Model 1 - Cardiac Excitation
Model Details
Model 1 is an Ordinary Differential Equation system that describes the electrical excitation of cardiac cells, characterised by action potentials across their membranes. The system, based on the Nobel model, is defined and described in Simitev and Biktashev (2010). Please see this paper for full details about the model.
There are 3 observed variables; E (the transmembrane voltage), h (a gating variable) and n (another gating variable), and 12 parameters to infer; k1, k2, k3, E1, ENa, Edagger, Estar, Fh, Fn, GNa, g21 and g22. The differential equations are given in Simitev and Biktashev (2010), equations (40a-c). However, the diffusion term (the term in the far right of equation (40a)) is omitted for this event. In order for there to be no confusion, equations (40a-c) have been rewritten to remove this term and can be found here - Model 1 Differential Equations. For Cside 2018, ε is kept fixed at the value 1.
The time course [0,900] and the initial conditions of the system (-10,1,0) are fixed for this event and therefore competitors should not change these. The time course was originally set by allowing the solver (ode15s in Matlab) to choose the incrementation. However, this can result in slightly different spacings from run to run. Hence, the time course has been hard coded to a time course indicative of this problem, based on a previous run. This results in 205 observations being generated by solving the system.
Cside 2018 Competition Parameters
The parameter values that generated the competition data for Model 1 are:
| Parameter | Value |
| k1 | 0.12 |
| k2 | 0.1 |
| k3 | 0.3 |
| E1 | -65 |
| ENa | 60 |
| Edagger | -60 |
| Estar | -20 |
| Fh | 0.25 |
| Fn | 0.015 |
| GNa | 50 |
| g21 | -7 |
| g22 | -5 |
Thank you
Thank you to Muhamad Hifzhudin Aziz and Radostin Simitev of the University of Glasgow for helping Cside 2018 to work with this model for this year's event. A special thanks to Muhamad for his code, as well as his time discussing the model and code.
Code
The code is run using Matlab. The compressed file contains CaricEq.m (the file that contains the differential equation) and CaricModelRun.m (the file that runs the solver). Competitors should only need to edit CaricModelRun.m for the purposes of the event.
Note: the default relative tolerance level in Matlab for solving the ODE using ode15s might be too large (1e-3), causing the numerical error in the solution to be large. The subsequent likelihood landscape would cause optimisers/samplers to perform poorly. To avoid this, please use a relative tolerance level no larger than 1e-5 (this is what will be used when generating the competition data). The code has been updated to use this lower relative tolerance level.
You can download a .zip file of the code here - CardiacExcitation.zip
You can download a .7z file of the code here - CardiacExcitation.7z