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.
Watch your horse before, during and after activities. When a horse lies down in paddock and wild, you will notice a trend. Horses rarely lie down on their own, and usually they do it when there is a horse near by. This is in relation to the fight or flight reaction. When they feel safe, they will relax and lie down, though one horse is always standing alert in case of danger. This too happens in paddock conditions.