{'fraction_non_alphanumeric': 0.018679119412941963, 'fraction_numerical': 0.00066711140760507, 'mean_word_length': 5.25, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Modeling heterogeneity of properties and random effects in drug dissolution.

PURPOSE
To investigate new models characterizing dissolution data obtained for heterogenous materials (model I) and under randomly time-varying conditions (model II).


METHODS
In model I, the heterogeneity of the dissolving substance introduces variation of the fractional dissolution rate. In model II, the fractional dissolution rate evolves randomly, and thus the dissolution has the characteristics of a stochastic process. This situation is studied for the constant and time-dependent means of the dissolution rate.


RESULTS
The time dynamics of the dissolved fraction is presented for model I. The standard characteristics of dissolution are derived under general conditions and for several examples. One of them is in accordance with a function found empirically (1). A duality between the time-dependency of the fractional dissolution rate and the heterogeneity of the substance is investigated. The mean and variance of the dissolved fraction are calculated for model II. A method for estimating the mean dissolution rate is proposed and illustrated using Monte-Carlo experiments.


CONCLUSIONS
It follows from model I that the heterogeneity, with the same mean properties, slows down the dissolution with respect to the homogeneous case. The second approach permits predictions about the role of the stochastic fluctuations of the dissolution rate and to establish the boundaries for the dissolution profiles.