Assessment of chemical equivalence in herbal materials using chromatographic fingerprints by combination of three similarity indices and three-dimensional kernel density estimation

An intuitive and practical way to control chemical equivalence of secondary metabolites in herbal materials based on chromatographic fingerprints deserves a thorough discussion, yet it is relatively unexplored. For the first time, we propose a mixture of three similarity indices, the congruence coefficient, the average of the peak area ratios, and the larger value between the maximum peak area ratio and the reciprocal of the minimum peak area ratio, to make up for the weak points of some widely used similarity indices and to evaluate the chemical equivalence of two fingerprints from various perspectives. The three similarity values are fed into a three-dimensional kernel density estimation to determine the quality of herbal materials. This estimation enables precise detection of anomalies in the absence of prior quality determination experience. Forty Atractylodes samples similar in appearance and indiscriminately used for medical purposes were used to demonstrate the effectiveness of the developed approach. After a reference sample was postulated, a quality assessment of the 40 samples was performed using the three similarity values and the estimated kernel density. The samples that were judged by the developed approach to be of good quality were compared with those chosen by the most popular approach using decision criterion of a single similarity index. The benefits of the proposed approach were evident in that the qualified samples had the composition ratio and individual concentrations of multi-components closer to those of the reference in general, and their inter-sample deviation was significantly smaller.