Each normal cardiac cycle is started by an action potential that is initiated in the sino-atrial (SA) node by automaticity of the SA nodal cells. This action potential then propagates from the SA node into the surrounding atrial cells. We have done numerical simulations of electrically coupled cells to understand how a small SA node can be spontaneously active and yet be sufficiently electrically coupled to the surrounding quiescent atrial cells to initiate an action potential in the atrial cells. Our results with a simple model of two coupled cells and a more complex model of a two-dimensional sheet of cells suggest that some degree of electrical uncoupling of the cells within the SA node may be an essential design feature of the normal SA-atrial system.

Conduction of impulses in myelinated axons has been studied by a new method of computer simulation. The contributions of nodal and internodal characteristics and parameters were examined. Surprisingly, the conduction velocity, theta, was found to be quite insensitive to the nodal area or the exact description of its excitable processes. The conduction velocity also is relatively insensitive to the internodal length but much more sensitive to the myelin capacitance and axoplasm conductance. Qualitative change in theta with temperature depended on which temperature-sensitive parameters were included in the simulation.

SUMMARY It has been argued theoretically and confirmed experimentally that conduction velocity (0) should be proportional to nerve fibre diameter for myelinated fibre tracts, such as normal peripheral nerve, exhibiting 'structural similarity'. In some axons, however, the nodes of Ranvier are more closely spaced than in normal peripheral nerve. Analytic arguments have suggested that when internodal distance (L) alone is changed, the plot of 0 versus L should have a relatively flat maximum. This was confirmed by several previous computer simulations of myelinated axons, but internode lengths of less than half the normal case were not examined. In order to gain insight into impulse propagation in myelinated and remyelinated fibres with short internodal lengths, the present study examines the conduction velocity and spike configuration for a wide range of internodal lengths. As L becomes large, 0 falls and finally propagation is blocked; as L becomes small, 0 decreases more and more steeply. From this, it is predicted that for fibres with very short internodal lengths, small local changes in L should affect substantially the conduction velocity.

The effects of intercellular coupling conductance on the activity of two electrically coupled isolated rabbit sinoatrial nodal cells were investigated. A computer-controlled version of the "coupling clamp" technique was used in which isolated sinoatrial nodal cells, not physically in contact with each other, were electrically coupled at various values of ohmic coupling conductance, mimicking the effects of mutual interaction by electrical coupling through gap junctional channels. We demonstrate the existence of four types of electrical behavior of coupled spontaneously active cells. As the coupling conductance is progressively increased, the cells exhibit: (a) independent pacemaking at low coupling conductances, (b) complex dynamics of activity with mutual interactions, (c) entrainment of action potential frequency at a 1:1 ratio with different action potential waveforms, and (d) entrainment of action potentials at the same frequency of activation and virtually identical action potential waveforms. The critical value of coupling conductance required for 1:1 frequency entrainment was �0.5 nS in each of the five cell pairs studied. The common interbeat interval at a relatively high coupling conductance (10 nS), which is sufficient to produce entrainment of frequency and also identical action potential waveforms, is determined most by the intrinsically faster pacemaker cell and it can be predicted from the diastolic depolarization times of both cells. Evidence is provided that, at low coupling conductances, mutual pacemaker synchronization results mainly from the phase-resetting effects of the action potential of one cell on the depolarization phase of the other. At high coupling conductances, the tonic, diastolic interactions become more important. In the sinoatrial (SA) 1 node synchronization of the actia regular rate. The mechanisms by which cells with difvation of electrically coupled, spontaneously pacing ferent intrinsic rates of automaticity maintain this syncells is a required attribute of normal action potential chronization has been the subject of numerous studies using a variety of experimental and model systems. initiation. Individual isolated SA nodal cells display a Several experimental approaches have been used to large variety in action potential waveforms (Nakayama study the electrical interactions between cardiac cells as et Jongsma, 1986, 1995). Morea function of intercellular conductance without the over, individual cells may have irregular firing patterns, with a varying cycle length (Opthof, 1988; Wilders and complexity of a multidimensional syncytium. Studies using thin SA node strips (Jalife, 1984; Delmar et al., Jongsma, 1993), which is most likely due to differences 1986), with the central region of the strip sealed off in in the composition of membrane currents (Nathan, 1986;Honjo et al., 1996). For the SA node to maintain a compartment containing either ion-free sucrose solua stable and regular discharge pattern, individual cells tion or Tyrode solution containing heptanol, sh...

1. The propagation of action potentials through the branching regions of squid axons was examined experimentally and with computer simulations over a temperature range of 5-25 degrees C. 2. Above a critical ratio of postbranch to prebranch diameters, propagation of an action potential failed. The value of this critical ratio is very sensitive to temperature and is smaller at high temperatures. The experimentally measured Q10 of the critical ratio is 0.37 +/- 0.04. 3. Evaluation of a number of parameters of action-potential propagation showed that this effect is closely related to the change in the width of the action potential with temperature (Q10 = 0.29 +/- 0.01).

We used numerical integration techniques to simulate action potential propagation along one-dimensional strands of cells coupled with electrical junctions. We considered the standard case to be a series of cardiac cells (20 micrometer in diameter, 50 micrometers long) with intercellular coupling such that the effective longitudinal resistance was 200 omega cm. The membrane properties were represented by the model of Beeler and Reuter (1977) (Sharp and Joyner, 1980). By increasing Ri (and thus decreasing the space constant, L), we showed that effects due to the discrete cell length, delta X, became apparent when delta X/L was greater than about 0.2, producing an increased maximal dV/dt but a decrease in peak inward current. We also simulated the effects of a periodic spatial variation in Ri, representing a structure with groups of well-coupled cells but with minimal coupling between the groups. Even with a constant membrane model and cell size, variations in the spatial pattern of interconnection produced significant changes in action potential shape and velocity, with some patterns producing decremental conduction or propagation failure.

Understanding developmental changes in contractility is critical to improving therapies for young cardiac patients. Isometric developed force was measured in human ventricular muscle strips from two age groups: newborns (Ͻ2 wk) and infants (3-14 mo) undergoing repair for congenital heart defects. Muscle strips were paced at several cycle lengths (CLs) to determine the force frequency response (FFR). Changes in Na/Ca exchanger (NCX), sarcoplasmic reticulum Ca-ATPase (SERCA), and phospholamban (PLB) were characterized. At CL 2000 ms, developed force was similar in the two groups. Decreasing CL increased developed force in the infant group to 131 Ϯ 8% (CL 1000 ms) and 157 Ϯ 18% (CL 500 ms) demonstrating a positive FFR. The FFR in the newborn group was flat. NCX mRNA and protein levels were significantly larger in the newborn than infant group whereas SERCA levels were unchanged. PLB mRNA levels and PLB/SERCA ratio increased with age. Immunostaining for NCX in isolated newborn cells showed peripheral staining. In infant cells, NCX was also found in T-tubules. SERCA staining was regular and striated in both groups. This study shows for the first time that the newborn human ventricle has a flat FFR, which increases with age and may be caused by developmental changes in calcium handling. (Pediatr Res 65: 414-419, 2009)

The anisotropy that normally exists in the myocardium may be either enhanced in peri-infarction zones by loss of lateral cell connections or reduced by redistribution of gap junctions. To test how the degree of anisotropy affects the development of ectopic focal activity, we carried out computer simulations in which a model of an ectopic focus is incorporated as the central element of a two-dimensional sheet of ventricular cells. At low values of intercellular coupling conductance (G c ), the focus region is spontaneously active, but the limited intercellular current flow inhibits propagation. At high G c , automaticity is suppressed by the loading effects of the surrounding cells. At intermediate G c , the ectopic activity may propagate into the sheet. In the case of isotropic coupling, the minimum size of the focus region for propagation to occur (in terms of number of collaborating cells within the focus) is as small as approximately ten cells, and this number decreases with increasing anisotropy. Thus, the presence of anisotropy facilitates the development of ectopic focal activity. We conclude that the remodeling that occurs in peri-infarction zones may create a substrate that either facilitates (enhanced anisotropy) or inhibits (reduced anisotropy) the development of cardiac arrhythmias associated with ectopic focal activity.