Application Of Fuzzy Mathematics To The Diagnosis And Therapeutic Evaluation Of Knee Osteoarthritis

Objectives To apply fuzzy mathematical method to objectively quantify thesyndromes of traditional Chinese medicine of KOA. To preliminarily establishthe fuzzy mathematical recognition model for syndrome type differentiationand fuzzy mathematical evaluation model for clinical efficacy of KOA. Toexplore the fuzzy mathematical theory of KOA syndrome type’s concept. Toestablish a platform for the diagnosis and evaluation expert system, which candistinguish different syndrome types and evaluate curative effect of KOA.Methods1. Referring to “A Practical Guide to The Clinical Pathway of ChineseMedicine”, the common clinical syndromes of knee arthralgia(KOA) weresummarized as wind-cold-dampness arthralgia， wind-fever-dampnessarthralgia, syndrome of blood stasis, deficiency of liver and kidney. Accordingto " Diagnostics of Chinese Medicine "," Clinical Research Guiding Principleof TCM New Drug" and the characteristics of KOA, we formulated the TCMdiagnostic criteria and differentiation factors of KOA. The differentiationfactors of wind-cold-dampness arthralgia were10，wind-fever-dampnessarthralgia11, syndrome of blood stasis10, deficiency of liver and kidney15.Based on the important degree and the membership grade of differentiationfactors for syndrome types, eight clinical TCM experts filled out the statisticaltables of factor weight evaluation, then the weight values of differentiationfactor were calculated. With the threshold λ=0.500as the standard, the differentiation factors of each syndrome type were divided into major andsecondary elements.2. We took the clinical symptoms and signs of OA in " Clinical ResearchGuiding Principle of TCM New Drug" as template, restructured it into KOAdifferentiation factors integral table. According to4levels quantizationmethod, the major and secondary differentiation factors were respectivelyassigned0,2,4,6and0,1,2,3points. If the factor is difficult to quantize,assigned0,4or0,2points according to without it or with it. TCM total scoreis the sum of differentiation factor scores.3. Set U was used to express46differentiation factors of KOA, U={u1，u2，u3，…，u46}. The four syndrome types of KOA were expressed as: Aj=(A1, A2,A3, A4),(j=1,2,3,4). Based on the presence or absence of differentiationfactor and its typical degree of each syndrome type, we setted2piecewisefunctions and standard feature subset of four syndrome types respectively.Referring to Zhang Dingyi’s formula of individual pattern recognitionmathematical model, combined with direct fuzzy pattern recognition method,maximum membership principle and the threshold, we built mathematicalquantitative models and recognition of membership function for KOAsyndrome types.4. Quantitative levels of differentiation factor was defined as u (Zi), Piecewisequantization functions of differentiation factor were setted by4levelsquantization method, then we built fuzzy mathematical evaluation model byestablishment of KOA TCM syndrome severity index.5.105hospitalized KOA patients met the inclusion criteria KOA weredialectical with artificial recognition method and fuzzy mathematicsrecognition model. The patients whose diagnoses were consistent, werearranged to wind-cold-dampness arthralgia group, wind-fever-dampnessarthralgia group, syndrome of blood stasis group, deficiency of liver and kidney group according to visit order. All patients were treated by thetreatment program for knee arthralgia(KOA) in “A Practical Guide to TheClinical Pathway of Chinese Medicine”. One course of treatment is6days, allpatients received2courses of treatment. Before and after treatment, the JOAknee osteoarthritis curative effect criteria, WOMAC index, TCM total scoreand KOA TCM syndrome severity index were be used to observe thecondition changes. Therapeutic effects were assessed by the criterion forcurative effect of osteoarthritis from " Clinical Research Guiding Principle ofTCM New Drug".Results1.105hospitalized KOA patients met the inclusion criteria KOA weredialectical with artificial recognition method and fuzzy mathematicsrecognition model. Two methods were consistent in90cases, diagnosiscoincidence rate was85.71%, wind-cold-dampness arthralgia group24cases,wind-fever-dampness arthralgia group13cases, syndrome of blood stasisgroup13cases, deficiency of liver and kidney group group with40cases. Theconsistency of them was examined by paired chi-square test, Kappa=0.795（P<0.01）.2. Using the Cronbach’s coefficient to test the internal consistency reliabilityof each dimension in KOA differentiation factors integral table. Cronbach’salpha coefficients of10factors in wind-cold-dampness arthralgia dimensionwere between0.531to0.764,11Cronbach’ s alpha coefficients ofwind-fever-dampness arthralgia dimension were in0.613～0.740, while insyndrome of blood stasis dimension, the score of “white and dry fur” was0,Cronbach’s alpha coefficients of other9factors were between0.709to0.783,Cronbach’s alpha coefficients of15factors in deficiency of liver and kidneydimension were in0.813～0.846. Cronbach’ s alpha coefficients of4syndrome dimensions were greater than0.700. 3. After treatment, the scores of JOA, WOMAC index, VAS in four groupswere significant different as before（P <0.05）. Except deficiency of liver andkidney group, the scores of physical function index in other groups weresignificant different as before（P <0.05）.Only the TCM total score in bloodstasis group had no statistical difference than pre-treatment（P>0.05）. Inwind-cold-dampness arthralgia group and wind-fever-dampness arthralgiagroup, the scores of KOA TCM syndrome severity index were significantdifferent as before（P <0.05）, the scores of other2groups had strikingdifference as before（P>0.05）. Total effective rate of each group were:wind-cold-dampness arthralgia group82.61%, wind-fever-dampnessarthralgia group58.33%, syndrome of blood stasis group84.62%, deficiencyof liver and kidney group group78.95%. Total effective rate of all patientswas77.91%.4. Through Pearson linear correlation analysis, the correlation coefficient ofKOA TCM syndrome severity index and JOA score were:wind-cold-dampness arthralgia group-0.389（P>0.05）, wind-fever-dampnessarthralgia group-0.733（P <0.01）, syndrome of blood stasis group-0.842（P<0.01）, deficiency of liver and kidney group group-0.700（P <0.01）, thecorrelation coefficient of86cases was-0.511（P <0.01）. The correlationcoefficient of KOA TCM syndrome severity index and WOMAC index scorewere: wind-cold-dampness arthralgia group0.413（P=0.05）,wind-fever-dampness arthralgia group0.745（P <0.01）, syndrome of bloodstasis group0.853（P <0.01）, deficiency of liver and kidney group group0.631（P <0.01）, all of86cases0.505（P <0.01）. The correlation coefficientof TCM total score and JOA score were: wind-cold-dampness arthralgia group-0.544（P <0.01）, wind-fever-dampness arthralgia group-0.778（P<0.05）,syndrome of blood stasis group-0.877（P <0.01）, deficiency of liver andkidney group group-0.662（P <0.01）, all of86cases-0.650（P <0.01）. The correlation coefficient of TCM total score and WOMAC index score were:wind-cold-dampness arthralgia group0.529（P <0.01）, wind-fever-dampnessarthralgia group0.739（P<0.01）, syndrome of blood stasis group0.903（P<0.01）, deficiency of liver and kidney group group0.657（P <0.01）, all of86cases0.656（P <0.01）.5. By means of paired t-test, the effect sizes of TCM total score were:wind-cold-dampness arthralgia group-1.122（P <0.05）, wind-fever-dampnessarthralgia group-1.523（P<0.05）, deficiency of liver and kidney group group-0.489（P <0.05）, all of86cases-0.782（P <0.01）. The effect sizes of KOATCM syndrome severity index were: wind-cold-dampness arthralgia group-0.986（P <0.05）, wind-fever-dampness arthralgia group-1.186（P<0.05）,all of86cases-0.768（P=0.01）.Conclusions1. This study preliminarily developed a KOA differentiation factors integraltable. Through Cronbach alpha coefficient method, analysis of parallel validity,effect size, clinical trials had proved that the table has good reliability, validityand responsiveness. After further improvement, it can be used as a tool toevaluate the clinical efficacy of KOA.2. In this study, a fuzzy mathematical recognition model for syndrome typedifferentiation and a fuzzy mathematical evaluation model for clinical efficacyof KOA have been preliminary established. The higher consistency of theformer and expert diagnosis have been confirmed. Both models have strongcorrelation with JOA knee osteoarthritis curative effect criteria and WOMACindex. They can be prepared as a computer program and be made into expertdiagnosis system that can automatically recognize KOA syndrome types.3. Based on the theory of Chinese medicine, further research on the the KOAsyndrome types and efficacy evaluation should be deepened. By using themeans of multicenter large sample and various mathematics methods, continue to improve and amend the KOA syndrome element entries, quantifythem more scientifically and objectiveiy, optimize these two models.