Compositionality results for cardiac cell dynamics

Abstract : By appealing to the small-gain theorem of one of the authors (Girard), we show that the 13-variable sodium-channel component of the 67-variable IMW cardiac-cell model (Iyer-Mazhari-Winslow) can be replaced by an approximately bi-similar, 2-variable HH-type (Hodgkin-Huxley) abstraction. We show that this substitution of (approximately) equals for equals is safe in the sense that the approximation error between sodium-channel models is not amplified by the feedback-loop context in which it is placed. To prove this feedback-compositionality result, we exhibit quadratic-polynomial, exponentially decaying bisimulation functions between the IMW and HH-type sodium channels, and also for the IMW-based context in which these sodium-channel models are placed. These functions allow us to quantify the overall error introduced by the sodium-channel abstraction and subsequent substitution in the IMW model. To automate computation of the bisimulation functions, we employ the SOSTOOLS optimization toolbox. Our experimental results validate our analytical findings. To the best of our knowledge, this is the first application of δ-bisimilar, feedback-assisting, compositional reasoning in biological systems.
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https://hal.archives-ouvertes.fr/hal-01133219
Contributor : Antoine Girard <>
Submitted on : Wednesday, March 18, 2015 - 5:26:17 PM
Last modification on : Tuesday, October 29, 2019 - 11:10:04 AM

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Md. Ariful Islam, Abhishek Murthy, Antoine Girard, Scott Smolka, Radu Grosu. Compositionality results for cardiac cell dynamics. HSCC '14 - 17th International Conference on Hybrid systems: computation and control, Apr 2014, Berlin, Germany. pp.243-252, ⟨10.1145/2562059.2562138⟩. ⟨hal-01133219⟩

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