الفهرس 
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Abstract
Electrical stimulation aims to impart specific neuromodulatory effects on target regions, while leaving all other regions unaffected, in order to achieve desired therapeutic/rehabilitative goals. The ability of multi-elements phased antenna arrays to accurately shape electromagnetic fields motivated researchers to investigate the possibility of using multielectrodes setups in electrical brain stimulation applications for the same purpose. However, as the number of electrodes increases, the number of parameters governing an electrical stimulation setup also increases. Common experience/simulation-guided trial-and-error procedures are no longer acceptable as the parameters search space is quite large. Instead, a formal optimization procedure is needed to estimate multi-electrodes stimulation setup parameters. This problem is a challenging optimization problem. Even when a single region is targeted for excitation, the problem remains a constrained multi-objective optimization problem. The constrained nature of the problem results from safety concerns while its multi-objectives originate from the requirement that non-targeted regions should remain unaffected. A successful optimization procedure should be able to study the feasibility of the set optimization goals, as well as finding the optimal solution. If finding the optimal solution is not possible within the allowable time limit, the procedure should be at least able to assess the degree of optimality of the obtained solution. These features are best satisfied by linear programming and mixed integer linear programming approaches. The thesis adapts the complex brain stimulation optimization problem so that it is possible to solve it using a mixed integer linear programming (MILP) framework. The desirable capabilities of the framework (feasibility analysis and solutions degree of optimality assessment) help researchers in avoiding pursuing infeasible goals as well as premature convergence to non-optimal solutions which would otherwise drive them to seek unnecessarily complex stimulation setups. Moreover, the analysis of what goals are infeasible under what stimulation setups gives researchers “food for thought” and is expected to enrich their insight and knowledge. The framework is able to find the optimal electrodes currents and locations that maximize electrical stimulation focality. Furthermore, the thesis proposes a time division multiplexing (TDM)-based strategy to improve stimulation focality. The TDM-based strategy replaces the complex problem of simultaneous multi-target stimulation with a series of single target stimulation problems, each solved in a different time slot of the TDM scheme. The thesis adopts a cortical visual prosthesis design case study to highlight the merits of the proposed framework. The adopted detailed computational model within the case study is complex enough to capture the realistic biological challenges associated with the application but at the same time simple enough to allow for the extensive computations required by the used mathematically rigorous optimization procedures. We expect the proposed computational framework to be useful for other researchers to investigate their own innovative ideas.