Critical behaviour of the Rouse model for gelling polymers

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_{s}$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.

Critical Dynamics of Gelation

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $k=\phi-\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\phi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor changes

Dynamics of gelling liquids: a short survey

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some reference

Non-clinical and Pre-clinical Testing to Demonstrate Safety of the Barostim Neo Electrode for Activation of Carotid Baroreceptors in Chronic Human Implants

The Barostim neo™ electrode was developed by CVRx, Inc.to deliver baroreflex activation therapy (BAT)™ to treat hypertension and heart failure. The neo electrode concept was designed to deliver electrical stimulation to the baroreceptors within the carotid sinus bulb, while minimizing invasiveness of the implant procedure. This device is currently CE marked in Europe, and in a Pivotal (akin to Phase III) Trial in the United States. Here we present the in vitro and in vivo safety testing that was completed in order to obtain necessary regulatory approval prior to conducting human studies in Europe, as well as an FDA Investigational Device Exemption (IDE) to conduct a Pivotal Trial in the United States. Stimulated electrodes (10 mA, 500 μs, 100 Hz) were compared to unstimulated electrodes using optical microscopy and several electrochemical techniques over the course of 27 weeks. Electrode dissolution was evaluated by analyzing trace metal content of solutions in which electrodes were stimulated. Lastly, safety testing under Good Laboratory Practice guidelines was conducted in an ovine animal model over a 12 and 24 week time period, with results processed and evaluated by an independent histopathologist. Long-term stimulation testing indicated that the neo electrode with a sputtered iridium oxide coating can be stimulated at maximal levels for the lifetime of the implant without clinically significant dissolution of platinum or iridium, and without increasing the potential at the electrode interface to cause hydrolysis or significant tissue damage. Histological examination of tissue that was adjacent to the neo electrodes indicated no clinically significant signs of increased inflammation and no arterial stenosis as a result of 6 months of continuous stimulation. The work presented here involved rigorous characterization and evaluation testing of the neo electrode, which was used to support its safety for chronic implantation. The testing strategies discussed provide a starting point and proven framework for testing new neuromodulation electrode concepts to support regulatory approval for clinical studies

Sustained suppression of sympathetic activity and arterial pressure during chronic activation of the carotid baroreflex

Following sinoaortic denervation, which eliminates arterial baroreceptor input into the brain, there are slowly developing adaptations that abolish initial sympathetic activation and hypertension. In comparison, electrical stimulation of the carotid sinus for 1 wk produces sustained reductions in sympathetic activity and arterial pressure. However, whether compensations occur subsequently to diminish these responses is unclear. Therefore, we determined whether there are important central and/or peripheral adaptations that diminish the sympathoinhibitory and blood pressure-lowering effects of more sustained carotid sinus stimulation. To this end, we measured whole body plasma norepinephrine spillover and α1-adrenergic vascular reactivity in six dogs over a 3-wk period of baroreflex activation. During the first week of baroreflex activation, there was an ∼45% decrease in plasma norepinephrine spillover, along with reductions in mean arterial pressure and heart rate of ∼20 mmHg and 15 beats/min, respectively; additionally, plasma renin activity did not increase. Most importantly, these responses during week 1 were largely sustained throughout the 3 wk of baroreflex activation. Acute pressor responses to α-adrenergic stimulation during ganglionic blockade were similar throughout the study, indicating no compensatory increases in adrenergic vascular reactivity. These findings indicate that the sympathoinhibition and lowering of blood pressure and heart rate induced by chronic activation of the carotid baroreflex are not diminished by adaptations in the brain and peripheral circulation. Furthermore, by providing evidence that baroreflexes have long-term effects on sympathetic activity and arterial pressure, they present a perspective that is opposite from studies of sinoaortic denervation