# The Value of Fractal Analysis in Ultrasound Imaging: Exploring Intricate Patterns
## 3 Results
### Pregnancy  
The integration of advanced fractal analysis and Doppler ultrasound for evaluating umbilical artery blood flow has significantly enhanced the accuracy of fetal health monitoring [32]. Doppler ultrasound remains a noninvasive, reliable method for assessing vascular perfusion within the umbilical artery, which is critical for fetal well-being. By emitting ultrasound waves that reflect off moving red blood cells, the Doppler system measures shifts in frequency proportional to blood flow velocity, offering detailed insights into fetal circulation. Recent advancements in spectral analysis methods, including the use of the Hurst exponent for the calculation of fractal dimensions, have further refined the assessment of umbilical artery Doppler signals [32; 33]. [PERSON] et al. [33] explored the efficacy of these fractal dimension curves in comparison to traditional Doppler indices, demonstrating the superior sensitivity of the PSDHURST index in detecting blood flow changes during pregnancy. Doppler signals were collected from 20 pregnant women with normal pregnancies between 18-24 weeks and 32-40 weeks of gestation. Data acquisition was conducted using a Doppler ultrasound unit with a consistent insonation angle and preset ultrasound settings to ensure data integrity. Signal processing involved denoising using wavelet soft thresholding, spectral analysis through AR methods and extraction of maximum frequency envelopes. The traditional Doppler indices-resistance index (RI), pulsatility index (PI) and systolic-to-diastolic ratio (S) were calculated from these envelopes. Additionally, fractal dimension curves were derived using the Hurst exponent, providing a novel metric for evaluating umbilical artery blood flow [33]. Fractal analysis was performed to quantify the Doppler blood flow signal's complexity. The Hurst exponent was used to estimate fractal dimensions together with the variance fractal dimension (VFD). Power spectral density (PSD) graphics were generated using autoregressive methods and the Hurst exponent values from PSD curves (PSDHURST) were evaluated to monitor changes in blood flow velocity with gestational age. However, the PSDHURST index demonstrated higher sensitivity in detecting blood flow changes with ROC curve analysis, showing an area under the curve (AUC) of 0.97 for the PSDHURST index, compared to 0.931, 0.959 and 0.938 for RI, PI and S. The findings suggest that fractal dimension analysis and PSDHURST indices provide more robust metrics for evaluating fetal and placental circulation [33]. These methods offer a significant advancement over traditional Doppler indices, facilitating the earlier detection of potential complications in fetal development. Moreover, [PERSON] et al. [34] highlighted the critical role of fractal analysis in the detection of microcalcifications in the placenta during pregnancy [34]. Fractal dimension was used as a key feature in the analysis due to its ability to characterize the complexity and self-similarity of structures within the image. In the context of this study, fractal dimension is computed to capture the fine structural details of the microcalcifications, which are essential for accurate detection. The fractal dimension is particularly useful in edge enhancement, which is a crucial preprocessing step in this methodology. By applying the Sobel and Laplacian of Gaussian (LoG) filters, the edges of the gray level image were detected and the fractal dimension was computed after these filters were applied. The box-counting method was used to calculate the fractal dimension of the 2D US images. This method provides fractal dimension values in the range of 1 to 2, indicating the roughness and detail of the image [34]. In this study, a high-pass filtering method was implemented, followed by contrast enhancement to ensure that the small details, such as microcalcifications, were more visible. The fractal dimension, when combined with other textural features, contributed to the overall improvement in classification accuracy.