The pericardium was a membrane that enclosed the heart, which consisted of an outer fibrous layer and an inner double layer of serous membrane.
In 2151, a Xyrillian embryo that Charles Tucker III had been impregnated with integrated with his pericardium. This made it difficult for Phlox to remove in the absence of information on the Xyrillian gestation process. (ENT: "Unexpected")
In 2374, The Doctor was able to stabilize B'Elanna Torres' pericardium after Dejaren had reached into her chest and grabbed her heart. Later, back aboard the USS Voyager, he repaired the tissue damage and told Torres that her pericardium was as "clean as a whistle". (VOY: "Revulsion")