A terahertz time-domain study on the estimation of opto-mechanical properties of pharmaceutical tablets using the Hashin–Shtrikman bounds for refractive index: a case study of microcrystalline cellulose and starch acetate compacts

Abstract

This work highlights the use of Hashin–Shtrikman (H–S) bounds in the prediction and verification of the effective refractive index, the height and the Young’s modulus of given training sets of pharmaceutical compacts using the measured time delay of a THz pulse traversing the compacts. Set A consisted of 13 microcrystalline cellulose (MCC) compacts whereas set B was made up of 5 starch acetate (SA) compacts. MCC is a typical ingredient of many pharmaceutical tablets. In the case of the MCC compacts, tight and closely matched bounds were obtained between the experimental, the calculated upper, lower bound values for the effective refractive index, and the height values. This promising outcome has shown the high possibility of utilizing H–S bounds in the verification and prediction of the decision level of useful parameters, which can serve as a quality check for pharmaceutical tablets. For the SA compacts, although less tight bounds were observed, the experimental values for the effective refractive index and the Young’s modulus were closely matched with the upper and the lower bounds, respectively. We therefore speculate based on the above observations that the MCC tablets contain an almost evenly distributed spherically shaped air voids whereas in the SA compacts, this assumption might not necessary be true.