Abstract: Modeling, analyzing, and simulating biological neural networks have attracted significant interest because of their wide-ranging applications in neuroscience and computational systems. Understanding and replicating the intricate behavior of biological components, such as calcium dynamics in the synaptic bouton, is crucial for advancing our understanding of synaptic plasticity, neural signaling, and the underlying mechanisms of learning and memory. However, accurately capturing the complex non-linear behavior of these networks, especially at the cellular level, remains a significant challenge due to the interplay of various biochemical processes. In this work, we focus on calcium movement within the synaptic bouton and introduce a novel approach for implementing these dynamics, providing an efficient solution for digital hardware realization. The proposed model leverages a high-precision method to effectively compute the nonlinear components of cellular equations while ensuring compatibility with digital hardware such as FPGA platforms. Experimental simulations and FPGA-based hardware synthesis demonstrate that the enhanced model closely replicates the intricate dynamics of intracellular calcium signaling. This approach offers a reliable, scalable, and computationally efficient tool for further exploration of neural processes, supporting applications ranging from biological modeling to neuromorphic engineering and biologically inspired computing architectures.