Nikitas P, Pappa-Louisi A, Papageorgiou A
Department of Chemistry, Aristotle University of Thessaloniki, Greece.
J Chromatogr A. 2001 Mar 30;912(1):13-29. doi: 10.1016/s0021-9673(01)00524-6.
The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.
结合使用非线性最小二乘法对重叠峰进行反卷积，研究了选择合适的描述色谱峰的函数这一问题。结果表明，文献中提出的用于描述色谱峰的大多数函数并不适用于此目的。只有多项式修正高斯函数几乎可以描述每个峰，但除非对其进行适当重新定义，否则在数学上是不正确的。提出并讨论了两个新函数。还表明，使用非线性最小二乘法程序（如Microsoft Solver）可以高精度地完成重叠峰的反卷积，但只有当我们将峰最大值的位置以及未分离色谱峰中每个组分的峰面积（或高度）用作拟合参数时，才能实现这一目标。如果我们将描述多组分峰中每个单峰的所有参数用作拟合参数，那么Solver会得到更好的拟合结果，不过这并不对应于峰的最佳反卷积。最后，发现Solver给出的结果比免疫算法和遗传算法等现代方法要好得多。
