SPECIAL COMMUNICATION
LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport

José L. Puglisi1,2 and Donald M. Bers2

1 Department of Physiology and Biophysics, University of Illinois at Chicago, and 2 Department of Physiology, Loyola University Chicago, Stritch School of Medicine, Maywood, Illinois 60153


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES

An interactive computer program, LabHEART, was developed to simulate the action potential (AP), ionic currents, and Ca handling mechanisms in a rabbit ventricular myocyte. User-oriented, its design allows switching between voltage and current clamp and easy on-line manipulation of key parameters to change the original formulation. The model reproduces normal rabbit ventricular myocyte currents, Ca transients, and APs. We also changed parameters to simulate data from heart failure (HF) myocytes, including reduced transient outward (Ito) and inward rectifying K currents (IK1), enhanced Na/Ca exchange expression, and reduced sarcoplasmic reticulum Ca-ATPase function, but unaltered Ca current density. These changes caused reduced Ca transient amplitude and increased AP duration (especially at lower frequency) as observed experimentally. The model shows that the increased Na/Ca exchange current (INaCa) in HF lowers the intracellular [Ca] threshold for a triggered AP from 800 to 540 nM. Similarly, the decrease in IK1 reduces the threshold to 600 nM. Changes in Ito have no effect. Combining enhanced Na/Ca exchange with reduced IK1 (as in HF) lowers the threshold to trigger an AP to 380 nM. These changes reproduce experimental results in HF, where the contributions of different factors are not readily distinguishable. We conclude that the triggered APs that contribute to nonreentrant ventricular tachycardia in HF are due approximately equally (and nearly additively) to alterations in INaCa and IK1. A free copy of this software can be obtained at http://www.meddean.luc.edu/lumen/DeptWebs/physio/bers.html.

heart failure; excitation-contraction coupling; Na/Ca exchange; mathematical model


    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 (Em) modulates Ca transport, and the Ca transient also can feedback to alter Em. 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 (Ito) and Ca-activated Cl current [ICl(Ca)], as well as modification of the kinetics of T-type Ca channel (ICa,T), the rapid component of the delayed rectifier K current (IKr), and rescaling of several conductances to better match results in rabbit ventricle (see Table 1).

                              
View this table:
[in this window]
[in a new window]
 
Table 1.   Ionic currents and Ca transport mechanisms

Transient outward K current. Ito has been reported in rabbit ventricular myocytes (6, 9). It is also known as Ito1 to differentiate it from the Ca-activated Cl current [known as Ito2 or ICl(Ca)] that is activated at the same time during the AP (37). Ito can contribute to ventricular repolarization. We used the Ito formulation of Winslow et al. (34) for this current
I<SUB>to</SUB><IT>=G</IT><SUB>to</SUB><IT>×X</IT><SUB>to</SUB><IT>×Y</IT><SUB>to</SUB><IT>×</IT>(<IT>V−E</IT><SUB>K</SUB>) (1a)

&agr;<SUB>Xto</SUB><IT>=</IT>0.04561 exp(0.03577<IT>×V</IT>) (1b)

&bgr;<SUB>Xto</SUB><IT>=</IT>0.0989 exp(−0.06237<IT>×V</IT>) (1c)

&agr;<SUB>Yto</SUB><IT>=</IT>0.005415 exp<IT>−</IT>[(<IT>V+</IT>33.5)<IT>/</IT>5]<IT>/</IT> (1d)

{1<IT>+</IT>0.051335 exp<IT>−</IT>[(<IT>V+</IT>33.5)<IT>/</IT>5]}

&bgr;<SUB>Yto</SUB><IT>=</IT>0.005415 exp[(<IT>V+</IT>33.5)<IT>/</IT>5]<IT>/</IT> (1e)

{1<IT>+</IT>0.051335 exp[(<IT>V+</IT>33.5)<IT>/</IT>5]}
where Gto is the channel conductance, Xto and Yto are activation and inactivation parameters, respectively, and EK is the reversal potential for K.

Ca-activated Cl current. ICl(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). ICl(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 (ICa). We modeled this current as
I<SUB>Cl(Ca)</SUB><IT>=G</IT><SUB>Cl</SUB><IT>×</IT>(<IT>V−E</IT><SUB>Cl</SUB>)<IT>/</IT>(1<IT>+K</IT><SUB>mCa</SUB>/[Ca]<SUB>i</SUB>) (2)
where GCl is the Cl conductance set to 10 mS/µF, ECl is the reversal potential, and Ca dependence is incorporated as a Michaelis-Menten factor with KmCa = 0.10 µM. These values were chosen to fit experimental records obtained by Puglisi et al. (25).

T-type Ca current. Although ICa,T is not generally detectable in rabbit ventricular myocytes, we have included it to make a more complete theoretical model. The ICa,T equations are
I<SUB>Ca,T</SUB><IT>=G</IT><SUB>Ca,T</SUB><IT>×b×g×</IT>(<IT>V−E</IT><SUB>Ca</SUB>) (3a)
where ECa is the Nernst potential for Ca and the gating parameters are as follows
b<SUB>∞</SUB>=1/{1+exp[−(<IT>V+</IT>48)<IT>/</IT>6.1]} (3b)

&tgr;<SUB>b</SUB><IT>=</IT>0.1<IT>+</IT>(5.4<IT>/</IT>{1<IT>+</IT>exp[(<IT>V+</IT>100)<IT>/</IT>33]}) (3c)

g<SUB>∞</SUB>=1/{1+exp[(<IT>V+</IT>66)<IT>/</IT>6.6)]} (3d)

&tgr;<SUB>g</SUB><IT>=</IT>8<IT>+</IT>(32<IT>/</IT>{1<IT>+</IT>exp[(<IT>V+</IT>65)<IT>/</IT>5)]} (3e)
These equations are slightly different from those used by Zeng et al. (35), but they reproduce more accurately the I-V relationship for ICa,T.

The kinetics of IKr were modified as follows
I<SUB>Kr</SUB><IT>=G</IT><SUB>Kr</SUB><IT>×X×R×</IT>(<IT>V−E</IT><SUB>Kr</SUB>) (4a)

G<SUB>Kr</SUB><IT>=</IT>0.02612<IT>×</IT>([K]<SUB>o</SUB>/5.4)<SUP>0.5</SUP> (4b)

X<SUB>∞</SUB>=1/{1+exp[−(<IT>V+</IT>50)<IT>/</IT>7.5]} (4c)

R=1/{1+exp[(<IT>V+</IT>33)<IT>/</IT>22.4]} (4d)

&tgr;<SUB>X</SUB><IT>=</IT>1<IT>/</IT>(0.00138<IT>×</IT>(<IT>V+</IT>7)<IT>/</IT>{1<IT>−</IT>exp[−0.123<IT>×</IT>(<IT>V+</IT>7)]}<IT>+</IT>0.00061<IT>×</IT>(<IT>V+</IT>10)<IT>/</IT>(exp{0.145<IT>×</IT>[0.145<IT>×</IT>(<IT>V+</IT>10)]<IT>−</IT>1} (4e)
The rest of the parameters follow the same formulation as in Luo and Rudy, with some rescaling to better fit the rabbit myocyte characteristics (see Table 1).

The general scheme of LabHEART consists of a main menu (Fig. 1) from which the user can choose different tasks to perform. The main menu screen is a diagram with the major mechanisms involved in ECC, a series of icons (left), and a group of command buttons (right). The self-explanatory icons allow the user to alter the ionic concentration (top left), choose a voltage or current protocol (top right), or examine a particular mechanism, namely, SR, Ca channels, Na/Ca exchanger, sarcolemmal Ca-ATPase, Na and K channels, Na-K-ATPase, and ICl(Ca). The command buttons allow the user to access help screens, alter the cytosolic buffers, run an AP or voltage-clamp simulation, save a particular set of conditions, or exit the program. During the generation of an AP, it is also possible to simulate SR Ca release induced by caffeine application and the effects of some drugs [e.g., nifedipine, almokalant, TTX, exchange inhibitory peptide, and 4-aminopyridine to simulate variable block of ICa, IKr, Na current (INa), Na/Ca exchange current (INaCa), and Ito]. One can choose either current-clamp protocols to simulate APs or voltage-clamp protocols to study individual current properties.


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.

In every voltage-clamp simulation, typical plots such as I-V relationship or inactivation curves are built-in features. Also, bearing the novice user in mind, there are help options in each screen that explain possible choices and include a brief description of the mechanism under simulation or exploration. The default ionic concentrations were set as follows (in mM): [Na]o = 140, [Na]i = 10, [K]o = 5.4, [K]i = 145, [Ca]o =1.8, and resting [Ca]i = 120 nM, where o indicates extracellular and i indicates intracellular concentration. Currents are expressed in amperes per farad and voltages in millivolts.


    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 (ICa,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 Km 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 ICa,L and ICa,T or to quickly obtain the graph of the I-V set. Figure 2C shows superimposed I-V relationships for ICa,L and ICa,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 ICa,T is seen in these cells. However, the option is there to include ICa,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.

The second protocol under voltage clamp is the steady-state inactivation, or availability of the channel. Figure 3, A and C, shows this simulation for INa. Once the INa traces are obtained (Fig. 3A), the normalized peak amplitude of the current is plotted against the holding potential (Fig. 3C).


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.

Another attribute of some ionic channels is the recovery from inactivation (assessed by the third voltage-clamp protocol, Fig. 3, B and D). The standard method to evaluate recovery is to use a first pulse to produce inactivation and a second pulse to assess the availability of the current, after rests of different durations and holding Em. The time-dependent increase in test pulse INa shows how the channel recovers from inactivation. The longer the interval between the pulses and the more negative the holding Em, the faster the channel recovers. Figure 3B displays the INa traces, and Fig. 3D shows the graph of recovery from inactivation. Like the I-V plot, this graph can be either directly printed or saved as an ASCII file for further analysis.

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, ICa,L, INa, Na-K-ATPase current (INaK), and INaCa. A second screen (Fig. 4B) shows all of the K currents included in the model (Ito, IK1, IKr, IKs, and IKp). The third screen (Fig. 4C) portrays the Ca-related currents: ICa,L and ICa,T, background Ca current (ICab), ICl(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 ICa,L, ICab, and INaCa, the amount of Ca extruded by the sarcolemmal Ca pump and INaCa, 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 ICa,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 INa with an inset to illustrate the temporal relationship between Em, INa, and ICa,L during the first 10 ms of the AP. Figure 5C displays superimposed traces of ICa,L, ICa,T, INaK, and INaCa, 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 (Vmax) 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 INaCa, 24% reduction in SR Ca-ATPase function, 36% reduction in Ito, and 49% reduction in IK1. Maximum conductance or Vmax values were changed, and this new HF parameter set can be saved and recalled at any time.

Figure 6, A and B, shows how the steady-state Ca transient and AP are modified in HF compared with control. The mean Ca transient amplitude was reduced by 40% experimentally (Fig. 6, left) and slightly less than this in the simulation (Fig. 6, right). The prolonged AP duration in HF (Fig. 6C) also was well reproduced by the model, as was the shortening with frequency and convergence of AP duration at higher frequency.


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.

Figure 7A shows the Em dependence of INaCa in HF and control myocytes. Both inward and outward current are increased twofold in HF (21). The apparent reversal potential is unchanged and close to the predicted value based on the pipette and extracellular solutions. Figure 7B illustrates Ca transients and INaCa induced by a rapid caffeine application (31). In HF myocytes, a smaller Ca transient is accompanied by a higher INaCa. Figure 7C displays the Ca dependence of inward INaCa on [Ca]i. In HF, this current is much larger, indicating that INaCa is functionally upregulated during dynamic Ca transient. The enhanced inward current means that Na/Ca exchange is extruding more Ca in direct competition with the SR Ca pump. This causes a lower SR Ca content that contributes to the smaller Ca transient. The experimental data in Fig. 7, B and C, were acquired at 23°C (rather than at 37°C as in the model data and all of Fig. 7A). This may largely account for the larger INaCa values in the model and the more rapid decline of [Ca]i and inward INaCa in the model (at 37°C) vs. the data at 23°C. Other factors that could impact on the precision of INaCa predictions with the model are that 1) LabHEART 4.7 uses a common cytosolic Ca pool, whereas submembrane [Ca]i, in fact, may be higher than average [Ca]i during the SR Ca release (32), and 2) the expression used for Na/Ca exchange in the model may not have the correct dependence on [Ca]i (33). The higher INaCa level in HF implies that for any given spontaneous SR Ca release [e.g., during a delayed afterdepolarization (DAD)], a greater inward INaCa is expected. This could increase the likelihood that a DAD triggers an AP.


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.

K currents also are altered in HF as shown in Fig. 8. Ito is downregulated by 49% (Fig. 8, A and B). The faster inactivation kinetics in the simulation apparently result because the experimental data was recorded at 23°C, rather than at 37°C for the model. The inward rectifier current (IK1) is also decreased (49%), as plotted in Fig. 8C. Again, the experimental data are at 23°C vs. the model at 37°C. Because experimental data have not always been recorded at 37°C, it would be convenient to be able to alter temperature in the model. Although we hope to include this option in future versions of LabHEART, this would be a major challenge, because there would be so many required parameters that might have different temperature dependence. Because IK1 is important in stabilizing the resting Em, the decreased IK1 may facilitate depolarization during the initiation of triggered arrhythmias.


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.

To further examine the role of altered INaCa and IK1 in triggered arrhythmias like DADs, we simulated DADs in a manner analogous to our experimental approach (Fig. 9). Pogwizd et al. (22) applied caffeine pulses at different SR Ca loads to determine the threshold amount of [Ca]i rise (Delta [Ca]i) required to produce a given depolarization (Delta Em) or trigger an AP. Using different frequencies to alter the SR Ca content, they determined that there was a greater depolarization for any give Delta [Ca]i in HF, and the threshold Delta [Ca]i to produce an AP was reduced by ~50% (515 ± 59 nM control, 280 ± 30 nM HF; Fig. 9B, left). In our model (Fig. 9B, right), caffeine application was simulated by opening the release channel and setting the Vmax for SR Ca uptake at zero. Moreover, because we can control the amount of SR Ca release directly, the model does not require the different conditioning pulses. Decreasing IK1 by 49% reduced the Delta [Ca]i threshold by 25% [from 800 nM (control) to 600 nM]. When the Na/Ca exchange (NCX) was increased by 100%, the threshold value was reduced by 32% (540 nM). If these two changes are combined (as in HF), the Delta [Ca]i threshold is reduced by 52% with respect to control (to 380 nM). These values are quite similar to the experimental observations in HF vs. control. The simulation also allows us to infer that the two key effects (increased NCX and reduced IK1) contribute about equally and additively to the increased propensity for triggered arrhythmias in HF (24). The reduction of Ito or SR Ca-ATPase seen in HF did not change DADs appreciably (not shown).


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 IK1, Ito, INaCa, 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 Delta [Ca]i threshold for triggering an AP). We found that the reduced IK1 and enhanced INaCa contribute about equally to shifts in [Ca]i dependence of DADs and AP threshold (25-32% shifts of threshold Delta [Ca]i). Moreover, these two effects seem to be approximately additive, because when both changes are instituted together, the threshold Delta [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 Ito (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.


    ACKNOWLEDGEMENTS

We are grateful to Dr. T. R. Shannon for valuable comments on the manuscript.


    FOOTNOTES

This work was supported in part by American Heart Association Fellowship 9920452Z (to J. L. Puglisi), National Heart, Lung, and Blood Institute Grant HL-30077 (to D. M. Bers), and the National Space Biomedical Research Institute (to D. M. Bers).

Address for reprint requests and other correspondence: D. M. Bers, Dept. of Physiology, Loyola Univ. Chicago, Stritch School of Medicine, 2160 South First Ave., Maywood, IL 60153 (E-mail dbers{at}lumc.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 27 April 2001; accepted in final form 20 August 2001.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES

1.   Beeler, GW, and Reuter H. Reconstruction of the action potential of ventricular myocardial fibers. J Physiol 268: 177-210, 1977[ISI][Medline].

2.   Bers, DM. Excitation-Contraction Coupling and Cardiac Contractile Force (2nd ed.). Dordrecht, The Netherlands: Kluwer Academic, 2001, p. 427.

3.   Carmeliet, E. Cardiac ionic currents and acute ischemia: From channels to arrhythmias. Physiol Rev 79: 917-1017, 1999[Abstract/Free Full Text].

4.   Di Francesco, D, and Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil Trans R Soc Lond 307: 353-398, 1985[ISI][Medline].

5.   Hilgemann, DW, and Noble D. Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms. Phil Trans R Soc Lond 230: 163-205, 1987.

6.   Hiraoka, M, and Kawano S. Calcium-sensitive and insensitive transient outward current in rabbit ventricular myocytes. J Physiol 410: 187-212, 1989[Abstract].

7.   Hodgkin, L, and Huxley AF. A quantitative description of membrane currents and its application to conduction and excitation in nerve. J Physiol 117: 500-544, 1952[ISI].

8.   Jafri, MS, Rice JJ, and Winslow RL. Cardiac Ca dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74: 1149-1168, 1998[Abstract/Free Full Text].

9.   Kawano, S, and Hiraoka M. Transient outward currents and action potentials alterations in rabbit ventricular myocytes. J Mol Cell Cardiol 23: 681-693, 1991[ISI][Medline].

10.   Kawano, S, Hirayama Y, and Hiraoka M. Activation mechanism of Ca sensitive outward current in rabbit ventricular myocytes. J Physiol 486: 593-604, 1995[Abstract].

11.   Lindblad, DS, Murphy CR, Clark JW, and Giles WR. A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am J Physiol Heart Circ Physiol 271: H1666-H1696, 1996[Abstract/Free Full Text].

12.   Luo, CH, and Rudy Y. A model of the ventricular cardiac action potential, depolarization, repolarization and their interaction. Circ Res 68: 1501-1526, 1991[Abstract].

13.   Luo, CH, and Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res 74: 1071-1096, 1994[Abstract].

14.   McAllister, RE, Noble D, and Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol 251: 1-59, 1975[ISI][Medline].

15.   Nerbonne, JM. Molecular basis of functional voltage-gated K+ channel diversity in the mammalian myocardium. J Physiol 525: 285-298, 2000[Abstract/Free Full Text].

16.   Noble, D. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potential. J Physiol 160: 317-352, 1962[ISI].

17.   Noble, D, and Tsien RW. The kinetics and rectifier properties of the slow potassium current in cardiac Purkinje fibers. J Physiol 195: 185-214, 1968[ISI][Medline].

18.   Nordin, C. Computer model of membrane current and intracellular Ca flux in the isolated guinea pig ventricular myocytes. Am J Physiol Heart Circ Physiol 265: H2117-H2136, 1993[Abstract/Free Full Text].

19.   Nygren, A, Fiset C, Firek L, Clark JW, Lindblad DS, Clark RB, and Giles WR. Mathematical model of an adult human atrial cell. The role of K currents in repolarization. Circ Res 82: 63-81, 1998[Abstract/Free Full Text].

20.   Pogwizd, SM, Chung MK, and Cain ME. Termination of ventricular tachycardia in the human heart: insights from three-dimensional mapping of nonsustained ventricular tachycardias. Circulation 95: 2517-2527, 1997[Abstract/Free Full Text].

21.   Pogwizd, SM, Qi M, Yuan W, Samarel AM, and Bers DM. Upregulation of Na/Ca exchanger expression and function in an arrhythmogenic rabbit model of heart failure. Circ Res 85: 1009-1019, 1999[Abstract/Free Full Text].

22.   Pogwizd, SM, Schlotthauer K, Li L, Yuan W, and Bers DM. Arrhythmogenesis and contractile dysfunction in heart failure: roles of sodium-calcium exchange, inward rectifier potassium current and beta -adrenergic responsiveness. Circ Res 88: 1159-1167, 2001[Abstract/Free Full Text].

23.   Priebe, L, and Beuckelman DJ. Simulation study of cellular electric properties in heart failure. Circ Res 82: 1206-1223, 1998[Abstract/Free Full Text].

24.   Puglisi, JL, Pogwizd SM, Yuan W, and Bers DM. Increased Na/Ca exchange and reduced IK1 facilitate triggered action potentials in a rabbit model of heart failure (Abstract). Biophys J 78: 55A, 2000[ISI].

25.   Puglisi, JL, Yuan W, Bassani JWM, and Bers DM. Ca influx through Ca channels in rabbit ventricular myocytes during action potential clamp. Circ Res 85: e7-e16, 1999[Abstract/Free Full Text].

26.   Rush, S, and Larsen H. A practical algorithm for solving dynamic membrane equations. IEEE Trans Biomed Eng 25: 389-392, 1978[ISI][Medline].

27.   Shannon, TR, and Bers DM. A mathematical model describes the SR load-dependence of Ca dynamics in cardiac myocytes (Abstract). Biophys J 80: 594A, 2001[ISI].

28.   Shannon, TR, Ginsburg KS, and Bers DM. Reverse mode of the sarcoplasmic reticulum calcium pump and load-dependent cytosolic calcium decline in voltage-clamped cardiac ventricular myocytes. Biophys J 78: 322-333, 2000[Abstract/Free Full Text].

29.   Shannon, TR, Ginsburg KS, and Bers DM. Potentiation of fractional sarcoplasmic reticulum calcium release by total and free intra-sarcoplasmic reticulum calcium concentration. Biophys J 78: 334-343, 2000[Abstract/Free Full Text].

30.   Sipido, KR, Callewaert G, and Carmeliet E. [Ca]i transients and [Ca]i-dependent chloride current in single Purkinje cells from rabbit heart. J Physiol 468: 641-667, 1993[Abstract].

31.   Trafford, AW, Diaz ME, and Eisner DA. A novel, rapid and reversible method to measure Ca buffering and time course of total sarcoplasmic reticulum Ca content in cardiac ventricular myocytes. Pflügers Arch 437: 501-503, 1999[ISI][Medline].

32.   Trafford, AW, Diaz ME, O'Neill SC, and Eisner DA. Comparison of subsarcolemmal and bulk calcium concentration during spontaneous calcium release in rat ventricular myocytes. J Physiol 488: 577-586, 1995[Abstract].

33.   Weber, CR, Ginsburg KS, Philipson KD, Shannon TR, and Bers DM. Allosteric regulation of Na/Ca exchange current by cytosolic Ca in intact cardiac myocytes. J Gen Physiol 117: 119-131, 2001[Abstract/Free Full Text].

34.   Winslow, RL, Rice J, Jafri S, Marban E, and O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure. II. Model studies. Circ Res 84: 571-586, 1999[Abstract/Free Full Text].

35.   Zeng, J, Laurita R, Rosenbaum DS, and Rudy Y. Two components of the delayed rectifier K currents in ventricular myocytes of the guinea pig type: theoretical formulation and their role in repolarization. Circ Res 77: 140-152, 1995[Abstract/Free Full Text].

36.   Zygmunt, AC, and Gibbons WR. Calcium-activated chloride current in rabbit ventricular myocytes. Circ Res 68: 424-437, 1991[Abstract].

37.   Zygmunt, AC, and Gibbons WR. Properties of the calcium-activated chloride current in heart. J Gen Physiol 99: 391-414, 1992[Abstract].


Am J Physiol Cell Physiol 281(6):C2049-C2060
0363-6143/01 $5.00 Copyright © 2001 the American Physiological Society