# The Value of Fractal Analysis in Ultrasound Imaging: Exploring Intricate Patterns
## 3 Results
### [PERSON] et al. [38] showed a computer-aided diagnostic (CAD) system for the classification of thyroid nodules into benign and malignant categories using US images. Their system leveraged a combination of texture features, including fractal dimension, local binary pattern, Fourier spectrum descriptor and laws texture energy, to quantify local changes in texture characteristics. These features were then used to train various classifiers, such as a support vector machine (SVM), decision tree (DT), Sugeno fuzzy, Gaussian mixture model (GMM), K-nearest neighbor (KNN), radial basis probabilistic neural network (RBPNN) and naive Bayes classifier (NBC). The system achieved 100% accuracy for high-resolution ultrasound (HRUS) images and 98.1% accuracy for contrast-enhancement ultrasound (CEUS) images [38]. A novel integrated index, the thyroid malignancy index (TMI), was proposed to help clinicians make more objective distinctions between benign and malignant nodules. The main innovation was the use of histogram analysis and segmentation-based fractal texture analysis (SFTA), which are not dependent on the orientation of the ultrasound probe. The system was tested on 40 thyroid nodules (20 malignant and 20 benign) and used features such as histogram parameters, fractal dimension and mean brightness value in different grayscale bands. The study achieved an overall accuracy of 92.42% usingrandom forests and 94.64% using a support vector machine (SVM) with leave-one-out cross-validation, highlighting the limitations of fine needle aspiration (FNA) biopsy and suggesting that the CAD system could provide a valuable second opinion and thus reduce unnecessary surgeries [39]. [PERSON] et al. [40] developed a novel CAD system combining spatial gray-level dependence features (SGLDF) and fractal textures to analyze the intrinsic structure of thyroid lesions. The features were then subjected to marginal Fisher analysis (MFA) for dimensional reduction and ranking before classification [40]. The system achieved an average accuracy of 97.52%, a sensitivity of 90.32% and a specificity of 98.57% using the support vector machine (SVM) classifier. The study developed the thyroid clinical risk index (TCRI), a single numerical index, to differentiate between benign and malignant lesions effectively. The fusion of texture features with MFA significantly enhanced the classification performance, providing a robust tool for clinical use [40] (Figure 2).
[42] investigated the diagnostic performance of muscle echo intensity (EI) and fractal dimension derived from US images to identify frailty in older adults. Frailty, characterized by decreased muscle mass and strength, poses diagnostic challenges, which this study aimed to address using noninvasive US techniques. In this retrospective analysis of US scans, [PERSON] et al. [42] evaluated participants classified into nonfrail and frail groups based on [PERSON]'s criteria. Echo intensity was measured from the rects femoris muscle and the fractal dimension was calculated using D box-counting techniques. A positive correlation was found between muscle EI and fractal dimension (r = 0.38) and both parameters displayed distinct patterns when comparing nonfrail to frail individuals. In addition, EI showed significant diagnostic accuracy (AUC = 0.69) for categorizing frailty, with high intrarater and interrater reliability. While fractal dimension correlated with EI, it did not independently improve diagnostic accuracy over EI alone [42]. EI proved to be a useful marker for distinguishing nonfrail from frail individuals, while fractal dimension provided additional insights into the muscle architecture changes associated with frailty. Further validation and normative data are required for clinical application [42] (Figure 3).