Evaluation of microvascular invasion of hepatocellular carcinoma using whole-lesion histogram analysis with the stretched-exponential diffusion model

Objectives: To evaluate the potential role of histogram analysis of stretched exponential model (SEM) through whole-tumor volume for preoperative prediction of microvascular invasion (MVI) in single hepatocellular carcinoma (HCC). Methods: This study included 43 patients with pathologically proven HCCs by surgery who underwent multiple b-values diffusion-weighted imaging (DWI) and contrast-enhanced MRI.The histogram metrics of distributed diffusion coefficient (DDC) and heterogeneity index (α) from SEM were compared between HCCs with and without MVI, by using the independent t-test. Morphologic features of conventional MRI and clinical data were evaluated with chi-squared or Fisher’s exact tests. Receiver operating characteristic (ROC) and multivariable logistic regression analyses were performed to evaluate the diagnostic performance of different parameters for predicting MVI. Results: The tumor size and non-smooth tumor margin were significantly associated with MVI (all p < 0.05). The mean, fifth, 25th, 50th percentiles of DDC, and the fifth percentile of ADC between HCCs with and without MVI were statistically significant differences (all p < 0.05). The histogram parameters of α showed no statistically significant differences (all p > 0.05). At multivariate analysis,the fifth percentile of DDC was independent risk factor for MVI of HCC(p = 0.006). Conclusions: Histogram parameters DDC and ADC, but not the α value, are useful predictors of MVI. The fifth percentile of DDC was the most useful value to predict MVI of HCC. Advances in knowledge: There is limited literature addressing the role of SEM for evaluating MVI of HCC. Our findings suggest that histogram analysis of SEM based on whole-tumor volume can be useful for MVI prediction.

Holographic Dark Energy and Dark Matter Interaction in Anisotropic Bianchi Type-V Universe

In this study, we consider an holographic dark energy and dark matter interacting model in the Bianchi Type-V universe with a stretched exponential scale factor. We obtain the Hubble, shear, deceleration, and equation of state parameters based on the presented model and give the numerical solutions. We show that the anisotropy in the early universe plays an important role in the time evolution of the universe. Furthermore, we show that an interacting anisotropic model with stretched exponential scale factors can explain all epochs of the universe.

Application Value of Mathematical Models of Diffusion-Weighted Magnetic Resonance Imaging in Differentiating Breast Cancer Lesions

Objective. To determine the application value of the mono-exponential model, dual-exponential model, and stretched-exponential model of MRI with diffusion-weighted imaging (DWI) in breast cancer (BC) lesions. Methods. Totally 64 cases with BC admitted to our hospital between June 2019 and October 2020 were enrolled in this study. They had 71 lesions in total, including 40 benign tumor lesions (including 9 breast cyst lesions) and 31 malignant tumor lesions. After DWI examination, with normal glands as control, mono-exponential model (ADC) map, dual-exponential model (Standard-ADC) map, slow apparent diffusion coefficient (Slow-ADC) map, fast-apparent diffusion coefficient (Fast-ADC) map, and stretched-exponential model (DDC) map were processed, and corresponding values were generated. Then, the situation and significance of each parameter in breast cysts, benign breast tumor lesions, and malignant tumor lesions were analyzed. Results. The values of ADC, Standard-ADC, and DDC of breast cysts were higher than those of normal glands (all P < 0.05 ), and the values of ADC and DDC of benign breast tumor lesions were lower than those of normal glands ( P < 0.05 ). In addition, malignant breast tumor lesions had lower values of ADC, Standard-ADC, Slow-ADC, and DDC and a higher Fast-ADC value compared to normal glands (all P < 0.05 ). Compared with benign tumor lesions, malignant tumor lesions had lower values of ADC, Standard-ADC, Slow-ADC, and DDC and a higher value of Fast-ADC (all P < 0.05 ). Moreover, the receiver operating characteristic (ROC) curve-based analysis revealed that all the above models could be adopted to effectively evaluate the deterioration of benign breast tumor lesions (all P < 0.05 ), and DDC value had the most significant diagnostic effect on malignant tumor lesions ( P < 0.05 ). Conclusion. Both dual-exponential model and stretched-exponential model of DWI can help effectively evaluate the progression of benign breast tumors, and the stretched-exponential model is more effective in the diagnosis of malignant breast tumors. These models are of great help to the future clinical diagnosis of BC.

Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

Diffusion-weighted MRI for predicting pathologic response to neoadjuvant chemotherapy in breast cancer: evaluation with mono-, bi-, and stretched-exponential models

Background To investigate the performance of diffusion-weighted (DW) MRI with mono-, bi- and stretched-exponential models in predicting pathologic complete response (pCR) to neoadjuvant chemotherapy (NACT) for breast cancer, and further outline a predictive model of pCR combining DW MRI parameters, contrast-enhanced (CE) MRI findings, and/or clinical-pathologic variables. Methods In this retrospective study, 144 women who underwent NACT and subsequently received surgery for invasive breast cancer were included. Breast MRI including multi-b-value DW imaging was performed before (pre-treatment), after two cycles (mid-treatment), and after all four cycles (post-treatment) of NACT. Quantitative DW imaging parameters were computed according to the mono-exponential (apparent diffusion coefficient [ADC]), bi-exponential (pseudodiffusion coefficient and perfusion fraction), and stretched-exponential (distributed diffusion coefficient and intravoxel heterogeneity index) models. Tumor size and relative enhancement ratio of the tumor were measured on contrast-enhanced MRI at each time point. Pre-treatment parameters and changes in parameters at mid- and post-treatment relative to baseline were compared between pCR and non-pCR groups. Receiver operating characteristic analysis and multivariate regression analysis were performed. Results Of the 144 patients, 54 (37.5%) achieved pCR after NACT. Overall, among all DW and CE MRI measures, flow-insensitive ADC change (ΔADC200,1000) at mid-treatment showed the highest diagnostic performance for predicting pCR, with an area under the receiver operating characteristic curve (AUC) of 0.831 (95% confidence interval [CI]: 0.747, 0.915; P < 0.001). The model combining pre-treatment estrogen receptor and human epidermal growth factor receptor 2 statuses and mid-treatment ΔADC200,1000 improved the AUC to 0.905 (95% CI: 0.843, 0.966; P < 0.001). Conclusion Mono-exponential flow-insensitive ADC change at mid-treatment was a predictor of pCR after NACT in breast cancer.