Fractal dimension analysis of cerebellum in Chiari Malformation type I

Retina images classification based on 2D empirical mode decomposition and multifractal analysis

Diabetic retinopathy is an ocular disease caused by long-term damage to the retina due to high blood sugar levels. Elevated blood sugar can impair the microvasculature in the retina, leading to vascular abnormalities and the formation of abnormal new blood vessels. These changes can manifest in the retina as hemorrhages, leaks, vessel dilation, retinal edema, and retinal detachment. The retinas of individuals with diabetes exhibit different morphologies compared to those without the condition. Most histological images cannot be accurately described using traditional geometric shapes or methods. Therefore, this study aims to evaluate and classify the morphology of retinas with varying degrees of severity using multifractal geometry. In the initial experiments, two-dimensional empirical mode decomposition was employed to extract high-frequency detailed features, and the classification process was based on the most relevant features in the multifractal spectrum associated with disease factors. To eliminate less significant features, the random forest algorithm was utilized. The proposed method achieved an accuracy of 96%, sensitivity of 96%, and specificity of 95%.

Fractals in Neuroimaging

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

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.

Cognitive Functioning in Chiari Malformation Type I Without Posterior Fossa Surgery

Chiari Malformation type I (CM-I) is a neurological disorder characterized by a displacement of the cerebellar tonsils through the foramen magnum into the spinal canal. Most research has focused on physical symptomatology but few studies include neuropsychological examinations. Moreover, although current research highlights the involvement of the cerebellum on higher cognitive functions, little is known about cognitive consequences associated with CM-I. The aim of this study is to analyze cognitive functioning between 39 CM-I patients and 39 healthy controls, matched by gender, age and years of education. Participants have been examined on a large battery of neuropsychological tests, including executive functioning, verbal fluency, spatial cognition, language, verbal memory, processing speed, facial recognition and theory of mind. Results show a poorer performance of the clinical group compared to the control group, even after controlling the effect of physical pain and anxious-depressive symptomatology. The findings suggest the presence of a generalized cognitive deficit associated with CM-I, which makes it necessary to focus attention not only on physical consequences, but also on cognitive ones.

3D structural complexity analysis of cerebellum in Chiari malformation type I

Chiari malformation type I (CM-I), described by a descent of the cerebellar tonsils, is assumed to be a neurological developmental disorder. The aim of the present study was to investigate morphological variance in cerebellar sub-structures, including gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), using magnetic resonance (MR) images with three-dimensional (3D) fractal dimension (FD) analysis in patients with CM-I. MRI data of 16 patients and 15 control subjects were obtained, and structural complexity analyses were performed using a box-counting FD algorithm. Results showed that patients with CM-I had significantly reduced FD values for WM and CSF in comparison with controls, and statistically significant differences in cerebellar GM and CSF volumes between patients and controls were found. Moreover, a significant difference was not found between the WM volumes. This may suggest that there are changes in structural complexity in WM even when its volume is unaffected. We conclude that the findings of this preliminary study indicate the possibility of using FD analysis to understand the pathophysiology of CM-I in patients.