Skip Navigation

Cardiovascular Research 1997 35(2):256-272; doi:10.1016/S0008-6363(97)00093-X
© 1997 by European Society of Cardiology
This Article
Right arrow Abstract Freely available
Right arrow FREE Full Text (PDF) Freely available
Right arrow E-letters: Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when E-letters are posted
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Disclaimer
Google Scholar
Right arrow Articles by Shaw, R. M.
Right arrow Articles by Rudy, Y.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Shaw, R. M.
Right arrow Articles by Rudy, Y.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 1997, European Society of Cardiology

Electrophysiologic effects of acute myocardial ischemia: a theoretical study of altered cell excitability and action potential duration1

Robin M. Shaw and Yoram Rudy*

Cardiac Bioelectricity Research and Training Center, Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106-7207, USA

* Corresponding author. Tel. +1 216 368-4051; Fax +1 216 368-4969.

Received 13 August 1996; accepted 12 March 1997


   Abstract
Top
 Abstract
1 Introduction
 2 Methods
 3 Results
 4 Discussion
 References
 
Objective: To study the ionic mechanisms of electrophysiologic changes in cell excitability and action potential duration during the acute phase of myocardial ischemia. Methods: Using an ionic-based theoretical model of the cardiac ventricular cell, the dynamic LRd model, we have simulated the three major component conditions of acute ischemia (elevated [K]o, acidosis and anoxia) at the level of individual ionic currents and ionic concentrations. The conditions were applied individually and in combination to identify ionic mechanisms responsible for reduced excitability at rest potentials, delayed recovery of excitability, and shortened action potential duration. Results: Increased extracellular potassium ([K]o) had the major effect on cell excitability by depolarizing resting membrane potential (Vrest), causing reduction in sodium channel availability. Acidosis caused a [K]o-independent reduction in maximum upstroke velocity, (dVm/dt)max. A transition from sodium-current dominated to calcium-current dominated upstroke occurred, and calcium current alone was able to sustain the upstroke, but only after sodium channels were almost completely (97%) inactivated. Acidic conditions prevented the transition to calcium dominated upstroke by acidic reduction of both sodium and calcium currents. Anoxia, simulated by lowering [ATP]i and activating the ATP-dependent potassium current, IK(ATP), was the only process that could decrease action potential duration by more than 50% and reproduce AP shape changes that are observed experimentally. Acidic or anoxic depression of the L-type calcium current could not reproduce the observed action potential shape changes and APD shortening. Delayed recovery of excitability, known as ‘post-repolarization refractoriness’, was determined by the voltage-dependent kinetics of sodium channel recovery; Vrest depolarization caused by elevated [K]o increased the time constant of (dVm/dt)max recovery from {tau} = 10.3 ms at [K]o=4.5 mM to {tau} = 81.4 ms at [K]o=12 mM, reflecting major slowing of sodium-channel recovery. Anoxia and acidosis had little affect on {tau}. Conclusions: The major conditions of acute ischemia, namely elevated [K]o, acidosis and anoxia, applied at the ionic channel level are sufficient to simulate the major electrical changes associated with ischemia. Depression of membrane excitability and delayed recovery of excitability in the single, unloaded cell are caused by elevated [K]o with additional excitability depression by acidosis. Major changes in action potential duration and shape can only be accounted for by anoxia-dependent opening of IK(ATP).

KEYWORDS Myocardial ischemia; Hyperkalemia; Acidosis; Anoxia; Membrane excitability; Action potential duration; Potassium channel; ATP sensitive; Computer model


   1 Introduction
Top
 Abstract
 1 Introduction
2 Methods
 3 Results
 4 Discussion
 References
 
The major pathophysiological component conditions of acute myocardial ischemia are elevated extracellular potassium ([K]o), acidosis, and anoxia. These conditions cause the following electrical changes: reduction in membrane excitability, shortening of action potential duration (APD), and prolongation of recovery of excitability following an action potential [1–3]. Difficulties exist in determining the ionic mechanisms of the electrical changes, and the contribution of each pathophysiological condition to each electrical change. We have attempted to relate the electrical changes to the component conditions and to determine the ionic mechanisms, using a detailed theoretical model of acute myocardial ischemia. The model was developed by separately simulating the effects of each pathophysiological condition on individual ion-channel currents in a dynamic mathematical model of the cardiac ventricular action potential (the LRd model) [4–6]. A theoretical model allows pathophysiological conditions to be selectively evaluated so that mechanisms can be examined at the specific ionic current and channel level.

The broad experimental literature has generated extensive data on the ionic mechanisms associated with ischemic electrophysiologic changes. Membrane excitability and the action potential upstroke are typically determined by the fast sodium current (INa) [7]. In highly depressed ischemic tissue, calcium current (ICa(L)) plays a role in the upstroke [8, 9], and may even dominate action potential generation [10]. We are interested in the conditions that affect a transition from an INa-controlled upstroke to an ICa(L)-controlled upstroke.

Beyond the upstroke, APD is reduced by enhancement of the ATP-dependent potassium current (IK(ATP)) [11]. Other putative mechanisms of shortening include enhancement of outward potassium currents secondary to elevated [K]o and acidic and anoxic reduction of ICa(L). Following an action potential, membrane excitability normally recovers upon return to resting membrane potential, Vrest. Ischemic conditions can cause postrepolarization refractoriness [12, 13], extending membrane refractoriness hundreds of milliseconds beyond the return to Vrest. Elevated [K]o has been identified as the principal pathophysiological condition associated with postrepolarization refractoriness. Hypoxia at elevated [K]o has been associated with aggravating the postrepolarization refractoriness phenomenon [14], but the mechanism is not clear. In this study, we attempt to determine the relative contribution of each ischemic condition to APD shortening and delayed recovery of excitability.

Mapping experiments have shown that reentrant arrhythmias occur during the first 2–10 min of acute ischemia [2, 15, 16]. The studies contained here explore the mechanisms of altered excitability and action potential duration, which are important parameters in the initiation and sustenance of reentry. The mechanistic insights obtained, together with theoretical studies of action potential conduction [17]and the extensive information that is available from experimental observations, can provide a basis for a mechanistic approach to the treatment of fatal arrhythmias associated with acute myocardial ischemia.


   2 Methods
Top
 Abstract
 1 Introduction
 2 Methods
3 Results
 4 Discussion
 References
 
2.1 Ventricular cell model
The dynamic LRd model is a general mammalian ventricular cell model, based mainly on data taken from the guinea-pig. Included in the model are the membrane ionic channel currents, represented mathematically by a Hodgkin–Huxley type formalism, as well as ionic pumps and exchangers. In addition, processes that regulate ionic concentration changes, especially dynamic changes of intracellular calcium, are introduced. The model includes the recent development [6]to account for the two components of the delayed rectifier potassium current, IKr and IKs. A diagram of the cell model is provided in Fig. 1 where processes altered by the simulated ischemic conditions are identified by rectangular frames. Detailed tables of equations governing the model are provided in References [4–6].


Figure 1
View larger version (48K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 1 Schematic diagram of the LRd ventricular cell model. Processes affected by the simulated ischemic conditions are identified by rectangular frames. INa, fast sodium current; ICa(L), calcium current through L-type calcium channels; ICa(T), calcium current through T-type calcium channels; IKr, fast component of the delayed rectifier potassium current; IKs, slow component of the delayed rectifier potassium current; IK1, inward rectifier potassium current; IKp, plateau potassium current; IK(ATP), ATP sensitive potassium current; INaK, sodium–potassium pump current; INaCa, sodium–calcium exchange current; Ip(Ca), calcium pump in the sarcolemma; INa,b, sodium background current; ICa,b, calcium background current; Ins(Ca), nonspecific calcium-activated current; Iup, calcium uptake from the myoplasm to network sarcoplasmic reticulum (NSR); Irel, calcium release from junctional sarcoplasmic reticulum (JSR); Ileak, calcium leakage from NSR to myoplasm; Itr, calcium translocation from NSR to JSR. For details see references [4–6].

 
The ionic and metabolic conditions of ischemia have been approached as three different entities: (1) increase in extracellular potassium, (2) intracellular and extracellular acidosis, and (3) anoxia and metabolic blockade. The approach and theoretical implementation of each condition is presented in our study of conduction in an ischemic fiber [17], summarized in Appendix A, and discussed briefly below.

2.2 Increased extracellular potassium concentration, [K]o
Experimentally, [K]o undergoes a triphasic change (increase to about 10 mM, plateau, and secondary increase) during the first 15 min of acute ischemia [18, 19]. In our simulations we examine the range of extracellular potassium concentrations that occur during the triphasic change (4–20 mM). We assign a value of [K]o, analogous to the experimental technique of perfusing the tissue with a constant [K]o. Elevated [K]o directly enhances the conductances of IK1 (proportional to [K]o1/2) [4], IKr (proportional to [K]o1/2) [6], and IK(ATP) (proportional to [K]o0.24, see below). In addition, the potassium reversal potential (EK) is less negative and INaK is augmented in the direction of Na+ extrusion (an electrogenic outward current).

2.3 Acidosis
Intracellular and extracellular pH drop linearly with time during the first 10 min of acute ischemia, reaching at the 10 min mark a level about 1 pH unit below their normal value [2, 20]. Yatani et al. [21]observed in a study with rat ventricular cells that low extracellular pH both decreased maximum sodium current and shifted the sodium channel current-voltage curves to the right (i.e., to more positive potentials). In studies with guinea-pig ventricular tissue, Kagiyama et al. [22]found that a one unit drop in pH decreases the maximum conductance of INa by 25%, and shifts its voltage dependence by 3.4 mV (INa was assessed by recording maximum upstroke velocity of the action potential). Since the LRd mammalian ventricular cell model is based mostly on guinea-pig studies, we incorporated the specific effects of acidosis as noted by Kagiyama et al. [22].

Similar to the effect on the sodium current, acidosis reduces the magnitude of the L-type calcium current. Irisawa and Sato [23]found, for guinea-pig ventricular cells, a sigmoidal decrease in conductance (50% at pH=6.6) upon intracellular acidosis and no significant response to extracellular acidosis. They did not find a shift in the calcium current-voltage curves, and concluded that acidosis has no significant effect on calcium channel kinetics. We simulate the effects of acidosis on calcium current by reducing its maximum conductance, ICa(L), by up to 50%.

Independent of the above effects, acidosis also causes a 2–5 mV depolarization of resting membrane potential [1, 24], Vrest. The most likely cause of Vrest changes (independent of [K]o) is a decrease in intracellular potassium concentration, [K]i [18, 25]. Our acidic condition includes a decrease in [K]i from 144.8 to 125 mM, which results in a 3.8 mV depolarization of Vrest.

2.4 Anoxia
Many experimental protocols are conducted under conditions of hypoxia rather than complete anoxia. We model the consequences of abrupt and complete cessation of perfusion, and therefore refer to our simulation protocol as anoxia. The direct effects of anoxia are linked to its detrimental effect on cellular respiration and consequent decrease in ATP availability. In 1983, Noma reported a specific ATP-sensitive potassium channel (IK(ATP)) that is inactive in healthy ventricular tissue and is increasingly outward with decreasing levels of ATP [26]. IK(ATP) does not vary with time or voltage. Our formulation of IK(ATP), originally formulated in Reference [27], is


Formula

where FormulaK(ATP) is maximum channel conductance per unit capacitative membrane area (nS/µF) at 0 mM [ATP]i. Nichols et al. [28]determined FormulaK(ATP) of 195 nS/cell in whole cell guinea-pig recordings at [K]o=4.0 mM and physiologic concentrations of ADP, GDP and free Mg2+. The Nichols et al. [28]data adjusted to LRd cell size are used for single channel conductance estimates. In the LRd cell model which is 100 µm in length and 11 µm in diameter, FormulaK(ATP)=4 mS/µF. This conductance is on the same order as maximum sodium channel conductance, FormulaNa=16 mS/µF. PATP is the percentage availability of IK(ATP) channels at a given ATP concentration. PATP has sigmoidal dependence [28, 29]on [ATP]i and can be expressed with Hill-type formalism with a half-maximal saturation point (k1/2, mM), and Hill coefficient (H). Nichols et al. [28]determined k1/2=114 µM and H = 2. Metabolic factors present during acute ischemia decrease IK(ATP) sensitivity to [ATP]i-based inactivation (increase k1/2). These factors include ADP which was present in the Nichols et al. [28]preparation, intracellular acidosis [30](2x increase in k1/2) and intracellular lactate [31](3x increase in k1/2). We modified k1/2 to 250 µM to account for these additional ischemic effects. PATP reproduces with good accuracy the dependence of IK(ATP) on [ATP]i, as shown in Fig. 2A. In addition to PATP, conductance through IK(ATP) is a function of [K]o (similar to the IK1 and IKr conductances). This dependence is to the power of n = 0.24 in the guinea-pig ventricular cell [32]. Fig. 2B and 2C correspond to our theoretically formulated (2B) and to the measured [32](2C) single channel current-voltage curves at [ATP]i=0 mM and [K]o=5.4, 50 and 150 mM. In Fig. 2B, whole cell currents are converted to single channel currents by assuming a channel density of 1.36 channels/µm2. IK(ATP) channel density has been estimated from single patch data to be about three times higher [28, 29], and thus our formulation of IK(ATP) corresponds to a conservative estimate.


Figure 2
View larger version (20K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 2 IK(ATP) dependence on [ATP]i and [K]o. (A) Sigmoidal dependence of (normalized) IK(ATP) on [ATP]i. [K]o held constant at 4.0 mM. Filled circles are measured data by Nichols et al. [28], solid line is the theoretical curve and dashed line is the modified theoretical curve that accounts for acidosis and lactate. (B) Computed single channel current-voltage curves of IK(ATP) for three different values of [K]o at [ATP]i=0.0 mM. (C) Measured single channel current-voltage curves of guinea-pig IK(ATP) (Kakei et al. [32]) under similar conditions as in (B).

 
In addition to IK(ATP), ATP-dependence of the L-type calcium channel has been introduced into the model. Noma and Shibasaki [33]recorded the dependence of ICa(L) on [ATP]i using guinea-pig ventricular cells. We used a Hill-type fit, k1/2=1.4 mM and H = 2.6, to the Noma and Shibasaki [33]data for metabolic regulation of ICa(L). These parameters cause 12% ICa(L) reduction at [ATP]i=3 mM, very similar to the reduction of ICa(L) recorded by Ohya and Sperelakis [34]using vascular smooth muscle cells at similar [ATP]i. The complete formulation of IK(ATP), ATP-dependence of ICa(L), and associated parameters are provided in Appendix A.

2.5 Protocols and definitions
Transmembrane currents are computed using the modified Euler method of Rush and Larsen [35]with a constant time step of 2 µS. The cell is excited with a 0.5 ms intracellular current stimulus of –80 µA/µF, unless otherwise specified. (dVm/dt)max is always the largest slope computed during the entire upstroke, not a local maximum. Action potential duration, APD90, is the time between (dVm/dt)max and 90% repolarization from peak amplitude (peak potential minus resting potential). Control [K]o is 4.5 mM.


   3 Results
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
4 Discussion
 References
 
3.1 Resting membrane potential
The majority of increased [K]o-related effects during ischemia stem from a [K]o induced elevation of resting membrane potential, Vrest. We investigated how changes in [K]o during simulated ischemia affect Vrest. In Fig. 3, Vrest (solid line, as computed by the LRd model) and potassium reversal potential, Ek (dotted line), are plotted against [K]o. Ek was computed by the Nernst equation at a temperature of 37°C and [K]i=144.86 mM (parameters of the LRd model). It can be observed that Vrest closely follows Ek, reflecting the large resting membrane permeability to potassium through IK1. Vrest is less negative than Ek at [K]o≤6.5 mM, due to inward current from the sodium and calcium background currents, INa,b and ICa,b, and the sodium–calcium exchanger, INaCa (at control [K]o Ek is 1.6 mV more negative than Vrest which is slightly less but on the same order of 4 mV difference reported by Kléber [18]for guinea-pig heart). Increased IK1 channel conductance at higher [K]o and decreased driving force of the inward currents diminish the deviation of Vrest from Ek, and for [K]o >6.5 mM Vrest is within 1 mV of Ek. Experimental recordings of Vrest versus [K]o from guinea-pig ventricle [36]have been reproduced in Fig. 3 (filled triangles). The simulation closely approximates recorded Vrest as [K]o is varied.


Figure 3
View larger version (22K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 3 Resting membrane potential, Vrest, vs. [K]o for non-acidic and acidic conditions. Solid line and x-symbol line show resting membrane potential, Vrest, of LRd model as [K]o is varied under non-acidic ([K]i=144.8 mM) and acidic ([K]i=125 mM) conditions, respectively. Dashed line is computed potassium Nernst potential, EK (non-acidic conditions). Triangles are measured resting membrane potential values for different values of [K]o from healthy guinea-pig ventricle muscle by Gettes et al. [36]. Vrest is slightly more positive than Ek at the lower range of [K]o. As [K]o increases, Vrest follows and approaches Ek. [K]o and [K]i are the extracellular and intracellular potassium concentrations.

 
Ischemic Vrest is affected by conditions of acidosis, in addition to the condition of increased [K]o. Acidosis reduces [K]i which, from Fig. 3 (x symbols), depolarizes Vrest about 3.8 mV (3.7 mV depolarization at [K]o=3 mM and 4.0 mV depolarization at [K]o=16.0 mM). The other effects of acidosis (INa and ICa(L) changes) and all effects of anoxia (IK(ATP)) have minimal effect on Vrest.

3.2 Action potential upstroke
In Fig. 4 we investigate the effect of Vrest depolarization on the action potential upstroke parameters. The figure contains peak upstroke velocity ((dVm/dt)max, solid line), maximum sodium current (long dashed line, mostly obscured by (dVm/dt)max), and resting sodium channel availability ((h·j)rest, short dashed line) versus resting potential. h and j are the fast and slow inactivation gates of INa, respectively [4, 37]. Their product provides the fraction of available sodium channels. [K]o values corresponding to the resting potential are also shown on the abscissa. Moderate increases in [K]o to [K]o<6 mM cause a slight increase in (dVm/dt)max due to reduced depolarization time to threshold without resting sodium channel inactivation. Further [K]o elevation, up to [K]o=15 mM, causes a decrease in resting sodium channel availability which reduces peak INa and (dVm/dt)max. In this range of [K]o (dVm/dt)max is coincident with INa,max, i.e., the action potential upstroke is supported by INa. In regions of [K]o >15 mM an interesting phenomenon occurs, (dVm/dt)max becomes independent of INa,max. At [K]o=15 mM, the action potential upstroke is ‘taken over’ by calcium current. That is, ICa(L),max (not shown) is greater than INa,max (for [K]o=17 mM, ICa(L),max is 15.5 µA/µF and INa,max is 5.4 µA/µF). At all values of [K]o >15 mM, (dVm/dt)max is coincident with ICa(L),max. Calcium takeover at [K]o=15 mM is highlighted in the inset of Fig. 4.


Figure 4
View larger version (24K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 4 Upstroke dependence on resting potential. Maximum upstroke velocity (dVm/dt)max (thick solid line), sodium channel availability (h·j)rest (short dashed line), and maximum sodium current during the upstroke, INa,max (long dashed line), for different resting potentials altered by raising extracellular potassium [K]o. (dVm/dt)max is dominated by INa until Vm~–60 mV at which (h·j)rest is 3%. This is the point of ICa(L) takeover.

 
Because acidosis reduces sodium channel and calcium channel conductances, it should affect the calcium takeover potentials and the viability of the upstroke. The effects of combined acidosis and elevated [K]o on (dVm/dt)max are shown in Fig. 5. The two large curves correspond to a control cell subjected to elevated [K]o (curve 1) and an acidic cell subjected to elevated [K]o (curve 2). Stimulus strength in this simulation was reduced to –50 µA/µF to reflect suppressed source current from neighboring cells during acute ischemia in the (multicellular) myocardium. Two observations can be made from Fig. 5: acidic (dVm/dt)max is less than control (dVm/dt)max at any [K]o, and calcium takeover does not occur in acidic cells. Acidic (dVm/dt)max is less than control (dVm/dt)max because acidosis reduces FormulaNa. Calcium takeover for the non-acidic cell occurred at [K]o=15 mM. Because (dVm/dt)max is reduced (INa is suppressed), takeover for the acidic cell would have occurred earlier, at [K]o=12.5 mM, if ICa(L) were not affected by acidosis. However, calcium current under acidic conditions is compromised and is insufficient to sustain the upstroke. The result is excitation failure. This is further illustrated in Fig. 5 by showing the first 10 ms of action potential upstrokes for [K]o=8, 11 and 13.5 mM. At [K]o=8 mM the upstrokes for the control (1) and acidic (2) action potentials are similar. At [K]o=11 mM, acidic slowing of the upstroke (2) is readily apparent. At [K]o=13.5 mM, sodium current brings the control cell (1) into the range of calcium activation and calcium current supports the latter half of the upstroke. In the acidic cell (2), the stimulus fails to evoke a sodium response and calcium current is unable to support further excitation, resulting in excitation failure and return to Vrest.


Figure 5
View larger version (20K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 5 Depression of maximum upstroke velocity as extracellular potassium is raised for control and acidic conditions. (dVm/dt)max for control (solid line, curve 1) and acidic (dotted line, curve 2) conditions with increasing [K]o. Acidosis causes a [K]o independent depression of (dVm/dt)max and prevents calcium takeover which would otherwise occur at [K]o~13 mM. The first 10 ms of the control (1) and acidic (2) upstrokes are shown for [K]o=8 mM, 11 mM, 13.5 mM (insets). Stimulus current was reduced to –50 µA/µF to reflect decreased excitatory current during acute ischemia.

 
To determine the impact of anoxia on membrane excitability of the isolated cell, we computed (dVm/dt)max for a full range of ischemic [ATP]i (2–10 mM) with and without the conditions of elevated [K]o and acidosis. Data are shown in Fig. 6. The top curve corresponds to simulations with anoxic conditions alone, via activation of IK(ATP). The middle curve corresponds to anoxic conditions together with acidosis (corresponding to pH=6.5), and the bottom curve corresponds to anoxia with elevated [K]o ([K]o=12 mM). The stimulus was constant at –80 µA/µF for all simulations. It is apparent from the down shift of the (dVm/dt)max curves that acidosis causes minor (19%) and elevated [K]o causes major (70%) depression of excitability. Anoxia has little effect on excitability. When [ATP]i is reduced from 10–2 mM, (dVm/dt)max is reduced by only 1.6%, 2.3%, and 2.7% for the top, middle, and bottom curves, respectively. Fig. 6 illustrates that if anoxia depresses membrane excitability by activation of IK(ATP), it does so at [ATP]i below the ischemic range.


Figure 6
View larger version (19K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 6 Effect of anoxia on maximum upstroke velocity. (dVm/dt)max computed as a function of [ATP]i. Reduced [ATP]i causes opening of IK(ATP). The top, middle, and bottom curves correspond to conditions of (pH~7.4, [K]o=4.5 mM), (pH~6.5, [K]o=4.5 mM), and (pH~7.4, [K]o=12.0 mM), respectively. At the entire ischemic range of [ATP]i, acidosis causes marginal reduction in (dVm/dt)max and elevated [K]o causes major reduction in (dVm/dt)max. For each condition, [ATP]i reduction has minor effect on (dVm/dt)max. ‘Normal’ indicates control, non-ischemic conditions.

 
3.3 Action potential duration (APD)
Ischemic shortening of action potential duration is the result of increased net outward current during the plateau, reflecting some combination of increased outward current and decreased inward currents. Elevated [K]o increases outward current by a direct effect on the [K]o dependent potassium currents, IK1 and IKr. Also, outward current is enhanced by the anoxic decrease in available [ATP]i, which opens the normally dormant IK(ATP). Inward current reduction is the result of both acidic and anoxic reduction of ICa(L). We evaluated the quantitative influence of these three processes on APD. Results are shown in Fig. 7. Panels A, B and C contain APD versus [K]o, [ATP]i and ICa(L), respectively. The gray zone in each panel corresponds to the range of values assumed by each parameter during acute ischemia. In Panel A, elevated [K]o contributes to APD shortening in a linear fashion proportional to [K]o. However its contribution is small, causing a 20 ms reduction of APD at [K]o=12 mM. Similarly, acidosis-related reductions in ICa(L) reduce APD (Panel C) in a linear fashion, causing 20 ms APD reduction at 50% ICa(L) reduction. Further reductions of ICa(L) to about 20–30% of maximum cause significant reduction of APD, but it is unlikely that ICa(L) is reduced to this degree during acute ischemia. [ATP]i reductions, within the ischemic range, have a marked effect on APD (Panel B). The solid and dotted lines in Panel B correspond to effects of [ATP]i on IK(ATP) alone and on both IK(ATP) and ICa(L), respectively. Comparison of the two lines indicates that the predominant effect of [ATP]i on APD is due to IK(ATP). Furthermore, at [ATP]i=7 mM, APD shortening is the same as that obtained from 25% acidic reduction of ICa(L) (i.e., 75% in Fig. 7C). At [ATP]i=4.5 mM, APD shortening is the same as from [K]o elevation to 12 mM. The steepness of the IK(ATP) Hill coefficient (indicating cooperative binding, Fig. 2A) causes a rapid decline of APD at [ATP]i<4.5 mM. At [ATP]i=2mM, the lower end of feasible ATP concentration during acute ischemia, APD is reduced to 72 ms.


Figure 7
View larger version (42K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 7 Changes in action potential duration for the three major component conditions of acute ischemia. (A) Hyperkalemia. Action potential duration computed from time of (dVm/dt)max to 90% repolarization (APD90) versus extracellular potassium concentration. (B) Anoxia. APD90 versus [ATP]i. [ATP]i reduction due to anoxia increases the conductance of the ATP-dependent potassium channel, IK(ATP), and decreases conductance of ICa(L). Solid line corresponds to anoxic regulation of IK(ATP) alone and dotted line corresponds to anoxic regulation of both IK(ATP) and ICa(L). (C) Acidosis. APD90 versus maximum conductance of the L-type calcium current, ICa(L). The conductance is decreased by intracellular acidosis. The shaded regions in each panel correspond to the range of values during acute ischemia.

 
The APD relationships in Fig. 7 suggest that IK(ATP) is the dominant cause of ischemic APD shortening. In Fig. 8, we further explore not only the degree of shortening but also action potential shape changes under ischemic conditions. Fig. 8A contains the action potentials recorded by Friedrich et al. [11]of isolated guinea-pig cells subjected to complete anoxia. Data are shown at 0, 3, 6 and 9 min from the onset of APD shortening. Simulated action potentials that correspond to the ischemic range of %ICa(L) and IK(ATP), i.e., the gray zones of Fig. 7, are shown in Fig. 8B (solid lines) and Fig. 8C, respectively. It can be immediately observed that ischemic reductions of ICa(L) fail to cause significant APD reduction (Fig. 8B). The dashed curve in Fig. 8B corresponds to an action potential at 0% ICa(L), illustrating that decreased ICa(L) can cause major APD reduction, but at levels well beyond the ischemic range. Furthermore, the characteristics of APD shortening in the experimental data (Fig. 8A) are similar to those computed during IK(ATP) induced shortening (Fig. 8C). It is very different from the behavior during decreased-ICa(L) induced shortening. Action potential amplitude decreases in the Friedrich data (Fig. 8A) and in the IK(ATP)-influenced action potential (Fig. 8C), but not in the ICa(L)-influenced action potentials (Fig. 8B). Due to its driving force, IK(ATP) is largest at peak Vm, at the start of the plateau. Thus IK(ATP) exerts its major effect early in the plateau which accelerates early repolarization. In contrast, both ICa(L) driving force and recovery from inactivation increase with repolarization from peak Vm. This explains the late plateau and phase-III effects of reduced ICa(L) (Fig. 8B). Note that during most of the plateau, action potentials for different degrees of ICa(L) suppression overlap with no apparent amplitude changes. Differentiation of these action potentials occurs only very late. The inconsistency with the experimental observation of the simulated ICa(L)-dependent shape changes and degree of APD reduction indicates that this current can not be responsible for ischemic action potential shortening. The fact that IK(ATP) alone can reproduce these changes faithfully (Figs. 7 and 8Go), strongly indicates that IK(ATP) is the major mechanism of ischemic APD shortening.


Figure 8
View larger version (27K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 8 Comparison of action potential shape changes between experimental anoxic conditions, simulated reduction in ICa(L) and simulated effect of IK(ATP) at different [ATP]i. (A) Action potentials recorded by Friedrich et al. [11]of isolated guinea-pig ventricular cells under conditions of anoxia. 0 min corresponds to the time of first action potential shortening. (B) Action potentials computed after decreasing maximum ICa(L) conductance within the range that occurs during acute ischemia (0–50% decrease). The extreme case of complete ICa(L) block, which is outside the range of ischemic conditions, is shown for reference (dashed curve). (C) Action potentials computed after decreasing [ATP]i from 6 mM to 2 mM (in steps of 1 mM), the range of values likely to occur during acute ischemia.

 
3.4 Recovery of excitability
Cardiac membrane normally recovers excitability on the tail of a preceding action potential. Full excitability begins with the return to resting potential. Elevated [K]o and other conditions of ischemia delay the recovery of excitability beyond the return to Vrest, a phenomenon known as ‘post-repolarization refractoriness’. In Fig. 9, we investigate the delay in recovery of excitability caused by elevated [K]o. In each set of simulations a conditioning action potential is initiated at time=0 by stimulus S1 and secondary action potentials are obtained with a second stimulus S2 at increasing diastolic intervals (DI, time between 95% repolarization of the first action potential and the start of S2). Panels A and B correspond to control conditions ([K]o=4.5 mM) and Panels C and D correspond to conditions of elevated potassium ([K]o=12 mM). Under control conditions the first successful S2 action potential occurs at S1–S2=181 ms (DI=–1.8 ms, which corresponds to 93% repolarization of the first action potential). Beyond 181 ms, (dVm/dt)max, a measure of membrane excitability, is restored rapidly in a monoexponential fashion with a time constant of {tau} = 10.3 ms (Panel B). Therefore (dVm/dt)max is 44% recovered at DI=10 ms and 89% recovered at DI=20 ms. In Panel 9B we show the product of the two sodium channel inactivation gates (h·j) immediately prior to the S2 stimulus (this product provides the degree of INa recovery and the fraction of available sodium channels). (h·j)S2 recovered with a time constant {tau} = 12.5 ms, similar to the time constant of (dVm/dt)max recovery, indicating that recovery of excitability is achieved by recovery from sodium channel inactivation. Time constants of the sodium channel inactivation gates depend on the membrane potential. Because [K]o determines resting membrane potential, it is then expected that elevated [K]o will alter the time constant of INa recovery. Panels 9C and 9D contain simulations run at [K]o=12 mM. The first successful S2 action potential for [K]o=12 mM occurred at S1–S2=171 ms (DI=22 ms). Thereafter (dVm/dt)max recovery occurred with a time constant of 81.4 ms, close to the (h·j)S2 time constant of 88.8 ms (Panel 9D). Note the eight fold increase in {tau} of (h·j)S2 relative to control which is due to the change in Vrest from –91 mV ([K]o=4.5 mM) to –66 mV([K]o=12 mM).


Figure 9
View larger version (31K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 9 Recovery of excitability under control conditions (left) and for elevated [K]o (right). (A) and (C) Action potentials obtained with a double (S1S2) pulse protocol where stimulus S1 initiates the conditioning action potential and S2 is the premature stimulus. (B) and (D) Recovery of (dVm/dt)max (solid line) and sodium channel availability prior to the S2 stimulus (h·j)S2 (dotted line) computed from action potentials in (A) and (C), respectively. Diastolic interval (DI) of 0 corresponds to 95% repolarization of the conditioning action potential. (A) and (B) were computed at [K]o=4.5 mM and (C) and (D) were computed at [K]o=12 mM.

 
Acidosis and anoxia affect the action potential shape and the sodium current, and therefore will modify recovery of excitability. In Fig. 10, the effect of these two conditions are evaluated when superimposed on control conditions (Panel A) and on elevated [K]o (Panel B). Each panel shows (dVm/dt)max versus S1–S2 interval for the condition of [K]o alone, [K]o with acidosis, and [K]o with anoxia. A horizontal line is drawn at the bottom of each curve from the start of excitability to 95% repolarization of the previous action potential (DI=0 ms, indicated by an arrow). Both anoxia and acidosis reduce APD (reflected in the shortened S1–S2 interval) and acidosis reduces (dVm/dt)max, yet at normal [K]o the shortest DI (start of excitability relative to DI=0) is similar for all conditions (–1.8 ms, –1 ms and –0.8 ms for control, anoxic and acidic conditions, respectively). When [K]o is elevated to 12 mM, however, the shortest DIs are different (23.2, 28.0 and 30.1 ms for control, anoxic and acidic conditions, respectively). Thus both anoxia and acidosis delay the start of excitability, and acidosis has a slightly greater effect than anoxia. After the start of excitability, the time constants of recovery are the same for all conditions at normal [K]o, and show small differences between conditions at elevated [K]o. At [K]o=4.5 mM, {tau} was 10 ms for all conditions. At [K]o=12 mM, {tau} increased from 81 ms to 83 ms for anoxia and decreased to 80 ms for acidosis.


Figure 10
View larger version (23K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 10 Effect of acidosis and anoxia on recovery of excitability. Maximum upstroke velocity, (dVm/dt)max, for control, anoxic ([ATP]i=3 mM) and acidic (approximating pH~6.5) conditions at normal [K]o=4.5 mM (A) and elevated [K]o=12 mM (B). Time constants of recovery of excitability, {tau}, are shown for each curve. S1–S2 interval corresponds to protocol defined in Fig. 8. Note, in absolute terms, anoxia causes earlier onset of recovery relative to time of S1 due to APD shortening and acidosis decreases maximum (dVm/dt)max. However neither anoxia nor acidosis significantly affect the time course of recovery, {tau}, with only minor effects on time to start of recovery from the end of the action potential. Horizontal lines at the beginning of each curve indicate time to start of recovery from 95% repolarization of the action potential (DI=0, arrows).

 
3.5 Integrated ischemic model
To this point, we attempted to differentiate the electrophysiologic effects of the three major individual components of acute ischemia. Much of the difficulty in elucidating a cause and effect relationship between the metabolic and ionic conditions of ischemia and the ischemic electrical changes lies in the complicated interrelationships between events. For example, APD shortening can be due to acidotically reduced ICa(L), and/or an enhanced outward IK(ATP) and/or elevated [K]o. To combine the conditions, we selected individual parameter values that correspond to approximately the same time during the acute ischemic period. At 10 min of ischemia, tissue and cellular preparations retain a highly depressed but still viable electrical excitability during which [K]o is approximately 12 mM, the acidic pH is about 6.5 and anoxia reduces [ATP]i to 3.0 mM [1, 2, 38, 39]. Assigning typical single values to represent these conditions does not reflect ischemic heterogeneity, but is useful to assess the relative roles of these three component conditions in ischemic electrophysiological changes. Fig. 11 contains action potentials resulting from the three different conditions of ischemia in isolation and in different combinations. Panel A is the control action potential and Panels B, C and D correspond to action potentials subject to [K]o=12 mM, pH=6.5 and [ATP]i=3 mM, respectively. Panels E, F and G reflect the combined contributions of two ischemic conditions; elevated [K]o and acidosis, elevated [K]o and anoxia, and acidosis and anoxia, respectively. Panel H corresponds to the action potential in the presence of all three conditions of simulated ischemia. A plot of the control action potential from Panel A (light line) is provided in Panel H for direct comparison.


Figure 11
View larger version (19K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 11 Action potentials corresponding to different components of ischemia. Action potentials obtained from cell model corresponding to different combinations of the three components of ischemia: (A) control; (B) elevated [K]o; (C) acidic effects on sodium channel, calcium channel and [K]i; (D) influence of IK(ATP) at [ATP]i=3 mM; (E)–(H) combinations of elevated [K]o, acidic and anoxic components. In (H) the fully integrated ischemic action potential (dark curve) and the control action potential (light curve) from (A) are superimposed for direct comparison. The abscissa and ordinate for all panels are adjusted to the scales indicated in (A). IK(ATP) is the ATP-dependent potassium current. [K]o and [K]i are the extracellular and intracellular concentrations of potassium.

 
Inspection of Fig. 11 allows visual estimation of the influence of each ischemic component. It is evident that elevated [K]o contributes significantly to resting depolarization, causes reduction in upstroke velocity and slight APD shortening (Panels A and B). The isolated effect of acidosis is minimal (Panels A and C) and anoxia, in isolation, causes APD shortening (Panel A and D). When present with elevated [K]o, acidosis magnifies the [K]o-induced upstroke depression (Panels B and E). Acidosis has little additional effect on the upstroke or APD when present in conjunction with anoxia (Panels D and G). To generalize, elevated [K]o affects all characteristics of the ischemic action potential by depolarizing Vrest, depressing the upstroke and reducing APD. Acidosis depresses the upstroke, and anoxia, the third ischemic condition, reduces APD.

A quantitative summary of the visual data in Fig. 11 is provided in Table 1. The complete ischemic conditions (last row) depolarize normal Vrest by 29 mV and reduce (dVm/dt)max and APD90 by 82% and 51%, respectively. These values are within the experimental range for ischemic depression of electrical activity, 10 min into the onset of perfusion block. From Table 1 it is clear that anoxia has little effect on the action potential upstroke. Anoxia reduced (dVm/dt)max from 379 V/s to 376 V/s when applied in isolation, and reduced (dVm/dt)max from 38 V/s to 36 V/s when applied in the presence of elevated [K]o and acidosis. Although both elevated [K]o and acidosis contribute to reductions in (dVm/dt)max, the effect of elevated [K]o is greater. Individually, [K]o and acidosis reduce (dVm/dt)max by 70% and 20%, respectively, a ratio of 3.5:1. With respect to APD, elevated [K]o reduces APD from 173 ms to 147 ms, but APD reduction is dominated by anoxia and the associated IK(ATP). The ratio of anoxia induced APD shortening to elevated [K]o induced APD shortening is 2.2:1. Acidosis has little effect on APD.


View this table:
[in this window]
[in a new window]

  		Table 1 Effect of elevated [K]o, acidosis and anoxia on rest potential (Vrest), maximum upstroke velocity ((dVm/dt)max), and action potential duration (APD90)

 
Major ionic currents during an ischemic action potential are shown in Fig. 12, left panel. These data show ionic current behavior under conditions of acute ischemia and can be compared to the respective currents under control conditions (right panel). The fast sodium current INa (Panel B) is significantly reduced (due to elevated [K]o and acidosis) and, consequently, ICa(L) (Panel C) supports the last portion of the upstroke (at Vm >0 mV). Note that ICa(L) is increased during ischemic conditions in spite of acidic depression of the maximum channel conductance. This reflects an increased driving force during the lower plateau of the ischemic action potential. The inward rectifier potassium current, IK1 (Panel D), is enhanced as a direct result of elevated [K]o. Anoxia results in activation of IK(ATP) which contributes a repolarizing current during the entire action potential (Panel C). The fast component of the delayed rectifier current, IKr (Panel E), is relatively unchanged due to a balance between reduced driving force (depolarized EK and reduced action potential amplitude) and direct enhancement from elevated [K]o. Because the slow component of the delayed rectifier (IKs) is not directly enhanced by elevated [K]o, reduction in driving force and slower activation at decreased plateau potentials significantly reduce IKs during the ischemic action potential.


Figure 12
View larger version (23K):
[in this window]
[in a new window]
[Download PowerPoint slide]
  		Fig. 12 Major ionic currents during an ischemic action potential. An ischemic action potential (A) and the principal ionic currents are shown for conditions of [K]o=12 mM, pH=6.5, and [ATP]i=3 mM. The fast sodium and slow L-type calcium currents are in (B) and (C), the inward rectifier and ATP-dependent potassium currents are in (D), and the fast and slow components of the delayed rectifier potassium current are in (E). A control, non-ischemic action potential and corresponding currents are shown in (F)–(J) for comparison. Current symbols are identified in Fig. 1.

 

   4 Discussion
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
References
 
The results suggest that the major electrical changes of acute myocardial ischemia can be reproduced by the conditions of elevated [K]o, acidic changes of the fast sodium and L-type calcium currents, acidic reduction of [K]i, anoxia induced activation of a time independent outward current (IK(ATP)), and slight anoxic reduction of ICa(L). These conditions of ischemia in a cell-model formulated from otherwise non-pathological conditions successfully produced: (a) Vrest depolarization at elevated [K]o, (b) [K]o depression of (dVm/dt)max with additional depression from acidosis, (c) APD shortening similar to that of isolated anoxic cells, and (d) delayed recovery of excitability (post-repolarization refractoriness). The model was developed from mostly single channel and single cell recordings of individual processes. The similarity of the simulated electrical behavior to observed ischemic electrical activity supports the use of the model to investigate mechanisms of electrophysiological changes due to ischemic conditions. Mechanistic insights gained from the simulations and limitations of the study are discussed below.

4.1 Membrane excitability
This study, in part, focused on the transition from INa to ICa(L) dominated upstrokes in single cells (‘space-clamped’ conditions). Without the complications of intercellular coupling, the results suggest that unmodified calcium current can maintain the upstroke at [K]o values that are elevated within the range of acute ischemia. Calcium current dominates the upstroke when ICa(L),max >INa,max. Because INa,max is normally ~400 µA/µF and ICa(L),max is normally ~10 µA/µF, INa needs to be ~97% inactivated (essentially fully inactive) before ICa(L) is required to support the rising phase. Therefore the transition from INa to ICa(L) dominance occurs only when INa fails due to resting inactivation. Acidosis depresses INa at any [K]o, and therefore ICa(L) is required at lower [K]o in the presence of acidosis for the upstroke to be maintained. Yet acidosis also depresses ICa(L). The combination of depressed ICa(L) and more negative Vrest (lower [K]o) decreases the likelihood that ICa(L) can activate and sustain the upstroke when INa fails. This is evident in Fig. 5 where the non-acidic transition to calcium upstrokes occurred at [K]o=15 mM. The acidic transition would have occurred at [K]o=12.5 but failed due to depressed ICa(L). The result was action potential failure.

These findings support the major role of INa in depressed upstrokes of acute ischemia at any Vrest at which INa is still viable. Early studies such as those by Cranefield [40]suggested a major role of the L-type calcium current because action potentials were found in isolated cardiac fibers superfused with elevated [K]o and catecholamines (calcium current agonists). Ischemic cardiac regions have elevated [K]o and high norepinephrine levels due to sympathetic nerve catecholemine release following coronary occlusion. Thus during ischemia, conditions exist that would facilitate ICa(L). However more recent evidence suggests that depressed upstrokes are supported by depressed sodium current. In vascularized hamster cardiac transplants, Gilmour and Zipes [41]could suppress depressed action potentials with the sodium channel blocker tetrodotoxin, but not with the calcium channel blocker verapamil. Kléber et al. [7]found that ischemic porcine ventricular cells become unresponsive at average Vrest≥–60.3 mV, slow response action potentials only began to appear at Vrest≥–48.5 mV. Lidocaine depressed or abolished action potentials in the ischemic regions of isolated porcine hearts [42], suggesting a primary dependence on inward sodium current.

In this study we have shown that at [K]o values within the ischemic range, a transition potentially exists from INa to ICa(L) upstrokes. The transition occurs at the point of INa failure, and is less likely in the presence of acidosis. These results were obtained in a single, ‘space-clamped’ cell in the absence of intercellular coupling and electrical loading. In a multicellular ischemic preparation it may be expected that the depolarizing source current is not as strong as the direct stimulus used in this study. In addition, loading by surrounding cells will reduce availability of local inward current for depolarization. For these reasons we expect that ICa(L)-dominated upstrokes in depressed membranes are even less likely to occur in a multicellular environment during acute ischemia. Future studies will be directed at determining the effects of source and sink currents from surrounding cells on properties of ischemic membranes.

A result that may counter conventional wisdom is that activation of IK(ATP) within the ischemic range of [ATP]i (2–10 mM), although having a major effect on action potential duration, does not affect membrane excitability (Fig. 6). The reason that outward IK(ATP) does not significantly counteract inward INa during the upstroke is based on the difference in reversal potential between INa and IK(ATP). Subthreshold depolarization occurs relatively close to resting potential which is very close to potassium reversal potential and very far from sodium reversal potential. In the extreme case that membrane conductances of INa and IK(ATP) are identical (an exaggeration of ischemic IK(ATP)), during subthreshold depolarization, the sodium current will still be much greater than that of the potassium current. At Vm=–60 mV, for example, the INa:IK(ATP) ratio of transmembrane driving forces is 4:1.

In the simulations we determined membrane excitability for the isolated cell by applying a brief strong stimulus, usually –80 µA/µF for 0.5 ms. In multicellular tissue, cells are excited by weaker, greater duration electrotonic current supplied from adjoining excited cells. IK(ATP), by reducing plateau amplitude and duration of excited cells, can decrease voltage gradients between excited and unexcited cells, decreasing the electrotonic source current. We have shown [17]that activation of IK(ATP) at [ATP]i levels that are within the ischemic range can cause propagation failure when INa is reduced. The results presented here support the principle that ischemic IK(ATP) exerts its effect by reduction of the electrotonic source current, not by direct reduction of membrane excitability.

4.2 Action potential duration
There is a general consensus, though not universal, that IK(ATP) is the major current responsible for action potential duration shortening during acute ischemia [11, 19, 33]. Reservations about the role of IK(ATP) during acute ischemia are based on the Kd (half maximal saturation) of this current that is in the micromolar (25–500 µM) [26, 32, 43]range whereas [ATP]i remains in the millimolar range (~2–5 mM) [44, 45]during the ischemic period. Also, sulfonylureas that are used in studies to block IK(ATP) may affect cell metabolism [19, 46], causing secondary changes in APD that are inadvertantly attributed to IK(ATP) [39].

Our results provide three reasons for supporting IK(ATP) as the dominant factor in ischemic APD shortening. (1) Process of elimination. Elevation of [K]o and anoxic and acidic reduction of ICa(L) to values within the range of acute ischemia do not cause significant APD shortening (Fig. 7). Our model did not suggest, and we are not aware of, other means of APD shortening (in a single cell). IK(ATP) alone can cause 50% (86 ms) APD shortening at [ATP]i=2.25 mM. At [ATP]i=3 mM, IK(ATP) caused a 56 ms reduction in APD whereas similar extreme values of acidosis and elevated [K]o caused only 13 ms and 31 ms shortening, respectively (Table 1). (2) IK(ATP) has a pronounced role in APD shortening even though its formulated conductance in the model is very conservative. Channel density, and hence maximum conductance, was taken from whole cell measurements which are approximately one third of the density estimate from single patch data (see Section 2). Even with this conservative formulation, the computed 50% APD shortening at [ATP]i=2.25 mM corresponds to only 1.2% activation of IK(ATP) (comparing favorably to experimental estimates of 0.7–1% IK(ATP) activation required for 50% APD shortening [28, 47]). (3) Only IK(ATP) can cause shape changes in the computed action potential that are similar to the shape changes observed in anoxic guinea-pig cells. ICa(L) reductions cause changes late in the action potential plateau whereas IK(ATP) causes changes early in the plateau similar to those measured in anoxic cells (Fig. 8).

Yan et al. [39]demonstrated in rabbit papillary muscle that APD shortening during acute no-flow ischemic conditions could be disassociated from cellular [ATP] levels, and that [K]o accumulation combined with hypoxia can be responsible for APD shortening without involvement of IK(ATP). [K]o increases alone did not, in our cellular model, cause significant APD shortening despite inclusion of [K]o dependent channels (IK1, IKr, IK(ATP)) and appropriate upstroke changes at different [K]o. It is possible that hypoxia in the elevated [K]o/hypoxia preparation [39]caused intracellular acidic changes which included Vrest depolarization and ICa(L) inhibition. With combined elevated [K]o and acidosis, APD is reduced by 24% (Table 1). Therefore although only IK(ATP) can cause major (>50%) APD shortening, the combined effect of acidosis and elevated [K]o remains quantitatively significant.

An effect of acidosis not incorporated into the simulations is inhibition of the sodium–calcium exchange current, INaCa, by intracellular protons. Cytoplasmic acidosis of pH=6.5 causes a 3–5 fold inhibition of INaCa from control conditions, and INaCa is almost completely inhibited at pH=6.0 [48, 49]. We found (simulation data not shown) that specific INaCa block of a non-paced cell increased APD of a single action potential by only 3%. However, we caution that the effect of INaCa on APD will vary significantly based on experimental conditions and protocol. For instance, lengthening of APD in this example is a result of decreased INaCa transport of calcium into the cell during the action potential upstroke and consequent reduction of SR calcium release and of calcium-dependent inactivation of ICa(L). If, when INaCa is blocked, calcium release from the SR is kept identical to that when INaCa is not blocked, APD decreases by 4%. In another example, if INaCa is altered by exchange of 50% of the extracellular sodium ions with lithium ions during the early plateau of an action potential, APD decreases by 20% [50](a result duplicated by our model simulation). The APD decreases significantly with this intervention since INaCa remains outward (rather than becoming inward) during the late plateau phase of the action potential. These examples suggest that the effect of acidotic INaCa on APD is marginal. They also illustrate that the INaCa effects must be carefully considered in context of the specific protocol and in relation to other currents, especially that of ICa(L) and its calcium-dependent inactivation.

4.3 Postrepolarization refractoriness
In vivo cardiac cells, whether or not ischemic, are subject to repetitive firing. Under normal conditions cell refractoriness is a function of INa availability and extends little beyond the recovery of resting potential. During acute ischemia the refractory (absolute and relative) period prolongs despite continued shortening of the APD and may outlast full repolarization by hundreds of milliseconds. Kodama et al. [14]reported an increase in the time constant of (dVm/dt)max recovery in guniea-pig papillary muscle from {tau} = 18.2 ms at [K]o=5 mM to {tau} = 74.6 ms at [K]o=12 mM. Our simulations computed similar changes in {tau}, ranging from {tau} = 10.3 ms at [K]o=4.5 mM to {tau} = 81.4 ms at [K]o=12 mM (Fig. 9). We found the mechanism of delayed recovery of excitability to be almost exclusively due to the voltage-dependence of the recovery kinetics of the sodium channel inactivation gates, h and j. Vrest depolarization by elevated [K]o slows the recovery of h and j following an action potential. A stimulus prior to complete h and j recovery encounters a lower (h·j)rest than under steady-state conditions which results in reduced sodium channel availability and reduced excitability.

In addition to the effect of elevated [K]o on {tau}, Kodama et al. [14]found that hypoxia in combination with elevated [K]o causes greater prolongation of recovery. For example, at [K]o=12 mM, 15 min of hypoxia increased {tau} from 75 ms to 134 ms [14]. In contrast, Sano et al. [51]did not find in dog ventricle significant hypoxia-induced prolongation of {tau}. Consistent with Sano et al. [51], we found that anoxia did not significantly prolong {tau} at any [K]o. With the addition of anoxic conditions, computed {tau} at [K]o=12 mM increased only 2% from 81 to 83 ms (Fig. 10).

We suggest that regional inhomogeneities of [K]o may have been present in the Kodama et al. [14]preparation to explain their observation of a synergistic effect of hypoxia and elevated [K]o on postrepolarization refractoriness. In superfused preparations, such as those of Kodama et al. [14], intramuscle [K]o and CO2 may increase to values larger than that recorded at the muscle surface [52]. Under conditions of elevated [K]o and hypoxia, intramuscle cells could experience sufficient [K]o elevation to become inexcitable. Therefore cells closer to the perfusate will be subjected to constant load from intramuscle cells, and respond with delayed recovery of excitability. This suggests that hypoxia induced delay in recovery of excitability may be caused by electrotonic influences due to ischemic heterogeneity rather than by an intrinsic cellular mechanism.

The effect of acidosis on postrepolarization refractoriness, like that of anoxia, was marginal. Acidosis has two direct effects on the sodium current, it (1) reduces maximum conductance and (2) causes an apparent negative shift in observed membrane potential. Reduced maximum conductance lowers the maximum obtainable (dVm/dt)max, however it does not affect INa activation and inactivation kinetics and therefore reduced conductance does not affect time course of recovery. The shift in membrane potential counters somewhat [K]o-induced depolarization of resting potential. At [K]o=12 mM, the addition of acidosis reduced {tau} from 81 to 80.0 ms. This reduction, of 1.2%, is not significant relative to [K]o-induced prolongation of (dVm/dt)max recovery.

4.4 Additional ischemic conditions
The conditions of ischemia studied in our theoretical simulations are not an exhaustive representation of all ischemic conditions. There are several conditions we have elected not to include because either their effects require further experimental characterization or their presence is not relevant during the acute phase of ischemia. The accumulation of lipid metabolites such as palmitoylcarnitine and lysophosphatidylcholine may have direct inhibitory effects on INa [53]and ICa(L) [54]. When these conditions are further elucidated and quantified, they can be incorporated into theoretical models of ischemia.

The effect of acidosis on the cardiac potassium currents is unclear. An increase in the time dependent outward current (IK) during intracellular acidosis has been reported [55], an effect oppostite to the observed [56]decrease in the time-independent outward current (IK1) in the presence of intracellular and extracellular acidosis. The opposite effects of IK and IK1 would have opposite effects on APD. The net effect on APD may be very small [57]and requires further experimental investigation. In this study we have chosen to neglect any direct affect of acidosis on the IKr, IKs and IK1 potassium currents.

There is considerable evidence that pH-linked accumulation of [Na]i and [Ca]i is related to arrhythmias during reperfusion and reoxygenation [58]. However, during the acute phase of ischemia studied in this paper, intracellular Na and Ca accumulation is not significant to overall ischemic electrophysiology. A rise in [Ca]i under ischemic conditions is coincident with the secondary phase of [K]o rise, electrical inexcitability, rapid depletion of [ATP]i and irreversible cell damage (cell death) [59]. Recent data suggest that intracellular calcium may contribute to electrical abnormalities associated with acute ischemia [60]. However these data remain preliminary and the role of intracellular calcium requires further study.

The activation of IK(ATP) and its major effect on APD raise the possibility that modulation of other ATP-dependent electrogenic processes might influence the action potential during ischemia. In particular, the possibility of a suppressed sodium/potassium pump, INaK, should be evaluated. Typically, [ATP]i drops 40–60% [44](to about 2.5 mM) during acute ischemia. Millimolar concentrations of ATP are adequate for supporting pump function and it has been shown that the pattern of [K]o rise and fall in acutely ischemic myocardium is consistent with a functioning Na/K pump [18]. This implies that during the acute phase, significant inhibition of the Na/K pump and a consequential change in INaK do not occur and should not be included in the simulations. It is important to recognize that the high sensitivity of IK(ATP) to changes in [ATP]i is due to its extremely high channel-density (comparable to that of INa). In fact, at [ATP]i=3.0 mM IK(ATP) is only 0.8% activated yet, due to its large density, its effect on APD is very significant.

Finally, the direct effects of ischemia on certain membrane ionic currents (Fig. 1) might lead to major, indirect changes in other ionic currents during the action potential. An example is shown in Fig. 12, where IKs is greatly reduced secondary to changes in the ischemic action potential (e.g., reduced amplitude). The large effect of ischemia on IKs, in the absence of direct modulation of this current (Fig. 1), serves as an example of the complexity of electrical changes under ischemic conditions. Such indirect changes should be carefully considered in the interpretation of experimental observations and in the identification of targets for pharmacological management of ischemic arrhythmias.

Time for primary review 42 days.

Appendix A
Modeling ischemic conditions with the LRd model [4–6]: parameter values and formulation of IK(ATP).Elevated [K]o


[K]ovaried between control (4.5 mM) and 16 mM,
[K]o=12.0 mM for integrated ischemic model.

Acidosis (pH=6.5)


[K]i=125.0 mM,
Vm,acid=Vm–3.4 for all sodium current computations (m{infty}, h{infty}, j{infty}, {tau}m, {tau}h, {tau}j, and driving force),
FormulaNa,acid=0.75·FormulaNa for integrated ischemic model,
FormulaCa,acid=0.75·FormulaCa for integrated ischemic model.

Anoxia-formulation of IK(ATP)


IK(ATP)=FormulaK(ATP)·(Vm–Ek),
FormulaK(ATP)=GK(ATP)·PATP·([K]o/[K]o,normal)n,
GK(ATP)=195·10–6/Nicholsarea (nS/cm2),
Table 3
Ek=potassium reversal potential,
Nicholsarea=5·10–3 cm2, Reference [28],
[ATP]i=3.0 mM for integrated ischemic model,
[K]o,normal=4.0 mM, n = 0.24, H = 2, k0.5=0.250 µM.

Anoxia-formulation of PCa(L),(ATP)


Table 4
[ATP]i=3.0 mM for integrated ischemic model,
H = 2.6, k0.5=1.4 mM.


   Acknowledgements
 
We thank Xiaoqin Zou and Jinglin Zeng for many helpful discussions and suggestions. We also wish to thank Robert Harvey and Matthew Levy for valuable discussions. This work was supported by the National Institutes of Health grants HL-49054 and HL-33343 (National Heart, Lung, and Blood Institute).


   Notes
 
1 Previously published in abstract form (Biophysical Journal 1997;72:A47). Back


   References
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 References
 

  1. Gettes LS, Cascio WE. Effect of acute ischemia on cardiac electrophysiology. In: Fozzard HA, Jennings RB, Haber E, Katz AM, Morgan HE, editors. The heart and cardiovascular system. New York: Raven Press, 1992:2021–2054.
  2. Wit AL, Janse MJ. The ventricular arrhythmias of ischemia and infarction: electrophysiological mechanisms. New York: Futura Publishing Company, 1992:648.
  3. Cascio WE, Johnson TA, Gettes LS. Electrophysiologic changes in ischemic ventricular myocardium: I. Influence of ionic, metabolic and energetic changes. J Cardiovasc Electrophys (1995) 6:1039–1062.[Web of Science][Medline]
  4. Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res (1994) 74:1071–1096.[Abstract/Free Full Text]
  5. Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ Res (1994) 74:1097–1113.[Abstract/Free Full Text]
  6. Zeng J, Laurita KR, Rosenbaum DS, Rudy Y. Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea-pig type: theoretical formulation and their role in repolarization. Circ Res (1995) 77:140–152.[Abstract/Free Full Text]
  7. Kléber AG, Janse MJ, Wilms Schopmann FJ, Wilde AA, Coronel R. Changes in conduction velocity during acute ischemia in ventricular myocardium of the isolated porcine heart. Circulation (1986) 73:189–198.[Abstract/Free Full Text]
  8. Kléber AG, Janse MJ, Van Capelle FJ, Durrer D. Mechanism and time course of S-T and T-Q segment changes during acute regional myocardial ischemia in the pig heart determined by extracellular and intracellular recordings. Circ Res (1978) 42:603–613.[Free Full Text]
  9. Arita M, Kiyosue T. Modification of ‘depressed fast channel dependent slow conduction’ by lidocaine and verapamil in the presence or absence of catecholamines-evidence for alteration of preferential ionic channels for slow conduction. Jpn Circ J (1983) 47:68–81.[Medline]
  10. Cranefield PF. The conduction of the cardiac impulse. Mount Kisco, NY: Futura Publishing, 1975:404.
  11. Friedrich M, Benndorf K, Schwalb M, Hirche H. Effects of anoxia on K and Ca currents in isolated guinea pig cardiocytes. Pflugers Arch (1990) 416:207–209.[CrossRef][Web of Science][Medline]
  12. Schütz E. Elektrophysiologie des Herzens bei einphasischer Ableitung. Ergebn Physiol (1936) 38:493–620.
  13. Downar E, Janse MJ, Durrer D. The effect of acute coronary artery occlusion on subepicardial transmembrane potentials in the intact porcine heart. Circulation (1977) 56:217–224.[Abstract/Free Full Text]
  14. Kodama I, Wilde A, Janse MJ, Durrer D, Yamada K. Combined effects of hypoxia, hyperkalemia and acidosis on membrane action potential and excitability of guinea-pig ventricular muscle. J Mol Cell Cardiol (1984) 16:247–259.[CrossRef][Web of Science][Medline]
  15. Pogwizd SM, Corr PB. Reentrant and nonreentrant mechanisms contribute to arrhythmogenesis during early myocardial ischemia: results using three-dimensional mapping. Circ Res (1987) 61:352–371.[Abstract/Free Full Text]
  16. Kaplinsky E, Ogawa S, Balke CW, Dreifus LS. Two periods of early ventricular arrhythmia in the canine acute myocardial infarction model. Circulation (1979) 60:397–403.[Abstract/Free Full Text]
  17. Shaw RM, Rudy Y. Electrophysiologic effects of acute myocardial ischemia: a mechanistic investigation of action potential conduction and failure. Circ Res (1997) 80:124–138.[Abstract/Free Full Text]
  18. Kléber AG. Resting membrane potential, extracellular potassium activity, and intracellular sodium activity during acute global ischemia in isolated perfused guinea pig hearts. Circ Res (1983) 52:442–450.[Abstract/Free Full Text]
  19. Wilde AA, Escande D, Schumacher CA, et al. Potassium accumulation in the globally ischemic mammalian heart. A role for the ATP-sensitive potassium channel. Circ Res (1990) 67:835–843.[Abstract/Free Full Text]
  20. Yan GX, Kléber AG. Changes in extracellular and intracellular pH in ischemic rabbit papillary muscle. Circ Res (1992) 71:460–470.[Abstract/Free Full Text]
  21. Yatani A, Brown AM, Akaike N. Effect of extracellular pH on sodium current in isolated, single rat ventricular cells. J Membr Biol (1984) 78:163–168.[CrossRef][Web of Science][Medline]
  22. Kagiyama Y, Hill JL, Gettes LS. Interaction of acidosis and increased extracellular potassium on action potential characteristics and conduction in guinea pig ventricular muscle. Circ Res (1982) 51:614–623.[Abstract/Free Full Text]
  23. Irisawa H, Sato R. Intra- and extracellular actions of proton on the calcium current of isolated guinea pig ventricular cells. Circ Res (1986) 59:348–355.[Abstract/Free Full Text]
  24. Grant AO, Strauss LJ, Wallace AG, Strauss HC. The influence of pH on the electrophysiological effects of lidocaine in guinea pig ventricular myocardium. Circ Res (1980) 47:542–550.[Free Full Text]
  25. Skinner RB Jr., Kunze DL. Changes in extracellular potassium activity in response to decreased pH in rabbit atrial muscle. Circ Res (1976) 39:678–683.[Abstract/Free Full Text]
  26. Noma A. ATP-regulated K+ channels in cardiac muscle. Nature (1983) 305:147–148.[CrossRef][Medline]
  27. Shaw RM, Rudy YR. Electrophysiological changes of ventricular tissue under ischemic conditions: a simulation study. Comp Cardiol (1994) 16:641–644.
  28. Nichols CG, Ripoll C, Lederer WJ. ATP-sensitive potassium channel modulation of the guinea pig ventricular action potential and contraction. Circ Res (1991) 68:280–287.[Abstract/Free Full Text]
  29. Weiss JN, Venkatesh N, Lamp ST. ATP-sensitive K+ channels and cellular K+ loss in hypoxic and ischaemic mammalian ventricle. J Physiol (Lond) (1992) 447:649–673.[Abstract/Free Full Text]
  30. Lederer WJ, Nichols CG, Smith GL. The mechanism of early contractile failure of isolated rat ventricular myocytes subjected to complete metabolic inhibition. J Physiol (Lond) (1989) 413:329–349.[Abstract/Free Full Text]
  31. Han J, So I, Kim EY, Earm YE. ATP-sensitive potassium channels are modulated by intracellular lactate in rabbit ventricular myocytes. Pflugers Arch (1993) 425:546–548.[CrossRef][Web of Science][Medline]
  32. Kakei M, Noma A, Shibasaki T. Properties of adenosine-triphosphate-regulated potassium channels in guinea-pig ventricular cells. J Physiol (Lond) (1985) 363:441–462.[Abstract/Free Full Text]
  33. Noma A, Shibasaki T. Membrane current through adenosine-triphosphate-regulated potassium channels in guinea-pig ventricular cells. J Physiol (Lond) (1985) 363:463–480.[Abstract/Free Full Text]
  34. Ohya Y, Sperelakis N. ATP regulation of the slow calcium channels in vascular smooth muscle cells of guinea pig mesenteric artery. Circ Res (1989) 64:145–154.[Abstract/Free Full Text]
  35. Rush S, Larsen H. A practical algorithm for solving dynamic membrane equations. IEEE Trans Biomed Eng (1978) 25:389–392.[Web of Science][Medline]
  36. Gettes LS, Buchanan JW Jr. Saito T, Kagiyama Y, Oshita S, Fujino T. Studies concerned with slow conduction. In: Zipes DP, Jalife J, editors. Cardiac electrophysiology and arrhythmias. Orlando, FL: Grune and Stratton, 1985:81–87.
  37. Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol (Lond) (1977) 268:177–210.[Abstract/Free Full Text]
  38. Nichols CG, Lederer WJ. Adenosine triphosphate-sensitive potassium channels in the cardiovascular system. Am J Physiol (1991) 261:H1675–H1686.[Web of Science][Medline]
  39. Yan GX, Yamada KA, Kléber AG, McHowat J, Corr PB. Dissociation between cellular K+ loss, reduction in repolarization time, and tissue ATP levels during myocardial hypoxia and ischemia. Circ Res (1993) 72:560–570.[Abstract/Free Full Text]
  40. Cranefield PF, Wit AL, Hoffman BF. Conduction of the cardiac impulse. 3. Characteristics of very slow conduction. J Gen Physiol (1972) 59:227–246.[Abstract/Free Full Text]
  41. Gilmour RF Jr., Zipes DP. Electrophysiological response of vascularized hamster cardiac transplants to ischemia. Circ Res (1982) 50:599–609.[Abstract/Free Full Text]
  42. Cardinal R, Janse MJ, Van Eeden I, Werner G, d'Alnoncourt CN, Durrer D. The effects of lidocaine on intracellular and extracellular potentials, activation, and ventricular arrhythmias during acute regional ischemia in the isolated porcine heart. Circ Res (1981) 49:792–806.[Free Full Text]
  43. Nichols CG, Lederer WJ. The regulation of ATP-sensitive K channel activity in intact and permeabilized rat ventricular myocytes. J Physiol (1990) 423:91–110.[Abstract/Free Full Text]
  44. Allen DG, Morris PG, Orchard CH, Pirolo JS. A nuclear magnetic resonance study of metabolism in the ferret heart during hypoxia and inhibition of glycolysis. J Physiol (Lond) (1985) 361:185–204.[Abstract/Free Full Text]
  45. Elliott AC, Smith GL, Allen DG. Simultaneous measurements of action potential duration and intracellular ATP in isolated ferret hearts exposed to cyanide. Circ Res (1989) 64:583–591.[Abstract/Free Full Text]
  46. Venkatesh N, Lamp ST, Weiss JN. Sulfonylureas, ATP-sensitive K+ channels, and cellular K+ loss during hypoxia, ischemia, and metabolic inhibition in mammalian ventricle. Circ Res (1991) 69:623–637.[Abstract/Free Full Text]
  47. Faivre JF, Findlay I. Action potential duration and activation of ATP-sensitive potassium current in isolated guinea-pig ventricular myocytes. Biochim Biophys Acta (1990) 1029:167–172.[Medline]
  48. Philipson KD, Bersohn MM, Nishimoto AY. Effects of pH on Na+–Ca2+ exchange in canine cardiac sarcolemmal vesicles. Circ Res (1982) 50:287–293.[Abstract/Free Full Text]
  49. Doering AE, Lederer WJ. The mechanism by which cytoplasmic protons inhibit the sodium–calcium exchanger in guinea-pig heart cells. J Physiol (1993) 466:481–499.[Abstract/Free Full Text]
  50. Le Guennec JY, Noble D. Effects of rapid changes of external Na+ concentration at different moments during the action potential in guinea-pig myocytes. J Physiol (1994) 478(3):493–504.[Abstract/Free Full Text]
  51. Sano T, Hiraoka M, Sawanobori T. Effects of anoxia and metabolic inhibitors on reactivation of the fast sodium system. In: Kobayashi T, Sano T, Dhalla NS, editors. Recent advances in studies on cardiac structure and metabolism, Vol. 11. Baltimore: University Press, 1978:79–83.
  52. Cascio WE, Yan GX, Kléber AG. Early changes in extracellular potassium in ischemic rabbit myocardium. The role of extracellular carbon dioxide accumulation and diffusion. Circ Res (1992) 70:409–422.[Abstract/Free Full Text]
  53. Sato T, Kiyosue T, Arita M. Inhibitory effects of palmitoylcarnitine and lysophosphatidylcholine on the sodium current of cardiac ventricular cells. Pflugers Arch (1992) 420:94–100.[CrossRef][Web of Science][Medline]
  54. Wu J, Corr PB. Influence of long-chain acylcarnitines on voltage-dependent calcium current in adult ventricular myocytes. Am J Physiol (1992) 263:H410–H417.[Web of Science][Medline]
  55. Sato R, Noma A, Kurachi Y, Irisawa H. Effects of intracellular acidification on membrane currents in ventricular cells of the guinea pig. Circ Res (1985) 57:553–561.[Abstract/Free Full Text]
  56. Harvey RD, Ten Eick RE. On the role of sodium ions in the regulation of the inward-rectifying potassium conductance in cat ventricular myocytes. J Gen Physiol (1989) 94:329–348.[Abstract/Free Full Text]
  57. Whalley DW, Wendt DJ, Grant AO. Electrophysiological effects of acute ischemia and reperfusion and their role in the genesis of cardiac arrhythmias. In: Podrid PJ, Kowey PR, editors. Cardiac arrhythmias: mechanisms, diagnosis, and management. Baltimore: Williams and Wilkins, 1994:109–130.
  58. Tani M, Neely JR. Role of intracellular Na+ in Ca2+ overload and depressed recovery of ventricular function of reperfused ischemic rat hearts. Possible involvement of H+–Na+ and Na+–Ca2+ exchange. Circ Res (1989) 65:1045–1056.[Abstract/Free Full Text]
  59. Steenbergen C, Murphy E, Watts JA, London RE. Correlation between cytosolic free calcium, contracture, ATP, and irreversible ischemic injury in perfused rat heart. Circ Res (1990) 66:135–146.[Abstract/Free Full Text]
  60. Maruyama T, Cascio WE, Knisley SB, Buchanan J, Gettes LS. Effects of ryanodine and BAY K 8644 on membrane properties and conduction during simulated ischemia. Am J Physiol (1991) 261:H2008–H2015.[Web of Science][Medline]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Circ Arrhythmia ElectrophysiolHome page
A. S. Barth and G. F. Tomaselli
Cardiac Metabolism and Arrhythmias
Circ Arrhythmia Electrophysiol, June 1, 2009; 2(3): 327 - 335.
[Full Text] [PDF]

Home page
 Exp PhysiolHome page
S. A. Niederer, M. Fink, D. Noble, and N. P. Smith
A meta-analysis of cardiac electrophysiology computational models
Exp Physiol, May 1, 2009; 94(5): 486 - 495.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Physiol. Renal Physiol.Home page
A. Edwards and T. L. Pallone
Mechanisms underlying angiotensin II-induced calcium oscillations
Am J Physiol Renal Physiol, August 1, 2008; 295(2): F568 - F584.
[Abstract] [Full Text] [PDF]

Home page
 Circ. Res.Home page
K. Gima and Y. Rudy
Ionic Current Basis of Electrocardiographic Waveforms: A Model Study
Circ. Res., May 3, 2002; 90(8): 889 - 896.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow FREE Full Text (PDF) Freely available
Right arrow E-letters: Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when E-letters are posted
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Disclaimer
Google Scholar
Right arrow Articles by Shaw, R. M.
Right arrow Articles by Rudy, Y.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Shaw, R. M.
Right arrow Articles by Rudy, Y.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?