Effective medium approach for heterogeneous reaction-diffusion media

Compound Stability in Nanoparticles: The Effect of Solid Phase Fraction on Diffusion of Degradation Agents into Nanostructured Lipid Carriers

The stability of active compounds encapsulated in nanoparticles depends on the resistance of the particles to diffusion of environmental degradation agents. In this paper, off-lattice Monte Carlo simulations are used to investigate a suspension of nanostructured lipid carriers (NLC) composed of interspaced liquid and solid lipid domains, immersed in a solution containing molecules representing oxidative or other degradation agents. The simulations examine the diffusion of the degradation agents into the nanoparticles as a function of nanoparticle size, solid domain fraction, and domain size. Two types of suspensions are studied: one (representing an infinitely dilute nanoparticle suspension) where the concentration of oxidative agents is constant in the solution around the particle and the other, finite system where diffusion into the nanoparticle causes depletion in the concentration of degradation agents in the surrounding solution. The total number of degradation agent molecules in the NLCs is found to decrease with the solid domain fraction, as may be expected. However, their concentration in the liquid domains is found to increase with the solid domain fraction. Since the degradation reaction depends on the concentration of the degradation agents, this suggests that compounds encapsulated in nanoparticles with high liquid content (such as emulsions) will degrade less and be more stable than those encapsulated in NLCs with high solid domain fraction, in agreement with previous experimental results.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Nanostructured lipid carriers: effect of solid phase fraction and distribution on the release of encapsulated materials

Emulsions, solid lipid nanoparticles (SLN), and nanostructured lipid carriers (NLC) containing a mix of liquid and solid domains are of interest as encapsulation vehicles for hydrophobic compounds. Studies of the release rate from these particles yield contradictory results: Some find that increasing the fraction of solid phase increases the rate of release and others the opposite. In this paper we study the release of encapsulated materials from lipid-based nanoparticles using Monte Carlo simulations. We find that, quite surprisingly, the release rate is largely insensitive to the size of solid domains or the fraction of solid phase. However, the distribution of the domains significantly affects the rate of release: Solid domains located at the interface with the surrounding solution inhibit transport, while nanoparticles where the solid domains are concentrated in the center enhance it. The latter can lead to release rates in NLCs that are faster than in the equivalent emulsions. We conclude that controlling the release rate from NLCs requires the ability to determine the location and distribution of the solid phase, which may be achieved through choice of the surfactants stabilizing the particles, incorporation of nucleation sites, and/or the cooling rates and temperatures.

Front propagation in one-dimensional spatially periodic bistable media

Front propagation in heterogeneous bistable media is studied using the Schlögl model as a representative example. Spatially periodic modulations in the parameters of the bistable kinetics are taken into account perturbatively. Depending on the ratio L/l (L is the spatial period of the heterogeneity, l is the front width), appropriate singular perturbation techniques are applied to derive an ordinary differential equation for the position of the front in the presence of the heterogeneities. From this equation, the dependence of the average propagation speed on L/l as well as on the modulation amplitude is calculated. The analytical results obtained predict velocity overshoot, different cases of propagation failure, and the propagation speed for very large spatial periods in quantitative agreement with the results of direct numerical simulations of the underlying reaction-diffusion equation.

Propagation limits and velocity of reaction-diffusion fronts in a system of discrete random sources

The effect of spatially randomizing a system of pointlike sources on the propagation of reaction-diffusion fronts is investigated in multidimensions. The dynamics of the reactive front are modeled by superimposing the solutions for diffusion from a single point source. A nondimensional parameter is introduced to quantify the discreteness of the system, based on the characteristic reaction time of sources compared to the diffusion time between sources. The limits to propagation and the average velocity of propagation are expressed as probabilistic quantities to account for the influence of the randomly distributed sources. In random systems, two- and three-dimensional fronts are able to propagate beyond a limit previously found for systems with regularly distributed sources, while a propagation limit in one dimension that is independent of domain size cannot be defined. The dimensionality of the system is seen to have a strong influence on the front propagation velocity, with higher dimensional systems propagating faster than lower dimensional systems. In a three-dimensional system, both the limit to propagation and average front velocity revert to a solution that assumes a spatially continuous source function as the discreteness parameter is increased to the continuum limit. The results indicate that reactive systems are able to exploit local fluctuations in source concentration to extend propagation limits and increase the velocity in comparison to regularly spaced systems.

Scaling properties of conduction velocity in heterogeneous excitable media

Waves of excitation through excitable media, such as cardiac tissue, can propagate as plane waves or break up to form reentrant spiral waves. In diseased hearts reentrant waves can be associated with fatal cardiac arrhythmias. In this paper we investigate the conditions that lead to wave break, reentry, and propagation failure in mathematical models of heterogeneous excitable media. Two types of heterogeneities are considered: sinks are regions in space in which the voltage is fixed at its rest value, and breaks are nonconducting regions with no-flux boundary conditions. We find that randomly distributed heterogeneities in the medium have a decremental effect on the velocity, and above a critical density of such heterogeneities the conduction fails. Using numerical and analytical methods we derive the general relationship among the conduction velocity, density of heterogeneities, diffusion coefficient, and the rise time of the excitation in both two and three dimensions. This work helps us understand the factors leading to reduced propagation velocity and the formation of spiral waves in heterogeneous excitable media.

Effects of reduced discrete coupling on filament tension in excitable media

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.