Controllability and state feedback control of a cardiac ionic cell model.

A phenomenon called alternans, which is a beat-to-beat alternation in action potential (AP) duration, sometimes precedes fatal cardiac arrhythmias. Alternans-suppressing electrical stimulus protocols are often represented as perturbations to the dynamics of membrane potential or AP duration variables in nonlinear models of cardiac tissue. Controllability analysis has occasionally been applied to cardiac AP models to determine whether different control or perturbation strategies are capable of suppressing alternans or other unwanted behavior. Since almost all previous cardiac controllability studies have focused on low-dimensional models, we conducted the present study to assess controllability of a higher-dimensional model, specifically the Luo Rudy dynamic (LRd) model of a cardiac ventricular myocyte. Higher-dimensional models are of interest because they provide information on the influence of a wider range of measurable quantities, including ionic concentrations, on controllability. After computing modal controllability measures, we found that larger eigenvalues of a linearized LRd model were on average more strongly controllable through perturbations to calcium-ion concentrations compared with perturbations to other variables. When only membrane potential was adjusted, the best time to apply perturbations (in the sense of maximizing controllability of the largest alternans eigenvalue) was near the AP peak time for shorter cycle lengths. Controllability results were found to be similar for both the default model parameters and for an alternans-promoting parameter set. Additionally, we developed several alternans-suppressing state feedback controllers that were tested in simulations. For the scenarios examined, our controllability measures correctly predicted which strategies and perturbation timings would lead to better feedback controller performance.

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

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.