Luo-Rudy model is a very robust computational model for cardiac myocyte, which is designed for the ventricle of guinea pig. Many later models were constructed based on the ionic descriptions given by Luo-Rudy model even for different parts of heart and species. For the updating of Luo-Rudy model, many efforts have been made. First note that in the Luo-Rudy model the opening time of Calcium-Induced-Calcium-Release (CICR) from sarcoplasmic reticulum (SR) is not determined “dynamically” by the transmembrane potential or calcium concentration; After the imposed duration “2 ms” from the upstroke of action potential, the CICR occurs. To modify this drawback, some key features for the ryanodine release channels (RyRs) on the SR, through which CICR occurs, must be depicted: graded release, fractional release, and variable gain. Graded release of CICR means that the magnitude of Ca2+ entry via the L type calcium channel “ICa(L)” determines the number of RyRs openings; thus small ICa(L) results in small SR release compared to large ICa(L) resulting in large SR release. The fractional release of SR release means the ratio between the release amount of Ca2+ through CICR and the total Ca2+ content in SR. It has been shown experimentally that the dependence of fractional SR release as a function of SR Ca2+ content is strongly nonlinear. Gain is the ratio between the amount of Ca2+ released from the SR and the amount of Ca2+ entry into the myocyte that triggers SR release. In myocytes, it has been observed that for the same amount of triggering Ca2+, the magnitude of release can vary as a function of the transmembrane potential, a property called “variable gain”. To describe the above RyRs’ properties, various hypotheses or formula have been proposed, e.g., activation and inactivation behaviors induced by the Ca2+ buffer in SR and Ca2+ in cytoplasm.
It was found that the Ca2+ concentration near the t-tubule is extraordinarily high compared to the other part of the cytoplasm. Therefore the “common pool” model was proposed (see ). That is, besides the two compartments SR and cytoplasm, another compartment “common pool” or “subspace” between the cell member in t-tubule and SR is added in the model.
Since the development of molecular biology and more clear structure of the protein structure of ion channel, various Markov chain models for various ions channels of cardiac myocytes have been proposed. However the signaling pathways inside the cell are very complicated and so the models with these coupling networks are also very intricate. In , the equations number is more than 100.
The newest Luo-Rudy series models are ,  derived by Y. Rudy’s lab.
Note that besides the electrophysiological viewpoint of heart, mechanics effects should also be considered in the cardiac model and the mutual feedbacks exist between them. The excitation-contraction-coupling (ECC) and mechano-electrical-feedback (MEF) are famous and have been incorporated into several models (, ).
. Cortassa S, Aon MA, O'Rourke B, Jacques R, Tseng HJ, Marbán E, Winslow RL. A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte. Biophys J. 2006 Aug 15;91(4):1564-89.
. Greenstein JL, Hinch R, Winslow RL. Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophys J. 2006 Jan 1;90(1):77-91.
. Greenstein JL, Wu R, Po S, Tomaselli GF, Winslow RL. Role of the calcium-independent transient outward current I(to1) in shaping action potential morphology and duration. Circ Res. 2000 Nov 24;87(11):1026-33.
. Greenstein JL, Winslow RL. An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. Biophys J. 2002 Dec;83(6):2918-45.
 Faber GM, Rudy Y. Calsequestrin mutation and catecholaminergic polymorphic ventricular tachycardia: a simulation study of cellular mechanism. Cardiovasc Res. 2007 Jul 1;75(1):79-88.
 Faber GM, Silva J, Livshitz L, Rudy Y. Kinetic properties of the cardiac L-type Ca2+ channel and its role in myocyte electrophysiology: a theoretical investigation. Biophys J. 2007 Mar 1;92(5):1522-43.
This article’s version needs a lot of work. Below are some comments that will help to make a better version for further review. In addition, we direct the author to other model articles already in Scholarpedia for ideas about format and style. http://www.scholarpedia.org/article/Noble_model http://www.scholarpedia.org/article/Barkley_model http://www.scholarpedia.org/article/FitzHugh-Nagumo_model and http://www.scholarpedia.org/article/Models_of_cardiac_cell
1. The article in many places is written more in the style of a historical report rather than as a scholarly article. We do not need to know about a graduate student’s complaints or the author’s perception of the scientific community’s response to the model, for instance. Ans: What is the definition of scholarly article? A scholarly article cannot accept any history concerned about why the model is created to incite the interest of the readers. I deserver the reviewer's opinion but no change of the content. 2. The article mentions differences in ion channel expression and kinetics associated with different species. This is one of the key problems from earlier models, as there was not enough information in the literature from a single species. As one of the model creators, the author is in an excellent position to clarify the sources of the data used to construct the model. Which currents were specifically drawn from guinea pig data, and which species were utilized to formulate the expressions of the remaining currents? Ans: I do not think the website should provide such a detailed inforamtion about the speciese of each current for general knowledgement provided. People who need the professional inforamtion in details can read the original papers in the journals.
3. The article should clarify how the model relates to previously published models. The Luo-Rudy-1 model has essentially the same equations as the Beeler-Reuter model, just with some different parameter values. How do the Luo-Rudy dynamic model equations for concentrations and pumps relate to the DiFrancesco-Noble model? When the author mentions that the Luo-Rudy dynamic model introduces pumps and exchangers, its make it sound as if it was the first time these were included in a model, whereas DiFrancesco and Noble did so almost 10 years earlier. Ans: Yes, I temptly do not raise the issue of DiFrancesco and Noble model published in 1985. A disk to access this model costed about US$1000, but almost no one used DF model happily and scientists still used Beeler and Reuter. I am quite gentle not to directly say Luo-Rudy as the first dynamic models but it is true. Please guess someone publishing something that cannot be used or very difficult to be used, people could doubt the reality of the model itself. DF did publish the dynamic model but the experimental data of ion channels were not sufficient to from a dynamic models at that moment. If DF can revise their model in five years, Luo-Rudy model is no longer existed maybe. So, this is the reason I do not mention DF model. If I want to mention this model, the criticism must be added. This is not what I want as well as a scholoarpedia wants. Please allow me to jump DF model indirectly. Scholoarpedia perhaps can invite someone to write DF model.
4. The author calls the Luo-Rudy-1 model a passive model “because the ion concentrations inside the cell model is unchanged.” That is not completely true, as it has a varying calcium concentration.
5. The article must be edited substantially to conform with standard English usage. This point cannot be over-emphasized. Perhaps it would be a good idea if the author invites Yoram Rudy to co-author the article.
1. The article appears to be formatted improperly. Table of contents is absent, headings do not appear in heading format, etc.
2. Some numbered citations are made but the corresponding references are not included. More references should be added throughout the article. Statements such as “Several famous labs announced the calcium ion channels but they were quite scattering …” need to be substantiated. Also internal citations to other Scholarpedia articles could be made.
3. “Active” and “passive” should be described at their first mention as these terms are not used in the usual sense.
4. The generic description of an action potential is probably unnecessary, as this has been discussed in more detail elsewhere.
5. The last section, concerning DNA, is confusing and should be rewritten or eliminated. What is the relevance to a discussion of the Luo-Rudy model?
In relation to Reviewer C’s comments, I agree that one of the major problems of the Luo-Rudy-II model is the non-autonomous function for the CICR given by the 2ms measurement time after an upstroke. While un-physiological, another main problem appears in simulations in 2D and 3D where non-autonomous functions can give erroneous results due to electrotonic effects. These problems and shortcomings may need to be addressed, but I believe that a long and technical discussion of this nature may not be necessary for this kind of article, which after all has to deal mostly with the model (see for example the Noble, Barkley and FHN model articles).
Reviewer B (Editor):
I agree with the Referees A and C and believe that the paper may be approved for publication after their comments are taken into account.