The Application Value Of Fractional-order Calculus Diffusion Mode In Breast Lesions

Purpose:To assess the feasibility of three parameters(D,β,and μ)derived from the fractional-order calculus(FROC)diffusion model for improving the differentiation between benign and malignant breast lesions.And further analyze the associationsbetween FROC-derived parameters and prognostic factors(ER,PR,HER2,Ki-67)and molecular subtypes of breast cancer.The parameters of this model in the diagnosis of breast lesions were compared with the intravoxel incoherent motion(IVIM)imaging(Bi-exponential model)and diffusion-weighted imaging(mono-exponential model).Materials and methods:In our study,a total number of 207 patients with breast lesions confirmed by pathology were enrolled.All patients performed complete MRI scans.Detailed MR protocols include T1WI,T2WI,contrast enhanced T1WI and DWI.The apparent diffusion coefficient(ADC),slow diffusion coefficient(Dslow),fast diffusion coefficient(Dfast),perfusion fraction(f),diffusion coefficient(D),fractional-order derivative in space(β)and spatial parameter(μ)were obtained,respectively.The detailed parameters of the DWI were as the followings:TR/TE/FA:4036ms/75.3ms/90°;Matrix/FOV:100×240/160×320 mm2;In total,12 b values were applied including 0,50,100,200,400,600,800,1200,1600,2000,2500 and 3000 s/mm2.Then the FROC-DWI derived metrics were calculated according to the fitting formular previously reported and the three parameter maps were generated.For comparison,the ADC obtained at b-values 50 and 800 s/mm2 using a conventional mono-exponential model.Meanwhile,for IVIM model,b values were applied including 0,50,100,150,200,250,300,400,600,800,1000 and 1200 s/mm2.The regions of interest(ROIs)were placed on the solid part of tumors in the DWI images of b800,and then the volumes of interest(VOIs)were created for each tumor by using 3D slicer(version 4.8.1),an open-source image processing software(www.slicer.org).A total number of 102 patients with breast lesions(including 48malignant lesions and 54 benign lesions)were recruited and included in the first part of the study.Intra-class correlation coefficients were calculated for assessing the agreement of parameters quantified by two radiologists.Then the metrics were statistically compared between the two subgroups with the Mann-Whitney U test.The ROC(receiver operating characteristic curve)analysis was performedto assess the performance of individual parameters for diagnosing malignant breast lension.A total of 105 breast cancer patients with histopathological features(ER,PR,HER2,Ki-67)were recruited and included in the second part of the study.For analysis of histopathological features,the MannWhitney U test was used P<0.05 was considered statistically significant.The parameters of different molecular subtypes were compared by Kruskall-Wallis test,and the Mann-Whinet U parameters with statistical significance were analyzed in pairs,and the significance was set as P<0.05.Results:The ADC,Dslow,D,β,and μ values all exhibited significant differences between benign lesions and malignant lesions(P<0.001).The ADC,Dslow,D,and β values were significantly lower in the malignant lesions than those in the benign lesions,whereas the μ values were higher in the malignant lesions.Among the individual parameters,The sensitivity of μ value was the highest(95.83%),and the specificity of β value was the highest(72.77%)when the parameters were evaluated separately by ROC curve analysis.Among the three parameters of the FROC model,the area under the curve of D value is largest(0.836),which is larger than the ADC value of traditional mono-exponential model.In addition,the combination of D values and β values of the FROC related parameters produced a higher AUC(0.836)and the highest diagnostic sensitivity(97.92%).The Dfast and D values of patients with ER-positive group were lower than that of ER-negative group(P=0.001,0.030).Compared with the PR-negative group,the Dfast and D values of the PR-positive group were significantly decreased(P=0.002,0.017)and f value was significantly increased(P=0.042).For HER2 expression,there was no statistically significant difference between the positive and negative groups.The ADC,Dslow,f,and D values all exhibited significant differences between Ki-67 low expression group and high expression group(P=0.001,0.000,0.012,0.009),and the ADC,Dslow,f and D values of Ki-67 low expression group were higher than those in the highexpression group.It was also found that ADC,Dfast and D values of breast cancer exhibited significant differences among different molecular subtypes(P=0.040,0.000,0.032).Further comparison showed that Luminal Blike had the lowest ADC value,and was significantly lower than Luminal A-like and HER2 positive types(P=0.032,0.009).At the same time,Luminal B-like breast cancer showed lowest D than other types,and significantly lower than HER2 positive type(P=0.004).Triple negative breast cancer produced the highest Dfast value and was significantly higher than the other three subtypes(P=0.001,0.001,0.018,respectively).Conclusion:1.This study demonstrated the feasibility of using a set of FROC-derived diffusion parameters D value,β value and μ value to improve the accuracy of identifying malignant breast lesions.This model has the ability to improve the diagnostic sensitivity and specificity,and the diagnostic efficacy of parameter D value is better than that of the ADC value.The combination of D value and β value showed the highest diagnostic sensitivity.2.Traditional ADC value,IVIM-derived parameters,and FROC-derived parameters can provide a reference for the evaluation of the prognostic factors andmolecular subtypes of breast cancer.FROC-derived diffusion parameters D value have potential value for predicting the expression of prognostic factors ER,PR,and Ki-67 and molecular typing in breast cancer.