Epilepsy is a chronic neurological disorder characterized by recurrent seizures resulting from abnormal electrical activity in the brain. All experimental models for seizure generation are based on the administration of drugs (e.g. pilocarpine), on artificial increase in the concentrations of extracellular K+ (Ko) or on direct electric stimulation, to name a few. However, all these approaches may not accurately reflect the in vivo conditions, where otherwise normal neuronal activity can generate occasional seizures. It is thus important to better understand the pathological changes that may be responsible for seizure generation during normal in vivo neuronal activity without any artificial external intervention. One possible mechanism is a pathological change in Ko homeostasis, which is crucial for maintaining the electrochemical gradient across neuronal membranes. As demonstrated with animal models, this can lead to prolonged membrane depolarization, increased neuronal excitability, and a higher susceptibility to seizures. However, it is not clear if and to what extent this process may occur in vivo during normal behavioral activities. To shed light on this process in hippocampal CA1 pyramidal neurons, we have implemented and validated a realistic computational model to investigate the conditions under which a local dendritic accumulation of Ko in response to synaptic inputs, as they can occur in vivo, can give rise to seizure-like activity similar to what is observed experimentally. The model makes the experimentally testable predictions that a change in the time constants for the mechanisms responsible for the extracellular K+ dynamics can eventually bring the neuron close to a state that may occasionally generate seizure-like activity during occasional bursts of synaptic activity, which would not normally cause any problem. The result suggests that basal dendrites and the apical trunk are the most sensitive to this effect, and that pharmacological intervention targeting the mechanisms responsible for Ko accumulation may restore normal conditions.