Observability analysis and state observer design for a cardiac ionic cell model

Abstract

To gain insights into cardiac arrhythmias, researchers have developed and employed various measurement techniques, such as electrocardiography, optical mapping, and patch clamping. However, there are no measurement methods that allow simultaneous recording of all cellular quantities, including intracellular ionic concentrations and gating states, that may play an important role in arrhythmia formation. To help address this shortcoming, we applied observability analysis, a method from control theory, to the Luo–Rudy dynamic (LRd) model of a cardiac ventricular myocyte. After linearizing the time-integrated LRd model about selected periodic orbits, we computed the observability properties of the model to determine whether past system states could be reconstructed from different hypothetical sets of measurements. Under the simplifying assumption that only one dynamical variable could be measured periodically, we found that intracellular potassium concentration generally yielded the largest observability values and thus contained the most information about the dominant modes of the system. The impacts on observability of measurement timings, inter-stimulus interval length, and an alternans-promoting parameter shift were also studied. Pole-placement state observer algorithms were designed and tested in simulations for several scenarios, and we found that it is possible to infer unmeasured variables from potassium-concentration measurements, and to an extent from membrane-potential measurements, both for longer periods that represent normal rhythms and shorter periods associated with tachyarrhythmias. Our results could lead to improved data assimilation algorithms that combine model predictions with measurements to estimate quantities that are difficult or impossible to measure during in vitro experiments.