Chinese Medicine (CM) has been widely used as an important avenue for disease prevention and treatment in China especially in the form of CM prescriptions combining sets of herbs to address patients’ symptoms and syndromes. However, the selection and compatibility of herbs are complex and abstract due to intrinsic relationships between herbal properties and their overall functions. Network analysis is applied to demonstrate the complex relationships between individual herbal efficacy and the overall function of CM prescriptions. To illustrate their connections and correlations, prescription function (PF), prescription herb (PH), and herbal efficacy (HE) intranetworks are proposed based on CM theory to identify relationships between herbs and prescriptions. These three networks are then connected by PFPH and PHHE interlayer networks adopting herb dosage to form a multidimensional heterogeneous network, a PrescriptionHerbFunction Network (PHFN). The network is applied to 112 classic prescriptions from
Traditional Chinese Medicine (TCM) formula is a common approach in traditional medical treatment and has gained widespread clinical applications [
CM embraces a holistic approach and uses complicated herb prescriptions for treatment targeting complex disease phenomena. Ma et al. mined syndrome differentiating principles from TCM clinical data [
Former studies on prescription analysis are based on gene or protein databases, unable to uncover the traditional combination theory of CM. Moreover, the dosage and properties of herbs on the effect of prescriptions have been neglected. The simultaneous application of herbs is usually in different dosages traditionally identified in a prescription with different roles. One of the key subjects of prescription research focuses on compatibility regularity while the dosage of herbs has joint action on the overall efficacy of prescriptions. The structure of Monarch, Minister, Assistant and Guide are traditional theories giving compatibility principles of prescriptions. Therefore, herb dosage needs to be integrated with combination rules to investigate the comprehensive mechanism of prescriptions.
We propose a structure of a PrescriptionHerbFunction Network (PHFN) with 3 intra networks corresponding to the effects of prescriptions, herb combinations and herbal efficacies with interlayers to illustrate the internal law of compatibility. The research is (1) to build a network model that accurately illustrates the prescriptions, herbs, efficacy and their complex relationships, providing a unified analysis model for an indepth study of formula compatibility; (2) to introduce a concept of relative dosage to reflect the relative intensity of each herb, and to provide a unified criterion for herb quantity evaluation; (3) to study herbs and their combinations in terms of multivariate tuples and weighted edges in network model to reflect relationships amongst herbs in prescriptions.
Definitions of relative dosage and relative interaction intensity are first introduced, followed by herbefficacy (HE), prescriptionherb (PH), prescriptionfunction (PF) intra networks and PFPH, PHHE interlayer networks. The network model comprising various concepts of TCM such as herbs and efficacies are then constructed. Each of the network is explained as follows.
Definition 1: Relative dosage. Standardized herb dosage that compares the actual dosage with its normal dosage range. Relative dosage is a standardized value ranging (0, 1]. Normally the larger the actual dosage of an herb, the larger the relative dosage prescribed related to patients’ symptoms and clinician’s medication experience. Considering that the negative exponential function features nonlinear, continuous, monotone decreasing and asymptotic, the calculation is defined as
where x and Y(x) are the actual dosage and the standardized dosage, respectively. Y(x) indicates that the efficacy of an herb is enhanced with the increase of herb dosage to 1 as the standardized maximum value. λ is chosen to define a range that Y(x) increases rapidly with x, and the increase becomes less significant when x goes further beyond the particular range. The parameters are chosen as follows, β = 2 and
where [a, b] is the routine dosage range of an herb [
Definition 2: Relative interaction intensity. The relative dosage of a particular herb to the sum of relative dosage of all herbs in a prescription. Relative interaction intensity describes the relative dosage of an herb in a prescription in proportion to all the other relative dosages, and its range of value is (0, 1]. For a prescription with n number of herbs, and the relative dosage of an herb is denoted as x_{j}, so the relative interaction intensity of i^{th} herb is
Based on the calculation of herb dosage in each formula according to Def. 1, taking Cassia Twig Decoction as an example, according to the original record it is composed of cassia twig 46.875 g, debark peony root 46.875 g, fresh ginger 46.875 g, Chinese date 12 g, and licorice 31.25 g. Based on research of dosage in
Definition 3: Intralayer Network. Intralayer networks include herbefficacy, prescriptionherb, prescriptionfunction networks. PH network demonstrates a set of herbs and their associations based on the composition of prescriptions under analysis. Prescriptionherb network is defined as
where Y is a set of nodes representing herbs appearing in all prescriptions, and R_{y} for herbtoherb relationships. r_{i,j} = <n_{1}, φ_{m}> is in the form of a tuple representing the relationship between herb y_{i} and herb y_{j} where n_{1} is the total number of coexistence of y_{i} and y_{j} in all prescriptions under analysis, and φ_{m} includes a set of prescriptions where they coexist and the corresponding original and relative dosage of herb y_{i} and herb y_{j}.
Prescription function network demonstrates associations between functions according to their cooccurrences in prescriptions. It is represented as
where G is a set of functions, and R_{g} is a set of relationships between them where g_{i,j} includes the number of cooccurrences and a set of prescriptions where they coexist. Likewise, herbal efficacy network shows associations between efficacies defined as N_{HE} = <E, R_{x}> where E is a set of efficacies, and R_{x} represents their relationships between them including cooccurrences from herbs in the scope of the analysis.
Definition 4: Interlayer Network. PHHE interlayer network represents the relationships between and prescriptionherb and herbefficacy network. PHHE interlayer network is represented as
where Y and E are a set of herbs and a set of herbal efficacies respectively, and matrix R_{y−x} represents the relationships between Y and E. If the herb y_{i} from Y has efficacy x_{i} from E, the corresponding element in R_{y−x} is set as 1 denoting there is a weightless edge between them.
PFPH interlayer network presents relationships of key herbs in prescriptions and functions of the prescriptions where they are in. It is represented as
where Y and G are a set of herbs and a set of prescription functions, respectively. Herbs in each prescription are sorted according to their relative interaction intensities, and main herbs accounting for more than 60% cumulative relative interaction intensities are linked to establish associations with the functions of corresponding prescription. R_{y−g} stores these herbfunction connections in the matrix, each element in the form of a tuple as R_{y−g} = <n, φ_{m}> where n is the total number of cooccurrences of particular herb y and a particular function g taking account of all prescriptions, and φ_{m} is the set of prescriptions where they coexist.
PrescriptionHerbFunction Network (PHFN) is a multidimensional heterogeneous network integrating herbefficacy, prescriptionherb, prescriptionfunction networks and their interlayer networks.
In order to realize elastic and scalable massive prescription analysis, the prescription data storage and analysis system adopts a distributed database and computing framework, which can be combined with a variety of analysis tools to realize interactive or batch data analysis, machine learning model construction, and graph analysis. As the association between nodes is sparse, in order to optimize the storage efficiency and ensure that the data can be queried interactively, the Cassandra database is adopted as shown in
PH network is created as an example for intra networks. According to Definition 3, each herb in PH network is a node, and the relationships between herbs are edges whose information is stored in R_{y}. Each element r in R_{y} is in the form of <n, φ_{m}>. The pseudocode of establishing R_{y} is shown in
Line No.  Algorithm pseudocode 

Input: All prescriptions with herbs and dosage 
Interlayer networks including PFPH and PHHE are based on intra networks previously constructed. The PFPH interlayer network is created as an example shown in
Line No.  Algorithm pseudocode 

Input: PF network, PH network, list A 
As PHFN model stores information of prescription functions, compositions and dosage with internal associations, the constructed network can be seen as a dataset with various relationships. Using the metadata of networks, users could query the stored data by specified herbs or prescriptions to retrieve a subnetwork with connected information. As the data of a related network is often in largescale, the data query component facilitates subgraphs to be displayed in the visualization component. The following queries are based on PHFN to extract information of prescriptions or herbal combinations as shown in
Line No.  Algorithm pseudocode 

Input: Specified herb x, PH network, PF network, Interlayer network PHPF 
According to Definition 3, the weight of edges in PH network stores the number of the coexistence of all possible twoherb combinations in all prescription data set. The frequency of herb combinations can be obtained by scanning the weight of edges in R_{y} from PH network_{.} The algorithm of herb pair query is shown in
Line No.  Algorithm pseudocode 

Input: PH Matrix R_{y}, frequency threshold m 
For a given formula and PFPH interlayer networks, main herbs accounting for cumulative relative interaction intensities and the functions of prescriptions can be obtained. Traversing herbs and functions in PH and PF networks respectively will provide further related information. The pseudocode of the algorithm is shown in
Line No.  Algorithm pseudocode 

Input: specified prescription 
112 prescriptions in
HerbHerb  Herb combinations in PH network 

cassia twig 
[(0, 1), 19, 
Promote sweating and relieve muscles  Dispel wind  Harmonize construction and defense  Engender fluid  Release the exterior  Relieve asthma  Warm 


Promote sweating and relieve muscles  /  [4, [0,1,4,5]]  [2, [0,1]]  [1, [1]]  [1, [2]]  [1, [2]]  [1, [5]] 
Dispel wind  /  /  [2, [0,1]]  [1, [1]]  /  /  [1, [5]] 
Harmonize construction and defense  /  /  /  [1, [1]]  /  /  / 
Engender fluid  /  /  /  /  [1, [8]]  /  / 
Release the exterior  /  /  /  /  /  [2, [2,7]]  / 
Promote sweating and relieve muscles  Dispel wind  Harmonize construction and defense  Engender fluid  Release the exterior  

Cassia twig  [5, [0,1,2,4,5]]  [4, [0,1,4,5]]  [3, [0,1,6]]  [2, [1,8]]  [7, [2,3,8,10,12,14,36]] 
Peony root  [2, [0,2]]  [1, [0]]  [2, [0,6]]  /  [1, [2]] 
Licorice root  [5, [0,1,2,4,5]]  [4, [0,1,4,5]]  [2, [0,1]]  [3, [1,8,106]]  [11, [2,3,8,9,10,11,12,14,36,70,92]] 
Jujube  [3, [1,2,4]]  [2, [1,4]]  [1, [1]]  [2, [1,8]]  [4, [2,8,9,14]] 
10 Daqinglong decoction, 36 Cassia twig and ginseng decoction, 70 Mahuang Lianchi Xiaodou Decoction, 92 Ephedra, aconite and licorice decoction, 106 Sini plus ginseng decoction 
Herbal efficacy 1–Herbal efficacy 2  Frequency  Herbs  Herb chinese name 

Promote sweating and relieve exterior– 
1  Ephedra  Ma Huang 
Clear spleen and clear heat– 
2  Gypsum, 
Shigao, 
To compare with other herb dosage standards, we compare our results with a rule that standardizes each herb dosage by d_{i}/(d_{max}+d_{min} ), where
PHFN model demonstrates rich information of prescription dataset. Herb combinations are more various than function or efficacy combinations. As networks are sparse with most of prescription functions or herbal efficacies taken only once or twice, for illustration herb combinations for more than three times in prescriptions are shown in
The significant associations in
In our network, the TCM information components, such as prescription functions, herbs, and efficacies are represented as nodes, and their cooccurrences or contributions are represented as weighted edges. The associations can be analyzed with graph theory to extract their attribute information. It can be inferred that the sum of weights of all edges in PH network is equal to the sum of the total number of possible combinations of any two herbs appearing in the prescriptions. Furthermore, a function node from a prescription is at least connected with an herb node to form PH interlayer network. Though 112 classical prescriptions in
Most of the recent network modeling are based on network pharmacology to integrate drugdisease and traditional knowledge of herbal medicines to identify the rationale of herb combinations. Cheng et al. [
The study on selection of multiple herbs are important for understanding the enhanced and harmonized therapeutic effect. The network is an initial step to integrate herbs, prescriptions, and functions with potential extensions including domain knowledge, such as herb properties (e.g., herb nature and flavor, channel tropism), symptoms and diagnosis to establish a whole treatment framework. Huge volumes of literature and records of the theoretical concepts and practical skills provide data support for analysis of the relationships in prescription composition. Future research will include other network measures, such as correlation and feature analysis, clustering and community detection in weighted networks. We will also focus on the feature extraction and modeling to analyze a treatment network in depth integrating diagnostic information to analyze relationships between treatment and differentiation.
PHFN model is proposed to manifest the relationships among prescriptions, herbs, and herbal efficacies to show their internal and mutual associations, and is applied to 112 classical prescriptions in
The network supported by distributed storage and processing is capable of manifesting a range of knowledge of prescriptions in a large scale, and the compatibility rules withdrawn are enriched with a refined summary of CM medication experience. The combinations extracted from the aforementioned research offer insight of the rules and patterns of herbs in CM treatment, also provide a reference for clinical practice and future pharmacological studies. As CM is an experiencebased medical system that focuses on clinical observation, summary, and individual differences, these rules and patterns inherited from classics also provide therapeutic evidence of CM in the potential to assist therapy selection and to standardize and clarify the diagnosis and treatment of CM.
Authors thank Le Deng for data input.
This work was supported by grants from National Key Research of Development Projects (2017YFC1703306), Scientific Research Program of Traditional Chinese Medicine in Hunan Province (2020002), Scientific Research Fund of Hunan University of Chinese Medicine (2019XJJJ029), and Scientific Research Projects of Changsha City (No. 468).
The authors confirm contribution to the paper as follows: study conception and design: XH, LL; data collection: HL; analysis and interpretation of results: XH, ST, XC; draft manuscript preparation: XH, CD. All authors reviewed the results and approved the final version of the manuscript.
The data that support the findings of this study are available from the corresponding author, CD, upon reasonable request.
The authors declare no conflict of interests.