药物作用量-效关系的Thiele型连分式插值法分析

Estimation of the drug dose-effect relationship by thiele-type continued fraction interpolation

目的:提出Thiele型连分式插值法,研究并建立新的量-效关系分析方法。方法:以原卟啉钠(NAPP)抑制人肝癌细胞株SMMC-7721细胞增殖的实验数据为例,基于Thiele型连分式插值,求出量-效关系表达式并绘制量-效曲线图;预测最大抑制率,计算半抑制浓度(half inhibitory concentration,IC50)和半效浓度(half effective concentration,EC50);求导并绘制导数图,研究抑制率随药物浓度变化的快慢程度。结果:通过Thiele型连分式插值法,得出NAPP作用于SMMC-7721细胞24、48、72 h的量-效关系表达式,预测不同时间下最大抑制率分别为43.75%,55.97%,64.93%;EC50分别为1.04 mg/L、0.36 mg/L、0.30 mg/L;作用48 h、72 h后IC50分别为16.46 mg/L、8.26 mg/L。导数图表明NAPP浓度在10 mg/L内,抑制率随浓度变化速度快,药效不稳定;大于10 mg/L后,变化不明显,药效稳定,出现平台期。结论:Thiele型连分式插值法简单、实用,逼近效果好,可作为研究药物量-效关系的一种新方法。

Objective： To design a thiele-type continued fraction interpolation for estimation of the dose-effect relationship of drugs.Methods： The experimental data on the inhibitive effect of protoporphyrin disodium（ NAPP） on human hepatoma carcinoma strain of SMM-7721 cells in vitro were collected and thiele-type continued fraction interpolation was used to prepare the equation of dose-effect and plot the curves,and to estimate the maximum value of inhibition rate.Half inhibitory concentration（ IC50） and half effective concentration（ EC50） were computed,and the derivative was driven and the derivative graph was developed for examining changes of inhibition rate with the level of NAPP. Results： Thiele-type continued-fraction interpolation obtained the equation of dose-effect relationship pertaining to the inhibitive effect of NAPP on SMM-7721 cells at 24,48 and 72 h,and prediction of the maximum value of inhibition rate at the corresponding time point by 43.75%,55.97% and 64.93%,respectively.The EC50 was 1.04 mg / L,0.36 mg / L and 0.30 mg / L; and IC50 at 24-hour and 48-hour,16.46 mg / L and 8.26 mg / L.The derivative graph indicated that the inhibition rate changed with NAPP concentration at 10 mg / m L,yet the drug effect appeared unstable.The variation was not significant,and the drug effect remained stable and in plateau derivative as the NAPP concentration excelling 10 mg / L. Conclusion： Thiele-type continued-fraction interpolation is simple,practical and effective,with a good approximation effect in comparison with other algorithms,and can be used as a new method for the study of dose-effect relationship of drugs.