Recent advances in neuroscience have underscored the role of single neurons in information processing. Much of this work has focused on the role of neurons' dendrites to perform complex local computations that form the basis for the global computation of the neuron. Generally, artificial neural networks that are capable of real-time simulation do not take into account the principles underlying single-neuron processing. In this paper we propose a design for a neural model executed on the graphics processing unit (GPU) that is capable of simulating large neural networks that utilize dendritic computation inspired by biological neurons. We subsequently test our design using a neural model of the retinal neurons that contribute to the activation of starburst amacrine cells, which, as in biological retinas, use dendritic computational abilities to produce a neural signal that is directionally selective to stimuli moving centrifugally.