基于残差拆分思想的中医“证”与临床指标关联关系再分析的数学模型的建立及应用

doi:10.3736/jcim20110805

Abstract

Studying the essence of syndromes (Zheng) in traditional Chinese medicine (TCM) is a fundamental challenge in basic theoretical research of TCM. The relationship between any given syndrome and biochemical indicators is one of the important aspects of the study. As the indexes selected in each study are specific to a particular Western medical disease diagnosis, and the disease factor is inevitably introduced into the study, the effect of disease factor on the index changes cannot be assessed effectively by traditional data processing methods. This is known as “the same syndrome with different reasons”, which has resulted in confusion in TCM research. This study aimed at providing a mathematical tool to address this issue. Based on information theory and the residual-split method, the syndrome information, which was covered in the index variation, was quantitatively calculated in this paper as an independent part of the disease factor. A mathematical model capable of objectively assessing and statistically testing the effect of the syndrome factor on the index changes was established. Applying this model to literature data of studies on the relationship between cyclic nucleotides and yang-deficiency syndrome showed following results. First, the values of yang-deficiency syndrome information were negative for cyclic adenosine monophosphate (cAMP) while positive for cyclic guanosine monophosphate (cGMP) in all included literature. This indicated that the group of yang-deficiency syndrome was correlated with an obvious trend of reduced cAMP levels and increased cGMP levels. Second, the statistical test results of yang-deficiency syndrome information of the two indexes were different among the literature included. The quality of original data was considered as a possible reason. Third, the significant differences between the yang-deficiency group of a specific disease and the normal group may, in some cases, be caused by a disease factor rather than a syndrome factor. The mathematical model provided a reasonable mathematical tool for the analysis of disease factor and syndrome factor in clinical research of TCM, suggesting that the mathematical model may give rise to innovative ideas and methods in the study of syndromes.

Key words: mathematical model, essence of syndrome, residual split, yang deficiency, cyclic nucleotides

Rui Jin, Bing Zhang, Sen-mao Liu, Chun-miao Xue, Qian Zhao. A mathematical model for re-analysis of the relationship between essence of syndromes in traditional Chinese medicine and clinical biochemical indicators based on the residual-split method and its application. Journal of Chinese Integrative Medicine, 2011, 9(8): 838-846.

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No.	Lead author	Time	Disease	Case load	Syndrome
1	Kuang et al^[10]	1980	Primary hypertension	35	Yang-deficiency
2	Bi et al^[11]	1981	Chronic nephritis	44	Deficiency of kidney yang
3	Kuang et al^[12]	1981	Coronary heart disease	25	Yang-deficiency
4	Liao et al^[13]	1982	Chronic obstructive pulmonary disease	54	Deficiency of kidney yang (1) Deficiency of spleen yang (2)
5	Kuang et al^[14]	1982	Acute myocardial infarction	114	Yang-deficiency
6	Ding et al^[15]	1996	Chronic renal failure	58	Deficiency of kidney yang
7	Li et al^[16]	2004	Chronic heart failure	68	Yang-deficiency
8	Yan et al^[17]	2005	Chronic bronchitis	89	Deficiency of kidney yang (1) Deficiency of spleen yang (2)
9	Dong et al^[18]	2005	Chronic obstructive pulmonary disease	92	Deficiency of lung yang

No.	Results of original literature				Results of mathematical analysis
No.	x⁽^Z⁾±s⁽^Z⁾	x⁽ⁿ⁾	x⁽^d⁾	P₁ value	x⁽^d⁾	?_Z	t_ZHENG	P₂ value
1	19.54±7.4	23.30	21.46	—	—	–1.92	–1.35	0.186
2	24.28±11.46	23.72	—	>0.05	26.84	–2.56	–1.77	0.084
3	20.78±2.11	24.47	—	>0.05	21.28	–0.50	–2.94	0.007
4(1)	31.70±12.69	22.56	—	<0.05	30.22	1.48	0.96	1.481
4(2)	27.89±16.14	22.56	—	>0.05	30.22	–2.33	–0.63	0.529
5	22.73±6.38	23.56	—	—	23.46	–0.73	–1.48	0.139
6	24.18±7.13	22.38	—	<0.05	26.41	–2.23	–2.96	0.004
7	18.17±10.83	16.68	—	>0.05	16.85	1.32	0.64	0.522
8(1)	13.82±1.02	18.36	—	>0.05	14.91	–1.09	–8.75	<0.001
8(2)	13.84±1.02	18.36	—	>0.05	14.91	–1.07	–5.91	<0.001
9	22.02±5.26	24.503	—	>0.05	23.19	–1.17	–2.61	0.011

No.	Results of original literature				Results of mathematical analysis
No.	x⁽^Z⁾±s⁽^Z⁾	x⁽ⁿ⁾	x⁽^d⁾	P₁ value	x⁽^d⁾	?_Z	t_ZHENG	P₂ value
1	7.39±2.73	5.95	7.22	>0.05	—	0.17	0.27	0.792
2	Missing
3	12.05±1.25	6.80	—	>0.05	11.29	0.76	8.54	<0.001
4(1)	3.38±2.02	4.71	—	—	3.79	–0.41	–1.35	0.182
4(2)	5.6±4.04	4.71	—	—	3.79	1.81	2.65	0.011
5	14.93±7.63	6.65	—	<0.01	12.62	2.31	5.43	<0.001
6	7.68±3.71	4.47	—	<0.01	6.78	0.90	2.58	0.013
7	19.51±9.36	5.74	—	<0.01	15.17	4.34	1.79	0.077
8(1)	5.42±0.3	4.44	—	<0.01	4.63	0.79	24.77	<0.001
8(2)	4.11±0.27	4.44	—	<0.01	4.63	–0.52	–11.16	<0.001
9	5.626±1.187	3.813	—	<0.01	4.75	0.87	8.42	<0.001

A mathematical model for re-analysis of the relationship between essence of syndromes in traditional Chinese medicine and clinical biochemical indicators based on the residual-split method and its application

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