Functional stereotactic lesions in the central lateral nucleus of the medial thalamus have proved to be an effective treatment of neurogenic pain and other neurological disorders associated with thalamocortical dysrhythmia. The mechanisms underlying patient recovery after surgery are currently being explored using quantitative electroencephalography. Here we test the hypothesis that the particular role played by the non-specific medial thalamic nuclei in thalamocortical dysrhythmia is based on the divergent connectivity between these non-specific and reticular nuclei. We built a spiking computer model of the human thalamocortical system consisting of specific, non-specific and reticular thalamic nuclei. In our simulations of the thalamocortical system, deafferentation of peripheral thalamic afferents leads to hyperpolarization and subsequent bursting in the reticular nucleus. This provides strong inhibitory feedback to both the specific and the non-specific thalamic nuclei and initiates a feedback cycle of thalamic bursts in the theta frequency range. The divergent connections between the reticular and non-specific thalamic nuclei provide synchronization of the oscillating circuits. Functional silencing of the non-specific model nucleus limits reverberation and rescues the system from these oscillations. The same effect could be achieved by increasing the input to the non-specific nucleus from cortical areas. The model predicts that the invasiveness of functional neurosurgery can be reduced by targeting only deafferented areas in the medial nuclei as these are the key areas for generation and maintenance of pathological rhythms.