The Value of Fractal Analysis in Ultrasound Imaging: Exploring Intricate Patterns

Abstract

Fractal analysis is a mathematical approach employed to study and describe complex patterns and structures across various disciplines, including mathematics, physics, computer science, biology and finance. Introduced by mathematician Benoit Mandelbrot in the 1970s, fractals are intricate, self-similar patterns that repeat at different scales, exhibiting consistent structures upon magnification or reduction. This analysis involves generating fractals through iterative processes or recursive equations, resulting in highly detailed and complex formations. Fractal analysis enhances medical images by removing noise while preserving details and improving diagnostic quality in magnetic resonance and computed tomography scans. However, there is a lack of comprehensive studies on its application in ultrasound imaging, prompting this narrative review to investigate its use and methodology in this context. Selected papers on the use of fractal analysis in ultrasound imaging were analyzed. Out of 186 records screened, 60 duplicates were removed and 28 were discarded. The text content of 98 potentially eligible papers was checked, with 65 not meeting inclusion criteria. Finally, 33 studies were included in the review. Fractal analysis enhances ultrasound imaging by providing detailed tissue texture characterization, aiding in the diagnosis of conditions like breast and lung cancer, osteoporosis and hypertensive disorders in pregnancy. It quantifies biological structure complexity and improves diagnostic accuracy and reliability. This technique supports clinicians in making informed decisions by offering critical insights into various medical conditions.

Keywords

• fractal analysis
• ultrasound imaging
• ultrasonography
• texture analysis
• fractal dimension
• lacunarity