A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model has been written to be compatible with CMISS. Alone it cannot be run and a new version will have to be created.
Model Structure
ABSTRACT: A mathematical model of the cardiac ventricular action potential is presented. In our previous work, the membrane Na+ current and K+ currents were formulated. The present article focuses on processes that regulate intracellular Ca2+ and depend on its concentration. The model presented here for the mammalian ventricular action potential is based mostly on the guinea pig ventricular cell. However, it provides the framework for modeling other types of ventricular cells with appropriate modifications made to account for species differences. The following processes are formulated: Ca2+ current through the L-type channel (ICa), the Na(+)-Ca2+ exchanger, Ca2+ release and uptake by the sarcoplasmic reticulum (SR), buffering of Ca2+ in the SR and in the myoplasm, a Ca2+ pump in the sarcolemma, the Na(+)-K+ pump, and a nonspecific Ca(2+)-activated membrane current. Activation of ICa is an order of magnitude faster than in previous models. Inactivation of ICa depends on both the membrane voltage and [Ca2+]i. SR is divided into two subcompartments, a network SR (NSR) and a junctional SR (JSR). Functionally, Ca2+ enters the NSR and translocates to the JSR following a monoexponential function. Release of Ca2+ occurs at JSR and can be triggered by two different mechanisms, Ca(2+)-induced Ca2+ release and spontaneous release. The model provides the basis for the study of arrhythmogenic activity of the single myocyte including afterdepolarizations and triggered activity. It can simulate cellular responses under different degrees of Ca2+ overload. Such simulations are presented in our accompanying article in this issue of Circulation Research.
The original paper reference is cited below:
A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes, Ching-hsing Luo and Yoram Rudy, 1994, Circulation Research, 74, 1071-1097. PubMed ID: 7514509
cell diagram of the LR-II model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum
A schematic diagram describing the ionic currents, pumps and exchangers that are captured in the LR-II model. The intracellular compartment is the sarcoplasmic reticulum (SR), which is divided into the two subcompartments, the network SR (NSR) and the junctional SR (JSR). Ca2+ buffers are present in both the cytoplasm and the JSR.
The opening rate of the d gate.
The kinetics of the m gate.
The closing rate of the d gate.
The reversal potential for the channel.
The release flux from the junctional sarcoplasmic reticulum into the
cytosol.
The calcium component of the total L-type channel current.
The opening rate for the K1 gate.
The potassium component of the channel's current.
The opening rate of the f gate.
We need to use dV/dt in the calulation of calcium-induced
calcium-release, so we make it accessible here.
The maximum calcium component of the total L-type channel current.
Calculation of the exchanger current.
The maximum sodium component of the channel's current.
The gating kinetics for the channel.
The kinetics of for the j gate.
The reversal potential of the channel.
The maximum potassium component of the channel's current.
The kinetics of the h gate.
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
The steady-state kinetics of the K1 gate.
Assign the rate of change of potential for the differential
equation.
Calculation of the fast sodium current.
The change in calcium concentration in the junctional sarcoplasmic
reticulum.
The change in intracellular calcium concentration.
Calcium leak flux from the network sarcoplasmic reticulum into the
cytosol.
The kinetics of the f gate.
The total current through the channel.
Calculation of the channel conductance.
The closing rate for the h gate.
The change in intracellular potassium concentration.
The opening rate for the j gate.
The sodium component of the total L-type channel current.
Calculation of the release channel conductance. This is incorrect as
there is no CICR induced via the accumulation of calcium in the
cytosol in the period following max(dV/dt)
Calculation of the channel current.
Calculation of the current.
The reversal potential for the channel.
Calculation of the current.
The closing rate for the X gate.
The kinetics of the Xi gate.
The sodium component of the channel's current.
Calculation of the exchanger current.
Translocation flux from the network to the junctional sarcoplasmic
reticulum.
The opening rate for the h gate.
The closing rate for the j gate.
The maximum sodium component of the total L-type channel current.
The closing rate for the K1 gate.
The opening rate for the X gate.
Calculation of the current.
The total current of the L-type channel current.
The change in intracellular sodium concentration.
The closing rate of the f gate.
The opening rate for the m gate.
The conductance for the channel.
The kinetics of the fCa gate.
The calcium pump current.
The channel reversal potential.
Component grouping together the differential equations for the
various ionic concentrations that the model tracks.
The change in calcium concentration in the network sarcoplasmic
reticulum.
The kinetics of the d gate.
The potassium component of the total L-type channel current.
Calculation of reversal potential for the fast sodium channel.
The uptake flux into the sarcoplasmic reticulum from the cytosol.
The closing rate for the m gate.
Calculation of the channel reversal potential.
Calculation of the current.
The kinetics of the X gate.
The reversal potential for the channel.
The maximum potassium component of the total L-type channel current.