Luo-Rudy Mammalian Ventricular Model I 1991

In 1991, Ching-hsing Luo and Yoram Rudy published a mathematical model of the ventricular cardiac action potential. This original model is the first of the two Luo-Rudy models, and it has subsequently come to be known as the Luo-Rudy I model. It is a significant update of the Beeler-Reuter mammalian ventricular model (1977) (see Figure 1 below), and like the the Beeler-Reuter model, the Luo-Rudy I model uses Hodgkin-Huxley type equations to calculate ionic currents.

The complete original paper reference is cited below:

A Model of the Ventricular Cardiac Action Potential - Depolarisation, Repolarisation and Their Interaction,, Ching-hsing Luo and Yoram Rudy, 1991 Circulation Research, 68, 1501-1526. PubMed ID: 1709839

The raw CellML description of the Luo-Rudy I model can be downloaded in various formats as described in the section “Download This Model”. For an example of a more complete documentation for an electrophysiological model, see The Hodgkin-Huxley Squid Axon Model, 1952.

Figure 1. A schematic diagram describing the current flows across the cell membrane that are captured in the LR-I model.

Figure 2. The network defined in the CellML description of the Luo-Rudy I model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the notation guide.

The membrane physically contains the currents, as indicated by the blue arrows in Figure 2. The currents act independently and are not connected to each other. Four of the channels encapsulate and contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.

The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.

The CellML description of this model is available in a number of formats. If you have your browser set up to view text files served with the “text/xml” MIME type, then you can have a look at the XML file here. If not, you can save that file to disk by shift-clicking on the preceding link. A “pretty-printed” browsable HTML version of the XML file is available here — note that you cannot download and save this version for later viewing since it makes use of stylesheets for formatting. If you wish to save or print out the “pretty-printed” version of the XML, a PDF version is also available here. A gzipped tarball (the Unix equivalent of a winzip file) including this documentation, the raw XML and the pretty-printed PDF version of the XML is available here.

Here are those links again: