A battery of techniques such as EDX, WDX. XF, IR, SIMS,XRD, etc., alone or in combination,may serve the purpose. Each technique has its advantages and limitations. The researcher is advised to consult with a materials scientist before proceeding further.
Not to forget the non destructive methods for repeated evaluation: micro-computed tomography (synchrotron-based or with polychromatic x-ray source) or the more traditional x-ray methods: transverse microradiography (TMR) or longitudinal microradiography (LMR).
I am not an endodontist, but being an active researcher of this area I can comment on this question. As per the suggestion of Prof. @Karl-Heinz Kunzelmann it can be monitored using non-destructive testing methods.
Plenty of methods are available to quantify the results of testing using image processing and signal processing techniques.