Grassi Mario, Grassi Gabriele
University of Trieste, Department of Engineering and Architecture , Via Valerio 6/A, I - 34127, Trieste , Italy +39 040 558 3435 ; +39 040 569823 ;
Expert Opin Drug Deliv. 2014 Aug;11(8):1299-321. doi: 10.1517/17425247.2014.924497. Epub 2014 Jun 17.
This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems.
The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered.
Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.
本综述以数学建模概念为出发点，旨在对调控基质系统药物释放的最重要机制进行物理和数学描述。对释放机制的确切了解使我们能够建立强大的数学模型，而这些模型对于设计和优化合适的药物递送系统至关重要。
基质药物释放的基本机制包括药物扩散、基质溶胀、基质侵蚀、药物溶解并可能重结晶（例如无定形和纳米晶药物的情况）、基质内药物的初始分布、基质几何形状、基质尺寸分布（不同直径球形基质的情况）和渗透压。根据基质特性，上述变量在药物释放中可能发挥不同作用；因此，数学模型需要仅基于所考虑的特定基质的最相关机制来构建。
尽管制药行业的态度略显迟疑，但鉴于最新研究结果，我们认为数学建模可能会对制药领域产生巨大的潜在影响。我们坚信，数学建模在未来将变得越来越重要，尤其是考虑到个性化医疗的迅速兴起，这是一种旨在治疗每个个体患者而非“平均”患者的新型治疗方法。
