Figure 1.
Some events that occur during myocardial ischemia and reperfusion.
During ischemia, ATP depletion leads to inhibition of the sodium-potassium exchanger (NaK) and increased efflux through the ATP-regulated potassium channel () (1). Also, increased anaerobic metabolism produces a metabolic acidosis (1). Increased
and decreased NaK flux contribute to the accumulation of extracellular potassium (2) (larger font). In addition, intracellular acidosis drives increased flux through the sodium-proton exchanger (NHE), contributing to extracellular acidosis (larger font) and intracellular sodium accumulation (2), worsened by decreased NaK flux. Increased intracellular sodium results in the sodium-calcium exchanger (NCX) operating more in the reverse mode, contributing to increased myoplasmic calcium concentration (3). High intracellular calcium concentrations can lead to abnormal sarcoplasmic reticulum calcium cycling and proarrhythmic phenomena. Upon reperfusion, washout of acidotic, hyperkalemic extracellular fluid occurs (4), reducing the concentrations of extracellular potassium and protons (smaller font). The resulting proton gradient allows increased flux through the NHE, resulting in exacerbations of intracellular sodium (5) and calcium (6) overloads (larger font) and additional proarrhythmic phenomena. Note that numbers in this legend correspond to encircled numbers in figure, not references.
Figure 2.
The model is an LRd model (black), with additions and modifications that were implemented from the CS (green) [8] and TCS [6] models (red), as well as an improved SERCA pump from [13] (purple), late sodium current from [27] (grey), the implementation of ATP-modified L-type calcium channel availability from [26] (orange), and novel additions by the authors (blue). Shaded components represent those that are regulated by pH and/or phosphometabolites. The model includes systems of equations that regulate concentrations of ATP, ADP, AMP, inorganic phosphate, creatine, and phosphocreatine, as well as impermeant metabolites that affect water flux. Abbreviations: Anion: generic anion species produced during ischemia; NCX, sodium-calcium exchanger; NHE, sodium-hydrogen exchanger; NBC, sodium-bicarbonate symporter; CHE, chloride-hydroxide exchanger; AE, anion exchanger; CMDN, calmodulin; TRPN, troponin C; CSQN, calsequestrin; JSR, junctional sarcoplasmic reticulum; NSR, network sarcoplasmic reticulum.
Figure 3.
Representative action potentials from the control simulation (no NHE inhibition).
In (A), the last action potential prior to the onset of ischemia (black), at the end of ischemia (gray), and after ten minutes of reperfusion (red) are shown. Panel (B) shows four responses to stimulation during late ischemia, approximately half a minute before the onset of reperfusion. The resting membrane potential is highly depolarized, and only every other stimulus generates an action potential.
Figure 4.
Comparison of mathematical model behavior to experimental data.
Changes in (A) intracellular pH (), (B) extracellular pH (
), and (C) intracellular sodium (
) concentration during experimental (circles) and simulated (lines) ischemia (gray region) and reperfusion. For (A), the dashed line denotes the part of the simulation in which
was prescribed by the ischemia-reperfusion protocol (Eq. 3). The solid line represents the part of the simulation in which
evolved according to the model equations (Eq. 29). Data points and error bars were extracted from [30] using the DigitizeIt software (share-it!, Denmark). For (B), the dashed line denotes the part of the simulation in which
was prescribed by the ischemia-reperfusion protocol (Eq. 28). The solid line represents the part of the simulation in which
evolved according to the model equations (Eq. 4). Data points and error bars were extracted from [32] using the DigitizeIt software (share-it!, Denmark). For (C), data points and error bars were extracted from [33] using the DigitizeIt software (share-it!, Denmark).
Table 1.
Initial conditions.
Figure 5.
Changes in ion concentrations and pH during simulated reperfusion.
(A) intracellular sodium (), (B) maximum and minimum intracellular calcium (
), and (C) intracellular pH (
) during simulated ischemia (gray region) and reperfusion during four simulations: Control (with no NHE inhibition) (black), NHE inhibition beginning with reperfusion at 50 percent (blue) or 100 percent (green) reduction, and 100 percent NHE blockade beginning with ischemia (light blue). In (B), the three insets, plotted on the same vertical axis as the main figure, show 2000 ms of intracellular calcium transients corresponding to the regions denoted by the vertical dashed lines: just prior to the onset of ischemia (left); during late ischemia, demonstrating alternans (middle); and late in the observed reperfusion window (right).
Figure 6.
Changes in ion concentrations and pH: peak intracellular sodium during reperfusion (A), end-ischemic intracellular sodium (B), peak intracellular calcium during reperfusion (C), and intracellular pH after 10 minutes of reperfusion (D).
In addition to the control simulation (no NHE inhibition), simulations were performed in which NHE flux was either reduced by 50 percent or completely blocked beginning at the onset of reperfusion (blue), half-way through ischemia (red), or at the onset of ischemia (green).
Table 2.
Intracellular sodium.
Table 3.
Intracellular calcium.
Table 4.
Intracellular pH.
Figure 7.
Number of sodium ions moved during each simulated reperfusion by each of eight sodium components: the L-type calcium channel (
), rapid sodium current (
), background sodium current (
), late sodium current (
), sodium-potassium exchanger (NaK), sodium-calcium exchanger (NCX), sodium-bicarbonate symporter (NBC), and sodium-exchanger (NHE). In addition to the control simulation (no NHE inhibition), simulations were performed in which NHE flux was either reduced by 50 percent or completely blocked beginning at the onset of reperfusion (blue), half-way through ischemia (red), or at the onset of ischemia (green).
Table 5.
Net number of sodium moles moved (×).
Table 6.
Proportion of total number of sodium moles moved.
Figure 8.
Removing pH-induced inhibition of sodium-potassium exchange decreases sodium and calcium overload during simulated reperfusion.
Ischemic phase of simulations denoted by gray shading. The three simulations shown are: Control (with no NHE inhibition) (black), R0 (complete NHE block instituted at the beginning of reperfusion) (green), and R0, but with the NaK responding to a normal pH as opposed to an acidotic pH being sensed by the rest of the subcellular components (gray). Intracellular sodium concentrations are shown in (A), maximum and minimum intracellular calcium concentrations are shown in (B), and maximum and minimum current through the sodium-potassium exchanger () during each beat are shown in (C). If the sodium-potassium exchanger is not inhibited by intracellular acidosis, significant reductions in sodium and calcium overload during reperfusion are observed, due to increased ability of the exchanger to remove sodium from the cell. The left inset in (C) shows
over 150 ms, plotted on the same vertical axis as the main figure, during the last beat prior to the onset of ischemia. The right inset shows current traces, on the same scale, during the last beat of the simulation.
Table 7.
Intracellular bicarbonate.