Application of an innovative FPGA-optimized model on pancreatic β-cells: Validation via Lyapunov analysis and equilibrium stability

Presenting an ideal hardware model capable of mimicking behavior of biological cells and neurons holds great significance in neuromorphic engineering. This research introduces a novel and unique approach to digitally implementing a biological cell model with the goal of reducing hardware requirements and enhancing processing speed while maintaining signal accuracy. The method outlined focuses on minimizing the number of nonlinear terms in the original model, making it well-suited for digital implementation. Specifically, this approach is applied to the pancreatic $\beta$ cell model in this study. Both software simulation and hardware implementation results validate the effectiveness of the proposed method in reproducing the signal and behavior of the original $\beta$ cell model by decreasing the number of nonlinear terms without discarding any equations from the initial model. By consolidating them into a single form, this method reduces the number of non-linear terms to one through a common variable, making it highly suitable for digital implementation. To validate the mathematical simulation findings, the proposed model was synthesized and implemented on the Zynq XC7Z010 (3CLG400) reconfigurable board (FPGA). The results demonstrate the ability to more efficiently reproduce biological behavior at significantly lower execution costs. Implementing this technique on the Zynq board can enhance the speed of the suggested model by up to 2.187 times compared to the original model, while also achieving a 34.91% decrease in energy (power) usage.