从具有多种保留机制的随机扩散模型中获得色谱峰形状：解析时域表达式和导数
Chromatographic Peak Shape from a Stochastic-Diffusive Model with Multiple Retention Mechanisms: Analytic Time-Domain Expression and Derivatives
AI总结：
本文提出了一种基于随机扩散模型的色谱峰形状解析表达式，结合轴向扩散、有限初始空间方差和多种保留机制，通过高效评估方案提升了计算效率，并在多个文献峰拟合中表现出更优的精度。
摘要：
在随机扩散框架内，推导出色谱峰形状的时域解析表达式，考虑了轴向扩散（分子扩散和多路径/涡流扩散）、有限初始空间方差、高短时事件速率的保留机制以及任意数量的独立慢速保留机制，每种机制具有自身独特的长时事件速率。推导出该表达式的高效评估方案，在单慢机制情况下比之前的方法快两个到四个数量级。还获得了所有模型参数的解析导数，其计算成本与峰形状表达式相当。对三个文献峰的拟合结果表明，全轮廓RMSE值均低于指数修正高斯函数，在所有测试案例中最小值范围为峰高0.03至0.14个百分点，而参考模型为0.43至5.57个百分点。相较于单慢机制模型，允许多个慢机制可使数据依赖性改进，其中对一个峰的改进超过一个数量级。
英文摘要：
A time-domain analytic expression for chromatographic peak shapes is derived within a stochastic-diffusive framework that incorporates axial diffusion (molecular and multipath/Eddy), finite initial spatial variance, a retention mechanism characterized by a high rate of short-duration events, and an arbitrary number of independent slow retention mechanisms, each characterized by its own rate of infrequent, long-duration events. A highly efficient evaluation scheme is derived for this expression. In the single-slow-mechanism case, it is two to four orders of magnitude faster than the previously available analytic route. Analytical derivatives with respect to all model parameters are also obtained, and each can be evaluated at computational cost comparable to that of the peak-shape expression. Illustrative fits to three literature peaks yielded full-profile RMSE values lower than those of the exponentially modified Gaussian in all tested cases, with minima ranging from 0.03 to 0.14 percent of peak height, compared with 0.43 to 5.57 percent for the reference model. Relative to the one-slow-mechanism formulation, allowing more than one slow mechanism produced a data-dependent improvement that exceeded one order of magnitude for one of the peaks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
