A technical question, but is there an old hebrew word for the pericardium or some such related area?
Quite to my embarrassment, I didn't hear of such an organ as the pericardium until you asked. However, I've checked and found out that in Hebrew it may be translated as one of the following:
מֵסַב הלב (me-sav ha-lev) literally the heart's bearing.
כיס הלב (kis ha-lev) literally the heart's pocket
קרום הלב (kroom ha-lev) literally the heart's membrane.
I should say that all these are modern Hebrew terms. I asked a friend who has a deep knowledge of the Bible and linguistics. He said that he is not aware of an old Hebrew term for this organ.