Flowrate control in flexible bioelectronics with targeted drug delivery capabilities is essential to ensure timely and safe delivery. For neuroscience and pharmacogenetics studies in small animals, these flexible bioelectronic systems can be tailored to deliver small drug volumes on a controlled fashion without damaging surrounding tissues from stresses induced by excessively high flowrates. The drug delivery process is realized by an electrochemical reaction that pressurizes the internal bioelectronic chambers to deform a flexible polymer membrane that pumps the drug through a network of microchannels implanted in the small animal. The flowrate temporal profile and global maximum are governed and can be modeled by the ideal gas law. Here, we obtain an analytical solution that groups the relevant mechanical, fluidic, environmental, and electrochemical terms involved in the drug delivery process into a set of three nondimensional parameters. The unique combinations of these three nondimensional parameters (related to the initial pressure, initial gas volume, and microfluidic resistance) can be used to model the flowrate and scale up the flexible bioelectronic design for experiments in medium and large animal models. The analytical solution is divided into (1) a fast variable that controls the maximum flowrate and (2) a slow variable that models the temporal profile. Together, the two variables detail the complete drug delivery process and control using the three nondimensional parameters. Comparison of the analytical model with alternative numerical models shows excellent agreement and validates the analytic modeling approach. These findings serve as a theoretical framework to design and optimize future flexible bioelectronic systems used in biomedical research, or related medical fields, and analytically control the flowrate and its global maximum for successful drug delivery.
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