It's true that the brain uses glucose to function but under a state of ketosis, which is the metabolic state your body will go into when on a low-carb diet, your body will via the process of gluconeogenesis produce sufficient glucose for proper brain function and for other glucose requirements like in red blood cells and to maintain your glycogen stores in the liver.
In a ketotic low carb diet (i.e. 30 grams or less of carbohydrate a day or thereabouts) you are still getting plenty of basic glucose from the carbohydrate you eat, and of course this is added to by gluconeogenesis as necessary.
Which is wonderful news for us as diabetics because not only can we run quite happily on this alternative energy source (i.e. fats and protein) we will in doing so metabolise fats rather than store them, improve our HDL/LDL ratio and lose weight. The downs sides? Well, you'll annoy dieticians and some GPs...
Below is an extract in more detail about this, from a quick Google on gluconeogenesis:-
When carbohydrate supplies are inadequate, however, the liver naturally converts oxaloacetate to glucose via gluconeogenesis for use by the brain and other tissues. When acetyl CoA does not bind with oxaloacetate, the liver converts it to ketones (or ketone bodies), leading to a state of ketosis causing most cells in the body to use fatty acids as their primary energy source. At the same time, glucose is synthesized in the liver from lactic acid, glucogenic amino acids, and glycerol, in a process called gluconeogenesis. This glucose is used exclusively for energy by cells such as neurons and red blood cells.
I take around 22 units of Lantus at night and about 6 units of fast acting for each meal, but you need to work out what works for you. 10 units of fast acting insulin on a low carbohydrate diet sounds too high to me...
Lastly, if all of this weren't true about the brain and glucose formation; then a lot of us on this forum would be in a great deal of trouble; I for one (and I suspect others as well) use their brains quite a lot and would probably notice if they weren't functioning....
