Quantitatively analyze composition principle of Ma Huang Tang by structural equation modeling
Graphical abstract
Introduction
Traditional Chinese prescriptions organically combine various herbal drugs according to a certain composition principle. In the long history, a unique and integrated theoretical system has been evolved, that is, ‘monarch, minister, assistant and guide’.
The monarch drug is an essential ingredient in a prescription; it plays a leading curative role aiming at the cause or the main syndrome of a disease. The minister drug helps strengthen the curative effect of the monarch drug, or, it is used for treatment of accompanying symptoms. The assistant drug has three roles: first, an ingredient to cooperate with the monarch and minister drugs to strengthen the therapeutical effects or treat the accompanying diseases or syndromes; second, an ingredient to inhibit the drastic effects or toxicity of the monarch and minister drugs; and last, an ingredient to possess the properties and flavor opposite to those of the monarch drug, but play supplementing effect in the treatment when serious diseases due to excessive pathogenic factors make patients refuse the drug. The guide drug refers to the ingredient leading the other drugs in the prescription to the affected part, or the ingredient regulating the properties of other drugs. Various drugs in a prescription have their respective importance of effect in the order of ‘monarch, minister, assistant and guide’. Besides, the drugs in a recipe are related to one another: the monarch and minister drugs cooperate with each other, the assistant drug coordinates or inhibits the monarch and minister drugs, ensuring the integral and comprehensive curative effect of the recipe (Chen, 2007).
Ma Huang Tang (Ephedra Decoction, MHT), a famous classical formula from Shang Han Lun by Zhang Zhongjing in the Han Dynasty, is a typical representation reflecting the above composition principle. This prescription consists of four Chinese herbs: Herba Ephedrae (Ephedra, Ephedraceae), Ramulus Cinnamomi (Cassia twig, Lauraceae), Semen Armeniacae Amarum (Bitter apricot kernel, Rosaceae) and Radix Glycyrrhizae Praeparatae (Prepared licorice, Leguminosae) with a traditional dose ratio of 9:6:6:3. It has the good effect of inducing sweating, dispelling exogenous evils, freeing lung and relieving asthma, and is mainly used for treating exterior syndrome due to affection of exogenous wind-cold marked by aversion to cold, fever, headache, general aching, and asthma (Yang et al., 2009). The ancient physicians had come to an agreement on the roles of the drugs in the MHT recipe: Ephedra and Cassia twig are both pungent in flavor and warm in nature, capable of inducing sweating to dispel exogenous pathogenic factors and dispersing the lung to relieve asthma. But Ephedra bears a drastic efficacy with a large dose, and thus acts as the monarch drug to deal with the cause of the disease and the chief syndrome. Cassia twig, as the minister drug, not only helps Ephedra induce sweating to disperse pathogenic cold and expel exterior factors, but also warms the channels to reduce headache and pantalgia. Bitter apricot kernel, with a bitter taste and warm nature, produces the effects of lowering the adverse flow of lung-qi and strengthens the asthma-reducing effect of Ephedra as an assistant drug. Prepared licorice, as a guide drug with a sweet taste and warm nature, can mediate the other drugs properties, and alleviate excessive diaphoretic effects of Ephedra and Cassia twig. When combined, the four drugs clearly show their respective effects, primary or secondary, supplementing and restricting one another, thus forming a prescription which is vigorous in its formation and, though composed of simple drugs, has great therapeutic effects (Fan, 2002, Li, 2006).
However, in spite of its widespread application in the ancient medical system for centuries, the composition principle of ‘monarch, minister, assistant and guide’ of MHT as well as other Chinese compound prescriptions, is still studied in the aspects of clinical application (Yang et al., 2009), efficacy validation (Liu et al., 2005a, Liu et al., 2005b, Jia et al., 2010, Jia et al., 2011) or chemical components analysis (Wei et al., 2003, He and Luo, 2005, Wu et al., 2006), and it is necessary to be interpreted and deepened quantitatively by modern science and technology.
Structural equation modeling (SEM) is a multivariate statistical technique used to deal with complex relationships among multiple variables. The variables used in SEM can be observed variables (also named manifest variables) or latent variables (not observed, also called construct variables), which is one of the most important differences between SEM and other modeling techniques, since the classical data analysis procedures only model observable measurements. Another important aspect of SEM is its extension for estimating measurement errors by using factors or latent variables (Amorim et al., 2010, Kline, 2010, Stein et al., 2012).
As a general framework that involves simultaneously solving systems of linear equations and encompasses other techniques such as regression, factor analysis, and path analysis (Beran and Violato, 2010, Stein et al., 2012), SEM has been successfully used to elucidate causal relationships in disparate fields such as econometrics, sociology and psychology (Armey et al., 2009, Ledermann and Macho, 2009). In addition, it has been applied to biology as well as medical research like epidemiology (Aburatani, 2011, Amorim et al., 2010, Beran and Violato, 2010, Chavance et al., 2010, Tolvanen et al., 2012).
Application of SEM consists of various stages, including the development of a theoretical conceptual model, specification of the mathematical model, determination of the model's identifiability, the model's fit and evaluation of its goodness of fit (Fergusson, 1997). To achieve model specification which is a crucial step, structural equation modeling involves two major components, namely, the measurement equation and the structural equation. A mathematical expression of the measurement equation model is specified as follows:where x is an m×1 vector of indicators describing the q1×1 exogenous latent vector ξ and y is an n×1 vector of indicators that proxy the q2×1 endogenous latent vector η, Λx and Λy are m×q1 and n×q2 matrices of the loading coefficients as obtained from the regressions of x on ξ and y on η, respectively, and δ and ε are m×1 and n×1 random vectors of the measurement errors, respectively. The random vectors δ and ε are assumed to be independent and also uncorrelated with the latent variables ξ and η, respectively. Given the observed data for describing the vectors x and y, the measurement equations appropriately group together the correlated indicator variables to form the latent variables in ξ and η. This is done by assigning fixed parameters and defining unknown parameters in Λx and Λy.
The interrelationship among the latent factors is explained through a structural equation model. It is expressed in the mathematical formula given bywhere η is a q2×1 endogenous random vector of latent variables, ξ is a q1×1 exogenous random vector of latent variable, B is a q2×q2 matrix of coefficients relating the endogenous latent variables to one another in the structural relationship, Г is a q2×q1 matrix of coefficients relating the exogenous latent variables to the endogenous latent variables, and ζ is a q2×1 random vector of error measurements in the equations. It is assumed that B has zeros in the diagonal, (I−B) is required to be nonsingular, and ξ is uncorrelated with ζ (Yanuar et al., 2010, Bollen and Noble, 2011).
In SEM, path diagrams are available to manifest the complex mutual relationships more clearly, in which circles or ovals represent the latent variables and rectangles or squares represent the observable variables, while unidirectional arrows indicate the influence of one variable on another and bidirectional arrows indicate the correlation between variables. Generally, an intact path diagram involves three aspects: regression coefficient of exogenous variables on endogenous variables, measurement error related to manifest variables and residual error of predictive value of latent variables (Kaplan, 2000, Amorim et al., 2010, Beran and Violato, 2010).
SEM is a set of statistical techniques used to measure and analyze the relationships of observed and latent variables. Similar but more powerful than regression analyses, it examines the causal relationships among variables, while simultaneously accounting for measurement error. Although its application has been seen in many disciplines, it has not yet been used in academic research of traditional Chinese medicine.
In the present paper, SEM, the systematology analysis method to complex causality, was adopted to decipher the composition principle of MHT from the overall integral perspective for the first time. The diaphoretic, antispasmodic and analgesic effects were chosen as evaluation indicators for potency of MHT in concordance with clinical application and pharmacological literature.
Section snippets
Materials
The four Chinese herbs Ephedra sinica Stapf (batch number: 20111015), Cinnamomum cassia Presl (batch number: 20111008), Prunus armeniaca L. var. ansu. Maxim. (batch number: 20111011) and Glycyrrhiza uralensis Fischer (batch number: 20111005) were purchased from Hangzhou Fanghuichun Drug Store (Hangzhou, China), and authenticated by Prof. Kongrong Chen, College of Pharmaceutical Science, Zhejiang Chinese Medical University, where the voucher specimens are deposited. The crude slices of all drugs
Pharmacologic effects of 16 prescriptions of different dose ratios
There were significant differences in sweat point number, spasmolysis percentage and writhing number between all 16 MHT-treated groups and model group, or normal control groups, as illustrated in Table 3. The sweat point number in all MHT-treated groups was significantly high as compared to vehicle-treated group (P<0.05). At the same time, the spasmolysis percentage of the MHT-treated groups was significantly higher, while the writhing number was significantly lower than those in model groups (P
Conclusions
SEM is utilized in this study to analyze quantitatively the composition principle of traditional Chinese compound recipes such as MHT. By this way, the theory of ‘monarch, minister, assistant and guide’ can be verified and the integral therapeutic effect can be evaluated, which exhibit the thinking pattern of holistic view and systemic theory in traditional Chinese medicine. Application of SEM to analyze compound prescription not only marks the statuses of prescription ingredients, but also
Acknowledgments
This work was financially supported by National Natural Science Foundation of China (nos. 81102734, and 81173647), Zhejiang Provincial Natural Science Foundation of China (nos. Z2101201, and Y2111160), Zhejiang Province Key Science and Technology Innovation Team (2012R10044-06), and Zhejiang Provincial Program for Cultivation of High-level Innovative Health talents.
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