Simulating human brain is currently absolutely not feasible for several reasons (I'll detail later).
AFAIK the only successful simulations (meaning: simulated result matched what biologic Neural Network actually did to a reasonable degree) were done for very simple organisms, if memory assists the most complex was a snail with several thousand neurons.
These simulations, however, were done simulating effects of neurotransmitters and neuron membrane; Simulated Neuron Networks (SNN, the kind of Neuron Networks that are actually in use to solve many problems, including prepare weather forecasts) work in a completely different way, the abstract the actual working of a neuron in a "stylized" way which has nothing in common with real Neuron operation. They are models of the neuron leaving out a lot of details to capture general principles of operation.
They do a good job, enough to be real useful in building A.I.
They're powerful enough to scare people like Elon Musk and Bill Gates with perspective results.
There's a heated debate if these SNN really capture enough of neurons working to permit replication of a complex brain.
In general problems arising when trying to simulate human brain are at several levels:
- Scale Problems
- It is unclear if SNN really behave in a way comparable with biologic systems.
- Very large SNN contain several hundred thousand Simulated Neurons our brain is close to hundred billion neurons.
- Each SN has, at most, about 100 connections; typical neuron has more than 100 thousand connections.
- Physiological problems:
- We do not exactly know how neurons are connected in our brain.
- We have only a vague idea of function localization.
- We have understood some of the interaction between neurons and neurotransmitters in blood stream.
- We are recently starting to understand neurons not located in the brain (such as cardiac ganglia) have an important role in long-term memorization (thus giving a completely new meaning to the phrase "learn by hart").
- Similar importance for overall brain operation have abdominal ganglia.
- Philosophical problems:
- There still is no universal consensus (I have definite ideas on the subject though) if brain biochemistry can fully explain our subjective and objective behavior.
- There still is no consensus of what actually is that we call "Conscience".
- There still is no consensus if simulation can capture the relevant parts of what we cal "I".
The cited Hofstatter's book is a very interesting one and it is what spawned my interest on the subject, mut it is, IMHO, trying to hard to demonstrate a philosophical thesis ans thus it is, in the end, rather unconvincing.
Note: I summarized my personal understanding of the matter in a small site I wish I had more time to maintain. You'll find many references to published academic papers there.