The Shif-Fox model
Background
Alternans and calcium. There are several excellent cell models in the literature for a variety of cell types and conditions. However, a major limitation of these models is that they do not specifically address the properties of cardiac cells under rapid pacing. In particular, the important phenomenon of alternans, which is suspected to underlie various arrhythmias. See my NYAS paper for a review of alternans. Furthermore, Chudin and collaborators showed that alternans can be due purely from calcium cycling properties. Therefore, any serious attempt to describe alternans must include a model of calcium cycling valid at rapid stimulations rates.
To address this issue we developed a calcium cycling model which was based on direct experimental data from rabbit myocytes. The essential features of this model are:
1. Describes calcium alternans at rapid stimulations rates. The mechanism is built in using a steep SR release vs. SR load relationship. This mechanism has been verified experimentally by Eisner's group, although in a rather unphysiological setting.
2. The model is a local control model, not a single pool model, which in my opinion is the wrong approach. This is a critical aspect of the model which we spent a lot of time thinking about. Let me state the experimental facts: calcium release is due to thousands of calcium sparks. These are discrete release events occurring in dyadic junctions distributed throughout the cell. Cardiac excitation-contraction coupling cannot be understood or described without incorporating this fact. Our calcium model incorporates sparks in a phenomenological fashion, most models do not and are therefore inconsistent with experiments. See Stern's classic paper for a detailed discussion comparing common pool and local control models. Also, please read carefully the introduction and model development in our paper.
3. Since the model is phenomenological it is by design tractable and can be implemented in tissue simulations.
Bidirectional coupling. At rapid stimulation rates alternans can originate from a variety of mechanisms. Two distinct mechanisms are steep APD restitution and unstable calcium cycling. Remarkably, the bi-directional coupling between these components can lead to interesting single cell dynamics and some unexpected spatial instabilities. The main point here is that the bi-directional coupling between voltage and calcium endows the cardiac system with interesting properties. See our recent Circ. Res. paper on this issue, and our review article.
The model
To address these issues we coupled our calcium cycling cell model with Fox's dog action potential model. This is a good model which is based on currents from Luo-Rudy and papers from the Winslow group. The coupled model is now referred to as the Shif-Fox model (don't blame me, I did not name this!).
This model should be viewed as a quasi-minimal model which can be used to study dynamical features of voltage and calcium cyling. It does not represent a particular cell type. However, its features are more closely associated with rabbit and guinea-pig properties. The value of this model depends on the type of question you are asking. If you want to explore subtle features of the action potential shape, this is not the right model to use. However, if you are interested in basic features of calcium alternans dynamics during a spiral wave, then, in my opinion, this is an excellent model to use. This model will be most useful to explore basic dynamical mechanisms.
In my view this model strikes an excellent balance between realism and tractability. It has enough variables to account for many interesting dynamical features, yet can be easily implemented in 2d or 3d tissue simulations. To address specific cell types will require a minimal time investment to tune some of the currents. My goal is to setup a data base of similar cell models which researchers in the field can download and use. Hopefully, people can improve various aspects of the model and share their CODE.
Features
1. The model can be tuned so that alternans are due to either steep APD restitution or unstable Ca cycling. This can have dramatic effect on spatial patterns alternans as shown in our recent Biophysics letters paper. Here, restitution slope is modulated by adjusting the time constant of inactivation of the L-type calcium current. Ca cycling alternans originate from a steep SR release vs. SR load slope.
2. The model can be adjusted to exhibit both positive or negative Ca on APD coupling. This is a crucial parameter as spatiotemporal properties are extremely sensitive to coupling.
3. Based on the Fox model ion currents so AP shape is realistic. Also, APD and CV restitution properties are consistent with experiments.
CODE
FORTRAN code of the cell model incorporated in a 1d cable. The cell model is included in a subroutine. To study cell properties just make the cable short, or simply rewrite the code for 1 cell.
shif-fox-ca.f : Instability due to Ca cycling. Ca instability due to steep SR release vs. SR load relationship.
shif-fox-vol.f : Instability due to steep restitution. Restitution steepened by adjusting the time constant of Ca-induced inactivation of ICa.
Illustration of cell model is here. Illustration shows the more realistic local control picture along side the model reduction.
DOCUMENTATION: A description of the currents and model properties. Some parameters might have been changed.
Here is a c-code version courtesy of Dr. Trine Krogh-Madsen at Cornell. This was used in their Biophysical journal paper on discordant alternans in tissue: shiffox.c
Email me if you have any questions or comments.
UPDATES
The model code will be updated as feedback is received.
For students learning Fortran, download this code:
Some papers
Acknowledgement: This model was developed in collaboration with Alain Karma and Daisuke Sato at the Center for interdisciplinary research at Northeastern University, and with Alan Garfinkel, Zhilin Qu, and James N. Weiss in the David Geffen School of Medicine at UCLA.
Cardiac Cell Models
