The study of brain dynamics currently utilizes the new features of nanobiotechnology and bioengineering. New geometric and analytical approaches appear very promising in all scientific areas, particularly in the study of brain processes. Efforts to engage in deep comprehension lead to a change in the inner brain parameters, in order to mimic the external transformation by the proper use of sensors and effectors. This paper highlights some crossing research areas of natural computing, nanotechnology, and brain modeling and considers two interesting theoretical approaches related to brain dynamics: (a) the memory in neural network, not as a passive element for storing information, but integrated in the neural parameters as synaptic conductances; and (b) a new transport model based on analytical expressions of the most important transport parameters, which works from sub-pico-level to macro-level, able both to understand existing data and to give new predictions. Complex biological systems are highly dependent on the context, which suggests a "more nature-oriented" computational philosophy.
Keywords: bioengineering; brain; carrier transport; cognitive science; electrical circuits; memristor; neural geometry; neuro-nanoscience; theoretical modeling.