FPGA-Optimized Neuromorphic Modeling of Cardiac Purkinje Fibers for Next-Generation Bionic Implants

The optimized hardware implementation of neurons and biological cells in the neuromorphic domain is of significant importance. In this paper, a novel method is presented that reduces any number of nonlinear terms in the differential equations describing the behavior of neurons or biological cells with a common variable to a single nonlinear term with high precision. This approach significantly improves implementation efficiency by reducing hardware resource consumption while maintaining high frequency and accuracy. The proposed method was applied to Cardiac Purkinje Fiber Cells, and its validity was demonstrated through time-domain analysis, noise condition analysis, Lyapunov stability analysis, and bifurcation analysis to validate the model under various conditions. These validations ensure the accuracy and stability of the proposed approach across different operating conditions. To assess large-scale applicability, the model was tested in a 300-cell Purkinje fiber network, demonstrating accurate synchronization, equilibrium states, and cross-spectral consistency while maintaining computational efficiency. The digital hardware implementation on a Virtex-7 FPGA board demonstrated a frequency improvement of 3.49 times compared to the original model and 1.79 times compared to the best implementation of this model to date. We also simulated a network of 4500 cells to analyze correlation and implemented it on hardware to demonstrate that the proposed model, based on the method presented in this paper, can efficiently and accurately scale to large-scale applications. This efficient and scalable approach paves the way for applications in medical research, bioengineering, and neuromorphic hardware development, including the creation of hardware-accelerated tools for simulating biological systems, designing bio-inspired devices, and enabling large-scale real-time simulations for understanding and treating cardiac or neurological conditions.