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The content uniformity (CU) of blend and tablet formulations is a criticalproperty that needs to be well controlled in order to produce an acceptablepharmaceutical product. Methods that allow the formulations scientist topredict the CU accurately can greatly help in reducing the development efforts.This article presents a new statistical mechanical framework for predicting CUbased on first principles at the molecular level. The tablet is modeled as anopen system which can be treated as a grand canonical ensemble to calculatefluctuations in the number of granules and thus the CU. Exact analyticalsolutions to hard sphere mixture systems available in the literature areapplied to derive an expression for the CU and elucidate the different factorsthat impact CU. It is shown that there is a single ratio,{\lambda}\equiv<w^2.f^2>/<w.f>; that completely characterizes "granule quality"with respect to impact on CU. Here w and f denote the weight of granule and thefractional (w/w) assay of API in it. This ratio should be as small as possibleto obtain best CU. We also derive analytical expressions which show how thegranule loading impacts the CU through the excluded volume, which has beenlargely ignored in the literature to date. The model was tested againstliterature data and a large set of tablet formulations specifically made andanalyzed for CU using a model API. The formulations covered the effect ofgranule size, percentage loading, and tablet weight on the CU. The model isable to predict the mean experimental coefficient of variation (CV) with goodsuccess and captures all the elements that impact the CU. The predictions ofthe model serve as a theoretical lower limit for the mean CV (for infinitebatches or tablets) that can be expected during manufacturing assuming the bestprocessing conditions.

An exact model for predicting tablet and blend content uniformity based on the theory of fluctuations in mixtures