INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

SINCE THE SEMINAL WORK of Hodgkin and Huxley (7) describing Na and K currents mathematically in squid axon, several groups have extended this sort of modeling to cardiac ionic currents and action potential (AP) (1, 14, 16-18). The tremendous increase of experimental work elucidating the behavior of ionic currents in heart (3) has required the development of new and more sophisticated models (4, 5, 11-13, 34).

Ca also plays a crucial role in cardiac excitation-contraction coupling (ECC) (2), and it has become clear that there is a dynamic interplay between the AP and Ca regulation mechanisms. The membrane potential (E_m) modulates Ca transport, and the Ca transient also can feedback to alter E_m. Thus cardiac cell models of AP and ionic currents have progressively incorporated more detailed formulations of the Ca transport systems.

A number of laboratories have made substantial contributions to this overall development (8, 18, 19, 23, 34, 35). However, the model of Luo and Rudy (12, 13, 35) has become, perhaps, the standard through the late 1990s. Unfortunate common features of most existing models are their limited flexibility and accessibility. As the model increases in complexity, it is more difficult to modify parameters, conditions, and equations. The accuracy required to reproduce a particular physiological observation can hinder the versatility of the whole model. Accessibility limitations pertain not only to obtaining the computer code but also to how user-friendly the interface is. A readily accessible model should be easy enough to use that 1) students can quickly use it as a learning tool and 2) researchers can use it as a development tool to test its fidelity in reproducing experimental results and also to explore potentially new experiments.

To fill this gap, we have created a computer program that combines current scientific findings with a user-friendly interface. We developed LabHEART, a program that is very intuitive to use and in which modifications of key variables, stimulation protocols, and default conditions can be made with a click on an icon. Standard electrophysiological plots, such as current-voltage relationships (I-V sets) or steady-state activation and inactivation curves are built-in features. Ionic concentrations and maximal current densities can be altered while the simulation is running, which adds a dynamic edge to the program.

A second key goal is that the model reproduces faithfully the electrophysiological and Ca transport characteristics of rabbit ventricular myocytes. Rabbit ventricle is used extensively in experimental studies, but there is no currently available model. A third goal is to simulate data obtained from control vs. heart failure (HF) rabbit ventricular myocytes where K currents, Na/Ca exchange, and sarcoplasmic reticulum (SR) Ca-ATPase function are altered (21, 22). While this study is, in part, a further test of the rabbit ventricular myocyte model, it also helps to better understand the cellular basis of changes in AP, Ca transients, and the observed propensity for triggered arrhythmias that lead to ventricular tachycardia in HF (23).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

We adapted the equations from Luo and Rudy to rabbit ventricular myocytes using values obtained from the literature and from our laboratory. The model was implemented by using LabVIEW 5.0 graphical programming language from National Instruments (Austin, TX). Its inherent visual capabilities fit perfectly with our aim of intuitive use. We utilized the Rush and Larsen algorithm (26) to solve the set of differential equations. The main difference between our formulation and the one adopted by Luo and Rudy is the inclusion of transient outward K current (I_to) and Ca-activated Cl current [I_Cl(Ca)], as well as modification of the kinetics of T-type Ca channel (I_Ca,T), the rapid component of the delayed rectifier K current (I_Kr), and rescaling of several conductances to better match results in rabbit ventricle (see Table 1).

Transient outward K current. I_to has been reported in rabbit ventricular myocytes (6, 9). It is also known as I_to1 to differentiate it from the Ca-activated Cl current [known as I_to2 or I_Cl(Ca)] that is activated at the same time during the AP (37). I_to can contribute to ventricular repolarization. We used the I_to formulation of Winslow et al. (34) for this current

(1a)

(1b)

(1c)

(1d)

(1e)

where G_to is the channel conductance, X_to and Y_to are activation and inactivation parameters, respectively, and E_K is the reversal potential for K.

Ca-activated Cl current. I_Cl(Ca) has been reported in rabbit Purkinje cells (30) and atrial (36) and ventricular myocytes (10). It is strongly temperature dependent, being very small at room temperature but substantial at 35°C (25). I_Cl(Ca) can be suppressed by anion blockers such as DIDS or niflumic acid. Because of its Ca dependence, it also can be eliminated by blocking Ca current (I_Ca). We modeled this current as

(2)

where G_Cl is the Cl conductance set to 10 mS/µF, E_Cl is the reversal potential, and Ca dependence is incorporated as a Michaelis-Menten factor with K_mCa = 0.10 µM. These values were chosen to fit experimental records obtained by Puglisi et al. (25).

T-type Ca current. Although I_Ca,T is not generally detectable in rabbit ventricular myocytes, we have included it to make a more complete theoretical model. The I_Ca,T equations are

(3a)

where E_Ca is the Nernst potential for Ca and the gating parameters are as follows

(3b)

(3c)

(3d)

(3e)

These equations are slightly different from those used by Zeng et al. (35), but they reproduce more accurately the I-V relationship for I_Ca,T.

(4a)

(4b)

(4c)

(4d)

(4e)

View larger version (92K): [in this window] [in a new window]   Fig. 1.   The MAIN MENU screen shows a schematic diagram of the different mechanisms involved in cardiac excitation-contraction coupling (ECC) in a rabbit ventricular myocyte. SL, sarcolemma; Mito, mitochondrion; MF, myofilaments. By clicking on the icons located on the left, the user can 1) establish ionic concentrations, 2) set the stimulus waveforms, and visualize or alter 3) characteristics of the sarcoplasmic reticulum (SR) or 4) properties of Ca channels, 5) Na/Ca exchange, 6) sarcolemmal Ca pump, 7) Na Channel, 8) K channels, 9) Na-K-ATPase, or 10) Ca-activated Cl channel. By pressing the command buttons on the right, it is possible to obtain HELP screens, alter amounts of the Ca BUFFERS, RUN an action potential, SAVE a new set of default values under a new name, or EXIT the program.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Voltage clamp and current characterization. Under voltage-clamp mode, three protocols are available. The first protocol generates the I-V relationship of a channel. Figure 2 shows an example of this simulation for L- and T-type Ca channels. Figure 2A depicts the voltage waveforms used for this purpose. The protocol is set in a manner similar to experimental software; that is, the user selects the holding potential, "step to" voltage, duration of pulse, voltage increment (Delta V) between pulses, and number of iterations. Figure 2B illustrates the resulting L-type Ca current (I_Ca,L) traces. A particular current trace can be chosen with a cursor, and the specific current amplitude, voltage applied, and time of simulation appear on the screen (left). Some characteristics of the channel such as the conductance or the K_m for Ca-induced inactivation can be altered by directly typing the new value in the corresponding field. The voltage protocol can be changed on this screen without returning to the previous one. Default conditions can be restored by a command button (right); the other command buttons allow the user to toggle between I_Ca,L and I_Ca,T or to quickly obtain the graph of the I-V set. Figure 2C shows superimposed I-V relationships for I_Ca,L and I_Ca,T and indicates the characteristic differences in amplitudes and voltage-dependence for those two channels. This plot can be either directly printed or saved as an ASCII file for further analysis or presentation. For the normal rabbit ventricular myocyte, the maximum T-type Ca channel conductance is set to zero, since no I_Ca,T is seen in these cells. However, the option is there to include I_Ca,T, if it is observed under other conditions.

View larger version (90K): [in this window] [in a new window]   Fig. 2.   Ca current in voltage clamp. A: schematic representation of the WAVEFORM screen used to control the protocol to generate current-voltage (I-V) data. The user inputs the values for holding potential, "step to" voltage, duration of pulse, voltage increments (Delta V), and the number of iterations. The screens shown here (and in Figs. 3 and 4) are simplified versions of the actual computer screen displays. For example, the "knobs" for adjusting parameters on the actual screen show numbers and units, and the selected value is also displayed in a box below the knob. The values also can be changed by either typing in values or nudging a cursor. B: ICa,L traces obtained in the simulation. Conductances and affinity constant (KmCa) values can be altered by typing the new values in the respective fields (top left). The cursor allows the user to choose a particular current trace and observe the corresponding values in boxes (bottom left). One can also switch protocol parameters by using the controls (bottom), without returning to the protocol screen. C: I-V screen showing superimposed ICa,L and ICa,T I-V relationships.

View larger version (86K): [in this window] [in a new window]   Fig. 3.   Availability and recovery from inactivation. A: INa availability traces for different holding membrane potentials (Em). The PLOT command (right) generates the inactivation curve (C). B: recovery from INa inactivation traces. Clicking the PLOT (right) command generates the recovery from inactivation curve (D). All graphs can be either saved or printed directly.

Current clamp and AP simulations. In current-clamp mode, there are three options: single pulse, double pulse, and run continuously. In the single pulse mode, an AP is generated by applying a single current pulse that can be adjusted by the user (e.g., to study threshold). The currents underlying the AP are shown in four consecutives screens (Fig. 4). The first screen is a general one (Fig. 4A) that exhibits AP, Ca transient, I_Ca,L, I_Na, Na-K-ATPase current (I_NaK), and I_NaCa. A second screen (Fig. 4B) shows all of the K currents included in the model (I_to, I_K1, I_Kr, I_Ks, and I_Kp). The third screen (Fig. 4C) portrays the Ca-related currents: I_Ca,L and I_Ca,T, background Ca current (I_Cab), I_Cl(Ca), and the sarcolemmal Ca-pump current. Finally, a fourth screen (Fig. 4D) illustrates the amount of Ca that has been transported across the membrane: the integral of Ca that entered through I_Ca,L, I_Cab, and I_NaCa, the amount of Ca extruded by the sarcolemmal Ca pump and I_NaCa, and also the net or total Ca flux. This value helps to show when Ca is being accumulated into the cell (total >0) or when the cell has been depleted of Ca (total <0). Figure 4D also shows that the total Ca that enters the cell is mainly due to I_Ca,L and that the principal Ca extrusion mechanism is the Na/Ca exchange. In any of these four screens, each trace can be toggled on or off to focus on a particular aspect. Transition between these screens is accomplished by clicking the arrows on either side of the indicator bar. A particular trace can be chosen by a cursor, and its value is shown along with the appropriate units. The chosen traces, with their corresponding labels and scales, can be saved as an ASCII file. Figure 5 shows traces that have been exported and plotted using Prism 3.0 software (GraphPad). Figure 5A shows the AP and [Ca]_i. Figure 5B shows I_Na with an inset to illustrate the temporal relationship between E_m, I_Na, and I_Ca,L during the first 10 ms of the AP. Figure 5C displays superimposed traces of I_Ca,L, I_Ca,T, I_NaK, and I_NaCa, a combination that is not available in the four screens of this simulation. Finally, the five different K currents are presented in Fig. 5D with an inset of their behavior near the rapid upstroke of the AP. The single-pulse current-clamp mode also allows one to trigger SR Ca release directly at various times after the AP, thereby simulating spontaneous diastolic SR Ca release (or a caffeine-induced Ca transient). The second option (two pulses) follows the same design principles and is useful to study refractoriness. The third option (run continuously) presents the results as in a chart recorder, allowing the user to make on-line modifications of the ionic concentration to visualize the effects of some drugs.

View larger version (76K): [in this window] [in a new window]   Fig. 4.   Current clamp simulations: single pulse. A: simplified general screen of a default action potential (AP) simulation. This screen shows AP, intracellular Ca concentration ([Ca]i), ICa, INa, INaK, and INaCa. Each of these traces can be toggled "on" or "off" by clicking the buttons below the display if the user wants to focus on a particular trace(s). B: K currents during the generation of an AP. C: Ca-related currents [ICa,L, ICa,T, ICab, ICl(Ca), and the sarcolemmal Ca-pump current (SLCa)]. D: integrated amount of Ca transported by the Ca channels (L-type and background), Na/Ca exchange, and sarcolemmal Ca-ATPase. Transition between the different screens is achieved by pressing on the arrows located at the sides of the bar. Cursors also are on the screen (not shown here) that allow examination of values (with units) at any time point on any trace. The time scale also can be altered by overtyping with a new value (e.g., to expand the early part of the AP). All traces can be printed or saved as ASCII files.

View larger version (20K): [in this window] [in a new window]   Fig. 5.   Example of postprocessed AP traces. Different records were saved as ASCII files and plotted on selected scales. A: superimposed AP and [Ca]i. B: INa plotted alone and on an expanded time scale (inset) to show the temporal relationship of Em, INa, and ICa,L in the first 10 ms. C: AP, INaK (INaK-ATPase), ICa,L, and INaCa (INaCaX). This combination of traces is not present as a default condition but can be readily achieved this way. D: K currents, with an inset showing details at the onset of the AP.

Heart failure rabbit: a case study. Current densities or maximal rate of Ca uptake (V_max) values can readily be adjusted, and we took advantage of this feature to simulate electrophysiological and Ca transport changes that we have measured in HF, which was induced by combined aortic insufficiency and aortic stenosis (21, 22). Ventricular myocytes from these HF rabbits exhibit 100% increase in I_NaCa, 24% reduction in SR Ca-ATPase function, 36% reduction in I_to, and 49% reduction in I_K1. Maximum conductance or V_max values were changed, and this new HF parameter set can be saved and recalled at any time.

View larger version (23K): [in this window] [in a new window]   Fig. 6.   Experimental data (left) and simulated traces (right) of control (Ctl) and heart failure (HF) myocytes. Default values for Na/Ca exchanger, IK1, Ito, and SR Ca-pump rate were replaced with parameters measured in HF myocytes (see text). A: Ca transients. B: APs. C: effect of frequency on the AP duration (APD75). Experimental data are from Ref. 22.

View larger version (27K): [in this window] [in a new window]   Fig. 7.   Na/Ca exchange data (left) and simulations (right). A: INaCa measured in control and HF myocytes (data from Ref. 21). B: caffeine (Caff)-induced Ca transient and INaCa (data from Ref. 22). C: dynamic relation of INaCa with Ca transient from B (data from Ref. 22). Experimental data were recorded at 37°C in A and at 23°C in B and C. Simulations with LabHEART were all at 37°C.

View larger version (25K): [in this window] [in a new window]   Fig. 8.   K current alterations in HF. A: current traces of the Ito for normal (top) and HF (bottom) myocytes. B: I-V relationship for Ito. C: I-V relationship for IK1. Experiments were conducted at 23°C and simulations at 37°C. Ito and IK1 amplitudes used in the model were a compromise between these data (extrapolated to 37°C) and measurements from other studies and models at 37°C (notably, Ito kinetics are faster and IK1 amplitude is larger). NCX, Na/Ca exchange. Experimental data are from Ref. 22.

View larger version (24K): [in this window] [in a new window]   Fig. 9.   In the current-clamp single-pulse mode, one can simulate spontaneous SR Ca release (as in a caffeine application). The amount of Ca released into the myoplasm is extruded by INaCa, producing a depolarizing current. A: for larger Ca releases, this current produces increasing depolarizations (eventually triggering an AP). B: we measured the delayed afterdepolarizations (DADs) for given amounts of Ca release for control and HF conditions. The amount of Ca needed to trigger a given DAD or an AP is significantly lower in the HF myocytes than in control (800 nM control, 380 nM HF). Experimental data are from Ref. 22.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The three goals achieved in this study were to 1) create a new type of cardiac electrophysiology/Ca model that emphasizes the user interface, 2) create a new model that predicts the electrophysiological and Ca transport properties of rabbit ventricular myocytes, and 3) use this model to simulate and analyze altered function in an experimental model of HF in rabbits.

Computer models of this sort have two major aspects: elaboration and implementation. Elaboration of the equations that are used to describe the biological behavior of the channels and how they interact has been the focal point of most current cardiac AP models. Several excellent models have been developed for guinea pig, canine, and human ventricle and rabbit atrium (8, 11-13, 18, 23, 34, 35). Indeed, this is the context in which important mechanistic innovations in such models has almost invariably come. However, there is no currently available model for rabbit ventricular myocyte, a tissue that is widely used in many types of experimental studies. There are major differences in Ca transport, ionic currents, and APs among common species and cell types (2). In particular, rabbit ventricle has a different balance of K currents and AP shape (compared to rat, dog, human ventricle, and even rabbit atrium). The competition between the SR Ca-ATPase and Na/Ca exchange during [Ca]_i decline also differs dramatically among these tissues. Thus it is important to have a computer model that is tailored to these specific properties.

The second aspect of computer models, implementation, refers to the computer program itself and, importantly, how the user interacts with the model. In the present study, we emphasize this aspect by modifying a widely utilized system of equations to simulate rabbit ventricular myocyte properties and also by creating a novel and highly user-friendly interface. LabHEART has several features that may allow it to have particularly broad utility. First, it is readily accessible. The program can be downloaded from our lab homepage (http://www.meddean.luc.edu/lumen/DeptWebs/physio/bers.html). Second, it runs well on a fairly basic personal computer. Some computer models for biological systems require more sophisticated computer resources that are not always readily available in the biology departments where many end users are located. Third, LabHEART is useful for students at many levels, including those with relatively limited background in electrophysiology or computer modeling. The help screens and intuitive layout of Lab-HEART encourage both exploration and learning. This will help students understand the principles and the dynamic interactions that occur among the systems considered. Fourth, LabHEART is valuable for the active scientist working in this field, where it may be particularly helpful in developing new experimental hypotheses or insights. Indeed, the user may freely adjust ionic conditions, pulse protocols, and some ion channel properties. Thus the experimentalist does not have to independently develop an integrative model to study the impact of more discretely measured electrophysiological changes. Fifth, LabHEART is relatively up to date with respect to ion currents and Ca transport properties.

Using this new program, we were able to both simulate and analyze the mechanisms underlying the generation of triggered arrhythmias in HF myocytes. Electrical reentry can contribute to ventricular tachycardia in many pathophysiological states, but three-dimensional mapping studies show that most fatal arrhythmias in HF initiate by nonreentrant mechanisms such as DADs (20). By altering the default values of the I_K1, I_to, I_NaCa, and the SR Ca-ATPase in the manner measured in voltage clamp and Ca transient studies (21,22), we could simulate the changes in AP and Ca transients. Furthermore, by adjusting these parameters individually in LabHEART (in a manner that cannot be done readily in experiments), we could analyze the likely quantitative contributions of different changes to the size of DADs for a given spontaneous SR Ca release (and the [Ca]_i threshold for triggering an AP). We found that the reduced I_K1 and enhanced I_NaCa contribute about equally to shifts in [Ca]_i dependence of DADs and AP threshold (25-32% shifts of threshold [Ca]_i). Moreover, these two effects seem to be approximately additive, because when both changes are instituted together, the threshold [Ca]_i is reduced by 52% (and this matches the experimental observations where the two contributions cannot be readily differentiated) (22). This is only one example of the kind of additional analytical insight that can be gleaned from a computer model of this type.

It should also be acknowledged that this is an ongoing process and that LabHEART 4.7 as described here is a first major step on this path. We are actively developing new scientific expressions for modeling the ventricular AP and Ca transients (e.g., more appropriate equations for SR Ca transport and Na/Ca exchange) (28, 29, 33). Several ionic currents also need additional refinement. For example, there are at least two molecular contributors to I_to (15) that have different kinetics. Altered functional frameworks also will be necessary. For instance, it is clear that local [Ca]_i near the sarcolemma differs from the bulk [Ca]_i and possibly also from [Ca]_i in the cleft between junctional SR and the sarcolemma (32). We have begun preliminary incorporation of some of these novel aspects into the elaboration phase (27) and plan to eventually transport that much more complex model into the user-friendly LabHEART format. A long-term challenge is to allow the LabHEART user to readily simulate different cell types (from stored parameter sets) and also to be able to easily change the basic equations used for different channels, transporters, or buffers.