Pyramidal neurons in the brain's neocortex receive, on average, approximately 10,000 synaptic inputs. The majority of these are made onto dendritic spines, which are chemically and electrically isolated from other parts of the neuron. We present an extension to the IBM Neural Tissue Simulator that models details of neuron morphology and the dynamics of intracellular diffusible ions or molecules, and here, for the first time, we demonstrate the ability to simulate the functional role of spines and their calcium dynamics at a detailed whole neuron and tissue level. We create a multicompartment model of a neuron in which a realistic number of spines (∼10,000) are explicitly simulated as individual compartments (two compartments per spine) branching from the dendrites. Simulations of this model neuron run efficiently using a parallel computing infrastructure. Experimental data are used to constrain the geometry of each spine as a function of morphological class and to distribute spines in a statistically realistic manner along the dendrite. We show how the model behaves differently with and without spines of different classes and how transmembrane potential and calcium dynamics differ between the spine neck and shaft. These results suggest that spines impose a constraint on back-propagation of action potentials dependent on their morphology and neck resistance.