Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Ultrasonic Degradation of Poly(acrylic acid)

The ultrasonic degradation of poly(acrylic acid), a water-soluble polymer, was studied in the presence of persulfates at different temperatures in binary solvent Mixtures of methanol and water. The degraded samples were analyzed by gel permeation chromatography for the time evolution of the molecular weight distributions. A continuous distribution kinetics model based on midpoint chain scission was developed, and the degradation rate coefficients were determined. The decline in the rate of degradation of poly(acrylic acid) with increasing temperature and with an increment in the methanol content in the binary solvent mixture of methanol and water was attributed to the increased vapor pressure of the solutions. The experimental data showed an augmentation of the degradation rate of the polymer with increasing oxidizing agent (persulfate) concentrations. Different concentrations of three persulfates-potassium persulfate, ammonium persulfate, and sodium persulfate-were used. It was found that the ratio of the polymer degradation rate coefficient to the dissociation rate constant of the persulfate was constant. This implies that the ultrasonic degradation rate of poly(acrylic acid) can be determined a priori in the presence of any initiator.

The Parallel Complexity Of Propagation In Boolean Circuits

We consider the problem of deciding whether the output of a boolean circuit is determined by a partial assignment to its inputs. This problem is easily shown to be hard, i.e., co-Image Image -complete. However, many of the consequences of a partial input assignment may be determined in linear time, by iterating the following step: if we know the values of some inputs to a gate, we can deduce the values of some outputs of that gate. This process of iteratively deducing some of the consequences of a partial assignment is called propagation. This paper explores the parallel complexity of propagation, i.e., the complexity of determining whether the output of a given boolean circuit is determined by propagating a given partial input assignment. We give a complete classification of the problem into those cases that are Image -complete and those that are unlikely to be Image complete.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

Fatigue crack propagation analysis of plaque rupture

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy

The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R2=99.9% and R2=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.

Effect of electroslag refining on the fracture toughness and fatigue crack propagation rates in heat treated AISI 4340 steel

The AISI 4340 steel has been electroslag refined and the improvement in mechanical properties has been assessed. Electroslag refining (ESR) has improved tensile ductility, plane strain fracture toughness, Charpy fracture energy, and has decreased fatigue crack growth rates. The KIC values for the ESR steel are nearly twice those estimated in the unrefined steel and higher than those obtained in the vacuum arc remelted steel. Fatigue crack growth rates in region I and in region III are found to be decreased considerably in the ESR steel, while they are unaffected in region II. Measurements on heat treated samples have shown that the ESR steel has a better response to heat treatment. Both the suggested heat treatments namely austenitizing at 1140–1470 K as well as the conventional heat treatment of austenitizing at 1140 K have been followed. The improvement in the mechanical properties of ESR steel has been explained on the basis of removal of nonmetallic inclusions and reduction in sulfur content in the steel.

The effect of an in–shoe orthotic heel lift on loading of the Achilles tendon during shod walking

- Study Design Controlled laboratory study - Objective To investigate the effect of a 12–mm in–shoe orthotic heel lift on Achilles tendon loading during shod walking using transmission–mode ultrasonography. - Background Orthotic heel lifts are thought to lower tension in the Achilles tendon but evidence for this effect is equivocal. - Methods The propagation speed of ultrasound, which is governed by the elastic modulus and density of tendon and is proportional to the tensile load to which it is exposed, was measured in the right Achilles tendon of twelve recreationally–active males during shod treadmill walking at matched speeds (3.4±0.7 km/h), with and without addition of a heel lift. Vertical ground reaction force and spatiotemporal gait parameters were simultaneously recorded. Data were acquired at 100Hz during 10s of steady–state walking. Statistical comparisons were made using paired t–tests (α=.05). - Results Ultrasound transmission speed in the Achilles tendon was characterized by two maxima (P1, P2) and minima (M1, M2) during walking. Addition of a heel lift to footwear resulted in a 2% increase and 2% decrease in the first vertical ground reaction force peak and the local minimum, respectively (P<.05). Peak ultrasonic velocity in the Achilles tendon (P1, P2, M2) was significantly lower with addition of an orthotic heel lift (P<.05). - Conclusions Peak ultrasound transmission speed in the Achilles tendon was lower with the addition of a 12–mm orthotic heel lift, indicating the heel lift reduced tensile load in the Achilles tendon, thereby counteracting the effect of footwear. These findings support the addition of orthotic heel lifts to footwear in the rehabilitation of Achilles tendon disorders where management aims to lower tension within the tendon. - Level of Evidence Therapy, level 2a

Ultrasonic attenuation in strongly disordered electronic systems

The attenuation of long-wavelength phonons due to their interaction with electronic excitations in disordered systems is investigated here. Lattice strain couples to electronic stress, and thus ultrasonic attenuation measures electronic viscosity. The enhancement and critical divergence of electronic viscosity due to localization effects is calculated for the first time. Experimental consequences for the anomalous increase of ultrasonic attenuation in disordered metals close to the metal-insulator transition are discussed. In the localized regime, the appropriate model is one of electronic two-level systems (TLS’s) coupled to phonons. The TLS consists of a pair of states with one localized state occupied and the other unoccupied. The density of such low-excitation-energy TLS’s is nonzero due to long-range Coulomb interactions. The question of whether these could be significant low-energy excitations in glasses is touched upon.

Genetic control of propagation traits in a single Corymbia torelliana x Corymbia variegata family

Genetic control of vegetative propagation traits was described for a second-generation, outbred, intersectional hybrid family (N = 208) derived from two species, Corymbia torelliana (F. Muell.) K.D. Hill & L.A.S. Johnson and Corymbia variegata (F. Muell.) K.D. Hill & L.A.S. Johnson, which contrast for propagation characteristics and in their capacity to develop lignotubers. Large phenotypic variances were evident for rooting and most other propagation traits, with significant proportions attributable to differences between clones (broad-sense heritabilities 0.2-0.5). Bare root assessment of rooting rate and root quality parameters tended to have the highest heritabilities, whereas rooting percentage based on root emergence from pots and shoot production were intermediate. Root biomass and root initiation had the lowest heritabilities. Strong favourable genetic correlations were found between rooting percentage and root quality traits such as root biomass, volume, and length. Lignotuber development on a seedling was associated with low rooting and a tendency to poor root quality in cuttings and was in accord with the persistence of species parent types due to gametic phase disequilibrium. On average, nodal cuttings rooted more frequently and with higher quality root systems, but significant cutting type x genotype interaction indicated that for some clones, higher rooting rates were obtained from tips. Low germination, survival of seedlings, and rooting rates suggested strong hybrid breakdown in this family.

Clonal propagation and storage of subtropical pines in Queensland, Australia

Clonal forestry is the approach used for deployment of Pinus elliottii x P. caribaea hybrids in Queensland, Australia. Clonal forestry relies on the ability to maintain juvenility of stock plants while selections are made in field tests, so that genetic gains are not eroded by the effects of stock plant maturation. Two parallel approaches are employed in Queensland to maintain juvenility of clonal material. Firstly, the ortet and several ramets of each clone are maintained as archive hedges <20-cm height for the duration of field tests. Secondly, shoots from archive hedges are stored in tissue culture at low temperature and low irradiance to slow growth and slow maturation. Once the best clones have been identified, production hedges are derived from both archive hedges and tissue culture shoots. About 6 million rooted cuttings are produced annually, representing almost the entire planting program of Pinus in subtropical Queensland.

Propagation of Wollemi pine from tip cuttings and lower segment cuttings does not require rooting hormones

Domestication of the recently discovered and highly endangered Wollemi pine has relied almost entirely upon serial propagation of cuttings from a very small conservation collection. This study assessed the requirement for applied auxin to induce rooting in tip cuttings and lower segment cuttings of Wollemi pine. Both types of cuttings proved easy-to-root, with mean rooting of 71% for tip cuttings and 82% for lower segments. Auxin application (at 1.5, 3.0 or 8.0 g indole-3-butyric acid/L) did not accelerate root protrusion from propagation tubes or affect final rooting percentages.

In vitro propagation of Eucalyptus grandis L. by tissue culture

Multiple shoots were induced from nodal segments of five year old trees of Eucalyptus grandis L. on solid medium containing Murashige and Skoog's (MS) Basal medium supplemented with additional thiamine, BAP and NAA. Rooting could be achieved from shoot culture on half strength MS salts or white's medium supplemented with low auxins like IAA, IBA and NAA.

Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.