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LETTER TO THE EDITOR
The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue. Comments on "A model for human ventricular tissue" by K. H. W. J. ten Tusscher et al.
Comments on "A model for human ventricular tissue"
To the Editor: In the recent study "A model for human ventricular tissue" by ten Tusscher et al. (6), the authors present a comparison between their model of a cardiac ventricular action potential and that of Luo-Rudy (the LR model) (Refs. 2–4 and 7, http://rudylab.wustl.edu/). The comparison is summarized in Table 3 of their study. Several entries in the table provide inaccurate information that may confuse the readers and users of the models; they require clarifications that we provide here (1). The table states that the rapid delayed rectifier current (IKr) and slow delayed rectifier current (IKs) components of the delayed rectifier K+ current are not included in the LR model. This is incorrect; IKr and IKs were formulated as part of the LR model and published in the study "Two components of the delayed rectifier K+current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization." by Zeng and Rudy (7). Ten Tusscher et al. refer to this article as Ref. 71 in their study but do not include its development of IKr and IKs in the models' comparison (2). Similarly, Table 3 states that transient outward current (Ito) has not been incorporated in the LR model. The LR model is based mostly on data from guinea pig ventricular myocytes, which do not express Ito. However, an Ito formulation was incorporated in the LR model and used to simulate effects of its transmural heterogeneity on the action potential and electrocardiographic waveforms (1, 3, 5).
We appreciate providing this information to the readers of the American Journal of Physiology, so that the misinformation in the study by ten Tusscher et al. is rectified.
REFERENCES
In our study, we chose for the comparison between the original formulation of the Luo-Rudy phase 2 model published in Ref. 3, which we explicitly write in the title of Table 3. This original formulation of the Luo-Rudy model does not contain the mentioned IKr, IKs, and Ito. We of course acknowledge that later modifications of the Luo-Rudy phase 2 model do include these current formulations (1, 2, 4). Note also that the Priebe-Beuckelmann and Courtemanche model, with which we also compare our model in Table 3, are also based on the Luo-Rudy model, and they do incorporate these currents and in addition are adjusted to match conditions in human cardiac cells. We stated this explicitly for the Priebe-Beuckelmann on page H1573 of our study.
We use the rest of this letter to compare our model with the modified versions of the Luo-Rudy model that do include IKr, IKs, and Ito, which can be important for researchers actively using these models for simulations.
In regard to IKr, IKr was added to the Luo-Rudy model first by Zeng et al. (4). The formulation is based on experimental data for guinea pig ventricular and atrial cells. Our IKr formulation is based on experimental data for human ventricular cells. Differences between our IKr formulation and that of Zeng et al. are as follows: 1) the size of IKr conductance is a factor of 3.6 smaller in the Zeng et al. model; 2) the activation time constant is a factor of 4–7 smaller in the –80- to 20-mV range; and 3) they use a rectification factor for immediate inactivation, whereas we use fast time-dependent inactivation. We demonstrate that this results in the initial peak of IKr at the beginning of an action potential that is also recorded in action potential-clamp experiments but absent from all models in which inactivation is instantaneous. In addition, the voltage of half-inactivation used by Zeng et al. is –9 mV, whereas it is –88 mV in our model.
In regard to IKs, IKs was added to the Luo-Rudy model first by Zeng et al. (4). The formulation is based on experimental data for guinea pig ventricular and atrial cells. Our IKs formulation is based on experimental data for human ventricular cells. Differences between our IKs formulation and that of Zeng et al. are as follows: a 6.5-mV difference in half-activation voltage of the activation gate, and activation is a factor of 3–4 faster in the Zeng et al. IKs formulation, whereas deactivation is a factor of 4–10 slower in the Zeng et al. IKs formulation. This difference in dynamics has important consequences for the effect of IKs on action potential duration and restitution.
In regard to Ito, Ito was added to the Luo-Rudy model first by Dumaine et al. (1), and this formulation was later used by Gima et al. (2). Although not clearly stated, based on the experimental studies in the reference list, Dumaine et al.'s Ito formulation is based on data on human and canine ventricular cells. Our Ito formulation is fitted to experimental data for human cardiac cells. Differences between our Ito formulation and that of Dumaine et al. are as follows: 1) the use of three activation gates versus one activation gate; 2) the use of an extra outward rectification factor, which our model does not have; 3) a faster activation time; 4) and a slower recovery from inactivation compared with our epicardial and M cells. Most importantly, the Dumaine et al. formulation assumes no Ito in endocardial cells. Instead, our model includes a seperate formulation for endocardial Ito that is a factor of 4 smaller in size than epicardial Ito. In addition, steady-state inactivation is shifted toward more negative voltages, and recovery from inactivation is much slower for endocardial compared with epicardial cells. These differences between epicardial/M cell and endocardial Ito are based on experimentally found differences.
In conclusion, we did not intend to claim to be the first to develop formulations for IKs, IKr, and Ito. We gladly acknowledge that this has been done previously by Rudy and coworkers. Rather, we were interested in formulating these currents specifically for human ventricular cells. Here we have shown that indeed significant differences are present between our formulations for IKr, IKs, and Ito and those incorporated in the Luo-Rudy guinea pig ventricular cell model.
REFERENCES
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