Controllability and state feedback control of a cardiac ionic cell model

• Published in: Computers in biology and medicine 2021-12, Vol.139, p.104909-104909, Article 104909
• Main Authors: Vogt, Ryan, Guzman, Anthony, Charron, Clar, Muñoz, Laura
• Format: Article
• Language: English
• Subjects: Action potential; Action Potentials; Alternan; Arrhythmias, Cardiac; Cardiac electrophysiology; Computational science; Control algorithms; Control systems; Controllability; Eigenvalues; Electrical alternans; Electrical stimuli; Feedback; Feedback control; Heart; Heart Ventricles; Humans; Investigations; Mathematical biosciences; Mathematical models; Membrane potential; Membranes; Models, Cardiovascular; Myocytes; Myocytes, Cardiac; Parameters; Perturbation; Potassium; State feedback; Tissue analysis; Variables; Ventricle
• ISSN: 0010-4825; 1879-0534
• DOI: 10.1016/j.compbiomed.2021.104909

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. •Controllability properties were reported for an ionic model of a cardiomyocyte.•Perturbation strategies were used to suppress alternans and other large modes.•Impacts of stimulus period, strategy, and perturbation timings were examined.•Alternans was controllable from membrane potential perturbations at AP peak time.•Perturbing calcium concentrations was the best overall control strategy.