广义估计方程与多目标遗传算法在缓控释制剂处方优化中的研究
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摘要
随着药学技术的日新月异,制药研究进入了创新时代,新型的给药系统,如缓控释制剂越来越受人们的青睐,缓控释制剂可以有效减缓药物“峰-谷现象”,保持平稳持久的有效血浓度,治疗作用持久,给药次数减少,方便用药。然而,在制药研究过程中要涉及到设计、建模和优化的问题。由于影响的因素通常不止一个,所以设计的方案也是多因素的,目前较常用的有析因设计、正交设计、均匀设计、中心复合设计、混料设计等;在构建模型的过程中目前常用的方法有多重线性回归模型、二次型回归模型及高阶回归模型等,但这些模型都要求数据具有独立性。缓控释制剂是重复测量数据,常以累积释放度作为评价指标,测量不同时点的累积释放度,以此来进行处方工艺筛选,其不同时点的数据具有高度相关性,因此传统建模方法不能揭示其内在的特点,有时还会得到错误的结论;在缓控释制剂处方优化过程中,其不同时点累积释放度是一个多目标条件优化的问题,传统的多目标优化方法直接法、最速下降法等存在着极大的主观性;目前较常用的综合评分法是将各个目标加权,从而将多目标问题转换为单目标问题,再采用比较成熟的单目标优化算法进行优化。但它们有明显的缺点,如转换成单目标优化后每次计算只能产生一个解,而权重系数往往也无法确定。
     广义估计方程(genrealized estimating equations, GEE)是用于分析非独立数据的一种统计分析方法,可以处理重复测量资料、整群抽样资料等,目前主要用在临床医学、流行病学调查、卫生服务,生物医学的研究中,但在缓控释制剂领域的应用尚未见报道。
     遗传算法(Genetic Algorithm, GA)是一类借鉴生物界的进化规律演化而来的随机化搜索方法。多目标遗传算法能够通过对各个子目标进行折衷处理,为决策者提供一组可选择的、非受控的、最佳解决方案集。改进的非劣分类遗传算法(NSGA-Ⅱ)是一个比较新颖的多目标遗传算法,目前国外大量的应用于多目标优化问题中,取得了卓越的成果。但在缓控释制剂的多目标优化中应用有限。
     本课题将广义估计方程与多目标遗传算法用于缓控释制剂的处方优化,在广义估计方程建模的基础上,用多目标遗传算法寻找处方的最优组合。主要从以下三个方面对课题进行阐述和探讨:
     第一部分广义估计方程概念、原理。广义估计方程是在广义线性模型和纵向数据准似然估计的基础上发展起来的一种拟似然估计方法,可用于非独立重复测量数据分析。主要涉及到广义线性模型的基本结构和连接函数,广义估计方程的计算步骤,作业相关矩阵的类型等原理。
     第二部分基于遗传算法的多目标优化。介绍了多目标优化的概念,Pareto解的概念,遗传算法的基本原理,重点介绍了NSGA-Ⅱ算法的原理。
     第三部分基于广义估计方程与多目标遗传算法在缓控释制剂处方优化中的实例应用。针对三种不同动力学模型的缓控释制剂文献资料进行建模和优化。
     零级动力学模型,利用醋氯芬酸控释片最佳工艺的研究资料,分别用广义线性模型和可交换相关、自相关及无结构相关三种相关结构的广义估计方程建模,结果显示可交换相关结构的均方误差(MSE)和平均绝对误差(MAD)最小,分别为8.8036和2.3649,模型拟合效果较好,因此采用可交换相关结构的广义估计方程建模。利用NSGA-Ⅱ对模型进行多目标寻优:低分子量聚氧乙烯210.2mg、氯化钠28.9mg、聚乙二醇4.4g、包衣增重7.2%;此条件下得到Q2为9.96%,Q6为44.74%,Q12达到92.05%,搜索得到结果更接近最佳释放目标。
     一级动力学模型,利用格列齐特缓释片最佳工艺的研究资料,分别用广义线性模型和可交换相关、自相关及无结构相关三种相关结构的广义估计方程建模,结果显示可交换相关结构的均方误差(MSE)和平均绝对误差(MAD)最小,分别为6.4354和2.0829,模型拟合效果较好,因此采用可交换相关结构的广义估计方程建模。利用NSGA-Ⅱ对模型进行多目标寻优:HPMC100cps24.59mg、HPMC4000cps17.74mg、海藻酸钠7.34mg;此条件下得到Q2为16.5%,Q6为56.8%,Q12达到85.9%,搜索得到结果更接近最佳释放目标。
     Higuchi动力学模型,利用酮洛芬缓释片最佳工艺的研究资料,分别用广义线性模型和可交换相关、自相关及无结构相关三种相关结构的广义估计方程建模,结果显示可交换相关结构的均方误差(MSE)和平均绝对误差(MAD)最小,分别为2.6501和11.6378,模型拟合效果较好,因此采用可交换相关结构的广义估计方程建模。利用NSGA-Ⅱ对模型进行多目标寻优:羟丙甲纤维素28.53g、乳糖29.57g、乙基纤维36.88g;此条件下得到Q2为27.9%,Q6为59.2%,Q12达到99.9%,搜索得到结果更接近最佳释放目标。
     综上所述,广义估计方程充分考虑缓控释制剂数据相关性的特点,建模可行;多目标遗传算法突破药典中综合评分法单一优化的不足,较大程度克服了传统方法主观性的缺点;利用广义估计方程与多目标遗传算法对缓控释制剂进行建模和优化,效果理想,简便可行。
With the ever-changing pharmaceutical technology, pharmaceutical research hasentered a new era and new drug delivery systems, for example sustained-release formulation is more and more used by people. The sustained-release and controlled-release formulations can slow down the drug "peak-valley phenomenon" effectively, to maintain stable long-lasting effective blood concentration, lasting therapeutic effect, reducing the number of convenient medication. However, it involves problems of the design, modeling and optimization in the process of pharmaceutical research. The impact factors are usually more than one, so the designed programs are multi-factors. Often use factorial design, orthogonal design, uniform design, central composite design, mixture design and so on; Currently there are multiple linear regression, quadratic regression model and higher order regression model to be used in the process of building models, but they require the data is independent. The data of sustained-release and controlled-release formulations is the repeated measurement data, and its evaluation index is usually used as the cumulative release rate, measuring the cumulative release of the same prescription at different time points, in order to screen the formulation and process, its data of different time points is highly correlated. Therefore, the traditional modeling method can not reveal its inherent characteristics, and sometimes can get the wrong conclusion; The cumulative release at different point time is a multi-objective optimization problem in the process of optimization of sustained-release and controlled-release formulations prescription. The more commonly used is the weight of each objective, then multi-objective problem can be converted to a single objective, to optimize by the more mature single-objective optimization algorithm. But they have disadvantages obviously, such as converting into single objective optimization and each calculation can only produce a solution, furthermore the weight coefficients are often unable to determine.
     Genrealized Estimating Equations is a statistical analysis method for the analysis of non-independent data, and it can handle with repeated measurements, cluster sampling data and so on. Currently it is used in clinical medicine, epidemiology research, health services, biomedical research, but it has not been reported in the field of sustained-release and controlled-release formulations.
     Genetic Algorithm is a search method from the biological evolution discipline. Multi-objective genetic algorithm provides decision-makers with a set of alternative, non-controlled and the best solution set through balancing all the sub-objectives. NSGA-Ⅱ is a novel multi-objective genetic algorithm, which is used in multi-objective optimization problems to apply in a large number of foreign countries to achieve excellent results. But it is limited in the multi-objective optimization of sustained-release and controlled-release formulations.
     The topic will apply the generalized estimating equations and multi-objective genetic algorithm to the optimization of sustained-release and controlled-release formulations. On the basis of the generalized estimating equation modeling,it can search the optimal prescription by multi-objective genetic algorithm. There are3parts of the subject to describe and discuss:
     Part1The concepts and principles of generalized estimating equations. Generalized estimating equations is a quasi-likelihood estimation method based on generalized linear models and longitudinal data quasi-likelihood estimation and it can be used in the repeated measurement of non-independent data. In refers to the basic structure and link function of the GLM,the steps of GEE, the type of work correlation Matrix.
     Part2Multi-objective optimization base on Genetic algorithm. There are the concepts of multi-objective optimization, the basic concepts of Pareto solution,the basic principles of genetic algorithms. Focuses on the basic principles of NSGA-Ⅱ.
     Part3Instance of the application Sustained-Release Formulation Optimization Based On Generalized Estimating Equations combined with multi-objective genetic algorithm. The topic will model and optimize the data of sustained release preparation for the three different dynamics models.
     Zero-order dynamics model, the topic using aceclofenac sustained-release formulations can model by generalized estimating equation and generalized linear models of three related structures which are exchangeable correlation, autocorrelation and unstructure correlation.Results show that the MSE and MAD of exchangeable correlation structure are the minimum. They are respectively8.8036and2.3649, and the model is well fitted. So it uses the generalized estimating equation of the exchangeable correlation structure to model. Using NSGA-II to optimize the multi-objective model:Low molecular weight poly (ethylene oxide) is210.2mg; NaCl is28.9mg; polyethylene glycol is4.4g; the weight gain is7.2%; The result is9.96%of the Q2under this condition,44.74%in Q6,92.05%in Q12.The results were closed to the best release.
     One-order dynamics model, the topic using Gliclazide sustained-release formulations can model by generalized estimating equation and generalized linear models of three related structures which are exchangeable correlation, autocorrelation and unstructure correlation. Results show that the MSE and MAD of exchangeable correlation structure are the minimum. They are respectively6.4354and2.0829, and the model is well fitted. So it uses the generalized estimating equation of the exchangeable correlation structure to model. Using NSGA-Ⅱ to optimize the multi-objective model:HPMC100cps is24.59mg;HPMC4000cps is17.74mg and Sodium alginate is7.34mg; The result is16.5%of the Q2under this condition,56.8%in Q6,85.9%in Q12.The results were closed to the best release.
     Higuchi dynamics model, the topic using ketoprofen sustained-release formulations can model by generalized estimating equation and generalized linear models of three related structures which are exchangeable correlation, autocorrelation and unstructure correlation. Results show that the MSE and MAD of exchangeable correlation structure are the minimum. They are respectively2.6501and11.6378, and the model is well fitted. So it uses the generalized estimating equation of the exchangeable correlation structure to model. Using NSGA-Ⅱ to optimize the multi-objective model:Hypromellose is28.53g, Lactose is29.57mg, EC is36.88g; The result is27.9%of the Q2under this condition,59.2%in Q6,99.9%in Q12.The results were closed to the best release.
     In summary, the generalized estimating equations take full account of the correlation characteristics of the sustained-release and controlled-release preparation of data, modeling is feasible; the multi-objective genetic algorithm is better than the single optimization of the integrated score breakthrough Pharmacopoeia, and overcomes the subjective characteristics of the traditional method largely; The results of sustained-release and controlled-release formulations are satisfactory and simplefeasible by generalized estimating equation combining with the multi-objective genetic algorithm for modeling and optimization.
引文
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