Faculty Opinions recommendation of Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization.

Author(s):  
Jan Kucera
2014 ◽  
Vol 11 (97) ◽  
pp. 20140352 ◽  
Author(s):  
Alfonso Bueno-Orovio ◽  
David Kay ◽  
Vicente Grau ◽  
Blanca Rodriguez ◽  
Kevin Burrage

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.


2009 ◽  
Vol 297 (3) ◽  
pp. H1048-H1057 ◽  
Author(s):  
Lin Wu ◽  
Sridharan Rajamani ◽  
Hong Li ◽  
Craig T. January ◽  
John C. Shryock ◽  
...  

Reduction of repolarization reserve increases the risk of arrhythmia. We hypothesized that inhibition of K+ current ( IK) to decrease repolarization reserve would unmask the proarrhythmic role of endogenous, physiological late Na+ current (late INa). Monophasic action potentials (MAP) and 12-lead electrocardiogram were recorded from female rabbit isolated hearts. To block IK and reduce repolarization reserve, E-4031, 4-aminopyridine, and BaCl2 were used; to block endogenous late INa, tetrodotoxin (TTX) and ranolazine were used. E-4031 (1–60 nM) concentration-dependently prolonged MAP duration (MAPD90) and increased duration of the T wave from Tpeak to Tend (Tpeak-Tend), transmural dispersion of repolarization (TDR), and beat-to-beat variability (BVR) of MAPD90. E-4031 caused spontaneous and pause-triggered polymorphic ventricular tachycardia [ torsade de pointes (TdP)]. In the presence of 60 nM E-4031, TTX (0.6–3 μM) and ranolazine (5–10 μM) shortened MAPD90, decreased TDR, BVR, and Tpeak-Tend ( n = 9–20, P < 0.01), and abolished episodes of TdP. In hearts treated with BaCl2 or 4-aminopyridine plus E-4031, TTX (0.6–3 μM) shortened MAPD90 and decreased Tpeak-Tend. Ranolazine could not reverse the effect of E-4031 to inhibit human ether-a-go-go-related gene (HERG) K+ current; thus, the reversal by ranolazine of effects of E-4031 was likely due to inhibition of late INa and not to antagonism of the HERG-blocking action of E-4031. We conclude that endogenous, physiological late INa contributes to arrhythmogenesis in hearts with reduced repolarization reserve. Inhibition of this current partially reverses MAPD prolongation and abolishes arrhythmic activity caused by IK inhibitors.


Author(s):  
Kęstutis Kubilius ◽  
Yuliya Mishura ◽  
Kostiantyn Ralchenko

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jun Xi ◽  
Yanqing Chen ◽  
Jianwen Cao

It is well known that linear complementarity problem (LCP) involving partial integro differential equation (PIDE) arises from pricing American options under Lévy Models. In the case of infinite activity process, the integral part of the PIDE has a singularity, which is generally approximated by a small Brownian component plus a compound Poisson process, in the neighborhood of origin. The PIDE can be reformulated as a fractional partial differential equation (FPDE) under fractional diffusion models, including FMLS (finite moment log stable), CGMY (Carr-Madan-Geman-Yor), and KoBol (Koponen-Boyarchenko-Levendorskii). In this paper, we first present a stable iterative algorithm, which is based on the fractional difference approach and penalty method, to avoid the singularity problem and obtain numerical approximations of first-order accuracy. Then, on the basis of the first-order accurate algorithm, spatial extrapolation is employed to obtain second-order accurate numerical estimates. Numerical tests are performed to demonstrate the effectiveness of the algorithm and the extrapolation method. We believe that this can be used as necessary tools by the engineers in research.


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