Structure-function relationship in the sinus and atrioventricular nodes.

Recently published optical mapping studies of larger mammals, including humans, have identified functionally discrete sinoatrial exit pathways of activation. This is in line with earlier mapping studies of the dog and the human but in contrast with findings in the mouse and the rabbit, wherein a propagation wave front pattern of activation has been described. It underpins the complex three-dimensional (3D) organization of the cardiac pacemaking and conduction system in larger species, wherein sinoatrial and atrioventricular nodal physiologies both demonstrate identifiable activation pathways, which coincide with anatomic landmarks and histologic architecture, so that in addition to muscle fiber orientation and cell coupling, these intrinsic factors act to determine excitation pathways. This complex 3D organization increases the effect of source-to-sink mismatch both by greater variability in the space constant of tissue and by the 3D projection of this effect in all directions. Mathematical modeling provides a means to study these interactions, and newer models should incorporate these additional factors and their effect into the 3D structure of large mammal physiology.

Towards a computational reconstruction of the electrodynamics of premature and full term human labour.

We apply virtual tissue engineering to the full term human uterus with a view to reconstruction of the spatiotemporal patterns of electrical activity of the myometrium that control mechanical activity via intracellular calcium. The three-dimensional geometry of the gravid uterus has been reconstructed from segmented in vivo magnetic resonance imaging as well as ex vivo diffusion tensor magnetic resonance imaging to resolve fine scale tissue architecture. A late-pregnancy uterine smooth muscle cell model is constructed and bursting analysed using continuation algorithms. These cell models are incorporated into partial differential equation models for tissue synchronisation and propagation. The ultimate objective is to develop a quantitative and predictive understanding of the mechanisms that initiate and regulate labour.

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia.

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.

A model for glucose-induced wave propagation in pancreatic islets of Langerhans.

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action.

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.

Standing excitation waves in the heart induced by strong alternating electric fields.

We studied the effect of sinusoidal electric fields on cardiac tissue both experimentally and numerically. We found that periodic forcing at 5-20 Hz using voltage applied in the bathing solution could stop the propagation of excitation waves by producing standing waves of membrane depolarization. These patterns were independent of the driving frequency in contrast to classical standing waves. The stimulus strength required for pattern formation was large compared to the excitation threshold. A novel tridomain representation of cardiac tissue was required to reproduce this behavior numerically.

Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans.

In response to glucose application, beta-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of beta-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled beta-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.

[Study of fractal properties of single ionic channel gating mechanism by the fast Fourier transform]. / Issledovanie fraktal'nykh svoistv "vorotnogo" mekhanizma odinochnykh ionnykh kanalov metodom bystrogo Fur'e-preobrazovaniia.

Sets of the channel open times (tau o), closed times (tau c) and the full set of the channel open and closed times (tau o, tau c) in the activity of single Ca(2+)-activated K+ channels in cultured kidney cells Vero were analyzed using the fast Fourier transform. It was found that in the low-frequency range (about 0.01-10 Hz), power density can be described by the equation S(f) approximately f-alpha (as a rule, 0 < alpha < 1), and this part of the Fourier spectrum usually consists of narrow peaks at almost multiple frequencies. It was shown that the upper frequency boundary of this spectrum is determined by the kinetic parameters tau o [symbol: see text] tau c. The data obtained show that ion channel gating is a fractal process (correlated in time) and can be regarded as a random signal modulated by some periodical functions (sinuses). The data obtained by the Fourier method are in agreement with the earlier results obtained using the rescaled-range analysis.

Soliton-like regimes and excitation pulse reflection (echo) in homogeneous cardiac purkinje fibers: results of numerical simulations.

On the basis of numerical simulations of the partial McAllister-Noble-Tsien equations quantitatively describing the dynamics of electrical processes in conductive cardiac Purkinje fibers we reveal unusual - soliton-like - regimes of interaction of nonlinear excitation pulses governing the heart contraction rhythm: reflection of colliding pulses instead of their annihilation. The phenomenological mechanism of the reflection effects is that in a narrow (but finite) range of the system parameters the traveling pulse presents a doublet consisting of a high-amplitude leader followed by a low-amplitude subthreshold wave. Upon collisions of pulses the leaders are annihilated, but subthreshold waves summarize becoming superthreshold and initiating two novel echo-pulses traveling in opposite directions. The phenomenon revealed presents an analogy to the effect of reflection of colliding nerve pulses, predicted recently, and can be of use in getting insight into the mechanisms of heart rhythm disturbances.

Non-markovian gating of ca(2+)-activated k(+) channels in cultured kidney cells vero. Rescaled range analysis.

Using the patch-voltage clamp technique and the rescaled range method, activity of single large conductance Ca(2+)-activated K(+) channels (K(Ca) channels) was studied. For the sequences of alternating open and shut time intervals, the dependence R/S vs. N(τ) in the double logarithmic coordinates presented a curve with two slopes, H(1) =0.60 ± 0.04, and H(2) = 0.88 ± 0.21, where H(1) and H(2) characterized the Hurst exponents for shot and long time ranges, respectively. Similar results were obtained for reduced data sets consisting of only open or only shut intervals. Randomization of the experimental data resulted in a single slope, H, of 0.52 ± 0.02. Simulations were performed with eight-state Markovian model without memory. The calculated Hurst exponent presented in average 0.54 ± 0.02. The results suggest that the activity of single Ca(2+)-activated K(+) channel exhibits two regimes, with slight positive correlation at short time ranges (H(1) =0.6), and strong positive correlation at long time ranges (H(2) = 0.88); therefore the channel gating as a whole is not a steady-state Markovian process.

Analysis of electrical phenomena accompanying the growth of Neurospora crassa hyphae: theory and experiment.

To describe electrical phenomena observed in growth of Neurospora crassa hyphae, a theoretical model was developed considering the hypha as a one-dimensional electric cable with non-uniform longitudinal distribution of current sources reflecting the activity of proton pumps. A profile of the density of the pump current along the hypha is proposed, at which the results of simulation quantitatively coincide with the results of physiological experiments. The model values of energy coupling in the growth zones were estimated. The experimental dependence of the elongation rate of regenerating apical hypha fragments on their lengths was determined. Based on the comparison of these experimental results with the results of analysis of the model, the contribution of the axial metabolite transport, from the distal parts of the hypha to the apical part, to the dynamics of the apical cell growth was estimated. The possibility of evaluating the intensity of high-molecular-weight syntheses and/or accumulation of substances in granules was demonstrated. The growth rate of the regenerating hypha fragments was shown to correlate with the electric current flowing into the apical fragment 0.2-mm in length.

[Splitting of the back edge of a propagating excitation pulse]. / Rasshcheplenie zadnego fronta rasprostraniaiushchegosia impul'sa vozbuzhdeniia.

A new type of unstability of action potential propagating in spatially inhomogeneous electrically excitable media is announced. Numerical experiments with the FitzHugh-Nagumo model show that if the medium contains a region where membrane slow, outward currents are partially depressed then the back front of action potential passing through such a region can split forming a "burning drop"-solitary standing wave of depolarisation with finite "life duration".