Tug at your heartstrings

This term means to really get to you emotionally. But how did it come about? As far as I'm aware, the heart has no strings, so why would anyone come up with a saying like this?

From Merriam-Webster:

Main Entry: heart·string
Pronunciation: -"stri[ng]
Function: noun

The heart does have strings - there are 'strings' of tissue that, I recall, prevent certain valves turning inside out.

1 obsolete : a nerve once believed to sustain the heart - yeah? why not check the biology?

2 : the deepest emotions or affections -- pulled at his heartstrings (Figurative)

check out the biology - I recall that the heart has 'strings' even if that is not the correct term.