Atrial fibrillation (AF) is the most common sustained arrhythmia in humans affecting almost 2% of the population in the developed world . As the two major strategies ablation therapy and drug therapy fail to succeed in about one third of all patients, AF is still a major challenge motivating the search for new drugs. Current antiarrhythmic agents suffer from limited efficacy or severe side-effects such as provoking life-threatening torsades de pointes arrhythmia in the ventricles. Vernakalant is a new multichannel blocker for pharmacological cardioversion of AF and proved to be superior to both placebo and the existing intravenous agent amiodarone in several clinical studies . Despite its clinical efficacy, the underlying mode of action on atrial myocytes is not understood. One experimental study investigated the effect on isolated ion channels . Wettwer et al. assessed the effect on tissue preparations  and Dorian et al.  studied the effect on atrial and ventricular refractory period in humans. However, these results on different integration levels could not be linked until now. In this work, we try to elucidate the complex non-linear effects of vernakalant on the cellular level by linking the experimental data from the single channel level to tissue level data.
2.1 Electrophysiological model
Cellular electrophysiology was modeled using the Courtemanche-Ramirez-Nattel model of human atrial myocytes  in the Control case. To represent chronic AF (cAF) induced remodeling, several conductivities were altered as described before . In brief, Ito was reduced by 65%, IK1 was increased by 100%, IKs was increased by 100%, IKur was reduced by 50%, ICaL was reduced by 55%, INa, Ca was increased by 60%, and the SR leak current was increased by 50%. Furthermore, the cell capacitance was increased by 20%.
An implementation of the monodomain model  was utilized to simulate excitation propagation in a one-dimensional tissue strand of size 20 × 0.1 × 0.1mm3. The domain was discretized by cubic voxels with a side length of 0.1mm. The monodomain conductivity was set to 76 mS/m yielding a conduction velocity of 750 mm/s in theControl model without any drug-induced changes at a frequency of 1 Hz. Each voxel of the system was initialized in a single-cell environment for 50 beats followed by 5 beats in the tissue strand to adapt to the stimulation frequency. Stimuli were applied in voxels # 0..2, action potentials (APs) were evaluated in voxel # 150 as described before .
2.2 Drug model
Vernakalant reduces the conductance of several atrial ionic currents. We modeled its effect based on Hill’s equation:(1)
with Θ being the degree of channel blockage ranging from 0 to 1,IC50 being the half maximal inhibitory concentration, D being the free drug concentration, and nH being the Hill coefficient. The IC50/nH values for the different currents were extracted from literature for model 1 (M1): 21.0 μM / 0.92 for IKr , 13.0 μM / 0.92 for IKur , 30.0 μM / 0.82 for Ito , and 84.0 μM / 1.0 for ICaL . As a hypothesis, a second model M2 was defined with only ICaL being affected (42.0 μM / 1.0) besides the sodium channel block considered in both M1 and M2.
Due to the frequency dependence of INa block, it can not be represented by a single IC50/nH value pair. Instead, we chose to determine the degree of INa block (gNa reduction) by matching experimentally found reduction of the upstroke velocity dVm/dtmax for each frequency and vernakalant concentration individually. Towards this end, dVm/dtmax at zero drug concentration was taken as a reference value and the INa block in the drug model was tuned to match the experimentally found relative reduction in dVm/dtmax . This optimization was performed in the tissue strand environment described above. Using the degrees of block at 10μM and 30 μM, frequency-specific IC50 /nH value pairs were estimated.
The bisection-based tuning of g Na reduction aiming at a replication of experimentally observed dVm/dtmax reduction converged for all substrates, frequencies, and concentrations. The resulting degree of gNa block is shown in Table 2. The degree of INa block increased with increasing frequency as can be seen from the frequency-specific IC50 and nH values in Table 1. This effect is reflected in lower IC50 values as well as in reduced Hill coefficients. Figure 1 reveals that this resulted in a consistently higher degree of block for higher frequencies within a concentration range of 1 – 35μM. The frequency dependence was less pronounced in thecAF substrate than inControl.
The in-silico drug models were used to simulate a train of APs in the tissue strand environment (see Figure 2). In the Control substrate, 2:1 block occured at 3 Hz stimulation frequency using the drug model M1. For all other combinations, APs could be induced continuously, although alternans was observed in some of the models. Besides the upstroke velocity, 6 further AP markers were evaluated for the 6th AP: effective refractory phase (ERP), AP duration at 90% and 20% repolarization (APD90, APD20), AP amplitude (APA), resting membrane potential (RMP), and PLT20 defined as the mean potential in the time window between 20% and 30% repolarization. Table 2 shows the results in comparison to the experimentally observed values in . Model M1 reproduced the ERP prolongation seen in .
However, we did not observe the drug-induced increase of the divergence between ERP and APD90 (ERP prolongation accompanied by APD90 shortening) reported particularly for theControl substrate. Model M2 on the other hand covered the APD90 reduction as well as the increase of PLT 20whilst not replicating the ERP prolongation. The remaining AP markers were replicated sufficiently by both drug models.
We showed how vernakalant prolongs the atrial refractory period by blocking the potassium currents IKr, IKur, and Ito, as well as the L-type calcium current ICaL in a dose-dependent manner. Furthermore, INa is blocked frequency- and dose-dependently. This model based on literature data from the single channel level (M1) explains what can most probably be considered the major antiar-rhythmic mode of action: ERP prolongation. Our results are in line with the in-vivo human data from Dorian et al.  describing a dose dependency but no pronounced frequency dependency of atrial ERP prolongation at frequencies between 1.6 and 3.3 Hz. Atrial ERP was prolonged by between 12 and 14% in  for the higher investigated intravenous dose of 4.6 mg/kg.
Our second drug model M2 was comprised of only ICaL and INa block with values for ICaL not being based on subcellular experimental data but chosen to match experimentally observed AP morphology. This model provides a possible explanation of how APD90 and PLT20 are affected by vernakalant based on the delicate balance of inward and outward currents during the AP plateau and repolarization phase. PLT20 has to be considered with caution, though, as APD20 values differ significantly for some of the investigated combinations. Our findings are unlikely to be significantly affected by the choice of the atrial cell model as results using the model by Maleckar et al.  were very similar (data not shown).
While each of the models provides hypotheses for part of the experimentally observed characteristics, none of the setups is capable of reproducing and explaining the entirety of the observed effects. This fact reveals a missing piece of the puzzle in our understanding of vernakalant and throws up new questions. Future work might consider more complex drug models describing frequency-dependent block directly rather than using several Hill formulations. Another aspect, which might need to be covered in order to explain the experimentally observed increase in the difference between ERP and APD90 more comprehensively, is state-dependency.
In conclusion, our results foster the understanding of vernakalant’s cellular mode of action and point out relevant gaps in our current knowledge. This study will thus hopefully fuel and direct future in-silico and experimental research on this aspiring antiarrhythmic agent.
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.
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Published Online: 2015-09-12
Published in Print: 2015-09-01
Citation Information: Current Directions in Biomedical Engineering. Volume 1, Issue 1, Pages 418–422, ISSN (Online) 2364-5504, DOI: https://doi.org/10.1515/cdbme-2015-0101, September 2015