Himiniuc Loredana, Socolov Razvan, Ghizdovat Vlad, Agop Maricel, Anton Emil, Toma Bogdan, Ochiuz Lacramioara, Vasincu Decebal, Popa Ovidiu, Onofrei Viviana
Department of Obstetrics and Gynecology, "Grigore T. Popa" University of Medicine and Pharmacy Iasi, 700115 Iasi, Romania.
Department of Obstetrics and Gynecology, Faculty of Medicine, "Grigore T. Popa" University of Medicine and Pharmacy Iasi, 700115 Iasi, Romania.
Polymers (Basel). 2022 Apr 30;14(9):1848. doi: 10.3390/polym14091848.
The paper focuses on the development of a multifractal theoretical model for explaining drug release dynamics (drug release laws and drug release mechanisms of cellular and channel-type) through scale transitions in scale space correlated with experimental data. The mathematical model has been developed for a hydrogel system prepared from chitosan and an antimicrobial aldehyde via covalent imine bonds. The reversible nature of the imine linkage points for a progressive release of the antimicrobial aldehyde is controlled by the reaction equilibrium shifting to the reagents, which in turn is triggered by aldehyde consumption in the inhibition of the microbial growth. The development of the mathematical model considers the release dynamic of the aldehyde in the scale space. Because the release behavior is dictated by the intrinsic properties of the polymer-drug complex system, they were explained in scale space, showing that various drug release dynamics laws can be associated with scale transitions. Moreover, the functionality of a Schrödinger-type differential equation in the same scale space reveals drug release mechanisms of channels and cellular types. These mechanisms are conditioned by the intensity of the polymer-drug interactions. It was demonstrated that the proposed mathematical model confirmed a prolonged release of the aldehyde, respecting the trend established by in vitro release experiments. At the same time, the properties of the hydrogel recommend its application in patients with intrauterine adhesions (IUAs) complicated by chronic endometritis as an alternative to the traditional antibiotics or antifungals.
本文重点在于开发一种多重分形理论模型，用于通过与实验数据相关的尺度空间中的尺度转变来解释药物释放动力学（细胞和通道型的药物释放规律及药物释放机制）。该数学模型是针对由壳聚糖和一种抗菌醛通过共价亚胺键制备的水凝胶系统开发的。亚胺键的可逆性质使得抗菌醛能逐步释放，这由反应平衡向试剂方向的移动所控制，而反应平衡的移动又由抑制微生物生长过程中醛的消耗所触发。数学模型的开发考虑了醛在尺度空间中的释放动态。由于释放行为由聚合物 - 药物复合系统的内在性质决定，所以在尺度空间中对其进行了解释，表明各种药物释放动力学规律可与尺度转变相关联。此外，在同一尺度空间中薛定谔型微分方程的功能揭示了通道和细胞类型的药物释放机制。这些机制由聚合物 - 药物相互作用的强度决定。结果表明，所提出的数学模型证实了醛的缓释效果，符合体外释放实验所确立的趋势。同时，水凝胶的特性表明其可应用于并发慢性子宫内膜炎的宫腔粘连（IUA）患者，作为传统抗生素或抗真菌药物的替代品。
