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 cat lying on its back is leaving its belly exposed and vulnerable (to having some nasty critter rip the guts out). When a cat lies on his back and shows you his belly, he's saying that he trusts you not to attack him. And if he SLEEPS on his back, that means his level of trust for you is in the stratosphere!