Final answer:
The deep grey matter in the brain receives blood through the blood-brain barrier and reabsorbs waste through arachnoid granulations. This process is facilitated by the production and circulation of cerebrospinal fluid.
Step-by-step explanation:
The deep grey matter in the brain receives blood through the blood-brain barrier. This barrier limits the exchange of materials between blood vessels and the nervous tissue. Metabolic wastes are collected in cerebrospinal fluid which circulates through the central nervous system. The fluid is produced by filtering blood at the choroid plexuses in the ventricles of the brain and is reabsorbed into the blood through arachnoid granulations, removing waste from the deep grey matter.