Transdermal administration of drugs that penetrate, in this case directly into the blood circulation, has many advantages and is promising for many drugs thanks to its easy application and good patient compliance. (S)-8-Methyl-6,9-diazaspiro[4.5]decan-7,10-dione (alaptide), has been studied as a potential chemical permeation enhancer. Based on its structure, four selected piperazine-2,5-diones were synthesized by means of multi-step synthetic pathways. All the compounds were investigated on their ability to enhance the permeation of the model drug theophylline from the hydrophilic medium propylene glycol:water (1:1). In vitro experiments were performed using vertical Franz diffusion cells at constant temperature 34 ± 0.5 °C and using full-thickness pig (Sus scrofa f. domestica) ear skin. Withdrawn samples were analyzed by RP-HPLC for determination of the permeated amount of theophylline. All the compounds were applied in ratio 1:10 (w/w) relative to the amount of theophylline. One hour after application, the permeated amount of theophylline from formulations with alaptide and (3S,6S)-3,6-dimethylpiperazine-2,5-dione, was ca. 15- and 12-fold higher, respectively, than from the formulation without the tested compounds. Despite the enhancement ratio of both enhancers in a steady state was ca. 2.3, the pseudo-enhancement ratio in the time range from 1 to 3 h was 4.4. These enhancement ratios indicate that the compounds are able to enhance the permeation of agents through the skin; however, the short-term application of both compound formulations seems to be more advantageous. In addition, the screening of the cytotoxicity of all the prepared compounds was performed using three cell lines, and the compounds did not show any significant toxic effect.
Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of betweenness-uniform graphs. In particular, we show that every connected betweenness-uniform graph is either a cycle or a 3-connected graph. Also, we show that betweenness uniform graphs of high maximal degree have small diameter.
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