An Investigation on the Three-Dimensional Memristive Morris–Lecar Model With Magnetic Induction Effects: Simulation of Biological Behaviors and Cost-Effective Digital Circuit Implementation

Abstract

The use of FPGA technology is becoming more popular for integrating neuromorphic computing systems because of the parallel processing capabilities and flexibility it offers. This study investigates the implementation of the 3D-Morris Lecar neuronal system, known as Digital Optimized Morris Lecar (DOML), in circuits to characterize the magnetic induction flow induced by neuron membrane potential. By employing a combination of trigonometric functions, hyperbolic functions, power-2 based terms, and LUT-based modules, a high-performance circuit is achieved through the best approximation methods. The model’s effectiveness is verified through validation techniques and error analysis, demonstrating a low-error mechanism due to the approximation of nonlinear functions and the avoidance of multipliers, dividers, and high-cost terms. By utilizing the proposed DOML method in digital synthesized circuits, a potential reduction of up to 37% in FPGA hardware resource cost and a potential speed increase of up to 5 times are achievable. The models were digitally synthesized using the Xilinx FPGA Virtex-4 board for cost-frequency validation, showing that the proposed model outperforms the original ML3D model while preserving its essential characteristics. The novelty of this approach lies in applying the combined approximation methods to create a cost-effective circuit suitable for biological systems, offering high speed and low cost attributes. Then, this basic circuit is applied in a sample Network of DOMLs (as a case study) to simulate and realize the population approach in simple form. This research’s findings can have practical implications for the development of neuromorphic hardware in medical devices, particularly in brain-computer interfaces and neuroprosthetics, where high-performance, low-cost hardware is crucial. In large-scale networks, our proposed modeling can be applied which is investigated in case of DOML connections.