REGIONAL CEREBRAL BLOOD FLOW (RCBF RCBF): Regional cerebral blood flow monitoring may help boost the validity of the regional localization theory, in which specific parts of the brain control specific functions.. measure of the blood flow in a specific area of the brain, using positron emission tomography (PET scans) and/or single photon emission computed tomography.
If a dog goes on his back to you he is accepting you as his master. This is part of the answer but here's a little more in-depth version as reported by USA Today. In general, dogs lie on their back for three reasons.
A dog who is lying on his back during play with another dog might be communicating a number of things. It has long been believed that the dog on his back is being submissive and this is his way of telling the other dog that he isn't a threat.