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Computational biology has increasingly turned to agent-based modeling to explore complex biological systems. Biological diffusion (diffusion, decay, secretion, and uptake) is a key driver of biological tissues. GPU computing can vastly accelerate the diffusion and decay operators in the partial differential equations used to represent biological transport in an agent-based biological modeling system. In this article, we utilize OpenACC to accelerate the diffusion portion of PhysiCell, a cross-platform agent-based biosimulation framework. We demonstrate an almost 40× speedup on the state-of-the-art NVIDIA Ampere 100 GPU compared to a serial run on AMD's EPYC 7742. We also demonstrate 9× speedup on the 64-core AMD EPYC 7742 multicore platform. By using OpenACC for both the CPUs and the GPUs, we maintain a single source code base, thus creating a portable yet performant solution. With the simulator's most significant computational bottleneck significantly reduced, we can continue cancer simulations over much longer times. [ABSTRACT FROM AUTHOR]