A possible new cardiac heterogeneity as an arrhythmogenic driver.

Atrial fibrillation (AF) is the commonest cardiac arrhythmia, affecting 3 million people in the USA and 8 million in the EU (according to the European Society of Cardiology). So, why is it that even with the best medical care, around a third of the patients are treatment resistant. Extensive research of its etiology showed that AF and its mechanisms are still debatable. Some of the AF origins are ascribed to functional and ionic heterogeneities of the heart tissue and possibly to additional triggering agents. But, have all AF origins been detected? Are all accepted origins, in fact, arrhythmogenic? In order to study these questions and specifically to check our new idea of intermittency as an arrhythmogenesis agent, we chose to employ a mathematical model which was as simple as possible, but which could still be used to observe the basic network processes of AF development. At this point we were not interested in the detailed ionic propagations nor in the actual shapes of the induced action potentials (APs) during the AF outbreaks. The model was checked by its ability to exactly recapture the basic AF developmental stages known from experimental cardiac observations and from more elaborate mathematical models. We use a simple cellular automata 2D mathematical model of N × N matrices to elucidate the field processes leading to AF in a tissue riddled with randomly distributed heterogeneities of different types, under sinus node operation, simulated by an initial line of briefly stimulated cells inducing a propagating wave, and with or without an additional active ectopic action potential pulse, in turn simulated by a transitory operation of a specific cell. Arrhythmogenic contributions, of three different types of local heterogeneities in myocytes and their collaborations, in inducing AF are examined. These are: a heterogeneity created by diffuse fibrosis, a heterogeneity created by myocytes having different refractory periods, and a new heterogeneity type, created by intermittent operation of some myocytes. The developmental stages (target waves and spirals) and the different probabilities of AF occurring under each condition, are shown. This model was established as being capable of reproducing the known AF origins and their basic development stages, and in addition has shown: (1) That diffuse fibrosis on its own is not arrhythmogenic but in combination with other arrhythmogenic agents it can either enhance or limit AF. (2) In general, combinations of heterogeneities can act synergistically, and, most importantly, (3) The new type of intermittency heterogeneity proves to be extremely arrhythmogenic. Both the intermittency risk and the fibrosis role in AF generation were established. Knowledge of the character of these arrhythmogenesis agents can be of real importance in AF treatment.

Percolation and tortuosity in heart-like cells.

In the last several years, quite a few papers on the joint question of transport, tortuosity and percolation have appeared in the literature, dealing with passage of miscellaneous liquids or electrical currents in different media. However, these methods have not been applied to the passage of action potential in heart fibrosis (HF), which is crucial for problems of heart arrhythmia, especially of atrial tachycardia and fibrillation. In this work we address the HF problem from these aspects. A cellular automaton model is used to analyze percolation and transport of a distributed-fibrosis inflicted heart-like tissue. Although based on a rather simple mathematical model, it leads to several important outcomes: (1) It is shown that, for a single wave front (as the one emanated by the heart's sinus node), the percolation of heart-like matrices is exactly similar to the forest fire case. (2) It is shown that, on the average, the shape of the transport (a question not dealt with in relation to forest fire, and deals with the delay of action potential when passing a fibrotic tissue) behaves like a Gaussian. (3) Moreover, it is shown that close to the percolation threshold the parameters of this Gaussian behave in a critical way. From the physical point of view, these three results are an important contribution to the general percolation investigation. The relevance of our results to cardiological issues, specifically to the question of reentry initiation, are discussed and it is shown that: (A) Without an ectopic source and under a mere sinus node operation, no arrhythmia is generated, and (B) A sufficiently high refractory period could prevent some reentry mechanisms, even in partially fibrotic heart tissue.

Origin of post-ictal and post-anesthesia adverse effects and possibly of SUDEP.

The origin of post-ictal malfunctions is debatable. We want to propose a novel idea of a cause of these adverse results occurring following epileptic seizures and anesthesia. Previously we have put forward the idea that epileptic seizures termination is caused by the function of the glymphatic system in the brain. A new measurement shows that this system can be much faster than what was estimated before. Moreover, the method enabling this speeding was actually measured in brains of epilepsy subjects. So, the main objection to our model is relegated. As a possible consequence of the glymphatic process, there can be an excess cleaning of the brain's interstitial fluid. We discuss possible adverse results of this process. This over-cleaning (that can, to a lower extent, occur also during anesthesia) which results post-ictally from the previous overexpression of fluid materials by the neurons during their seizure operation, can reduce ingredients essential for regular neuronal functioning, thereby leading to function reduction and EEG suppression which last until those materials are replenished. We argue that this ingredients' scarcity is the cause of post-ictal generalized EEG suppression (PGES), of post-ictal immobility (PI) and possibly of Sudden Unexpected Death in Epilepsy Patients (SUDEP). Similarly, such cleaning can lead to morbidity and even mortality problems following anesthesia. If our assumption is correct, this understanding of the process of the problems' origin can lead to a method to remedy them by judicial supplement of the lost materials.

Transport in two-dimensional scattering stochastic media: simulations and models

Classical transport of neutral particles in a purely scattering two-dimensional stochastic media is studied. Results of numerical Monte Carlo simulations of transport in two-dimensional stationary, binary, purely scattering stochastic media with Markovian mixing statistics are reported. Partial Markovian descriptions are proposed as models for the transport process inside the stochastic media. In these models, the composition of the media is correlated on a finite length scale. The results obtained from the models are in good agreement with the results obtained from the two-dimensional simulations.

Scaling regimes in the distribution of galaxies.

If we treat the galaxies in published redshift catalogues as point sets, we may determine the generalized dimensions of these sets by standard means, outlined here. For galaxy separations up to about 5 Mpc, we find the dimensions of the CfA galaxy set to be about 1.2, with only a modest indication of multifractality. For larger scales, out to about 30 Mpc, there is also good scaling with a dimension of about 1.8. For even larger scales, the data seem too sparse to be conclusive, but we fmd that the dimension is climbing as the scales increase. We report simulations that suggest a rationalization of such measurements, namely that in the intermediate range the scaling behavior is dominated by flat structures (pancakes) and that the results on the smallest scales are a reflection of the formation of density singularities.

Cosmic lacunarity.

The present distribution of galaxies in space is a remnant of their formation and interaction. On a large enough scale, we may represent the galaxies as a set of points and quantify the structures in this set by its generalized dimensions [Beck and Schlogl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1986); Paladin and Vulpiani, Phys. Rep. 156, 147 (1987)]. The results of such evaluation are often taken to be evidence of a fractal (or multifractal) distribution of galaxies. However, those results, for some scales, may also reveal the presence of singularities formed in the gravitational processes that produce structure in the galaxy distribution. To try to make some decision about this issue, we look for the more subtle galactic lacunarity. We believe that this quantity is discernible in the currently available data and that it provides important evidence on the galaxy formation process. (c) 1997 American Institute of Physics.