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.

Stretched Exponential Dynamics in Online Article Views

Article view statistics offers a measure to quantify scientific and public impact of online published articles. Popularity of a paper in online community changes with time. To understand popularity dynamics of article views, we propose a decay dynamics based on a stretched exponential model. We find that a stretched exponent gradually decreases with time after online publication following a power-law scaling. Compared with a simple exponential or biexponential model, a stretched exponential model with a time-dependent exponent well describes long-tailed popularity dynamics of online articles. This result gives a useful insight into how popularity diminishes with time in online community.

Histogram analysis from stretched exponential model on diffusion-weighted imaging: evaluation of clinically significant prostate cancer

Objective: To evaluate the usefulness of histogram analysis of stretched exponential model (SEM) on diffusion-weighted imaging in evaluating clinically significant prostate cancer (CSC). Methods: A total of 85 patients with prostate cancer underwent 3 T multiparametric MRI, followed by radical prostatectomy. Histogram parameters of the tumor from the SEM [distributed diffusion coefficient (DDC) and α] and the monoexponential model [MEM; apparent diffusion coefficient (ADC)] were evaluated. The associations between parameters and Gleason score or Prostate Imaging Reporting and Data System v. 2 were evaluated. The area under the receiver operating characteristics curve was calculated to evaluate diagnostic performance of parameters in predicting CSC. Results: The values of histogram parameters of DDC and ADC were significantly lower in patients with CSC than in patients without CSC (p < 0.05), except for skewness and kurtosis. The value of the 25th percentile of α was significantly lower in patients with CSC than in patients without CSC (p = 0.014). Histogram parameters of ADC and DDC had significant weak to moderate negative associations with Gleason score or Prostate Imaging Reporting and Data System v. 2 (p < 0.001), except for skewness and kurtosis. For predicting CSC, the area under the curves of mean ADC (0.856), 50th percentile DDC (0.852), and 25th percentile α (0.707) yielded the highest values compared to other histogram parameters from each group. Conclusion: Histogram analysis of the SEM on diffusion-weighted imaging may be a useful quantitative tool for evaluating CSC. However, the SEM did not outperform the MEM. Advances in knowledge: Histogram parameters of SEM may be useful for evaluating CSC.