Mathematical models of the drug release have been used in the drug delivery (DD) field for more than 50 years by the scientists in the drug development process. These models not only help scientists to learn the dynamics of the drugs release, but also help them to save money and time by helping to design more effective experiments. There is no model in the literature that covers all drug release scenarios. Also, some system-specific models have complex mathematical equations and these models are not suitable for general use. Zero Order Model, First Order Model, Higuchi Model, Peppas Model and Hixon Crowell Model are used in 85% of drug release studies in total. The popularity of these models comes from their simplicity, easy mathematical expressions and implementation. In this review, mathematical derivations of these five models are shown in detail. The points to be considered during the derivation and the problems that may be encountered are carefully explained along with their solutions. In addition, the application of the models to drug release data and the points to be considered were obtained by writing from the scratch without using any ready software while obtaining the fit function. In this way, many problems are better understood, and their solutions are explained. Finally, the obtained fit functions are interpreted.

This study aimed to investigate the potential of Kluyveromyces lactis to be used as baker's yeast in production of lean bread (100% of wheat flour) and sucrose (10%), lactose (10%), or whey (13.35%) supplemented breads. The pH, total titratable acidity, baking loss, specific volume, color parameters, textural, and sensory properties of breads produced by K. lactis were measured and compared with those of breads produced by commercial baker's yeast. Type of yeast and dough formulation had significant influences on pH, specific volume, baking loss, textural parameters, and color parameters of breads. Commercial baker's yeast presented better results than K. lactis in lean bread. The investigated parameters of K. lactis leavened bread were improved with the addition of each ingredient. Whey and lactose added breads leavened by K. lactis had quality characteristics and sensory scores as good as or better than the breads leavened by commercial baker's yeast. Practical applications Several studies have focused on the increase in the nutritional value of wheat based bread. Fortification of dough with whey improves bread protein quality, but also may negatively affect the other quality characteristics of bread. Moreover, breads containing whey powder may not be suitable for people with lactose intolerance due to the high amount of lactose found in it. Kluyveromyces lactis has ability to utilize lactose as a source of carbon. In this study, whey powder fortified bread leavened by K. lactis was judged as acceptable by the sensory panel and received similar scores for odor, taste, and overall acceptability compared to commercial baker's yeast. The results of this study show that K. lactis is feasible yeast for the production of whey powder enriched bread, and thus, may help to use whey powder as a suitable ingredient in bread making.

Background: pH sensitive dendrimers attached to nanocarriers, as one of the drug release systems, has become quite popular due to their ease of manufacture in experimental conditions and ability to generate fast drug release in the targeted area. This kind of fast release behavior cannot be represented properly most of the existing kinetic mathematical models. Besides, these models have either no pH dependence or pH dependence added separately. So, they have remained one dimensional. Objective: The aim of this study was to establish the proper analytic equation to describe the fast release of drugs from pH sensitive nanocarrier systems. Then, to combine it with the pH dependent equation for establishing a two-dimensional model for whole system. Methods: We used four common kinetic models for comparison and we fitted them to the release data. Finding that, only Higuchi and Korsmeyer-Peppas models show acceptable fit results. None of these models have pH dependence. To get a better description for pH triggered fast release, we observed the behavior of the slope angle of the release curve. Then we puroposed a new analytic equation by using relation between the slope angle and time. Result: To add a pH dependent equation, we assumed the drug release is “on” or “off” above/below specific pH value and we modified a step function to get a desired behavior. Conclusion: Our new analytic model shows good fitting, not only one-dimensional time dependent release, but also two-dimensional pH dependent release, that provides a useful analytic model to represent release profiles of pH sensitive fast drug release systems.

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