Observability Analysis of Data Reconstruction Strategies for a Cardiac Ionic Model

Laura Munoz1, Anna Marks2, Julio Santiago-Reyes3, Mark Ampofo1, Elizabeth Cherry4
1Rochester Institute of Technology, 2Wake Forest University, 3The College of New Jersey, 4Georgia Institute of Technology


Motivation: The study of arrhythmia formation is impeded by limitations in sensor technology, given that not all quantities of interest, such as ionic concentrations and gating variables, can be measured directly and simultaneously from the same cell or tissue preparation. A possible remedy is to develop data assimilation algorithms that combine predictions of a dynamical model with available data to reconstruct unmeasured quantities. To learn more about prospects for data assimilation, we performed an observability analysis on the Shiferaw-Sato-Karma (SSK) model of a cardiac myocyte. The SSK model was of interest since it represents electrical alternans, which precedes certain arrhythmias, in addition to modeling different alternans mechanisms, including instabilities in membrane-potential dynamics (voltage-driven alternans) and intracellular calcium dynamics (calcium-driven alternans).

Aims: We aimed to determine which types of measurements yielded strongest observability, where observability is a model property that indicates whether the system state variables can be reconstructed from a proposed measured quantity. Another goal was to assess impacts of different alternans mechanisms on observability.

Methods: We numerically linearized the SSK model and computed modal observability measures for its largest modes over a range of simulated measurements, where each type of measurement consisted of recording the value of one dynamical variable once per inter-stimulus interval. We also examined whether alternans mechanisms affected observability.

Results: Observability rankings showed that a variety of assimilation strategies, such as inferring cellular variables from membrane potential, could be used to reconstruct other cellular variables. We found that the best strategies, in the sense of maximizing observability, were to measure the slow INa inactivation gate (during voltage-driven alternans) or the submembrane calcium concentration (during calcium-driven alternans).

Conclusion: Our results indicate that alternans mechanisms can affect which types of measurements are most informative, although various assimilation strategies were found to be viable for either mechanism.