Sources connected with the family tell us ... doctors performed tests Monday morning and determined the swelling on her brain has gone down. In addition, she has been able to "move her eyes" ... all important signs.
Perhaps most important ... we're told the oxygen levels in her brain have increased significantly -- 4 times better than Sunday.
But the family has been told ... because Bobbi Kristina was deprived of oxygen for anywhere between 2 to 5 minutes while she was submerged in a tub, doctors fear neurological damage.