Dispersion of cardiac action potential duration and the initiation of re-entry: A computational study

BACKGROUND: The initiation of re-entrant cardiac arrhythmias is associated with increased dispersion of repolarisation, but the details are difficult to investigate either experimentally or clinically. We used a computational model of cardiac tissue to study systematically the association between action potential duration (APD) dispersion and susceptibility to re-entry. METHODS: We simulated a 60 × 60 mm 2 D sheet of cardiac ventricular tissue using the Luo-Rudy phase 1 model, with maximal conductance of the K+ channel gKmax set to 0.004 mS mm-2. Within the central 40 × 40 mm region we introduced square regions with prolonged APD by reducing gKmax to between 0.001 and 0.003 mS mm-2. We varied (i) the spatial scale of these regions, (ii) the magnitude of gKmax in these regions, and (iii) cell-to-cell coupling. RESULTS: Changing spatial scale from 5 to 20 mm increased APD dispersion from 49 to 102 ms, and the susceptible window from 31 to 86 ms. Decreasing gKmax in regions with prolonged APD from 0.003 to 0.001 mS mm-2 increased APD dispersion from 22 to 70 ms, and the susceptible window from <1 to 56 ms. Decreasing cell-to-cell coupling by changing the diffusion coefficient from 0.2 to 0.05 mm2 ms-1 increased APD dispersion from 57 to 88 ms, and increased the susceptible window from 41 to 74 ms. CONCLUSION: We found a close association between increased APD dispersion and susceptibility to re-entrant arrhythmias, when APD dispersion is increased by larger spatial scale of heterogeneity, greater electrophysiological heterogeneity, and weaker cell-to-cell coupling

Complex patterns of spontaneous initiations and terminations of reentrant circulation in a loop of cardiac tissue

A two-component model is developed that consists of a discrete loop of cardiac cells that circulates action potentials together with a cardiac pacing mechanism. Physiological properties of cells such as restitutions of refractoriness and of conduction velocity are given via experimentally measured functions. The dynamics of circulating pulses and their interactions with the pacer are regulated by two threshold relations. Patterns of spontaneous initiations and terminations of reentry (SITR) generated by this system are studied through numerical simulations and analytical observations. These patterns can be regular or irregular; causes of irregularities are identified as the threshold bistability of reentrant circulation (T-bistability) and in some cases, also phase-resetting interactions with the pacer.Comment: 27 pages, 10 figures, 61 references; A version of this paper (same results) is to appear in the Journal of Theoretical Biology; arXiv V2 adds helpful commments to facilitate reading and corrects minor errors in presentatio

Recognition of fibrotic infarct density by the pattern of local systolic-diastolic myocardial electrical impedance

Myocardial electrical impedance is a biophysical property of the heart that is influenced by the intrinsic structural characteristics of the tissue. Therefore, the structural derangements elicited in a chronic myocardial infarction should cause specific changes in the local systolic-diastolic myocardial impedance, but this is not known. This study aimed to characterize the local changes of systolic-diastolic myocardial impedance in a healed myocardial infarction model. Six pigs were successfully submitted to 150 min of left anterior descending (LAD) coronary artery occlusion followed by reperfusion. 4 weeks later, myocardial impedance spectroscopy (1–1000 kHz) was measured at different infarction sites. The electrocardiogram, left ventricular (LV) pressure, LV dP/dt, and aortic blood flow (ABF) were also recorded. A total of 59 LV tissue samples were obtained and histopathological studies were performed to quantify the percentage of fibrosis. Samples were categorized as normal myocardium (50%). Resistivity of normal myocardium depicted phasic changes during the cardiac cycle and its amplitude markedly decreased in dense scar (18 ± 2 ·cm vs. 10 ± 1 ·cm, at 41 kHz; P < 0.001, respectively). The mean phasic resistivity decreased progressively from normal to heterogeneous and dense scar regions (285 ± 10 ·cm, 225 ± 25 ·cm, and 162 ± 6 ·cm, at 41 kHz; P < 0.001 respectively). Moreover, myocardial resistivity and phase angle correlated significantly with the degree of local fibrosis (resistivity: r = 0.86 at 1 kHz, P < 0.001; phase angle: r = 0.84 at 41 kHz, P < 0.001). Myocardial infarcted regions with greater fibrotic content show lower mean impedance values and more depressed systolic-diastolic dynamic impedance changes. In conclusion, this study reveals that differences in the degree of yocardial fibrosis can be detected in vivo by local measurement of phasic systolic-diastolic bioimpedance spectrum. Once this new bioimpedance method could be used via a catheter-based device, it would be of potential clinical applicability for the recognition of fibrotic tissue to guide the ablation of atrial or ventricular arrhythmias.Award-winningPostprint (published version

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network

Electrophysiological effects of 5-hydroxytryptamine on isolated human atrial myocytes, and the influence of chronic beta-adrenoceptor blockade

&lt;b&gt;1.&lt;/b&gt; 5-Hydroxytryptamine (5-HT) has been postulated to play a proarrhythmic role in the human atria via stimulation of 5-HT&lt;sub&gt;4&lt;/sub&gt; receptors. &lt;b&gt;2.&lt;/b&gt; The aims of this study were to examine the effects of 5-HT on the L-type Ca&lt;sup&gt;2+&lt;/sup&gt; current (&lt;i&gt;I&lt;/i&gt;&lt;sub&gt;CaL&lt;/sub&gt;) action potential duration (APD), the effective refractory period (ERP) and arrhythmic activity in human atrial cells, and to assess the effects of prior treatment with &#946;-adrenoceptor antagonists. &lt;b&gt;3.&lt;/b&gt; Isolated myocytes, from the right atrial appendage of 27 consenting patients undergoing cardiac surgery who were in sinus rhythm, were studied using the whole-cell perforated patch-clamp technique at 37&#186;C. &lt;b&gt;4.&lt;/b&gt; 5-HT (1 n-10 &#956;M) caused a concentration-dependent increase in &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;CaL&lt;/sub&gt;, which was potentiated in cells from &#946;-blocked (maximum response to 5-HT, E&lt;sub&gt;max&lt;/sub&gt;=299&#177;12% increase above control) compared to non-&#946;-blocked patients (E&lt;sub&gt;max&lt;/sub&gt;=220&#177;6%, P&#60;0.05), but with no change in either the potency (log EC&lt;sub&gt;50&lt;/sub&gt;: -7.09&#177;0.07 vs -7.26&#177;0.06) or Hill coefficient (&lt;i&gt;n&lt;/i&gt;&lt;sub&gt;H&lt;/sub&gt;: 1.5&#177;0.6 vs 1.5&#177;0.3) of the 5-HT concentration-response curve. &lt;b&gt;5.&lt;/b&gt; 5-HT (10 &#956;M) produced a greater increase in the APD at 50% repolarisation (APD50) in cells from &#946;-blocked patients (of 37&#177;10 ms, i.e. 589&#177;197%) vs non-&#946;-blocked patients (of 10&#177;4 ms, i.e. 157&#177;54%; P&#60;0.05). Both the APD&lt;sub&gt;90&lt;/sub&gt; and the ERP were unaffected by 5-HT. &lt;b&gt;6.&lt;/b&gt; Arrhythmic activity was observed in response to 5-HT in five of 17 cells (29%) studied from &#946;-blocked, compared to zero of 16 cells from the non-&#946;-blocked patients (P&#60;0.05). &lt;b&gt;7.&lt;/b&gt; In summary, the 5-HT-induced increase in calcium current was associated with a prolonged early plateau phase of repolarisation, but not late repolarisation or refractoriness, and the enhancement of these effects by chronic &#946;-adrenoceptor blockade was associated with arrhythmic potential

Fractal Rigidity in Migraine

We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.Comment: 4 pages, 6 figure

Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.Comment: 26 pages, 13 figures, appendix and 2 movies, as accepted to PLoS ONE 2011/08/0