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 gating variable for the time-independent potassium current - the K1 gate.
The reversal potential for the channel.
The opening rate for the K1 gate.
We need to use dV/dt in the calulation of calcium-induced
calcium-release, so we make it accessible here.
c.lloyd@auckland.ac.nz
The maximum calcium component of the total L-type channel current.
Calculation of the exchanger current.
Circulation Research1994-06-01
Fixed maths.
The gating kinetics for the channel.
The Luo-Rudy II Model of Mammalian Ventricular Cardiac Action
Potentials, 1994
Ventricular MyocyteMammalia
The kinetics of for the j gate.
The reversal potential of the channel.
The kinetics of the h gate.
This is the CellML description of Luo and Rudy's mathematical model of the mammalian cardiac ventricular action potential. It is a significant development on their original 1991 model. While this version of the model qualitatively compares well to the LR II paper for the action potential, the intracellular calcium dynamics have not been included correctly - namely there is no calcium-induced calcium-release (CICR) process in this version of the model. The original version of the model simulates CICR via a mechanism whereby CICR is induced if and only if the calcium accumulated in the cell in the 2 ms following (dV/dt)max exceeds a given threshold. This sort of process is a bit tricky to include in the CellML (or at least in a way that will work with the CellML abilitites of CMISS) so has been left out for now.
The background calcium current.
The time-dependent potassium reploarisation current.
MayCatherineLloyd
The opening rate of the f gate.
The calcium component of the total L-type channel current.
Assign the rate of change of potential for the differential
equation.
The voltage-dependent inactivation gate for the fast sodium channel -
the h gate.
Catherine Lloyd
The change in calcium concentration in the junctional sarcoplasmic
reticulum.
The change in intracellular calcium concentration.
7514509
The total current through the channel.
Calculation of the channel conductance.
The change in intracellular potassium concentration.
The time-dependent activation gate for the time-dependent potassium
current - the X gate.
2003-06-05c.lloyd@auckland.ac.nz
The maximum sodium component of the channel's current.
MayCatherineLloyd
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 current.
2002-03-28T00:00:00+00:00
The maximum potassium component of the channel's current.
A non-specific calcium activated channel - assumed impermeable to
calcium ions but permeable to sodium and potassium ions.
YoramRudy
Calculation of the current.
The closing rate of the d gate.
Catherine Lloyd
The potassium current active at plateau potentials.
2002-03-28
The sodium component of the channel's current.
The sodium-calcium exchanger current, exchanges three sodium ions
for one calcium ion.
The voltage-dependent inactivation gate for the L-type calcium
channel - the f gate.
Ching-hsingLuo
The main component for the model, contains all ionic currents and
defines the transmembrane potential.
The background sodium current.
The closing rate for the X gate.
The fast sodium current is primarily responsible for the upstroke of
the action potential.
Translocation flux from the network to the junctional sarcoplasmic
reticulum.
keyword
The time-independent potassium repolarisation current.
The closing rate for the j gate.
The closing rate for the K1 gate.
The University of Auckland, Auckland Bioengineering Institute
The opening rate for the X gate.
Calculation of the current.
The kinetics of the Xi gate.
The time-independent inactivation gate for the time-dependent
potassium current - the Xi gate.
The total current of the L-type channel current.
The L-type calcium channel. Primarily a calcium specific channel,
but with small potassium and sodium components, activated at plateau
potentials.
The closing rate for the h gate.
The maximum sodium component of the total L-type channel current.
The change in intracellular sodium concentration.
A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes7410711096.110000
The kinetics of the f gate.
The voltage-dependent slow inactivation gate for the fast sodium
channel - the j gate.
Fixed maths: alpha_J_calculation in fast_sodium_current_j_gate, beta_K1_calculation in time_independent_potassium_current_K1_gate, and i_NaK_calculation in sodium_potassium_pump.
The conductance for the channel.
MayCatherineLloyd7514509
The kinetics of the fCa gate.
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
The change in calcium concentration in the network sarcoplasmic
reticulum.
The University of AucklandAuckland Bioengineering Institute
The kinetics of the d gate.
Calculation of reversal potential for the fast sodium channel.
YoramRudy
The calcium pump current.
This is the CellML description of Luo and Rudy's mathematical model of the mammalian cardiac ventricular action potential. It is a significant development on their original 1991 model. While this version of the model qualitatively compares well to the LR II paper for the action potential, the intracellular calcium dynamics have not been included correctly - namely there is no calcium-induced calcium-release (CICR) process in this version of the model. The original version of the model simulates CICR via a mechanism whereby CICR is induced if and only if the calcium accumulated in the cell in the 2 ms following (dV/dt)max exceeds a given threshold. This sort of process is a bit tricky to include in the CellML (or at least in a way that will work with the CellML abilitites of CMISS) so has been left out for now.
The potassium component of the total L-type channel current.
The sodium/potassium exchanger current which extrudes three sodium
ions from the cell in exchange for two potassium ions entering the
cell.
The closing rate of the f gate.
Circulation Research
The opening rate for the m gate.
James Lawson
The voltage-dependent activation gate for the L-type calcium
channel - the d gate.
2003-07-30
Calcium leak flux from the network sarcoplasmic reticulum into the
cytosol.
The calcium-dependent inactivation gate for the L-type calcium
channel - the fCa gate.
1994-06-01
The release flux from the junctional sarcoplasmic reticulum into the
cytosol.
The closing rate for the m gate.
The reversal potential for the channel.
The channel reversal potential.
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
Ching-hsingLuo
Calculation of the channel reversal potential.
This model contains a delay element in its mathematical description of CICR. Discrete delay elements can not yet be represented in CellML (as of CellML version 1.1) as as such, this model is non-functional.
The University of Auckland, Auckland Bioengineering Institute
Calculation of the current.
Calculation of the channel current.
The potassium component of the channel's current.
The various calcium fluxes into and from the sarcoplasmic reticulum.
The sodium component of the total L-type channel current.
The kinetics of the X gate.
cardiacventricular myocyteelectrophysiology
Calculation of the fast sodium current.
A calcium pump for removal of calcium from the cytosol to the
extracellular space.
A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes7410711096
The reversal potential for the channel.
The uptake flux into the sarcoplasmic reticulum from the cytosol.
The opening rate for the h gate.
MayCatherineLloyd
The steady-state kinetics of the K1 gate.
The maximum potassium component of the total L-type channel current.
Calculation of the exchanger current.
The University of AucklandAuckland Bioengineering Institute
The opening rate for the j gate.
Component grouping together the differential equations for the
various ionic concentrations that the model tracks.