Mathematical models describing cellular membranes form the basis of whole tissue models to describe the electrical activity of entire organs, such as the heart. Numerical simulations based on these models are useful for both basic science and increasingly for clinical diagnostic and therapeutic applications such as targeting ablation therapy for atrial arrhythmias, defibrillator design and cardiac resynchronization therapy. A common bottleneck in such simulations arises from solving large stiff systems of ordinary differential equations (ODEs) thousands of times for numerous integration points (representing cells) throughout a three-dimensional tissue or organ model. For some electrophysiology simulations, over 80% of the time is spent solving these systems of ODEs. While a cluster provides the required interactive response time to solve the ODEs, a desktop sized platform would enhance usability of the software in a laboratory setting. The audience will benefit by learning how a real-world, complex, HPC application can directly benefit by the use of CUDA technology. Participants will learn which optimization techniques yielded the best performance results on an actual application. We will also explore the benefits and limits of the use of single precision in certain scientific applications.