中药复方成分提取动力学数学模型的初步研究

目的：建立中药复方成分提取动力学数学模型,并对补阳还五汤中黄芪甲苷的提取动力学参数进行研究和分析。方法：根据Fick定律、Noyes-whitney溶出理论和药材提取过程的实际情况,考虑到溶出成分的分解消除,建立包括代数式的微积分方程组的中药复方溶出动力学数学模型,求解得函数表达式,并对动力学参数求算进行分析。运用该模型研究了补阳还五汤中黄芪甲苷的动力学参数。结果：建立了包含3项e的指数形式的成分溶出浓度解析解及各参数分析方法。黄芪甲苷的动力学参数M,α,N,β,L,π,K,k₁′,k₂′,ρ₁ ,ρ₂,t^{max,c_max,AUC,w₀,P,D分别为0.061 27%,0.280 2 min-1,-1.027%,0.008 965 min}-1,1.077%,0.002 665 min^-1,3.451×10^-3 min^-1,3.188×10^-3 min^-1,0.375 9 min-1,1.420 min, 0.754 7 min,184.9 min,0.057 21 mg·mL^-1 ,289.9 min,0.070 11%,46.24%,22.35%。结论：封闭可溶中药复方扩散体系的成分溶出符合线性动力学数学模型,各参数可根据溶出浓度表达式关系计算得到。

Fundamentally study on mathematical kinetic model of component extraction from FTCM

OBJECTIVE: To establish the mathematical kinetic model of the components extracted from the FTMC (formulae of the traditional Chinese medicine) and analyze parameters of the astragaloside IV extracted from the BYHWD (Buyang Huanwu decoction). METHOD: The model, including algebra and differential groups, have been set up according to the FICK discipline and Noyes-whitney soluted theories, as well as two transfer diffusive processes ((1) from protoplasate to apoplasmic, also from material compartment interior cell membrane to outside compartment; (2) apoplasmic to solution, also from outside compartment to solvent compartment) on components extraction from the FTMC. The equation groups, according to laplace transform, have been given a expression as solutions, which indicate the quantitative changes of the component concentration in solvent vs. time. The model kinetic parameters have been analyzed, meanwhile the parameters of the astragaloside IV in the BYHWD under 100 degrees C, extracted by water, have been analyzed by way of this model: RESULT: It has been established a mathematical model that consists of three parts of e exponent. The kinetic parameters: M, alpha, N, beta, L, pi, K, k1', k2', rho1, rho2, tmax, Cmax, AUC, w0, P, D of the BYHWD were respectivelly 0.061 27% , 0.280 2 min(-1), - 1.027% , 0.008 965 min(-1), 1.077%, 0.002 665 min(-1), 3.451 x 10(-3) min(-1), 3.188 x 10(-3) min(-1), 0.375 9 min(-1), 1.420 min, 0.754 7 min, 184.9 min, 0. 0572 1 mg x mL(-1), 289.9 min, 0.070 11%, 46.24%, 22. 35%. CONCLUSION: The kinetic model, applied to isolated system, can have been of the rule of multiplex linear. Each parameters can be analyzed completely.