In his book "Mind Children" (1988) Hans Moravec described a process he calls "Transmigration". There is an online description of this process here http://www.leaderu.com/truth/2truth05.html.
The basic idea behind the transmigration, or neural replacement thought experiment, is that one at a time (or in small groups) you monitor the complete operating function of one or more neurons in a brain as it produces conscious awareness. Then you produce a programmed simulation of the set such that given the same set of inputs, the simulation produces the same set of responses. After it can be verified that the simulation is accurate and results in the same set of responses after a sufficient period of comparison time, you then implement some kind of transducer / switching system in which the real neuron(s) can be replaced with the simulated ones. This is done in a way that allows the downstream neurons to receive the same stimulus from the simulation they would otherwise receive from the real versions. The switching mechanism provides the ability to switch back and forth between the virtual and real ones, to verify proper identical operation, before the real ones are replaced with the simulation.
This replacement process is repeated for ever more neurons in the brain until the entire brain is finally only a virtual simulation.
This argument is often used to argue that such simulations result in consciousness since the behavior is indistinguishable from the original.
David Chalmers used this line of thinking as the cornerstone of his argument for his "Principle of Organizational Invariance" as represented in this Consciousness arises from any equivalent functional organization camp on the "Hard Problem".
Neural replacement scenarios along these lines have been discussed by many others such as Pylyshyn (1980), Savitt (1980), Cuda (1985), and Searle (1992).
Cuda, T. (1985). Against neural chauvinism. Philosophical Studies, 48, 111-27.
Searle, J.R. (1992). The Rediscovery of the Mind. Cambridge, MA: MIT Press.