@article {, title = {Alternans promotion in cardiac electrophysiology models by delay differential equations}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {27}, year = {2017}, pages = {093915}, abstract = {

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate{\textquoteright}s recovery between consecutive action potentials.

}, issn = {1054-1500}, doi = {10.1063/1.4999471}, url = {http://aip.scitation.org/doi/10.1063/1.4999471}, author = {Gomes, Johnny M. and dos Santos, Rodrigo Weber and Cherry, Elizabeth M.} } @article {, title = {Distinguishing mechanisms for alternans in cardiac cells using constant-diastolic-interval pacing}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {27}, year = {2017}, pages = {093902}, abstract = {

Alternans, a proarrhythmic dynamical state in which cardiac action potentials alternate between long and short durations despite a constant pacing period, traditionally has been explained at the cellular level using nonlinear dynamics principles under the assumption that the action potential duration (APD) is determined solely by the time elapsed since the end of the previous action potential, called the diastolic interval (DI). In this scenario, APDs at a steady state should be the same provided that the preceding DIs are the same. Nevertheless, experiments attempting to eliminate alternans by dynamically adjusting the timing of pacing stimuli to keep the DI constant showed that alternans persisted, contradicting the traditional theory. It is now widely known that alternans also can arise from a different mechanism associated with intracellular calcium cycling. Our goal is to determine whether intracellular calcium dynamics can explain the experimental findings regarding the persistence of alternans despite a constant DI. For this, we use mathematical models capable of producing alternans through both voltage- and calcium-mediated mechanisms. We show that for voltage-driven alternans, action potentials elicited from a constant-DI protocol are always the same. However, in the case of calcium-driven alternans, the constant-DI protocol can result in alternans. Reducing the strength of the calcium instability progressively reduces and finally eliminates constant-DI alternans. Our findings suggest that screening for the presence of alternans using a constant-DI protocol has the potential for differentiating between voltage-driven and calcium-driven alternans.

}, issn = {1054-1500}, doi = {10.1063/1.4999354}, url = {http://aip.scitation.org/doi/10.1063/1.4999354}, author = {Cherry, Elizabeth M.} } @article {, title = {Effects of model error on cardiac electrical wave state reconstruction using data assimilation}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {27}, year = {2017}, pages = {093911}, abstract = {

Reentrant electrical scroll waves have been shown to underlie many cardiac arrhythmias, but the inability to observe locations away from the heart surfaces and the restriction of observations to only one or two state variables have made understanding arrhythmia mechanisms challenging. Recently, we showed that data assimilation from spatiotemporally sparse surrogate observations could be used to reconstruct a reliable time series of state estimates of reentrant cardiac electrical waves including unobserved variables in one and three spatial dimensions. However, real cardiac tissue is unlikely to be described accurately by mathematical models because of errors in model formulation and parameterization as well as intrinsic but poorly described spatial heterogeneity of electrophysiological properties in the heart. Here, we extend our previous work to assess how model error affects the accuracy of cardiac state estimates achieved using data assimilation with the Local Ensemble Transform Kalman Filter. We focus on one-dimensional states of discordant alternans characterized by significant wavelength oscillations. We demonstrate that data assimilation can provide high-quality estimates under a wide range of model error conditions, ranging from varying one or more parameter values to using an entirely different model to generate the truth state. We illustrate how multiplicative and additive inflation can be used to reduce error in the state estimates. Even when the truth state contains underlying spatial heterogeneity, we show that using a homogeneous model in the data assimilation algorithm can achieve good results. Overall, we find data assimilation to be a robust approach for reconstructing complex cardiac electrical states corresponding to arrhythmias even in the presence of model error.

}, issn = {1054-1500}, doi = {10.1063/1.4999603}, url = {http://aip.scitation.org/doi/10.1063/1.4999603}, author = {LaVigne, Nicholas S. and Holt, Nathan and Hoffman, Matthew J. and Cherry, Elizabeth M.} }