A modeling framework for the nonlinear dynamics analysis and optimization of electrical stimulation protocol

Electrical stimulation (ES) is and will be even more a key part of biomedical technology---for advanced prosthetics and therapies. For such purposes and given the underlying system complexity, its effects are to be robustly modeled, studied, and predicted.;This work's primary goal is to identify the key features of efficient low-power ES. Identification of optimal low-stimulation-current waveforms impacts on the related medical and engineering efficiency. The latter has typically been addressed through computationally expensive iteration with uncertain and highly-variable outcome. To do better we also strived to achieve knowledge, understanding and insights by computational modeling at different scales---from single-neuron excitability to population activity patterns. Motivation for working at a neural population scale was provided by the need of a validated computational model to provide an in silico testing environment toward the design of cortical visual prostheses. In the latter, sensory thalamic input would be replaced by optimal-control-based direct ES of modeled cortical laminae---toward evoking natural-like activity patterns. Therefore, once again one encounters the subproblem of optimal low-power ES-current waveforms, which "closes the circle" of the main topics of interest. Such population-scale model also provides for fundamental questions like: Would lamina IV remain the primary stimulation target? Assuming a neocortical canonical functional micro-circuit is indeed put in place by evolution, would it determine uniquely the most efficient spatio-temporal patterns of activation?;This purposes provided the "red-thread" through the individual questions, whose answers---using appropriate approaches and tools (incl. original ones that we developed), constitute a research-and-development framework. The gist of results is as follows.;To determine efficient low-power ES, we employed the Least-Action Principle (LAP) of variational calculus. Thus we were able to derive in closed form a general solution for the globally optimal membrane-potential growth trajectory. Then for a given ionic-current model and protocol, one easily obtains the specific energy-efficient ES current waveform. Such a solution is model-independent by construction. The approach has been demonstrated successfully with the most popular ionic current models from the literature. Costly and uncertain iteration is replaced by a single quadrature of a system of ordinary differential equations (ODE's). The approach was further validated through a general comparison to the conventional simulation and optimization results from the literature. To these approaches we have also added one of our own, based on finite-horizon optimal control. Applying the LAP resulted in a number of general ES optimality principles.;Different voltage-gated sodium ion-channel subtypes play distinct functional roles in evolutional, developmental and metabolic challenges. To address the question: How does the Naupsilon ion-channel type distribution affect neuronal dynamic regimens, excitability and refractoriness? we used nonlinear dynamics analysis. A key meta-parameter was derived, which captures a key physical property---the membrane voltage level at which about 50% of the channels of a given subtype are asymptotically activated---a likely prime determinant of function. Continuous variation of this meta-parameter was linked to fundamental, computational and empirical properties of the studied parameterized family of ion channels. This analysis provided bridges toward the informed interpretation of the experimental observations.;We developed a computational model of primary visual activation by sensory stimulation, whose architecture was constrained by the existing knowledge about the quantitative neocortical anatomy. Such published anatomical accounts appears to support the canonical microcircuit concept. Inter-laminar connectivity in the model was estimated numerically through data-driven parameter identification---toward approximating experimentally observed cat electrophysiology data.