Synonyms for the term "O'Beirne's experiments sphincter" are not widely recognized or commonly used in the English language. It is unclear what specific term or concept "O'Beirne's experiments sphincter" refers to, as it does not correlate with any known phrase or scientific term. Therefore, it is challenging to provide accurate synonyms. It is advised to double-check the term for accuracy or provide more information about the intended context, so appropriate synonyms can be suggested.