The electrical restitution of the non-propagated cardiac ventricular action potential

Figures

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  Fig. 1. Steady-state rate dependence of APD. A APs (upper tracings) were recorded from guinea pig papillary muscle with standard microelectrodes, together with force of contraction (lower tracings). At each pacing frequency, time was allowed for the AP to reach the steady state (3–5 min) (figure from [125]. B APDs from panel A, measured at 90% of repolarization, are reported as a function of CL. Rate dependence curve is fitted with a mono-exponential. Note the bifurcation at CL = 100 ms (10 Hz) due to APD alternans at that pacing rate

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  Fig. 2. Restitution and potentiation. A Schematic representation of the experiment of Hoffmann and coworkers [63]. During constant BCL pacing, a single pre/post-mature stimulus is introduced (black arrow) at a given coupling interval (CI) after the last conditioning beat (LCB). Transmembrane potential (Vm) and isometric tension (T) are reported. B By adopting the same protocol, Kruta and Braveny studied the percent changes of T developed by the extrasystoolic (restitution R) and post-extrasystolic (potentiation P) beats when CI was made varying (results from [84]

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  Fig. 3. The ERS1-S2 curve. A top: after the LCB of a constant pacing train at BCL = 1000 ms (S1), a premature stimulus (S2, or CI = 333 ms) was applied and the test APD recorded. Bottom: an identical CI (BCL = 333 ms) was applied after a different BCL = 333 ms. Note that, since CI = BCL in this case, the test APD remains at its steady state and is identical to LCB (from [96]. B By applying the same S1–S2 pacing protocol, Boyett and Jewell measured the ER representation with the test APD as a function of CI (data from [17]

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  Fig. 4. Notation. A The different types of ER will be identified here with two subscripts, the first referring to the protocol used to measure it, the second to the beating parameter reported in the x-axis of the corresponding ER curve. For example, ERdyn,DI indicates electrical restitution measured with the dynamic protocol, and reported as APD versus DI. B An example of steady-state dog ventricular APD rate dependence (Erdyn,CI) is reported in figure with empty dots, superimposed to the ER curve measured with S1–S2 protocol (BCL = 2 s) (black dots) (data from [95]. Note that the x label CL represents CIs in the case of ERS1-S2, and BCLs in the case of ERdyn. C, left Example recorded in cat papillary muscle of restitution measured with S1–S2 protocol (BCL = 600 ms) and represented as APD vs CI. C, right Same data as in left panel, reported as APD vs DI (data from Franz et al. 1988)

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  Fig. 5. ERS1-S2,DI vs Erdyn,DI. A, top Dynamic (ERdyn,DI, empty dots) and standard (ERS1-S2,DI, filled dots) restitution optically measured in canine left ventricular wedge. A, bottom Slopes of the above curves (dotted line for ERdyn,DI and solid line for ERS1-S2,DI) (data from [188]. B Same for curves measured with MAP recordings in left ventricular epicardium of Langendorff-perfused guinea pig hearts by Soltysinska and colleagues [140]

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  Fig. 6. Comparison of ER formulations. In all panels, representative ER curves (black line, left y axis) and their slopes (red line, right y axis) are reported. (top) A generic ERS1-S2,CI has the same shape of the corresponding ERS1-S2,DI measured for the same cell at the same BCL. (bottom) The steady-state ERdyn,CI is unique for the same cell, different from the instantaneous ERS1-S2,CI, and also different from the corresponding ERdyn,DI

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  Fig. 7. BCL dependence of the ERS1-S2 curve. ERS1-S2 curves depends, by definition, on the BCL of the conditioning pacing. In figure, an example where differently delayed S2 stimuli were delivered, in turn, after a conditioning training at 3 different values (reported in figure) of BCL (3000, 750, and 370 ms) in superficial cells of cat papillary muscle. Data are fitted with mono-exponentials with time constants τ = 90, 170, and 300 ms respectively (data from Boyett and Jewel 1978)

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  Fig. 8. Species and spatial heterogeneity of ER. A Differences in ERS1-S2,DI and in steady-state ERdyn,CI, documented by Arpadffy-Lovas in microelectrode impaled tissue preparations from different species. B Differences in ERS1-S2,DI depending on the APD measured at CL = 1000 ms (insets) in the same species (human). ERS1-S2,DI curves were fitted by mono-exponentials. Time constants of ERS1-S2,DI curves averaged 63.9 ± 6.0 ms for APD < 250 ms (n = 10, filled squares), and 125.5 ± 9.1 for APD > 300 ms (n = 17, filled triangles) (data and figure from Arpadffy-Lovas et al. 2020)

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  Fig. 9. AP-clamp derived ER curve for ionic currents. Ideally, LCB and test APs should be recorded during a S1–S2 protocol (A) and applied as voltage clamp pulses after conditioning training (B). In a much easier version, two identical voltage clamp square pulses are used instead under calcium current Isi blockade, and the ionic current difference between the test beat and LCB used to describe the ER curve of Isi (right D panel). ERS1-S2 of APD is also reported on the left (figure from [138]

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  Fig. 10. The ER surface and the portrait. Restitution dynamics when pacing CL suddenly changes between two constant values (BCL1 and BCL2) can be though off as a function mapping the LCB at BCL1 (An) and the following DI (Dn) into a surface describing all the possible states of the test APD (An+1). ERdyn,DI, ERS1-S2,DI, and ERCB,DI can be derived as the intersections of this surface with the three flat surfaces An+1 = An (panel A), An = ALCB (panel B), and An + Dn = BCL2 (panel C) respectively. The restitution portrait results from the projection of these intersecting curves on the (An+1, Dn) plane and is therefore the collection of the three ER curves (panel D). These tend to coincide for large values of BCL1 (low pacing rate, not shown). At high pacing rate, though, they rotate with respect to each other around the point representing steady-state DI and APD at BCL1 (figures from [148]

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  Fig. 11. ERbtb and family of ERS1-S2 curves. The ten Tusscher human ventricular AP model [147] was paced with CL sequences varying A sinusoidally with small angular frequency (ω = 0.4), B sinusoidally with large angular frequency (ω = 2.4), and C randomly. The average CL (BCL) and its variability window (σ) were the same in the three instances. One hundred APs of each sequence are reported, superimposed, in the first column. Insets show detail of APD sequences. The second column reports APDn,CLn-1 values of five consecutive beats (see color code) and their corresponding ERS1-S2 curves. In the third column, all ERS1-S2 curves measured for each of the 100 beats are reported in red. The collection of the APDn,CLn-1 values for all beats is reported as black dots and form the corresponding ERbtb representations (data and figure from [185]. D, left The AP model was initially paced with a constant CL = 350 ms (lower panel). The initial steady-state APD (upper panel) was turned into APD alternans by switching off the current stimulus for one single beat (black star). APD alternans was removed by passing to pacing CL oscillating sinusoidally around 350 ms within a ± 50 ms range and at an angular…

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  Fig. 12. The restitution hypothesis. The scheme explains why, during constant BCL pacing, a single perturbation of the pacing rate (DI*) can make pacing parameters to alternate, converging or diverging from steady-state values (DIss and APDss) depending whether the slope of the ERS1-S2,DI curve (thick line) is smaller (left) or greater (right) than 1. The broken grey straight line represents APD = BCL – DI (modified from [65])