Discovery of the Hidden State in Ionic Models Using a Domain-Specific Recurrent Neural Network

Ionic models, the set of ordinary differential equations (ODEs) describing the time evolution of the state of excitable cells, are the cornerstone of modeling in neuro- and cardiac electrophysiology. Modern ionic models can have tens of state variables and hundreds of tunable parameters. Fitting ionic models to experimental data, which usually covers only a limited subset of state variables, remains a challenging problem. In this paper, we describe a recurrent neural network architecture designed specifically to encode ionic models. The core of the model is a Gating Neural Network (GNN) layer, capturing the dynamics of classic (Hodgkin-Huxley) gating variables. The network is trained in two steps: first, it learns the theoretical model coded in a set of ODEs, and second, it is retrained on experimental data. The retrained network is interpretable, such that its results can be incorporated back into the model ODEs. We tested the GNN networks using simulated ventricular action potential signals and showed that it could deduce physiologically-feasible alterations of ionic currents. Such domain-specific neural networks can be employed in the exploratory phase of data assimilation before further fine-tuning using standard optimization techniques.