Novel 3D GPU based numerical parallel diffusion algorithms in cylindrical coordinates for health care simulation

Modeling diffusion processes, such as drug deliver, bio-heat transfer, and the concentration change of cytokine for computational biology research, requires intensive computing resources as one must employ sequential numerical algorithms to obtain accurate numerical solutions, especially for real-time in vivo 3D simulation. Thus, it is necessary to develop a new numerical algorithm compatible with state-of-the-art computing hardware. The purpose of this article is to integrate the graphics processing unit (GPU) technology with the locally-one-dimension (LOD) numerical method for solving partial differential equations, and to develop a novel 3D numerical parallel diffusion algorithm (GNPD) in cylindrical coordinates based on GPU technology, which can be used in the neuromuscular junction research. To demonstrate the effectiveness and efficiency of the obtained GNPD algorithm, we employed it to approximate the real diffusion of the neurotransmitter through a disk shaped volume. This disk shaped volume is the synaptic gap, connecting the neuron and the muscle cell in the neuromuscular junction. Furthermore, we compared the speed and accuracy of the GNPD with the conventional sequential diffusion algorithm. Results show that the GNPD can not only significantly accelerate the speed of the diffusion solver via GPU-based parallelism, but also greatly increase the accuracy by employing the stream function of latest Fermi GPU cards. Therefore, the GNPD has a great potential to be employed in the design, testing, and implementation of health information systems in the near future. c ⃝ 2014 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).