Noble Purkinje Fibre Model 1962
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in COR, JSim and OpenCell to recreate the published results. The units have been checked and they are consistent.
Model Structure
In 1962, Denis Noble published one of the first mathematical models of a cardiac cell. By adapting the equations of the original Hodgkin-Huxley squid axon model (1952), Noble described the long lasting action and pace-maker potentials of the Purkinje fibres of the heart. The potassium-current equations differ from those of Hodgkin and Huxley in that the potassium ions are assumed to flow through two types of channel in the membrane. By contrast, the sodium current equations are very similar to those of Hodgkin and Huxley.
The main failure of the Noble (1962) model is that it only includes one voltage gated inward current, INa. Calcium currents had not yet been discovered, but there was a clue in the model that something was missing. The only way the model could be made to work was to greatly extend the voltage range of the sodium current by reducing the voltage dependence of the sodium activation process. In effect the sodium current was made to serve the function of both the sodium and the calcium channels as far as the plateau is concerned. There was a clear experimental prediction: either sodium channels in the heart are quantitatively different from those in neurons, or other inward current-carrying channels must exist. Both predictions are correct.
The original paper reference is cited below:
A Modification of the Hodgkin-Huxley Equations Applicable to Purkinje Fibre Action and Pace-maker Potentials, Noble, D. 1962
Journal of Physiology
, 160, 317-352. PubMed ID: 14480151
model diagram
A schematic cell diagram describing the current flows across the cell membrane that are captured in the Noble 1962 model. Note that this image is identical to the schematic diagram which describes the Hodgkin-Huxley 1952 model. This is because the Noble 1962 model is based on the HH 1952 model, and the ony differences are in the parameters of the model, and also the gating of the potassium channel - and these differences do not show in the schematic diagram.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Na}+\mathrm{i\_K}+\mathrm{i\_Leak})}{\mathrm{Cm}}$
$\mathrm{g\_Na}=m^{3}h\mathrm{g\_Na\_max}\mathrm{i\_Na}=(\mathrm{g\_Na}+140)(V-\mathrm{E\_Na})$
$\mathrm{alpha\_m}=\frac{100(-V-48)}{e^{\frac{-V-48}{15}}-1}\mathrm{beta\_m}=\frac{120(V+8)}{e^{\frac{V+8}{5}}-1}\frac{d m}{d \mathrm{time}}=\mathrm{alpha\_m}(1-m)-\mathrm{beta\_m}m$
$\mathrm{alpha\_h}=170e^{\frac{-V-90}{20}}\mathrm{beta\_h}=\frac{1000}{1+e^{\frac{-V-42}{10}}}\frac{d h}{d \mathrm{time}}=\mathrm{alpha\_h}(1-h)-\mathrm{beta\_h}h$
$\mathrm{i\_K}=(\mathrm{g\_K1}+\mathrm{g\_K2})(V+100)\mathrm{g\_K1}=1200e^{\frac{-V-90}{50}}+15e^{\frac{V+90}{60}}\mathrm{g\_K2}=1200n^{4}$
$\mathrm{alpha\_n}=\frac{0.1(-V-50)}{e^{\frac{-V-50}{10}}-1}\mathrm{beta\_n}=2e^{\frac{-V-90}{80}}\frac{d n}{d \mathrm{time}}=\mathrm{alpha\_n}(1-n)-\mathrm{beta\_n}n$
$\mathrm{i\_Leak}=\mathrm{g\_L}(V-\mathrm{E\_L})$
Peter
Villiger
J
Catherine
Lloyd
May
Auckland Bioengineering Institute
Catherine Lloyd
c.lloyd@auckland.ac.nz
2006-03-31
Journal of Physiology
This models has been curated using the unit checker in COR and is now unit-consistent.
1962-01-01
The University of Auckland
Auckland Bioengineering Institute
14480151
2007-09-07T00:00:00+00:00
James Lawson
A Modification of the Hodgkin-Huxley Equations Applicable to Purkinje Fibre Action and Pace-Maker Potentials
160
317
352
added metadata
2005-05-04
This is the CellML description of Noble's 1962 mathematical model of Purkinje fibre action and pace-maker potentials. The equations formulated by Hodgkin and Huxley (1952) to describe the electrical activity of squid nerve have been modified to describe the action and pace-maker potentials of the Purkinje fibres of the heart.
keyword
purkinje
Purkinje fibre
electrophysiology
pacemaker
cardiac
Hodgkin-Huxley
penny.noble@physiol.ox.ac.uk
This model has been curated by both Penny Noble and James Lawson and is known to run in COR and PCEnv 0.2.
Penny
Noble
2007-09-07T13:50:26+12:00
D
Noble
Penny
Noble
Oxford University