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.
The most common reason for a dog to hide under a bed is fear. It might be a thunderstorm, a stranger in the house or something getting dropped. Dogs can be overly skittish, especially if they've been abused. Some breeds are also known for running and hiding when they're scared.