利用有理样条插值法计算EC_(50)的研究  

Study on calculation of EC_(50) by rational spline interpolation method

作　　者：朱涛[1] 张澜[2] 赵前进[2] ZHU Tao ZHANG Lan ZHAO Qianjin(Coll of Med , Anhui Univ of Sci ＆ Tech , Huainan 232001, China Coll of Math and Big Date, Anhui Univ of Sci ＆ Tech, Huainan 232001, China)

机构地区：[1]安徽理工大学医学院,安徽淮南232001 [2]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《扬州大学学报（农业与生命科学版）》2017年第2期28-31,46,共5页Journal of Yangzhou University：Agricultural and Life Science Edition

基　　金：国家自然科学基金资助项目(60973050)

摘　　要：以2种典型的毒理学试验数据为例,利用有理样条插值法,求解参数后将试验数据纳入计算过程,求得有理插值样条表达式,并绘制浓度-抑制率曲线图。将计算出半效浓度(EC_(50))与概率单元法、曲线拟合法等计算结果进行比较。结果表明:有理样条插值法是一种计算EC_(50)的新方法,其基于变形能量最小建立的优化模型,适合于试验数据较少的情形。With the application of a case involving two typical toxicity data, the paper took the control data into the calculation process, calculated the expression of rational spline interpolation and draw the curve for the concentration- inhibition ratio by rational spline interpolation. The EC50 was compared with the results of the methods of curve-fitting, probit method, etc. The result indicated that the method of rational spline interpolation was a new method to calculate EC50, which established optimal mathematical model based on minimum strain energy, and was suitable for the case of less experimental data.

关 键 词：EC50 有理三次样条插值 保形 曲线拟合 概率单元法 

分 类 号：O241.3[理学—计算数学]