Schematic presentation of electrical propagation. The scheme depicts an excitable cylindrical structure conducting the action potential from left to right at a velocity of 0.5 m/sec. The change in membrane potential along the axis of the cylinder corresponding to the action potential upstroke is plotted above the cylinder. The inside of the cylinder is negatively charged at its resting potential. The inside of the excited segment is charged positively. This potential difference drives the axial or local circuit current, as symbolized by the closed loop. The local circuit current depolarizes the membrane to the threshold for excitation at the site marked with an asterisk. In such a way a new segment of the membrane gets excited and excitation propagates from left to right.

Electrical cable. Top: Cylindrical structure of cell membrane enveloping the intracellular medium. Point P marks the site of current injection, as explained in bottom panel. Middle: Equivalent electrical circuit. The extra‐ and intracellular spaces are represented by the resistances r_o and r_i, respectively. The membrane is represented by a parallel circuit of membrane capacitance, c_m, and membrane resistance, r_m. Bottom: Decrease of relative membrane voltage, V/V_o, during injection of intracellular current in a cable of infinite length. The voltage drops exponentially from the site of current injection at point P (X = 0), from the initial value V_o. The distance on the abscissa is given in the relative unit X, which corresponds to the distance x scaled by the space constant λ (X = x/λ).

Relation between the change in transmembrane potential, V_M, flow of ionic current, I_ion, flow of membrane current, I_M, and axial or local circuit current, I_A, in a continuous linear structure. The cell membrane is symbolized by a parallel circuit consisting of a capacitance and a changing resistance corresponding to a time‐ and voltage‐dependent ionic conductance. The cell interior is symbolized by an internal resistance. Simulation using the Luo‐Rudy model 7. Note that there is axial or local circuit current flow during the early phase of the action potential, which provides the transmembrane current for excitation, I_M. Once the threshold is reached and Na⁺ channels are activated, the Na⁺ inward current contributes to axial current (see text).

Schematic presentation of the effect of wavefront curvature on conduction. Left: A flat wavefront propagates at a basic velocity θ₀. Arrows denote direction of flow of local circuit current. Middle: Convex wavefront with dispersion of local current, resulting velocity θ is smaller than θ₀. Right: Concave wavefront with conversion of local current, resulting velocity θ is larger than θ₀.

Effect of point stimulation (left panel) versus linear stimulation (right panel) on activation spread. Stimulation with a single electrode (point stimulation) produces a convex excitation front. Stimulation with a line of electrodes (line stimulation) produces an almost flat excitation front. Numbers denote activation times in milliseconds relative to the earliest activation. The interval between isochrones is 3 msec. Average longitudinal velocity of curved wave is 13% lower than of flat wave.

Effect of the radius of a circular stimulation electrode on current threshold (panel A) and stimulus energy (panel B): Epicardial stimulation of the canine heart. At an electrode size below 0.1–0.4 mm, the current threshold is independent of electrode size; above this radius, which corresponds approximately to the radius of the liminal area, current threshold increases with increasing electrode size. The stimulus energy is lowest at the electrode radius which corresponds to the radius of the liminal area.

Isolated myocyte: Micrograph of immunostained, paraformaldehyde‐fixed disaggregated canine myocyte. Immunostaining of connexin43 reveals a pattern that conforms precisely to the distribution of intercellular gap junctions.

Laminar organization of ventricular myocardium. Micrographs of tangential surface of a ventricular specimen showing layered organization of myocytes, branching of layers (arrow) and collagen fibers between adjacent sheets.

Simulation of the effect of wavefront collision on the upstroke of the transmembrane action potential and the Na⁺ inward current. The values computed during uniform conduction (solid lines) are compared to the values computed at a collision site (dashed lines). Left top: Change of membrane potential, V_M, during action potential upstroke. Left bottom: maximal upstroke velocity of transmembrane action potential in Volts/sec. Right top: Na⁺ inward current, I_Na. Right bottom: time course of Na⁺ conductance, g_Na.

Simulation of the effect of wavefront dispersion on the upstroke of the transmembrane action potential and the Na⁺ inward current. A: Inset shows simulated two‐dimensional strand of excitable tissue emerging into a large area. Signals on panels A–D are simulated from sites 1–11 shown on the inset. Action potential upstrokes show a double component, which is most prominent at the expansion site. B: First time derivatives dV/dt from action potential upstrokes shown on panel A. C: Time course of Na⁺ conductance, g_Na. D: Time course of Na⁺ inward current, I_Na. Note increase of I_Na at expansion site, associated with a decrease of dV/dt_max.

Effects of resistive discontinuities on propagation. Top: A row of simulated excitable elements (abscissa denotes element number) is separated by resistors. A number N of elements is connected by resistors of low value (200 Ω cm). Each group of N elements is connected to the next group by a single resistor, , of high value. Discontinuity at a constant value of effective longitudinal resistance can be changed by the simultaneous increase of N and . Bottom: Propagation along the simulated row of excitable elements, as illustrated by the time course of dV/dt_max (upper trace) and the action potential upstroke (lower trace). The degree of discontinuity is increased from panel A to C, while the value of effective or total longitudinal resistance is kept constant. Note increasing delay between the two action potential upstrokes, and the discontinuous upstroke in C.

Effects of resistive discontinuities on conduction velocity, θ. Propagation velocity is simulated in the model shown in the upper panel of Figure 11 as a function of the overall or effective resistance R_i (expressed as a fraction of the low value resistance of 200 Ωcm shown in FIG. 11, R/200) The solid line depicts the decrease of θ in a continuous cable where θ² ∼ R_i. In curve A, the value for the high resistor, , is 5000 Ωcm, the numbers on the curve denote the number of elements N. In curve B, the degree of discontinuity is higher, because is 10,000 Ωcm. Note that in curve B, θ decreases above N = 16 and conduction block occurs when N >26 (see text).

Effects of resistive discontinuities on the maximal upstroke velocity of the transmembrane action potential, dV/dt_max (simulated in the model shown in the upper panel of FIG. 11). As a control, the dashed lines depict the dV/dt_max values for continuous cables (upper line R_i = 200 Ωcm, lower line R, = 4200 Ωcm). In all solid curves shown, the value of the high resistor is set to = 4200 Ωcm, and the curves differ with respect to their numbers of elements N. The curves are shown for N = 5, N = 9, and N = 51. With N = 51, there is dispersion of local current beyond the first resistive obstacle with a decrease of dV/dt_max, and collision before the next resistive obstacle (from N 40 to 51) with an increase in dV/dt_max. With a small number of N 5, the effect of dispersion and collision is minor and all of the dV/dt_max values are above the upper dashed line. This is due to the almost simultaneous excitation of all elements, similar to the situation of a space‐clamped action potential. N = 9 corresponds to an intermediate situation.

Simulated cell chain. Comparison of continuous with discontinuous conduction with decreasing cell‐to‐cell coupling. Effects of variations in axial (longitudinal) resistance on microscopic velocity (θmic, curve 1) and on average macroscopic velocity (θmac, curve 2). The microscopic velocity corresponds to the velocity inside a cell. The case of a continuous structure is shown for comparison on curve 3 and follows the inverse square root relation of continuous cable theory. The effective longitudinal resistance is changed by varying the disk resistance while the myoplasm resistance is kept constant at 200. Both effective longitudinal resistivity and the corresponding disk resistance are indicated.

Simulated chain of cells. Changes of maximal upstroke velocity with decreasing cell‐to‐cell coupling. Conduction velocity θ (dashed line) and dV/dt_max (solid line) are plotted as a function of the increasing effective resistance or the specific disk resistance (coupling resistance between simulated cells). There is a transient increase of dV/dt_max with increasing cell‐to‐cell uncoupling and decreasing velocity of propagation.

Experimental determination of conduction in a single cell chain. A: Reproduction of the microscopic appearance of a cultured cell chain. Dots and numbers denote positions of three light‐sensitive diodes (6.5 μm in diameter) separated by a distance of 30 μm. B: Optical recording of action potential upstrokes from diodes 1–3, measured as fluorescence change ΔF/F of a voltage‐sensitive dye (upper traces) and the first time derivatives (lower traces). Numbers 1–3 denote times of local activation. Note that the conduction delay across the cell border 2,3 is larger than delay within the cytoplasm 1,2. C: Histograms of cytoplasmic (upper graph) and junctional (lower graph) conduction times. The difference between the mean conduction times amounts to approximately 80 μsec and reflects the mean conduction time across the end‐to‐end cell junctions.

Experimental determination of conduction in a cell strand. A: Reproduction of the microscopic appearance of a cultured cell strand (4–5 cells in width). Dots and numbers denote positions of three light‐sensitive diodes (6.5 μm in diameter) separated by a distance of 30 μm. B: Optical recording of action potential upstrokes from diodes 1–3, measured as fluorescence change ΔF/F of a voltage‐sensitive dye (upper traces) and the first time derivatives (lower traces). Numbers 1–3 denote times of local activation. C: Histograms of cytoplasmic (upper graph) and junctional (lower graph) conduction times. With respect to the measurements shown in Figure 16 the mean cytoplasmic conduction time has increased from 38 μsec to 60 μsec and the mean junctional conduction time has decreased from 118 μsec to 80 μsec. This is explained by electrotonic current flow through lateral gap junctions (“ lateral averaging”; see text).

Propagation in a cellular network, simulation of intracellular excitation sequences. A, longitudinal conduction: Conduction from left to right is depicted on the upper trace, conduction from right to left is depicted on the lower trace. Isochrone lines are separated by 4 μsec. B, transverse conduction: Conduction from top to bottom is shown on the upper trace, propagation from bottom to top is depicted on the lower trace. Intracellular isochrones are separated by 3 μsec. During longitudinal propagation, there is a crowding of isochrones (slow propagation) at the beginning of propagation in the individual cells and acceleration of propagation toward the end of the cells. During transverse propagation, the arrows indicate preferential longitudinal propagation spread, with microcollisions occurring occasionally (asterisk).

Simulation of intracellular excitation sequences (A), intracellular distributions of dV/dt_max (B) and inward Na⁺ charge movements during excitation (C) in an anisotropic cellular network. The left graphs correspond to longitudinal propagation from left to right and the right graphs correspond to transverse propagation from top to bottom. Note the close correspondence between the isochrone spacing, dV/dt_max and inward Na⁺ charge movement during both transverse and longitudinal propagation: The dV/dt_max is relatively low where excitation is slow and vice versa. By contrast the locations of slow activation and low dV/dt_max correspond to large inward Na⁺ charge movements and vice versa.

Ratio of extracellular to intracellular resistance in compact ventricular tissue. The amplitude of the bipolar extracellular electrogram (upper trace, V_E) and the amplitude of the action potential upstroke (lower trace, V_M) are shown from an isolated, arterially‐perfused papillary muscle. The signals are measured in a muscle which is surrounded by an electrical insulator. The ratio of V_E/(V_M − V_E) which is approximately 1, corresponds to the ratio of extracellular: intracellular resistance, r_or_i. This demonstrates that the extracellular resistance in compact ventricular tissue is of approximately the same magnitude is the resistance of the intracellular space (including the gap junctions).

Effect of superfusion fluid on conduction velocity, θ, the maximal upstroke velocity of the transmembrane action potential dV/dt_max, and the time constant of the initial rise of the action potential, τ_foot. Panels (a) and (b) show action potentials measured at two sites along a cylindrical papillary muscle, between electrodes D and C, (D‐C), and between electrodes A and B, (A‐B). The bipolar extracellular electrogram is measured between the extracellular electrodes c and b, (b‐c). The muscle is either soaked in a large bulk solution (SF, closed circles) or covered only by a thin fluid layer (T, open circles). Panel (b) illustrates the curved wavefronts measured in the presence of the large bulk solution during propagation from left to right. Traces on the right correspond from top to bottom: τ_a‐b, dV/dt_{max, a‐b}, τ_d‐c dV/dt_{max d‐c}, θ₀ (conduction velocity at the surface) and θ_i (conduction velocity in the core of the fiber). Increasing the thickness of the fluid layer (electrical shunting, transition from T to SF) produces (1) an increase of θ₀ and θ_i; (2) an increase of τ_a‐b and τ_d‐c; (3) a decrease of dV/dt_max.

Three‐dimensional plot of simulated transmembrane voltage (Φm) after application of a point stimulus to two‐dimensional anisotropic tissue. The X‐axis corresponds to the longitudinal direction of the fibers, the Y‐axis to the transversal direction of the fibers. Panel A: Simulation of anisotropy with equal ratios of extracellular to intracellular conductivities. Panel B: Longitudinal conductivity ratio (σ_ex/σ_ix) 8 × 10⁻⁴:2 × 10⁻⁴; conductivity ratio (σ_ey/σ_iy) 2 × 10⁻⁴:2 × 10⁻⁵ Note that with an equal anisotropic ratio there is a drop of Φm with distance from current injection and a elliptical shape of Φm distribution in the x/y plane. In Panel B, which corresponds to the simulation using experimentally determined values of intra‐ and extracellular conductivities, there is a hyperpolarization of Φm in the × (longitudinal) and a depolarization in the Y (transverse) directions.

Dog‐bone shape of virtual electrode. Plots showing the shape of virtual electrodes caused by stimuli from 1–7 mA. The horizontal axis corresponds to the longitudinal direction of the anisotropic subepicardial layer of a dog, the vertical axis corresponds to the transverse fiber direction. Note that upon application of a central cathodal stimulus, the line where excitation starts to propagate, i.e. the virtual electrode, has a dog bone shape with a very large extension of the electrode in the transverse direction.

Interaction between an anisotropic medium and a bathing solution. A: Deviation of the isochrones of a wave propagating in the longitudinal direction (left side) and a wave propagating in the transverse direction (right side). Note that due to the anisotropy‐dependent differences in intra‐ and extracellular conductivities, wavefront bending in the longitudinal direction is significantly more expressed. In the absence of a bulk conductor, both longitudinal and transverse wavefronts are flat (not shown). B: Phase plane plots of dV/dt_max versus membrane potential in a model with unequal anisotropy. Superimposed are phase plane plots of action potentials propagating in the longitudinal direction (L), at angles of 30°, 45°, and 60° from the longitudinal direction and in the transverse direction (T). On the left hand side, the bathing fluid was absent. Note that all the traces almost superimpose. On the right hand side, a bathing fluid has been added to the boundary of the tissue. In this case there is a marked direction dependence of both the initial portion of the action potential of and of dV/dt_max.

Isochronal map of excitation spread from the sinoatrial node. Tones depict excitation intervals in steps of 5 msec, numbers correspond to activation times in msec. Configuration of action potentials is shown along the pathway of conduction from the sinus node to the atrium. The dashed line indicates the beginning of the atrial electrogram used as time reference. Toward the periphery, action potentials show an increase in amplitude and dV/dt_max and a decrease in rate of diastolic depolarization. The area in which two component action potentials were recorded is hatched in the activation map.

Spread of excitation in the right atrium. Isochronal map of the spread of excitation from the sinoatrial node (S. A. N.) over the epicardial surface of the right atrium made by Thomas Lewis in 1915. Although in general spread of activation is depicted as being radial, the isochrones deviate over the crista terminalis, indicating preferential conduction in that region.

Anatomy of the rabbit right atrium. The contrast of the preparation has been enhanced by supravital staining with methylene blue: ct, cut ends of the crista terminalis; ra, right auricle; fo, fossa ovalis; SVC, superior vena cava; ivc, inferior vena cava; ocs, ostium of the coronary sinus; vc, valve of the coronary sinus; ss, sinus septum; asl, attachment of the septal tricuspid leaflet (marked by a dotted line); SA, sinoatrial node (the letters inside surrounded by a dotted line indicate the approximate area of the compact node consisting of typical nodal cells); CN, cauda of the sinoatrial node; rb, right branch of the sinoatrial right bundle; lb, left (septal) branch of the sinoatrial ring bundle; tc, transitional cell zone of the atrioventricular node; mc, midnodal cells; lc, lower nodal cells; avb, atrioventricular bundle; ao, atrial overlay fibers.

Activation sequence in the right atrium. A: A photograph of the right atrium of a rabbit: the activation sequence has been mapped using a tenfold microelectrode assembly, with which 280 different atrial cells have been impaled during the course of the experiment. The specimen was opened by an incision along the lateral margin of the tricuspid valve, and pinned out in order not to interrupt the internodal tissues. After the experiment, the preparation was fixed before being photographed. The specimen is illuminated from behind to illustrate the thick and thin parts of the myocardium. B: A diagrammatic representation, in which the abbreviations are as follows: SVC, superior vena cava; IVC, inferior vena cava; FO, fossa ovalis; CS, coronary sinus; AVN, atrioventricular node; MS, membranous septum; IVS, interventricular septum; C and D: Activation maps made according to photographs taken while the preparation was in the tissue bath—hence the slight differences in shape when compared to the fixed specimen. The preparation was beating spontaneously for the construction of (C); in (D), the preparation was paced through an electrode placed above the ostium of the SVC. In both instances, the activation sequence, indicated by isochrone lines separating areas activated within 5 msec intervals, follows the thicker muscle bundles. These are the crista terminalis, the septal branch of the crista, and the thick muscle ridge between IVC and FO. The AV node receives a dual input. The localization of the pacemaker determines the dominant input. In C, during spontaneous sinus rhythm, the AV node is reached earliest by the posterior route. In D during driving from the SVC, the anterior limbus activates the AV node earlier.

Anatomy of the AV junction. A: Photograph and B sketch of a normal human heart showing the anatomical landmarks of the triangle of Koch. The approximate site of the compact AV node is indicated by the stippled area adjacent to the central fibrous body.

Propagation toward the AV node. Arrows indicate the four areas from which atrial fibers approach the specialized AV junctional area. The fourth area, indicated by the curved arrow, is from the left atrial aspect of the septum.

Action potential characteristics in the AV node: Action potentials of six types of AV nodal cells during periodic premature stimulation of the right atrium. Each section was obtained by superimposing (in decreasing order of coupling stimulation intervals [numbers at left in msec]) tracings corresponding to last basic and premature beat. Baseline of each subsequent tracing was shifted downward to help distinguish potentials. Action potential after premature potential in lower trace in AN (atrionodal) and H (His) was caused by an atrial re‐entrant beat. Note double components in N (nodal) cell of early premature responses. ANL, late AN cells; ANCO, AN cells with action potential upstroke with two components.

Activation of the AV node. Map showing sequence of normal antegrade conduction of rabbit AV node. Symbols indicate position of AV nodal cells from which action potentials were recorded and also in which 20 msec interval these cells were activated. Note dual input into AV node. CT, crista terminalis; IAS, interatrial septum; CS, ostium of coronary sinus; Tr. V., tricuspid valve; H, position of extracellular electrode on His bundle.

Conduction in the AV node. Two simultaneously recorded transmembrane potentials from the AV node of a Langendorff blood‐perfused canine heart at a superficial and a deep site at the same location. The atrium was paced at a basic cycle length of 600 msec, and a premature stimulus S₂ was applied at a coupling interval of 300 msec, either at the posterior input (“ slow pathway,” upper panel) or at the anterior input (“ fast pathway,” lower panel). Note double components, especially during premature stimulation, where the action potential of the superficial cell causes a slow prepotential in the deeper cell which during posterior stimulation is large enough to cause an action potential that is propagated to the His bundle (not shown), but that fails to reach threshold during antegrade stimulation.

Abnormal Wenckebach phenomenon. Three simultaneously recorded action potentials in posterior input (cell a), in anterior input (cell b), and in junctional area of these two inputs (cell c). Note the difference in timing and configuration of the action potentials of cells a and c and of the His bundle complex during the first and fifth beats. Double bars indicate block. Numbers are activation times in msec. Atr., recording electrode on crista terminalis from which the electrogram in the upper trace was recorded. His, position of electrode recording electrogram of His bundle (lower trace).

Cycle length dependence of AV‐nodal conduction. Action potentials illustrating dependency of first and second component in N cells upon late AN and early NH potentials. Signals 1 and 2 were recorded from AN cells, signals 3, 4, and 5 from N cells, and signal 6 from an NH cell. Inset shows position of cells. First component is largest in N cells close to AN zone; second component is largest in cells close to NH cells. Note that second component occurs later than upstrokes of action potentials in cell 6. Note also that duration of prepotential in cell 6 increases progressively in successive activation and that level at which prepotential breaks into a fast upstroke remains constant in all cycle lengths. Cells 4, 5, and 6 were recorded simultaneously. Cells 1, 2, and 3 were recorded separately, approximately 3 min earlier.

Cycle length dependence of AV nodal conduction. A: Classical ladder diagram used in electrocardiography to depict cycle length‐dependent conduction delay in the AV junction, in this case during a 4:3 Wenkenbach phenomenon. B: Modification of the ladder diagram to express saltatory nature of the cycle length‐dependent conduction delay.

Division of the left bundle branch. An illustration of the variation in the structure of the divisions of the left bundle branch in 20 different hearts.

Propagation across the Purkinje–muscle junction. Intracellular and extracellular recordings at Purkinje–ventricular muscle junctional sites. A: Action potential of a Purkinje fiber (P_i), coinciding with the Purkinje (P) deflection preceding the all‐negative ventricular muscle (V) deflection in the extracellular electrogram (e). s, Stimulus artifact. B: Action potential of a transitional cell (T_i), with an early slow component (arrow). C: Simultaneous intracellular recordings of an early (T_i) and a late (T_2i) transitional cell. The latter could also be classified as an early ventricular cell that is electrotonically influenced from the transitional cells, giving rise to the long, slow foot (arrow). D: Simultaneous intracellular recordings of a Purkinje fiber and a transitional cell with a slow foot (arrow) and an inherent low amplitude that is heightened on activation of the ventricular mass. E: Intracellular recording from a transitional cell that coincides with a small deflection in the extracellular electrogram during the Purkinje fiber–ventricular muscle delay period. F: Intracellular recording of a transitional cell with multiple components during the upstroke (arrow). Panels A–C derive from rabbit hearts, and panels D–F derive from pig hearts.

Structure of the Purkinje–muscle junction. Schematic representation of the structure of a rabbit Purkinje fiber–ventricular muscle junction. P, Purkinje fibers; T, transitional cells; V, ventricular myocardium.

Safety factor of propagation. Results of computer simulation of propagation in a cell chain. The cells are separated by a simulated gap junction resistor. A: Safety factor of propagation, SF, as a function of propagation velocity. Dashed line: Change of SF with a decrease of excitability. Solid line: Change of SF with decreasing conductance (increasing resistance) between cells. B: Change of SF as a function of propagation velocity in the absence and presence of I_Ca,L. Note that very low conduction velocities can only be achieved with flow of I _Ca,L. (See text.)

Supernormal excitability and conduction. A, B: Transmembrane action potentials. C, D: Strength interval curves. Time scale is identical for both traces. A: Recording from the His bundle. B: Recording from a Purkinje fiber running freely in a false tendon. C: Recording from a transitional type Purkinje fiber. D: Recording from a ventricular cell. The supernormal phase of excitability in B is associated with a supernormal conduction.

Relationship of excitability to conduction velocity during phase‐4 depolarization. Conduction time along a fixed distance of a Purkinje strand and maximal upstroke velocity of the transmembrane action potential, dV/dt_max of a Purkinje fiber are plotted as a function of the “ take‐off” potential during spontaneous phase 4 depolarization ranging from 92.5 to 105 mV. Note that with ongoing spontaneous depolarization (decrease of “ take‐off” potential”) there is a decrease of conduction time corresponding to an increase in conduction velocity and a decrease of dV/dt_max.

Change of longitudinal and transverse conduction velocity with increasing extracellular potassium concentration, [K⁺]_o. Measurements were made in an isolated perfused porcine heart. Note that propagation blocks at a [K⁺]_o of 11 mM.

Recovery of maximal upstroke velocity of the action potential, dV/dt_max. Action potentials were elicited at different times in the wake of the preceding action potential. Time 0 denotes the beginning of the preceding action potential. The curves depict the recovery curves of dV/dt_max with increasing time measured at different resting potentials. Note that recovery from activation becomes delayed with depolarization.

Unidirectional block in the wake of the preceding wavefront. Transmembrane potentials (V_m) and sodium channel conductance (gNa) computed after application of a premature stimulus (cell 1) in the wake of propagating action potential. In the antegrade direction (right panel) recordings were taken from cells 0.5 mm apart. In the retrograde direction (left panel) traces were recorded from cells 1 mm apart. At the time of premature stimulation, membrane excitability at cell 1 was less than 10% of the maximum excitability (compare gNa curves 1 and 5 on the left panel). In the retrograde direction, the action potential propagated a distance of 4 mm before reaching the region of fully excitable membrane. In the antegrade direction, membrane excitability gradually decreased and propagation extinguished. Note different gNa scales in the left and right panels.

Unidirectional block with asymmetric depression of excitability. Top: Injury is produced by a crushing probe. The line spacing on the Purkinje fiber indicates increasing degree of injury. Bottom: The influence of injury on the excitability threshold is illustrated. The amplitudes of the anterograde wavefront (C‐x‐B) are compared to the amplitudes of the retrograde wavefront (A‐x‐C). At y, the transition between normal cells and inexcitable, injured cells is abrupt. C represents decremental or augmental conduction, depending on direction, through a transitional zone of partial injury; x represents the point of transition between partially excitable cells and inexcitable cells (x‐y). A and B represent electrotonic transmission through inexcitable cells. The retrograde wave succeeds in conducting across, and the anterograde wave front fails.

Unidirectional block at a geometrical tissue expansion: The role of Ca⁺⁺‐inward current. A: Schematic representation of a cultured cell monolayer with geometrical expansion and overlaid photodiodes during antegrade (upper panel) and retrograde (lower panel) conduction. B and C: Action potential upstrokes recorded using a voltage‐sensitive dye in control conditions (B) and after administration of 5 μM nifedipine. In control conditions, the antegrade propagation was characterized by biphasic upstrokes and local slowing of conduction at the expansion (B). The blockage of Ca⁺⁺ current with nifedipine produced antegrade conduction block (C). The retrograde propagation was successful in both cases.

Unidirectional block in anisotropic tissue. Anisotropic conduction time curves obtained in human and canine atrial bundles. A: Uniform anisotropic pectinate muscle of a 12‐year‐old child. B: Non‐uniform anisotropic pectinate muscle of a 62‐year‐old man. C: Non‐uniform anisotropic muscle (christa terminalis) of an adult dog. In each preparation conduction times (msec per mm interelectrode distance) were obtained from analyzing the unipolar extracellular electrogram of two electrode pairs. As shown in the inset, the two electrode pairs were placed in longitudinal and transverse directions, respectively. Solid circles represent longitudinal propagation, open circles represent transverse propagation. Each preparation was stimulated at a basic rate, and premature action potentials were introduced at variable intervals, A₁–A₂. In the uniform anisotropic bundle (A) conduction times became longer with the shortening of the A₁–A₂ intervals, block occurred in both directions at the same interval. In the non‐uniform cases (B and C), block occurred in the longitudinal direction at a premature interval of 325 and 310 msec, respectively. At this prematurity, transverse propagation was still preserved.

Effect of microscopic resistive barriers on propagation. A: A phase‐contrast image of a cell culture (neonatal rat myocytes) with the overlaid diode array. Action potential upstrokes are measured at each diode location. The numbers 1–10 on the diode array correspond to the locations of the signals shown in D and E. In D and C, the location of these signals is indicated by the gray area. Two clefts in the central area (outlined in white in A) form an narrow isthmus of 40 μm. Activation maps of longitudinal and transverse conduction are shown in B and C respectively. Note slowing and deviation of the wavefront at the isthmus. Numbers denote separation of isochrones by 100 μsec. Selected recordings of action potential upstrokes during longitudinal and transverse conduction are shown in D and E, respectively. Discontinuities in the action potential upstrokes occur at the expansion site during transverse propagation.

Unidirectional conduction block at an “ isthmus.” Wave propagation across a narrow tissue isthmus in an isolated ventricular preparation of sheep heart. A: Map of activation spread before an isthmus was produced. B: Activation spread in the same preparation with the isthmus 2.26 mm wide. The isthmus was produced by two tissue cuts (gray zones). C: Activation spread after the isthmus was reduced to 0.88 mm. D: Local conduction velocity measured across the isthmus as a function of isthmus width.

Circus movement re‐entry around a large anatomical obstacle.

Effect of a premature impulse entering a re‐entrant circuit. The black and dotted areas show the absolute and relative refractory periods, respectively. In A and B, a premature impulse enters the circuit at the end of the relative refractory period and spreads in two directions. In the retrograde direction, the premature wave is annihilated by the circulating wave; in the anterograde direction, the premature impulse advances, resetting the tachycardia. In C and D, the premature impulse reaches the circuit closer to the state of absolute refractoriness. The impulse annihilates the retrograde wave and fails to propagate in the anterograde direction thereby terminating the tachycardia.

Initiation of functional re‐entry by premature stimulation in an isolated preparation of rabbit atrial muscle. A: Isochronal activation map of basic beat (interval 500 msec). Dots indicate sites of stimulation. Activation times (msec) are given relative to the stimulus onset. B: Map of premature beat (interval 56 msec). T bars indicate conduction block. C: First cycle of tachycardia. D: Refractory periods measured during basic rhythm (in msec).

Functional re‐entry and tachycardia. Activation map (right) and action potential recordings (left) obtained during steady‐state tachycardia. Cells in the central area of the re‐entrant circuit show double potentials of low amplitude (traces 3 and 4). Lower right: Schematic representation of the activation pattern. Double bars indicate conduction block.

Spiral waves. Spiral waves in chemical Belousov‐Zhabotinsky reaction (A) and in an isolated preparation of canine epicardial muscle (B).

Initiation of spiral wave in a simple model of cardiac excitation. A rectangular area R is excited overlapping the absolutely refractory tail of a propagating wave (A). The premature wave propagates in the retrograde direction (right to left) but blocks in the anterograde direction, forming a wave break that turns around the refractory area R (B). When the area R recovers, the excitation wave short‐circuits this area (C) and forms a spiral wave rotating around a linear line of block (D–F).

Initiation of a spiral wave by cross‐field stimulation in canine right ventricular myocardium. A: Isochronal maps of activation and repolarization during wave propagation induced by stimulation (S1) from a line of eight epicardial pacing sites. Solid lines depict isochronal activation lines; dashed lines depict isorecovery lines. Numbers indicate time in msec. B: Gradients of extracellular potential (in V/cm) produced by a unipolar cathodal shock (S2) of 150 V from a mesh electrode at the bottom. C: Pattern of activation spread following sequential application of S1 stimulus from the right and S2 shock from the bottom. The S1–S2 interval was 191 msec and the S2 strength was 150 V. Activation times (msec) are measured from the start of the 3 msec S2 shock. The heavy solid line represents the transition between successive activation maps. Isochrones are drawn at 10 msec intervals. The hatched line represents a zone of conduction block. The double‐headed arrow indicates the mean epicardial fiber orientation in the area of conduction block. The hatched area indicates the region assumed to be directly excited by the S2 shock field. Earliest post‐shock activation occurs distant from the S2 site, with no early activation wavefronts conducting away from the directly excited region located between the S2 site and the critical point. A counterclockwise re‐entrant circuit is formed around the region containing the critical point and the block line. The potential gradient equals 5.8 V/cm, and the pre‐shock interval equals 171 msec at the critical point (critical refractory period = 169 msec). D: Schematic representation of the re‐entry initiation by cross‐field stimulation. The row of pacing wires (S1) on the right creates parallel isorecovery lines (R₇ through R₂), with R₇ the least refractory and R₂ the most refractory. The S2 from the bottom creates parallel isogradient lines (G₇ through G₃), with G₇ the largest potential gradient and G₃ the weakest. The S2 shock produces direct excitation (DE), graded response (GR), or neither effect (NE). Activation fronts propagate from only one part of the directly excited area, not from the directly excited region abutting the area of graded response, thus forming a zone of unidirectional conduction block.

Initiation of a spiral wave at a pivoting point. Formation of a free wave break after wavefront detachment from the sharp edge of an inexcitable obstacle. Computer model with Luo‐Rudy ionic kinetics. The maximal sodium conductance was reduced to 6.6 mS/cm² A: Isochronal map of activation spread with an interval of 5 msec. B: Snapshot of activation at the moment marked by the asterisk in A. Black indicates the excited area defined by the activation of inward Na⁺ current. Gray indicates the area in the refractory state as defined by Na⁺ current inactivation. Point P marks the wave tip, defined as a point where excited, refractory, and resting states meet. The dashed line t shows the trajectory of the wave tip with the radius r_p

Dynamics of spiral wave rotation in mathematical models of cardiac excitation. A–C: Cellular automata model. Spiral wave rotation changes from circular (A) to meandering (B), and then to Z‐type (C) with increasing excitability. D–G: FitzHugh‐Nagumo model. The same types of rotation are observed when the wavelength of excitation is increased.

Drift of a spiral wave and the Doppler effect. A and B: Isochronal activation maps showing initiation (A) and the first rotation cycle (B) of a spiral wave in an isolated preparation of epicardial muscle. A stepwise inhomogeneity in refractory period was created by separate superfusion of two parts of the preparation with normal and quinidine‐containing solutions. Dashed line shows the border of inhomogeneity with larger refractoriness in the upper part. The asterisk shows the location of the stimulation electrode. C: Trajectory of the spiral wave tip during initiation (S₁) and three subsequent cycles of spiral wave rotation (V₁−V₃). D: Excitation intervals measured along the border of inhomogeneity during spiral wave drift (cycle V₂). Because of the drift, excitation intervals in front of the spiral wave are significantly shorter than intervals behind the spiral wave (Doppler effect).

Anchoring of a spiral wave. A: Electrocardiographic recordings showing that premature stimulation (S₂) produced polymorphic arrhythmic activity followed by a transition to sustained monomorphic tachycardia. B: Time‐space plot of activation spread obtained from video‐imaging of transmembrane potential (voltage‐sensitive dye). In these plots, the activity from the whole image is projected onto a single direction (vertical axis) and displayed as a function of time. White bands show a planar wave propagation while branching of bands indicates the presence of a spiral wave induced by the S₂ stimulus. As detected from the movement of the branching point, which marks the center of the spiral, the spiral drifted during the first seven cycles and became stationary thereafter.