Luo-Rudy Model for Ventricular Cells

One Cell

This model is used to simulate the activation of ventricular cells. As in the Hodgkin-Huxley and Beeler-Reuter applet , one can change the time for the second stimulus (S2) and conductances. Also, one can plot all 8 variables of the model.

In 1991 Luo and Rudy (1991) presented an ionic model (LR-I) for the cardiac AP in guinea pig ventricular cells based on the BR-model ( Circ. Res. Vol 68 pg 1501-1526, 1991 by C. Luo and Y. Rudy), but updated to include more recent experimental results. They reformulated the opening and closing rate coefficients for the sodium current from the BR-model making it a faster process and added three new currents: one plateau potassium current, one background current with constant conductance and an additional potassium current with a gate variable that can be approximated by its steady-state value due to a small time constant. They retained the BR formulation for the slow inward calcium current as well as the time-dependent potassium current. However, they allowed the possibility of changing the extracellular potassium concentration. In total, phase one of the Luo-Rudy model (LR-I) describes six different currents and uses nine variables, one of which is approximated by its steady state and is replaced by a function, so that only eight variables are needed in the calculation. Later, Luo and Rudy updated their model further to produce the LR-II model ( Luo, C.-H., Rudy, Y., 1994. A Dynamic Model of the Cardiac Ventricular Action Potential: I. Simulations of Ionic Currents and Concentration Changes. Circulation Research 74, 1071-1096.), since then many more processes including ionic pumps and exchangers have been added and is currently known as the LRd (dynamic) model (see for example Clancy, C., Rudy, Y., 2001. Cellular Consequences of HERG Mutations in the Long QT Syndrome: Precursors to Sudden Cardiac Death. Cardivas. Res. 50, 301-313. , and references therein).

The LR-I, in contrast to the BR model, produces an AP with a faster upstroke more consistent with experimental observations. From our experience with the BR model in the previous section, we expect that because of the faster sodium dynamics, the APD produced by the LR-I model will be longer and with higher depolarization. Therefore we can predict that this model will be more excitable and will be able to produce excitations at shorter S1-S2 coupling intervals. We can also anticipate that the change in APD size at shorter S1-S2 coupling intervals will be smaller than for the BR model, and indeed this is the case, as one can see by "playing" with the applet.