Novel mathematical model for the assessment of similarity of chromatographic fingerprints of volatile oil from Houttuynia cordata

Background: The analysis of similarities among fingerprints of Chinese herbal medicines is an important quality control tool to determine the authenticity of the herbal medicines. Objectives: In this study, we aimed to develop a novel mathematical model to analyze the similarity of the chromatographic fingerprints of Houttuynia cordata (HC). Materials and Methods: Total quantum statistical moment similarity (TQSMS) expressions were deduced to evaluate the similarities between two chromatographic fingerprints. The volatile oil samples of HC were analyzed with gas chromatography-mass spectrometry, and the fingerprints were constructed by the area under the peak of the chromatograms. Results: There were nine peaks in common, and a total of 733 chemical constituents observed among 15 batches of samples. The number of peaks in the chromatographic fingerprints of the 15 batches of HC was 49–137, with a relative standard deviation (RSD) of 30.13%. The sum of area under the peak was 1.159 × 10⁷–3.437 × 10⁸ μv × s, with an RSD 174.56%; MCRT_T was 9.410–18.602 min, with an RSD of 20.79%; and VCRT_T was 37.549–81.504, with an RSD of 23.27%. The volatile oil composition and content of HC showed strong fluctuation. Therefore, its quality control from the variety and content of the components is impractical. Since TQSMS method can characterize the sample similarity, we can quantitate the correct probability of positive and negative conclusions regardless of the population origin of the samples. Conclusion: Our results show that TQSMS can be an additional method that can be used to assess the similarity of two chromatographic fingerprints.