Many studies, using various instrumentation, are beginning to chart the unusual brain activity in people while they are performing as mediums or in deep meditation. I know of one study that took MRIs of a medium while she was in communication with the deceased. 

The short article below, published in the online journal, Frontiers  in Psychology (Nov 20, 2013), is a summary of the findings on brain activity of mediums using EEG. 

We need to know more about how this works, but for now, the electrical stream through which telepathy manifests seems to be the answer, at least for me.

Electrocortical activity associated with

subjective communication with the deceased

Arnaud Delorme^1,2*, Julie Beischel³, Leena Michel¹, Mark Boccuzzi³, Dean Radin¹ and Paul J. Mills⁴

• ¹Institute of Noetic Sciences, Petaluma, CA, USA
• ²Institute of Neural Computation, SCCN, University of California, San Diego, La Jolla, CA, USA
• ³Windbridge Institute, Tucson, AZ, USA
• ⁴Department of Psychiatry, University of California, San Diego, La Jolla, CA, USA

During advanced meditative practices, unusual perceptions can arise including the sense of receiving information about unknown people who are deceased. As with meditation, this mental state of communication with the deceased involves calming mental chatter and becoming receptive to subtle feelings and sensations. Psychometric and brain electrophysiology data were collected from six individuals who had previously reported accurate information about deceased individuals under double-blind conditions. Each experimental participant performed two tasks with eyes closed. In the first task, the participant was given only the first name of a deceased person and asked 25 questions. After each question, the participant was asked to silently perceive information relevant to the question for 20 s and then respond verbally. Responses were transcribed and then scored for accuracy by individuals who knew the deceased persons. Of the four mediums whose accuracy could be evaluated, three scored significantly above chance (p < 0.03). The correlation between accuracy and brain activity during the 20 s of silent mediumship communication was significant in frontal theta for one participant (p < 0.01). In the second task, participants were asked to experience four mental states for 1 min each: (1) thinking about a known living person, (2) listening to a biography, (3) thinking about an imaginary person, and (4) interacting mentally with a known deceased person. Each mental state was repeated three times. Statistically significant differences at p < 0.01 after correction for multiple comparisons in electrocortical activity among the four conditions were obtained in all six participants, primarily in the gamma band (which might be due to muscular activity). These differences suggest that the impression of communicating with the deceased may be a distinct mental state distinct from ordinary thinking or imagination.