Agent-based cellular models simulate tissue evolution by capturing the behavior of individual cells, their interactions with neighboring cells, and their responses to the surrounding microenvironment. An important challenge in the field is scaling cellular resolution models to real-scale tumor simulations, which is critical for the development of digital twin models of diseases and requires the use of High-Performance Computing (HPC) since every time step involves trillions of operations. We hereby present a scalable HPC solution for the molecular diffusion modeling using an efficient implementation of state-of-the-art Finite Volume Method (FVM) frameworks. The paper systematically evaluates a novel scalable Biological Finite Volume Method (BioFVM) library and presents an extensive performance analysis of the available solutions. Results shows that our HPC proposal reach almost 200x speedup and up to 36% reduction in memory usage over the current state-of-the-art solutions, paving the way to efficiently compute the next generation of biological problems.