No JKR info that I could find, but most likely it is Chordae Tendineae
The chordae tendineae are tendons linking the papillary muscles to the tricuspid valve in the right ventricle and the mitral valve in the left ventricle. As the papillary muscles contract and relax, the chordae tendineae transmit the resulting increase and decrease in tension to the respective valves, causing them to open and close. The chordae tendineae are string-like in appearance and are sometimes referred to as "heart strings." (source source)
Since dragon heart generally plays role in assorted lore, it makes sense that a wand core associated with an actual part of dragon's heart would be considered powerful.