Several studies suggest that action potential duration (APD) alternans play an important role in initiation of arrhythmias, while less is known about the alternans of early phases of action potential (AP) and phase relation between the two. Transmembrane potentials recorded from swine and canine ventricles were analyzed to determine the correlation and phase relation between alternans of early and late phases of an AP. In both species, for activation intervals ≤ 400 ms, action potential amplitude (APA) alternans occurred≥ 50% of times when APD alternans occurred and vice versa, both were mostly in phase. Also, alternans of APA and APD were mostly in phase with alternans of maximal rate of depolarization. The correlation between alternans in early and later parts of AP, however, was variable between species; APD10 and APD90 alternans were out of phase 81 % versus 34 % in canines and swines. These observations suggest that ionic mechanisms underlying alternans of depolarization and early repolarization phases may be distinct from those underlying later phases of repolarization. Simulations conducted to see the spatiotemporal effect of phase behavior between these alternans show that out of phase behavior suppresses oscillations in wavelength and minimizes the chances of spatial discordance.

In der vorliegenden Arbeit wurden dynamische Mechanismen der Entstehung von Kammerflimmern dargestellt. Es wurde erläutert, dass ein APD-Alternans für die Induktion von Spiralwellenbrüchen als elektrophysiologisches Korrelat von Kammerflimmern wichtig ist. Es konnte gezeigt werden, dass die Restitution der Aktionspotentialdauer und der Leitungsgeschwindigkeit wichtige Determinanten zur Ausbildung eines diskordanten APD-Alternans sind. Dieser diskordante APD-Alternans ist ein Alternans des Myokards bei dem verschiedene Myokardregionen außer Phase schlagen. Es wurde erläutert, dass die Generierung eines diskordanten APD-Alternans zu einer spatiotemporalen Heterogenität und damit zur Entstehung eines lokalen Leitungsblockes führt, der wiederum den initialen Schritt eines Spiralwellenbruchs darstellt. In der Arbeit konnte dargestellt werden, dass insbesondere durch die Applikation von bestimmten Stimulations-Sets ein diskordanter APD-Alternans provoziert werden konnte. Dies entstand typischerweise durch eine kurz-lang-kurz-lang-Sequenz. Es bildete sich in der Versuchsreihe unter dieser Stimulationsgabe ein diskordanter APD-Alternans zwischen dem rechten und linken Ventrikel des Hundemyokards aus, der dann in einem lokalem Leitungsblock und Kammerflimmern resultierte. / The Study describes the mechanism of the development of ventricular fibrillation. The Study shows that Alternans of Action Potential Duration (APD) is related to the breaking up of Spiral Waves.

<p>Sudden death from arrhythmia is a major cause of mortality in the United States. Unfortunately, no current diagnostic test can accurately predict risk for sudden arrhythmic death. Because ventricular arrhythmias often result from abnormalities of repolarization, assessment of myocardial repolarization using the electrocardiogram (ECG) can aid in prediction of arrhythmia risk. Non-linear, rate-dependent changes in myocardial repolarization can promote the development of arrhythmia, but few studies examine how these dynamic changes in repolarization affect the ECG. This dissertation describes the use of a computer model to investigate the effect of dynamic changes in myocardial repolarization on the ECG T wave.</p><p>To simulate action potential conduction from the endocardium to the epicardium of the free wall of the canine left ventricle, 1-dimensional multicellular computer fiber models were created. Each fiber model was composed of endocardial, midmyocardial, and epicardial cells. For each cell type, existing mathematical models were modified to approximate experimental data for four types of dynamic repolarization behavior: (1) dynamic restitution, the response to steady-state pacing; (2) S1-S2 restitution, the response to a premature or postmature stimulus; (3) short-term memory (STM), the response to an abrupt change in pacing rate; and (4) repolarization alternans, beat-to-beat alternation in cellular repolarization time. Repolarization times were obtained from endocardial, midmyocardial, and epicardial regions in the fiber model and compared to parameters measured from a computed transmural ECG.</p><p>Spatial differences in repolarization created two voltage gradients that influenced the ECG: an endocardial-midmyocardial (endo-mid) gradient and a midmyocardial-epicardial (mid-epi) gradient. Epicardial dynamic restitution changes altered the mid-epi gradient, influencing the rising phase of the ECG T wave, and endocardial dynamic restitution changes altered the endo-mid gradient, influencing the falling phase of the T wave. Changes in epicardial or endocardial repolarization due to S1-S2 restitution or STM caused transient changes in the rising or falling phase of the T wave, respectively.</p><p>During repolarization alternans, an alternating, asymmetric distribution of extracellular potential around the fiber influenced the measurement of T-wave alternans (TWA) in the ECG. Presence of a resistive barrier in the fiber model altered the magnitude of repolarization alternans as well as the TWA amplitude in the ECG with effects dependent on barrier location. The resistive barrier also modified the relationship between cellular repolarization alternans magnitude and TWA amplitude.</p><p>The results presented in this dissertation explain basic mechanisms by which dynamic changes in myocardial repolarization affect the ECG T wave. These mechanisms form the foundation for the development of techniques to identify arrhythmogenic, dynamic changes in the myocardium using the ECG. Future studies in higher-dimensional, more complex models will build upon these results by considering the influence of additional voltage gradients, more realistic tissue geometries, and heterogeneities in the volume conductor.</p> / Dissertation

Sudden Cardiac Death (SCD) is the largest cause of natural deaths in the USA, accounting for over 300,000 deaths annually. The major reason for SCD is Ventricular Arrhythmia (VA). Therefore, there is need for exploration of approaches to predict increased risk for VA. Alternans of the T wave in the ECG (TWA) is widely investigated as a potential predictor of VA, however, clinical trials show that TWA has high negative predictive value but poor positive predictive value. A possible reason that TWA has a large number of false positives is that a pattern of alternans known as concordant alternans, may not be as arrhythmogenic as another pattern which is discordant alternans. Currently, it is not possible to discern the pattern of alternans using clinical ECGs. Prior studies from our group have showed that alternans of the maximum rate of depolarization of an action potential also can occur when Action Potential Duration (APD) alternans occurs and the relationship between these two has the potential to create spatial discord. These results suggest that exploration of the co-occurrence of depolarization and repolarization alternans has the potential to stratify the outcome of TWA tests. In order to investigate the link between depolarization alternans and changes in ECGs, we used a mathematical model created previously in our research group which simulated ECGs from the cellular level changes observed in our experimental studies. These results suggest that the changes in ECGs should appear as alternating pattern of the amplitude of the R wave. Because there are a variety of factors which may also cause the R wave amplitude to change, we used signal analysis and statistical modeling to determine the link between the observed changes in R wave amplitude and depolarization alternans. Results from ECGs recorded from patients show that amplitude of the R wave can change as predicted by our experimental results and mathematical model. Using TWA as the marker of repolarization alternans and R Wave Amplitude Alternans (RWAA) as the marker of depolarization alternans, we investigated the phase relation between depolarization and repolarization alternans in clinical grade ECG and observed that this relationship does change spontaneously, consistent with our prior results from animal studies. Results of the present study support further investigation of the use of RWAA as a complementary method to TWA to improve its positive predictive value.

Atrial Fibrillation (AF) is rare amongst young people whilst epidemic in the elderly. Whilst much is known about the pathophysiology of AF, the mechanisms underlying the vulnerability to AF amongst older people in incompletely understood. Young (< 18 months, first quintile of life) and old (> 8 years, last quintile of life) Welsh mountain sheep were used to investigate changes in atrial electrophysiology with age. Old sheep were more vulnerable to induced AF than young sheep. On the surface ECG, p-wave duration increased with age suggesting increasing atrial size. The corrected sinus node recovery time increased with age, suggesting deteriorating sinus node function. These findings confirmed the validity of sheep as a model for human ageing. In isolated atrial myocytes, action potentials (APs) were recorded using the perforated patch clamp technique. AP duration increased with age, and an increase in AP amplitude was also seen at the lowest stimulation rates. Right atrial AP durations were prolonged compared to those from left atrial myocytes, and the inter-atrial difference was similar between old and young. However, when right atrial monophasic APs were recorded from anaesthetised sheep in vivo, no difference in AP duration was seen between age groups. Alternans occurred at lower stimulation rates in old compared to young myocytes and was of greater magnitude. These age-related differences were present in isolated myocytes and in vivo. Alternans mechanisms were explored by simultaneously recording APs and intracellular calcium concentration. Atrial alternans was driven by alternans of Ca2+ cycling at low stimulation rates. However, despite disabling Ca2+ cycling using thapsigargin, alternans could still be elicited from myocytes during rapid stimulation. Right atrial conduction velocity (CV) was assessed in vivo and found to increase with age. A key determinant of CV, the Na+ current INa was investigated using the whole cell patch clamp technique. INa increased with age in left atrial myocytes and recovered faster from inactivation. Protein expression was investigated using Western blotting. Expression of the Na+ channel α-subunit did not change with age. The gap junction protein Cx43 was expressed less in older subjects, but Cx40 expression was similar. This work has cast light on several aspects of atrial electrophysiology in which the effects of age have not been thoroughly investigated. The longer cellular APs seen with age decrease the wavelength of potential re-entrant circuits which could be seen as protective against AF. However, AP prolongation is also associated with afterdepolarisations which could serve to trigger AF. The increase in alternans behaviour may set the stage for wavebreak, leading to re-entrant circuit formation. The increase in CV was surprising and might be seen as protective against AF as it increases arrhythmia wavelength, and is likely to be caused by the increased INa.

<p>Instability in the propagation of nonlinear electro-chemical waves in the heart is responsible for life-threatening disease. This thesis describes an investigation of the effects of boundaries on cardiac wave propagation that arises from a site where an electrical stimulus is applied or from boundaries beyond which current does not flow. It is generally believed that the spatial scale for boundary effects is approximately equal to the passive length constant, lambda, of the tissue, the distance over which a a voltage pulse decays when it is below the threshold for wave generation. From the results of <em>in vitro</em> experiments with bullfrog cardiac tissue and through numerical simulations, I find that boundaries affect wave propagation over a much larger spatial scale and that the spatial variation in some cardiac restitution properties is correlated statistically with the onset of alternans, a possible precursor to fibrillation in the human heart.</p><p>An optical imaging system using novel illumination based on LEDs is used to determine the spatial dependence of action potential duration (APD) and the slope of the dynamic restitution curve S_DRC, which describes the relationship between steady-state APD and diastolic interval. For tissue with nearly identical cells, I find that APD is longest near the stimulus and shortest near the physical boundary with significant changes (~100 ms) over a distance of ~10lambda. S_DRC decreases with distance from the stimulus at a constant rate (~0.1-1.5 /mm) over the surface of the tissue. Simulations using a two-variable cardiac model confirm that spatial patterns of APD and S_DRC can be induced by boundaries.</p><p>Additional measurements with the simultaneous impalement of two microelectrodes are used to determine the spatial differences of other restitution properties. These studies indicate that APD and S_DRC, as well as the slopes of the constant-BCL and S1S2 restitution curves, vary in space and that the spatial differences and onset of alternans at rapid pacing are correlated. If similar correlations are evident in humans, such measurements may identify patients who are susceptible to arrhythmias and allow for early treatment.</p> / Dissertation

<p>While alternans in a single cardiac cell appears through a simple</p><p>period-doubling bifurcation, in extended tissue the exact nature</p><p>of the bifurcation is unclear. In particular, the phase of</p><p>alternans can exhibit wave-like spatial dependence, either</p><p>stationary or traveling, which is known as <italic>discordant</italic></p><p>alternans. We study these phenomena in simple cardiac models</p><p>through a modulation equation proposed by Echebarria-Karma. In</p><p>this dissertation, we perform bifurcation analysis for their</p><p>modulation equation.</p><p>Suppose we have a cardiac fiber of length l, which is</p><p>stimulated periodically at its x=0 end. When the pacing period</p><p>(basic cycle length) B is below some critical value B_c,</p><p>alternans emerges along the cable. Let a(x,n) be the amplitude</p><p>of the alternans along the fiber corresponding to the n-th</p><p>stimulus. Echebarria and Karma suppose that a(x,n) varies</p><p>slowly in time and it can be regarded as a time-continuous</p><p>function a(x,t). They derive a weakly nonlinear modulation</p><p>equation for the evolution of a(x,t) under some approximation,</p><p>which after nondimensionization is as follows: </p><p> &partial_t a = σ a + <bold>L</bold> a - g a <super>3</super>,</p><p>where the linear operator</p><p> <bold>L</bold> a = &partial_xxa - &partial_x a -Λ<super>-1</super> ∫ <super>0</super> _x a(x',t)dx'.</p><p>In the equation, σ is dimensionless and proportional to</p><p>B_c - B, i.e. σ indicates how rapid the pacing is,</p><p>Λ<super>-1</super> is related to the conduction velocity (CV) of the</p><p>propagation and the nonlinear term -ga<super>3</super> limits growth after the</p><p>onset of linear instability. No flux boundary conditions are</p><p>imposed on both ends.</p><p>The zero solution of their equation may lose stability, as the</p><p>pacing rate is increased. To study the bifurcation, we calculate</p><p>the spectrum of operator <bold>L</bold>. We find that the</p><p>bifurcation may be Hopf or steady-state. Which bifurcation occurs</p><p>first depends on parameters in the equation, and for one critical</p><p>case both modes bifurcate together at a degenerate (codimension 2)</p><p>bifurcation.</p><p>For parameters close to the degenerate case, we investigate the</p><p>competition between modes, both numerically and analytically. We</p><p>find that at sufficiently rapid pacing (but assuming a 1:1</p><p>response is maintained), steady patterns always emerge as the only</p><p>stable solution. However, in the parameter range where Hopf</p><p>bifurcation occurs first, the evolution from periodic solution</p><p>(just after the bifurcation) to the eventual standing wave</p><p>solution occurs through an interesting series of secondary</p><p>bifurcations.</p><p>We also find that for some extreme range of parameters, the</p><p>modulation equation also includes chaotic solutions. Chaotic waves</p><p>in recent years has been regarded to be closely related with</p><p>dreadful cardiac arrhythmia. Proceeding work illustrated some</p><p>chaotic phenomena in two- or three-dimensional space, for instance</p><p>spiral and scroll waves. We show the existence of chaotic waves in</p><p>one dimension by the Echebarria-Karma modulation equation for</p><p>cardiac alternans. This new discovery may provide a different</p><p>mechanism accounting for the instabilities in cardiac dynamics.</p> / Dissertation

No description available.

The presented studies investigate dynamics of action potential duration (APD) tobetter understand the underlying mechanism for repolarization alternans.We recorded trans-membrane potentials (TMP) in canine endocardial muscle tissueusing standard glass microelectrode under the control of an explicit diastolic interval (DI)control pacing protocol, i.e. feedback protocol. During sequential sinusoidal DI activation,the trajectory of APD dynamics has multiple values of APD correspondent to the sameDI, i.e. restitution is a bi-modal relationship. Our results indicate that: 1) there is a delay,similar to hysteresis, of change in APD responding to change in DI, 2) and the timecourse of the delay is asymmetric for fast or slow pacing history. The alternans wasobserved during constant DI pacing, i.e. the DI preceding each APD was invariant orchanged within a limited range. This finding suggests that alternans of APD do not needthe oscillation of preceding DI, i.e. DI dependent restitution is not a necessary conditionfor the alternans. This result implies that DI independent component exists in themechanism of the alternans. Nonetheless, the amplitude of alternans was statisticallylarger during constant pacing cycle length (PCL) pacing than that during constant DIpacing, even though both PCL and DI pacing trials used similar average activation rate.These results also demonstrate the ability of the feedback protocol to analyze the memoryeffects and dissect different components in the mechanism of alternans.Two computational models, Luo-Rudy dynamics (LRD) and cardiac ventricle model(CVM) were used to study the hysteresis in restitution. By perturbing membrane current:L-type calcium current, rapid and slow potassium rectifier, and intracellular calciumtransfer rate in sarcoplasmic reticulum (SR) and using sinusoidal DI pacing sequence, weshowed that the asymmetric calcium current across the membrane and its interaction withcalcium buffer in SR during increasing and decreasing DI phase plays an important rolein the hysteresis. CVM was used to study the alternans during constant DI pacing.However CVM failed to replicate the alternans that occurred in the experiments. Thisresult implies that CVM lacks the electrophysiological kinetics related to alternans thatwas shown in our experiment.

Ventricular fibrillation is one of the leading causes for Sudden Cardiac Death and is characterized by multiple activation wavefronts. Multiple activation wavefronts originate from a reentrant circuit which requires the presence of a unidirectional block in the path of a propagating excitation wave. It has been proposed that at the cellular level beat to beat alternation in the action potential duration at rapid pacing rates can result in a conduction block. Various mechanisms have been postulated to show the mechanisms of alternans. We use simulated activation in a one dimensional tissue fiber to show the existence of a new mechanism via which alternans can result. We used a new pacing protocol to eliminate alternans at the pacing site, and thus eliminating restitution of action potential duration at this site to reveal existence of alternans down the fiber. Effects on alternans of manipulations of specific ionic currents such as the sodium current (INa), calcium current (ICaL), potassium current (Ikr) and of the diffusion co-efficient (Dx) which simulates reduced expression of connexin 43 were determined. Decrease in sodium conductance, i.e. in excitability by half caused the alternans to occur at the pacing site itself even though APD restitution was eliminated. An increase or decrease in calcium current (ICaL) eliminated alternans throughout the fiber. The use of a novel pacing approach in investigation of alternans, as in this study, furthers our understanding of the mechanism of alternans and may prove helpful in the development of better anti-arrhythmic drugs in the future.