Research

IONIC CHARGE CONSERVATION AND MODEL STABILITY

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Hund, T. J., J. P. Kucera, et al. (2001). "Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model." Biophys J 81(6): 3324-31.

"It has been reported in the literature that dynamic cell models, which account for changes in intracellular ion concentrations, show a nonphysiological drift in computed parameters (Yehia et al., 1999; Endresen et al., 2000; Rappel, 2001). This drift occurs during rapid pacing for prolonged periods of time (Yehia et al., 1999; Rappel, 2001). The results of the present study establish that such drift is due to a nonconservative implementation of the stimulus, and not to an intrinsic property of the LRd model. The drift disappears when ions carried by the stimulus current are accounted for in the computation of ion concentrations. In general, when using a dynamic model, any source of charge (such as the stimulus) must also be considered a source of ions. Failure to do so violates conservation and may produce a nonphysiological behavior due to drift of model parameters. In this study, the problem is easily corrected by incorporating the stimulus current into the total K+current in the LRd formulation. Assuming that other ions in the system (Na+ and Ca2+) to be the stimulus charge carrier is also consistent with the conservation principle, as long as these ions are accounted for in the formulation."
FIGURE 5 (A) Vm,dia as a function of time during pacing with a current stimulus at a BCL of 300 ms using the algebraic method (solid line) and the differential method (dashed line indicated with arrow). In both cases, the stimulus current carries K+ ions into the cell and contributes directly to computed changes in intracellular ion concentrations. Note the lack of drift and identical results for both methods. An additional simulation is shown using the differential method and a current stimulus that does not carry a particular ion species into the cell (dash-dot line). Notice that computed parameters drift if charges carried by the stimulus current are not taken into account in the computation of ion concentration changes.

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