on average the same results as the standard PC-GE. However, the limits of repeatability of PC-SSFP were significantly larger than those of PC-GE (2 l/min and 0.5 l/min, respectively, P=.001). The multiecho approach introduced some specific problems in vivo. The difference in echo times made the velocity maps sensitive for water-fat shifts and B(0)-drifts, which in turn made velocity offset correction problematic. Also, the addition of a single bipolar gradient cancelled the flow compensated nature of the SSFP sequence. In combination with the prolonged TR, this resulted in flow artifacts caused by high and pulsatile through-plane flow, affecting repeatability. Given the significantly lower repeatability of PC-SSFP, cardiac output in turn is less reliable, thus impairing the use of multiecho PC-SSFP.     

Arsenic speciation in chinese seaweeds using HPLC-ICP-MS and HPLC-ES-MS

Three common Chinese edible seaweeds, one brown (Laminaria japonica) and two red (Porphyra crispata and Eucheuma denticulatum), were examined for their total arsenic content. The As species were extracted with yields of 76.4, 69.8 and 25.0%, respectively. Anion-exchange and cation-exchange high-performance liquid chromatography (HPLC) in combination with inductively coupled plasma mass spectrometry (ICP-MS) were used for the separation of the different arsenic species in two of the three seaweed extracts (Laminaria and Porphyra). The main arsenic species in the algal extracts are arseno sugars, although it has been shown that the Laminaria seaweed contains significant amounts of dimethylarsinic acid (DMA). HPLC was coupled with electrospray mass spectrometry (ES-MS) for structural confirmation of the arsenic species. The mass spectrometer settings for the arseno sugars were optimised using standards. The conclusions drawn on the basis of HPLC-ICP-MS were confirmed by the HPLC-ES-MS data. The HPLC-ES-MS method is capable of determining both arseno sugars and DMA in the seaweeds. The unknown compounds seen in the HPLC-ICP-MS chromatogram of Laminaria could not be ascribed to trimethylarsenic oxide or tetramethylarsonium ion.     

Enumerating Regular Mixed-Cell Configurations

By means of the Cayley Trick the problem of enumerating all regular fine mixed subdivisions is reduced to enumerating all regular triangulations. The set of all regular triangulations is well understood thanks to the bijection with the vertices of the secondary polytope. However, since we are only interested in the configurations of mixed cells in a mixed subdivision, we want to avoid dealing with other cells. We propose an operator derived from the bistellar flip for regular triangulations to modify a mixed-cell configuration. Received June 30, 1997, and in revised form December 1, 1997.     

Renormalization of soliton theories

We present a general proof of the renormalizability of the one soliton sector, based on a new quantization scheme for solitons in two space time dimensions.     

Study of the O(N) linear \sigma model at finite temperature using the 2PPI expansion

We show that a new expansion, which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear -model at finite temperature. We prove that this expansion can be renormalized with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self-energy of the -meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation. Received: 22 March 2001 / Revised version: 3 September 2001 / Published online: 14 December 2001     

Spreading of proteins and its effect on adsorption and desorption kinetics

The kinetics of adsorption of lysozyme and alpha-lactalbumin from aqueous solution on silica and hydrophobized silica has been studied. The initial rate of adsorption of lysozyme at the hydrophilic surface is comparable with the limiting flux. For lysozyme at the hydrophobic surface and alpha-lactalbumin on both surfaces, the rate of adsorption is lower than the limiting flux, but the adsorption proceeds cooperatively, as manifested by an increase in the adsorption rate after the first protein molecules are adsorbed. At the hydrophilic surface, adsorption saturation (reflected in a steady-state value of the adsorbed amount) of both proteins strongly depends on the rate of adsorption, but for the hydrophobic surface no such dependency is observed. It points to structural relaxation ("spreading") of the adsorbed protein molecules, which occurs at the hydrophobic surface faster than at the hydrophilic one. For lysozyme, desorption has been studied as well. It is found that the desorbable fraction decreases after longer residence time of the protein at the interface.     

Covariant stringlike dynamics of scroll wave filaments in anisotropic cardiac tissue

It has been hypothesized that stationary scroll wave filaments in cardiac tissue describe a geodesic in a curved space whose metric is the inverse diffusion tensor. Several numerical studies support this hypothesis, but no analytical proof has been provided yet for general anisotropy. In this Letter, we derive dynamic equations for the filament in the case of general anisotropy. These equations are covariant under general spatial coordinate transformations and describe the motion of a stringlike object in a curved space whose metric tensor is the inverse diffusion tensor. Therefore the behavior of scroll wave filaments in excitable media with anisotropy is similar to the one of cosmic strings in a curved universe. Our dynamic equations are valid for thin filaments and for general anisotropy. We show that stationary filaments obey the geodesic equation.