Topological Modeling and Parallelization of Multidimensional Data on Microelectrode Arrays

Microelectrode arrays (MEAs) are physical devices widely used in various science and engineering fields. One common computational challenge when applying a high-density MEA (i.e., a larger number of wires, more accurate locations of abnormal cells) is how to efficiently compute those resistance values provided the nonlinearity of the system of equations with the unknown resistance values per the Kirchhoff law. This paper proposes an algebraic-topological model for MEAs such that we can identify the intrinsic parallelism that cannot be identified by conventional approaches. We implement a system prototype called Parma based on the proposed topological methodology. Experimental results show that Parma outperforms the state-of-the-practice in time, scalability and memory usage: the computation time is two orders of magnitude faster on up to 1,024 cores with almost linear scalability and the memory is much better utilized with proportionally less warm-up time with respect to the number of concurrent threads.