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He Y, Miao F, Fan Y, He J, Zhang F, Wang Z, Wu Y, Zhao Y, Yang P. Analysis of Acupoint Selection and Combinations in Acupuncture Treatment of Piriformis Syndrome: A Protocol for Data Mining. J Pain Res 2023; 16:3265-3272. [PMID: 37790189 PMCID: PMC10544196 DOI: 10.2147/jpr.s422857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2023] [Accepted: 07/22/2023] [Indexed: 10/05/2023] Open
Abstract
Background Piriformis syndrome (PS) is a neuromuscular condition characterized by discomfort in the gluteal region. The efficacy of acupuncture as a treatment modality for PS has been substantiated through a multitude of clinical trials. However, certain queries persist, such as the optimal approach for identifying the most efficacious acupoints. The objective of this study is to perform an initial data mining analysis aimed at identifying the optimal acupoint selection and combinations for the treatment of PS. Methods We will search 7 electronic bibliographic databases (PubMed, Embase, Cochrane Library, China National Knowledge Infrastructure, Wanfang Database, Chinese Biomedical Literature Database and Chongqing VIP Database) from inception to June 2023. We will select clinical trials that evaluate the efficacy of acupuncture therapy in the management of PS. Exclusions will be made for reviews, protocols, animal trials, case reports, systematic reviews, and meta-analyses. The primary outcome measure will be clinical outcomes associated with PS. Descriptive statistics will be performed in Excel 2019. Association rule analysis will be performed in SPSS Modeler 18.0. Exploratory factor analysis and cluster analysis will be performed in SPSS Statistics 26.0. Results This study will investigate the most effective acupoint selection and combinations for patients with PS. Conclusion Our findings will provide evidence for the effectiveness and potential treatment prescriptions of acupoint application for patients with PS, helping clinicians and patients make a more informed decision together.
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Affiliation(s)
- Yujun He
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Furui Miao
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Yushan Fan
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Jiujie He
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Fangzhi Zhang
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Zibin Wang
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Yu Wu
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Yiping Zhao
- Faculty of Acupuncture, Moxibustion and Tui Na, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
| | - Pu Yang
- Graduate School, Guangxi University of Chinese Medicine, Nanning, People’s Republic of China
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Liu Y, Zhang Z, Lin W, Liang H, Lin M, Wang J, Chen L, Yang P, Liu M, Zheng Y. A novel FCTF evaluation and prediction model for food efficacy based on association rule mining. Front Nutr 2023; 10:1170084. [PMID: 37701374 PMCID: PMC10493461 DOI: 10.3389/fnut.2023.1170084] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 08/16/2023] [Indexed: 09/14/2023] Open
Abstract
Introduction Food-components-target-function (FCTF) is an evaluation and prediction model based on association rule mining (ARM) and network interaction analysis, which is an innovative exploration of interdisciplinary integration in the food field. Methods Using the components as the basis, the targets and functions are comprehensively explored in various databases and platforms under the guidance of the ARM concept. The focused active components, key targets and preferred efficacy are then analyzed by different interaction calculations. The FCTF model is particularly suitable for preliminary studies of medicinal plants in remote and poor areas. Results The FCTF model of the local medicinal food Laoxianghuang focuses on the efficacy of digestive system cancers and neurological diseases, with key targets ACE, PTGS2, CYP2C19 and corresponding active components citronellal, trans-nerolidol, linalool, geraniol, α-terpineol, cadinene and α-pinene. Discussion Centuries of traditional experience point to the efficacy of Laoxianghuang in alleviating digestive disorders, and our established FCTF model of Laoxianghuang not only demonstrates this but also extends to its possible adjunctive efficacy in neurological diseases, which deserves later exploration. The FCTF model is based on the main line of components to target and efficacy and optimizes the research level from different dimensions and aspects of interaction analysis, hoping to make some contribution to the future development of the food discipline.
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Affiliation(s)
- Yaqun Liu
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Zhenxia Zhang
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Wanling Lin
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Hongxuan Liang
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Min Lin
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
- School of Laboratory Medicine, Youjiang Medical University for Nationalities, Baise, Guangxi, China
| | - Junli Wang
- School of Laboratory Medicine, Youjiang Medical University for Nationalities, Baise, Guangxi, China
| | - Lianghui Chen
- School of Laboratory Medicine, Youjiang Medical University for Nationalities, Baise, Guangxi, China
| | - Peikui Yang
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Mouquan Liu
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
| | - Yuzhong Zheng
- School of Food Engineering and Biotechnology, Hanshan Normal University, Chaozhou, Guangdong, China
- School of Laboratory Medicine, Youjiang Medical University for Nationalities, Baise, Guangxi, China
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Cho Y, Han Y, Kim Y, Han S, Oh K, Chae H, Hongmin C, Ryu M. Anatomical structures and needling method of the back-shu points BL18, BL20, and BL22 related to gastrointestinal organs: A PRISMA-compliant systematic review of acupoints and exploratory mechanism analysis. Medicine (Baltimore) 2022; 101:e29878. [PMID: 36316824 PMCID: PMC9622668 DOI: 10.1097/md.0000000000029878] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
BACKGROUND Acupuncture treatment on back-shu points (BSPs) has received attention owing its ability to control the function of visceral organs. We aimed to conduct a systematic review to provide detailed information on the effectiveness and safety of BL18, BL20, and BL22 on the digestive system in terms of soft tissue and anatomical structure and assist in the appropriate application. METHODS Medline, Cochrane Library, EMBASE, OASIS, RISS, and CNKI were searched from their inception to July 2021. This systematic review included randomized controlled trials, controlled clinical trials, case series, and case reports that addressed anatomical structures or needling methods of BL18, BL20, and BL22. RESULTS In total, 115 articles were included from the 7 electronic databases. One hundred eight articles described the depth and method. A total of 96 articles described depth, 86 articles described the angle, and 74 articles described both. Seventy-nine articles described the target muscles and anatomical structure. Acupuncture on BSP is effective in gastrointestinal diseases because of compression of the spinal nerve, sympathetic nerve hyperactivity, and connection of the diaphragm. By reviewing each study's acupuncture method and target muscles, we analyzed the angle and depth of the needle that effectively leads to therapeutic response. CONCLUSIONS This study provides guidance on applying needles in terms of anatomical structures to yield therapeutic responses. However, few studies have assessed how to effectively stimulate BSP to trigger digestive effects and their mechanisms. Additional studies on the relationship between BSP and the digestive system are needed to use these acupoints for digestive diseases.
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Affiliation(s)
- Yeonwoo Cho
- College of Korean Medicine, Dongguk University, Ilsan City, Republic of Korea
| | - Yaejin Han
- College of Korean Medicine, Dongguk University, Ilsan City, Republic of Korea
| | - Yeji Kim
- College of Korean Medicine, Dongguk University, Ilsan City, Republic of Korea
| | - Sihyun Han
- College of Korean Medicine, Dongguk University, Ilsan City, Republic of Korea
| | - Kichang Oh
- College of Korean Medicine, Dongguk University, Ilsan City, Republic of Korea
| | - Hyocheong Chae
- Academic Affairs Board, Korean Medical Society of Soft Tissue, Seoul, Republic of Korea
| | - Chu Hongmin
- Academic Affairs Board, Korean Medical Society of Soft Tissue, Seoul, Republic of Korea
- Daecheong Island Branch Office of a Ongjin Public Health Center, Incheon, Republic of Korea
- *Correspondence: Chu Hongmin, Daecheong Island Branch Office of a Ongjin Public Health Center, 3, Daecheong-ro, Daecheong-myeon, Ongjin-gun, Incheon, Republic of Korea (e-mail: )
| | - Myungseok Ryu
- Academic Affairs Board, Korean Medical Society of Soft Tissue, Seoul, Republic of Korea
- Daemyung Korean Medicine Clinic, Seoul, Republic of Korea
- *Correspondence: Chu Hongmin, Daecheong Island Branch Office of a Ongjin Public Health Center, 3, Daecheong-ro, Daecheong-myeon, Ongjin-gun, Incheon, Republic of Korea (e-mail: )
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Analysis of Acupoints Combination for Cancer-Related Anorexia Based on Association Rule Mining. EVIDENCE-BASED COMPLEMENTARY AND ALTERNATIVE MEDICINE 2022; 2022:4251458. [PMID: 36304134 PMCID: PMC9596268 DOI: 10.1155/2022/4251458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 09/25/2022] [Accepted: 09/29/2022] [Indexed: 11/06/2022]
Abstract
We investigated the acupoint selection regulations and workable core acupoint combinations in cancer-related anorexia (CA) treatment. The Apriori algorithm, complemented by the FP-growth algorithm, was used to mine association rules based on retrieved randomized control trials (RCTs) and clinical control trials (CCTs). We searched the following databases for acupuncture treatment regimens for CA: PubMed, Embase, Cochrane Central, Web of Science, WanFang Data, VIP, China Journal Full-Text Database (CNKI), and SinoMed (CBM). We extracted acupoints prescriptions from the 27 enrolled RCTs and CCTs for analysis. There have been 38 acupoints refined from 27 prescriptions. The pinnacle three regularly chosen acupoints were Zusanli (ST36), Zhongwan (RN12), and Sanyinjiao (SP6). We investigated 10 association rules, and the consequences confirmed that {RN4} ≥ {RN12}, {PC6} ≥ {ST36}, {RN12, SP6} ≥ {RN4}, {HT7} ≥ {RN12}, and {DU20} ≥ {RN12} had been the most frequent associated rules in the adoption literature. Zusanli (ST36), Sanyinjiao (SP6), Guanyuan (RN4), Zhongwan (RN12), Neiguan (PC6), Shenmen (HT7), and Baihui (DU20) would be regarded as acupuncture prescriptions in the treatment of CA.
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Li S, Zhu H. Enterprise Operating State Evaluation Based on Association Rule Algorithm and Data Set. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:1300068. [PMID: 36188681 PMCID: PMC9522508 DOI: 10.1155/2022/1300068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Revised: 08/25/2022] [Accepted: 09/06/2022] [Indexed: 11/28/2022]
Abstract
In order to further improve the evaluation quality of enterprise operating efficiency, reduce the error items and invalid items of partition, and improve the objectivity of operating condition evaluation, this study takes listed enterprises as an example and proposes an evaluation method of operating efficiency based on association rule algorithm and data set. In this method, the results of operating efficiency are scientifically analyzed from horizontal and vertical dimensions. The operating cost of total assets of listed companies is taken as indicators, and the correlation test is carried out by Kendall's tau_b. From the longitudinal comparison results, it can be seen that only 12 of the 19 enterprises in the study have small-scale changes and increase year by year, accounting for 63.16%. At the same time, there are also 6 enterprises with an overall trend of decline, which objectively reflects the reasonable operation status and operation scale of enterprises in the study.
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Affiliation(s)
- Shoubo Li
- School of Management, Wuzhou University, Wuzhou, Guangxi 543002, China
| | - Haiyan Zhu
- School of Business, Wuzhou University, Wuzhou, Guangxi 543002, China
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Fei R. Sports Medical Image Modeling of Injury Prevention in Dance Learning and Sports Training. SCANNING 2022; 2022:7027007. [PMID: 35950088 PMCID: PMC9348966 DOI: 10.1155/2022/7027007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Revised: 07/09/2022] [Accepted: 07/16/2022] [Indexed: 06/15/2023]
Abstract
In order to effectively prevent injuries in dance learning and sports training, this paper proposes a method based on sports medical image modeling. This method solves the problem of injury prevention in dance learning by studying the association analysis algorithm, medical image information system, and CT technology and analyzing the role of data mining technology in the medical image information system. The experimental results show that the average prediction error of CT and US is about 5%, which can be considered that the model can predict accurately. The error of MR is as high as 28.2%, and the prediction is relatively inaccurate. Conclusion. the model can effectively prevent the injury in training.
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Affiliation(s)
- Renying Fei
- Liupanshui Normal University, Liupanshui, Guizhou 553004, China
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Lai WD, Li DM, Yu J, Huang L, Zheng MZ, Jiang YP, Wang S, Wen JJ, Chen SJ, Wen CP, Jin Y. An Apriori Algorithm-Based Association Analysis of Analgesic Drugs in Chinese Medicine Prescriptions Recorded From Patients With Rheumatoid Arthritis Pain. FRONTIERS IN PAIN RESEARCH 2022; 3:937259. [PMID: 35959238 PMCID: PMC9358686 DOI: 10.3389/fpain.2022.937259] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Accepted: 06/21/2022] [Indexed: 11/13/2022] Open
Abstract
Chronic pain, a common symptom of people with rheumatoid arthritis, usually behaves as persistent polyarthralgia pain and causes serious damage to patients' physical and mental health. Opioid analgesics can lead to a series of side effects like drug tolerance and addiction. Thus, seeking an alternative therapy and screening out the corresponding analgesic drugs is the key to solving the current dilemma. Traditional Chinese Medicine (TCM) therapy has been recognized internationally for its unique guiding theory and definite curative effect. In this study, we used the Apriori Algorithm to screen out potential analgesics from 311 cases that were treated with compounded medication prescription and collected from “Second Affiliated Hospital of Zhejiang Chinese Medical University” in Hangzhou, China. Data on 18 kinds of clinical symptoms and 16 kinds of Chinese herbs were extracted based on this data mining. We also found 17 association rules and screened out four potential analgesic drugs—“Jinyinhua,” “Wugong,” “Yiyiren,” and “Qingfengteng,” which were promised to help in the clinical treatment. Besides, combined with System Cluster Analysis, we provided several different herbal combinations for clinical references.
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Affiliation(s)
- Wei-dong Lai
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Dian-ming Li
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Jie Yu
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Lin Huang
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Ming-zhi Zheng
- Hangzhou AI Center, China Academy of Information and Communications Technology, Hangzhou, China
| | - Yue-peng Jiang
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Song Wang
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Jun-jun Wen
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Si-jia Chen
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
| | - Cheng-ping Wen
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
- *Correspondence: Cheng-ping Wen
| | - Yan Jin
- The Second Clinical Medical College of Zhejiang Chinese Medical University, Hangzhou, China
- College of Basic Medical Science, Zhejiang Chinese Medical University, Hangzhou, China
- Yan Jin
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Wang Y, Shi X, Efferth T, Shang D. Artificial intelligence-directed acupuncture: a review. Chin Med 2022; 17:80. [PMID: 35765020 PMCID: PMC9237974 DOI: 10.1186/s13020-022-00636-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 06/18/2022] [Indexed: 11/10/2022] Open
Abstract
Acupuncture is widely used around the whole world nowadays and exhibits significant efficacy against many chronic diseases, especially in pain-related diseases. With the rapid development of artificial intelligence (AI), its implementation into acupuncture has achieved a series of significant breakthroughs in many areas of acupuncture practice, such as acupoints selection and prescription, acupuncture manipulation identification, acupuncture efficacy prediction, and so on. The paper will discuss the significant theoretical and technical achievements in AI-directed acupuncture. AI-based data mining methods uncovered crucial acupoint combinations for treating various diseases, which provide a scientific basis for acupoints prescription in clinical practice. Furthermore, the rapid development of modern TCM instruments facilitates the integration of modern medical instruments, AI techniques, and acupuncture. This integration significantly improves the quantification, objectification, and standardization of acupuncture as well as the delivery of clinical personalized acupuncture therapy. Machine learning-based clinical efficacy prediction of acupuncture can help doctors screen patients who may benefit from acupuncture treatment. However, the existing challenges require additional work for developing AI-directed acupuncture. Some include a better understanding of ancient Chinese philosophy for AI researchers, TCM acupuncture theory-based explanation of the knowledge discoveries, construction of acupuncture databases, and clinical trials for novel knowledge validation. This review aims to summarize the major contribution of AI techniques to the discovery of novel acupuncture knowledge, the improvement for acupuncture safety and efficacy, the development and inheritance of acupuncture, and the major challenges for the further development of AI-directed acupuncture. The development of acupuncture can progress with the help of AI.
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Affiliation(s)
- Yulin Wang
- College of Pharmacy, Dalian Medical University, 9 South Lvshun Road Western Section, Dalian, 116044, People's Republic of China.
| | - Xiuming Shi
- Renaissance College, University of New Brunswick, 3 Bailey Drive, P.O. Box 4400, Fredericton, NB, E3B 5A3, Canada
| | - Thomas Efferth
- Department of Pharmaceutical Biology, Institute of Pharmaceutical and Biomedical Sciences, Johannes Gutenberg University, 55128, Mainz, Germany
| | - Dong Shang
- Clinical Laboratory of Integrative Medicine, First Affiliated Hospital of Dalian Medical University, 222 Zhongshan Road, Dalian, 116011, People's Republic of China. .,College of Integrative Medicine, Dalian Medical University, Dalian, 116044, People's Republic of China.
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Lu PH, Chen YY, Tsai FM, Liao YL, Huang HF, Yu WH, Kuo CY. Combined Acupoints for the Treatment of Patients with Obesity: An Association Rule Analysis. EVIDENCE-BASED COMPLEMENTARY AND ALTERNATIVE MEDICINE : ECAM 2022; 2022:7252213. [PMID: 35341146 PMCID: PMC8947926 DOI: 10.1155/2022/7252213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 01/28/2022] [Accepted: 02/15/2022] [Indexed: 11/21/2022]
Abstract
Obesity is a prevalent metabolic disease that increases the risk of other diseases, such as hypertension, diabetes, hyperlipidemia, cardiovascular disease, and certain cancers. A meta-analysis of 11 randomized sham-controlled trials indicates that acupuncture had adjuvant benefits in improving simple obesity, and previous studies have reported that acupoint combinations were more useful than single-acupoint therapy. The Apriori algorithm, a data mining-based analysis that finds potential correlations in datasets, is broadly applied in medicine and business. This study, based on the Apriori algorithm-based association rule analysis, found the association rules of acupoints among 11 randomized controlled trials (RCTs). There were 23 acupoints extracted from 11 RCTs. We used Python to calculate the association between acupoints and disease. We found the top 10 frequency acupoints were Extra12, TF4, LI4, LI11, ST25, ST36, ST44, CO4, CO18, and CO1. We investigated the 1118 association rule and found that {LI4, ST36} ≥ {ST44}, {LI4, ST44} ≥ {ST36}, and {ST36, ST44} ≥ {LI4} were the most associated rules in the data. Acupoints, including LI4, ST36, and ST44, are the core acupoint combinations in the treatment of simple obesity.
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Affiliation(s)
- Ping-Hsun Lu
- Department of Chinese Medicine, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei City, Taiwan
- School of Post-Baccalaureate Chinese Medicine, Tzu Chi University, Hualien, Taiwan
| | - Yu-Yang Chen
- Department of Mathematics National Central University, Taoyuan, Taiwan
| | - Fu-Ming Tsai
- Department of Research, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei City, Taiwan
| | - Yuan-Ling Liao
- Department of Chinese Medicine, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei City, Taiwan
| | - Hui-Fen Huang
- Department of Chinese Medicine, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei City, Taiwan
- School of Post-Baccalaureate Chinese Medicine, Tzu Chi University, Hualien, Taiwan
| | - Wei-Hsuan Yu
- Department of Mathematics National Central University, Taoyuan, Taiwan
| | - Chan-Yen Kuo
- Department of Research, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei City, Taiwan
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