This paper describes a way to map users' queries to relevant Medical Subject Headings (MeSH terms) used by the National Library of Medicine to index the biomedical literature. The method, called SENSE (SEarch with New SEmantics), transforms words and phrases in the users' queries into primary conceptual components and compares these components with those of the MeSH vocabulary. Similar to the way in which most numbers can be split into numerical factors and expressed as their product--for example, 42 can be expressed as 2*21, 6*7, 3*14, 2*3*7,--so most medical concepts can be split into "semantic factors" and expressed as their juxtaposition. Note that if we split 42 into its primary factors, the breakdown is unique: 2*3*7. Similarly, when we split medical concepts into their "primary semantic factors" the breakdown is also unique. For example, the MeSH term 'renovascular hypertension' can be split morphologically into reno, vascular, hyper, and tension--morphemes that can then be translated into their primary semantic factors--kidney, blood vessel, high, and pressure. By "factoring" each MeSH term in this way, and by similarly factoring the user's query, we can match query to MeSH term by searching for combinations of common factors. Unlike UMLS and other methods that match at the level of words or phrases, SENSE matches at the level of concepts; in this way, a wide variety of words and phrases that have the same meaning produce the same match. Now used in PaperChase, the method is surprisingly powerful in matching users' queries to Medical Subject Headings.