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.
cardiac
ventricular myocyte
electrophysiology
Ching-hsing
Luo
The conductance for the channel.
The channel reversal potential.
Circulation Research
The time-dependent potassium reploarisation current.
The kinetics of the d gate.
The opening rate for the h gate.
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
The closing rate of the f gate.
Component grouping together the differential equations for the
various ionic concentrations that the model tracks.
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 calcium pump current.
The steady-state kinetics of the K1 gate.
The maximum sodium component of the channel's current.
7514509
The potassium current active at plateau potentials.
Calculation of the current.
The change in intracellular calcium concentration.
The maximum potassium component of the total L-type channel current.
The Luo-Rudy II Model of Mammalian Ventricular Cardiac Action
Potentials, 1994
Ventricular Myocyte
Mammalia
The background sodium current.
The closing rate for the m gate.
The various calcium fluxes into and from the sarcoplasmic reticulum.
The time-dependent activation gate for the time-dependent potassium
current - the X gate.
The total current of the L-type channel current.
The opening rate for the K1 gate.
The University of Auckland
Auckland Bioengineering Institute
The background calcium 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.
Catherine
Lloyd
May
The kinetics of the h gate.
Calculation of the channel conductance.
A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes
74
1071
1096
The reversal potential for the channel.
Catherine
Lloyd
May
We need to use dV/dt in the calulation of calcium-induced
calcium-release, so we make it accessible here.
The reversal potential for the channel.
The time-independent potassium repolarisation current.
The closing rate for the h gate.
7514509
Ching-hsing
Luo
The voltage-dependent slow inactivation gate for the fast sodium
channel - the j gate.
1994-06-01
The kinetics of the X gate.
The change in intracellular sodium concentration.
The voltage-dependent inactivation gate for the fast sodium channel -
the h gate.
Calculation of the exchanger current.
The voltage-dependent activation gate for the L-type calcium
channel - the d 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.
James Lawson
The potassium component of the total L-type channel current.
The main component for the model, contains all ionic currents and
defines the transmembrane potential.
c.lloyd@auckland.ac.nz
The release flux from the junctional sarcoplasmic reticulum into the
cytosol.
The opening rate for the X gate.
The potassium component of the channel's current.
The kinetics of the Xi gate.
The gating variable for the time-independent potassium current - the K1 gate.
2002-03-28
The kinetics of the m gate.
The calcium-dependent inactivation gate for the L-type calcium
channel - the fCa gate.
Calculation of the current.
Yoram
Rudy
Calculation of the 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)
Catherine Lloyd
The calcium component of the total L-type channel current.
The kinetics of the f gate.
The closing rate for the X gate.
Calculation of the exchanger current.
Fixed maths.
The change in calcium concentration in the network sarcoplasmic
reticulum.
The L-type calcium channel. Primarily a calcium specific channel,
but with small potassium and sodium components, activated at plateau
potentials.
The closing rate of the d gate.
The kinetics of the fCa gate.
The sodium component of the channel's current.
The opening rate for the j gate.
Calculation of the channel current.
The University of Auckland, Auckland Bioengineering Institute
The change in intracellular potassium concentration.
The fast sodium current is primarily responsible for the upstroke of
the action potential.
Calculation of reversal potential for the fast sodium channel.
Catherine
Lloyd
May
The sodium-calcium exchanger current, exchanges three sodium ions
for one calcium ion.
The opening rate of the f gate.
The gating kinetics for the channel.
The maximum sodium component of the total L-type channel current.
The voltage-dependent inactivation gate for the L-type calcium
channel - the f gate.
Calculation of the channel reversal potential.
Catherine
Lloyd
May
Assign the rate of change of potential for the differential
equation.
keyword
The kinetics of for the j gate.
The uptake flux into the sarcoplasmic reticulum from the cytosol.
Calculation of the fast sodium current.
2003-06-05
The University of Auckland, Auckland Bioengineering Institute
The opening rate for the m gate.
A non-specific calcium activated channel - assumed impermeable to
calcium ions but permeable to sodium and potassium ions.
The sodium/potassium exchanger current which extrudes three sodium
ions from the cell in exchange for two potassium ions entering the
cell.
The University of Auckland
Auckland Bioengineering Institute
The maximum calcium component of the total L-type channel current.
2002-03-28T00:00:00+00:00
A Dynamic Model of the Cardiac Ventricular Action Potential I. Simulations of Ionic Currents and Concentration Changes
74
1071
1096
The closing rate for the K1 gate.
c.lloyd@auckland.ac.nz
The time-independent inactivation gate for the time-dependent
potassium current - the Xi gate.
2003-07-30
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 total current through the channel.
Yoram
Rudy
The maximum potassium component of the channel's current.
1994-06-01
A calcium pump for removal of calcium from the cytosol to the
extracellular space.
The reversal potential for the channel.
The change in calcium concentration in the junctional sarcoplasmic
reticulum.
The reversal potential of the channel.
The sodium component of the total L-type channel current.
The closing rate for the j gate.
Translocation flux from the network to the junctional sarcoplasmic
reticulum.
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
Catherine Lloyd
The opening rate of the d gate.
Calculation of the current.
Circulation Research
Calcium leak flux from the network sarcoplasmic reticulum into the
cytosol.