As you well may know, the biopsies the determine whether or not a patient has celiac disease are very invasive. These biopsies are not a practical long-term way to monitor the state of the small intestine, so doctors have been trying to come up with easier and quicker ways. In one line of research, doctors monitor FABP levels in the person with celiac disease. FABPs, or fatty acid binding proteins, come in several varieties. Researchers found that intestinal FABPs and liver FABPs circulate in much higher concentrations in people with untreated biopsy-proven celiac disease than in healthy people.
The articles on this research do not say which non-invasive method detects FABP levels, but urine tests are about as bad as non-invasive procedures get. All you need to know? A non-invasive type of celiac disease diagnosis is not yet available, but in the future you can expect that diagnosis will be a lot less painful.