In my ECG recordings, I periodically add increasing concentration of high calcium ringer's solution with an interval of 10 minutes for each concentration. I noticed that for an increase of concentration of Calcium, the interbeat interval between each beat becomes longer. For 10mmol/L (my highest concentration), beat skipping happens in a random manner. In line with this, would it be possible to model my data as a differential equation? Or any appropriate mathematical model? Or if there's any available mathematical model, please let me know. Thank you very much to all of you!!
Best,
Pocholo
Your beat skipping for the highest concentration could be of fractional order.Look up research work by F Mainardi, Podlubny and Gorenflo for further information on how to model using fractional differential equations. If you could give detailed data, I might even be able to help you in the modelling, as I have been working on fractional order differential equations.
Article Fractional and operational calculus with generalized fractio...
As the ecg is based on the cardiac action potential. You need the equations for the cardiac action potential. There are many versions for these equations depending on whether you are dealing with the purkinje fibres, the ventricles and which animal you are dealing with.
As an example of these equations see
http://rsta.royalsocietypublishing.org/content/367/1896/2225
You need to read about the works Dennis Noble who developed the original cardiac action potential models.
see http://physiologyonline.physiology.org/content/19/4/191
Once you have got the right mathematical model for the tissue you are looking at in the animal you are looking at then you can try to re create your finding with the models by altering the calcium currents etc
There are simpler models eg Bonhoeffer-van der Pol oscillator model
see
http://www.ncbi.nlm.nih.gov/pubmed/8177060
and see
http://www.wseas.org/multimedia/journals/systems/2012/56-146.pdf
Though simpler, than the experimentally derived models, this model does not actually model the underlying currents in any great detail if at all. This model has similar dynamical properties to the cardiac action potential.
The ECG graphs are continuous every where but nowhere differentiable. So the way to analyze it mathematically use of jumarie type fractional derivative.
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