Fractal analysis of plaque border, a novel method for the quantification of atherosclerotic plaque contour irregularity, is associated with pro-atherogenic plasma lipid profile in subjects with non-obstructive carotid stenoses

Fractal Dimension Analysis of Melanocytic Nevi and Melanomas in Normal and Polarized Light-A Preliminary Report

Clinical diagnosis of pigmented lesions can be a challenge in everyday practice. Benign and dysplastic nevi and melanomas may have similar clinical presentations, but completely different prognoses. Fractal dimensions of shape and texture can describe the complexity of the pigmented lesion structure. This study aims to apply fractal dimension analysis to differentiate melanomas, dysplastic nevi, and benign nevi in polarized and non-polarized light. A total of 87 Eighty-four patients with 97 lesions were included in this study. All examined lesions were photographed under polarized and non-polarized light, surgically removed, and examined by a histopathologist to establish the correct diagnosis. The obtained images were then processed and analyzed. Area, perimeter, and fractal dimensions of shape and texture were calculated for all the lesions under polarized and non-polarized light. The fractal dimension of shape in polarized light enables differentiating melanomas, dysplastic nevi, and benign nevi. It also makes it possible to distinguish melanomas from benign and dysplastic nevi under non-polarized light. The fractal dimension of texture allows distinguishing melanomas from benign and dysplastic nevi under polarized light. All examined parameters of shape and texture can be used for developing an automatic computer-aided diagnosis system. Polarized light is superior to non-polarized light for imaging texture details.

Fractal dimension of diffusion-limited aggregation clusters grown on spherical surfaces

In this work we study the fractal properties of diffusion-limited aggregation (DLA) clusters grown on spherical surfaces. Diffusion-limited aggregation clusters, or DLA trees, are highly branched fractal clusters formed by the adhesion of particles. In two-dimensional media, DLA clusters have a fractal dimension D_{f}=1.70 in the continuous limit. In some physical systems, the existence of characteristic lengths leads us to model them as discrete systems. Such characteristic lengths may result also from limitations in measuring instruments, for example, the resolution of biomedical imaging systems. We simulate clusters for different particle sizes and examine the influence of discretization by exploring the systems in terms of the relationship between the particle size r and the radius of the sphere R. We also study the effect of stereographic projection on the fractal properties of DLA clusters. Both discretization and projection alter the fractal dimension of DLA clusters grown on curved surfaces and must be considered in the interpretation of photographic biomedical images.

Trabecular complexity as an early marker of cardiac involvement in Fabry disease

AIMS

Fabry cardiomyopathy is characterized by glycosphingolipid storage and increased myocardial trabeculation has also been demonstrated. This study aimed to explore by cardiac magnetic resonance whether myocardial trabecular complexity, quantified by endocardial border fractal analysis, tracks phenotype evolution in Fabry cardiomyopathy.

METHODS AND RESULTS

Study population included 20 healthy controls (12 males, age 32±9) and 45 Fabry patients divided into three groups: 15 left ventricular hypertrophy (LVH)-negative patients with normal T1 (5 males, age 28±13; Group 1); 15 LVH-negative patients with low T1 (9 males, age 33±9.6; Group 2); 15 LVH-positive patients (11 males, age 53.5±9.6; Group 3). Trabecular fractal dimensions (Dfs) (total, basal, mid-ventricular, and apical) were evaluated on cine images. Total Df was higher in all Fabry groups compared to controls, gradually increasing from controls to Group 3 (1.27±0.02 controls vs. 1.29±0.02 Group 1 vs. 1.30±0.02 Group 2 vs. 1.34±0.02 Group 3; P<0.001). Group 3 showed significantly higher values of all Dfs compared to the other Groups. Both basal and total Dfs were significantly higher in Group 1 compared with controls (basal: 1.30±0.03 vs. 1.26±0.04, P =0.010; total: 1.29±0.02 vs. 1.27±0.02, P=0.044). Total Df showed significant correlations with: (i) T1 value (r=-0.569; P<0.001); (ii) LV mass (r=0.664, P<0.001); (iii) trabecular mass (r=0.676; P <0.001); (iv) Mainz Severity Score Index (r=0.638; P<0.001).

CONCLUSION

Fabry cardiomyopathy is characterized by a progressive increase in Df of endocardial trabeculae together with shortening of T1 values. Myocardial trabeculation is increased before the presence of detectable sphingolipid storage, thus representing an early sign of cardiac involvement.

Shear rate is a better marker of symptomatic ischemic cerebrovascular events than velocity or diameter in severe carotid artery stenosis

OBJECTIVE

This study was designed to test the hypothesis that the high shear rate of flow in the area of carotid stenosis is associated with the incidence of ischemic symptoms in patients with a high degree of carotid stenosis.

METHODS

This is a case-control study of patients with >70% stenosis of the internal carotid artery (ICA) identified by duplex ultrasound in an Intersocietal Accreditation Commission-accredited laboratory during 1 year. Symptomatic patients were included in the study group, and asymptomatic patients served as controls. Shear rates were calculated from high-resolution ultrasound images. Descriptive statistics and univariate and multivariate analysis were performed to account for confounding factors. Receiver operating characteristic curves were used to compare diagnostic values of shear rate, velocities, and diameters of the ICA.

RESULTS

The study included 308 patients (55.5% male; mean age, 73 ± 10 years); 209 of them were asymptomatic and 99 were symptomatic. The mean shear rate was 7930 s^-1 for asymptomatic and 9338 s^-1 for symptomatic patients. Receiver operating characteristic curve identified a cutoff value of 8000 s^-1 to differentiate between symptomatic and asymptomatic patients; 92% of asymptomatic patients and 8.0% of symptomatic patients had a shear rate of <8000 s^-1 compared with 48.5% asymptomatic and 51.5% symptomatic who had a shear rate ≥8000 s^-1. Patients who had a shear rate higher than this cutoff value were 12 times more likely to be symptomatic than those with a shear rate <8000 s^-1 (odds ratio, 12.1; 95% confidence interval, 6.12-24.09). Sensitivity and specificity were 84.8% and 61.2%, respectively.

CONCLUSIONS

In patients with >70% ICA stenosis, the shear rate is associated with the prevalence of symptomatic cerebrovascular ischemic events. A shear rate of 8000 s^-1 and above may be used as a predictor for having symptomatic cerebrovascular ischemic events. Further validation as well as further study of the pathologic mechanism connecting the high shear rate and ischemic cerebrovascular events is needed.