I have done a cursory research on this and cannot find anything. I do know that interpretation of some designs is arbitrary. There is a wonderful website with listings of books on the subject of gravestone symbolism. The website is www.gravestonestudies.org and is the site of the Association of Gravestone Studies which strives to preserve the historical and artistic legacy of cemeteries and gravestones. You may wish to peruse this site and explore all the information they offer up.
I am sorry I could not answer your question directly, but I will continue to research for you as well.