Over the course of this award PI’s Mathematics for Engineering Applications (MEA) research laboratory produced four journal papers in peer-reviewed journals with good impact factors as well as four conference proceedings papers and four abstracts/posters. This included four of PI’s undergraduate research assistants becoming co-authors on publications including journal papers. Two of them traveled to present their research despite of the pandemic and one of them made three in person poster presentations with another two accepted for presentation early next year. Finally, support from this award made possible preparation, submission, and/or revision of two patent applications one of which was already issued in June 2021 as the first ever patent not only for Diné College but, to the best of PI’s knowledge, for any tribal college or university.

The major goal of this project was to optimize the design of concentric ring electrodes, novel sensors gaining increased recognition in the area of noninvasive electrophysiological measurement for diagnostic purposes. More specifically, this project provided an innovative solution (ability to optimize all of the parameters of the concentric ring electrode simultaneously) to improve the accuracy of an acquired signal (surface Laplacian estimate) to inform future sensor design decisions. This was accomplished by successfully fulfilling two specific aims: 1) expanding the solutions of the previously proposed general inter-ring distances optimization problem for a wide range of conditions and 2) incorporating the radius of the central disc and individual widths of the concentric rings (the last two parameters that were previously not included into the concentric ring electrode model used for optimization purposes) into the concentric ring electrode design optimization process along with the previously included parameters such as the number of rings and inter-ring distances. Specifically, for the first specific aim, the inter-ring distances optimization problem has been solved for pentapolar (4 rings) and sextopolar (5 rings) concentric ring electrode configurations using a wide range of truncation error percentiles ranging from 1st to 25th. Moreover, previously obtained solutions for tripolar (2 rings) and quadripolar (3 rings) configurations have been expanded to cover the same percentile range. Finally, a way to estimate the optimal ranges of inter-ring distances for electrode configurations with 6 or more rings was proposed and illustrated using septapolar (6 rings) configuration as an example. For the second specific aim, a realistic finite dimensions model of the concentric ring electrode was proposed as opposed to the previously used simplistic negligible dimensions model. It was also used as a basis for solving a comprehensive electrode design optimization problem with resulting optimal configurations constituting the bulk of the issued patent. These optimal configurations were directly compared to both the previously proposed configurations and to the models approximating the dimensions of the currently available commercial bipolar (1 ring) and tripolar concentric ring electrodes. The advantage of the optimal configurations with respect to the accuracy of the Laplacian estimation was confirmed using finite element method modeling. All of these results have been successfully disseminated via the aforementioned publications.

MEA lab’s intellectual merit of contributing to advancing post-secondary learning goes beyond paid research assistantships that provide students with cutting edge research experience. MEA lab also provides STEM tutoring to current Diné College students (both undergraduate and graduate) and promotes STEM disciplines to prospective ones via participation in biannual STEM festivals. During these festivals MEA lab members introduce visiting high-school students to electric circuits by building models of renewable energy power plants.

Broader impacts of MEA lab go beyond adding to the publications record and intellectual property portfolio of the School of STEM. Thanks to this award, MEA lab continued establishing itself as one of the primary research hubs of Diné College as well as one of the leading laboratories working with concentric ring electrode technology in the world.

Last Modified: 12/23/2023
Modified by: Oleksandr Makeyev