Box-Counting Fractal Analysis: A Primer for the Clinician

Blue skies: Does the visual composition of sky guide subjective judgments of naturalness in the environment?

Expanding on previous findings, that highlighted the significance of sky in environmental perception, our analysis investigated whether the visual composition of the sky shapes perceptions of environmental naturalness. The study employed a novel, free-selection task in which participants viewed a series of environmental images with varying levels of natural and urban elements, as well as different sky visibility conditions, and were asked to identify "nature" within these images. The task procedure also involved subjective ratings of each scene. Using previously gathered data, we reassessed 105 participants' selection of the sky as "nature" across 96 photos of diverse outdoor scenes to understand which visuospatial features influence these perceptions. Utilizing the Boruta feature selection algorithm, we identified key characteristics-fractal dimensions, brightness, and entropy in brightness, hue, and saturation-that significantly predicted the selection of sky as "nature", irrespective of the environment type (urban or natural). Results indicated that lower fractal dimensions are preferred for sky selected as "nature", inversely affecting the naturalness judgment of scenes with the additional effect of brightness. These findings enhance our understanding of how visuospatial features influence environmental perception, offering implications for future research directions and theoretical advancements in understanding environmental perception.

Simulated deep CT characterization of liver metastases with high-resolution filtered back projection reconstruction

Early diagnosis and accurate prognosis of colorectal cancer is critical for determining optimal treatment plans and maximizing patient outcomes, especially as the disease progresses into liver metastases. Computed tomography (CT) is a frontline tool for this task; however, the preservation of predictive radiomic features is highly dependent on the scanning protocol and reconstruction algorithm. We hypothesized that image reconstruction with a high-frequency kernel could result in a better characterization of liver metastases features via deep neural networks. This kernel produces images that appear noisier but preserve more sinogram information. A simulation pipeline was developed to study the effects of imaging parameters on the ability to characterize the features of liver metastases. This pipeline utilizes a fractal approach to generate a diverse population of shapes representing virtual metastases, and then it superimposes them on a realistic CT liver region to perform a virtual CT scan using CatSim. Datasets of 10,000 liver metastases were generated, scanned, and reconstructed using either standard or high-frequency kernels. These data were used to train and validate deep neural networks to recover crafted metastases characteristics, such as internal heterogeneity, edge sharpness, and edge fractal dimension. In the absence of noise, models scored, on average, 12.2% ( α = 0.012 ) and 7.5% ( α = 0.049 ) lower squared error for characterizing edge sharpness and fractal dimension, respectively, when using high-frequency reconstructions compared to standard. However, the differences in performance were statistically insignificant when a typical level of CT noise was simulated in the clinical scan. Our results suggest that high-frequency reconstruction kernels can better preserve information for downstream artificial intelligence-based radiomic characterization, provided that noise is limited. Future work should investigate the information-preserving kernels in datasets with clinical labels.

Point of Care Testing (POCT) in Psychopathology Using Fractal Analysis and Hilbert Huang Transform of Electroencephalogram (EEG)

Research has shown that relying only on self-reports for diagnosing psychiatric disorders does not yield accurate results at all times. The advances of technology as well as artificial intelligence and other machine learning algorithms have allowed the introduction of point of care testing (POCT) including EEG characterization and correlations with possible psychopathology. Nonlinear methods of EEG analysis have significant advantages over linear methods. Empirical mode decomposition (EMD) is a reliable nonlinear method of EEG pre-processing. In this chapter, we compare two existing EEG complexity measures - Higuchi fractal dimension (HFD) and sample entropy (SE), with our newly proposed method using Higuchi fractal dimension from the Hilbert Huang transform (HFD-HHT). We present an example using the three complexity measures on a 2-minute EEG recorded from a healthy 20-year-old male after signal pre-processing. Furthermore, we showed the usefulness of these complexity measures in the classification of major depressive disorder (MDD) with healthy controls. Our study is in line with previous research and has shown an increase in HFD and SE values in the full, alpha and beta frequency bands suggestive of an increase in EEG irregularity. Moreover, the HFD-HHT values decreased in those three bands for majority of electrodes which is suggestive of a decrease in irregularity in the frequency-time domain. We conclude that all three complexity measures can be vital features useful for EEG analysis which could be incorporated in POCT systems.

Complex Morphologic Analysis of Cerebral Aneurysms Through the Novel Use of Fractal Dimension as a Predictor of Rupture Status: A Proof of Concept Study

BACKGROUND

Aneurysm morphology has been correlated with rupture. Previous reports identified several morphologic indices that predict rupture status, but they measure only specific qualities of the morphology of an aneurysm in a semiquantitative fashion. Fractal analysis is a geometric technique whereby the overall complexity of a shape is quantified through the calculation of a fractal dimension (FD). By progressively altering the scale of measurement of a shape and determining the number of segments required to incorporate the entire shape, a noninteger value for the dimension of the shape is derived. We present a proof-of-concept study to calculate the FD of an aneurysm for a small cohort of patients with aneurysms in 2 specific locations to determine whether FD is associated with aneurysm rupture status.

METHODS

Twenty-nine aneurysms of the posterior communicating and middle cerebral arteries were segmented from computed tomography angiograms in 29 patients. FD was calculated using a standard box-counting algorithm extended for use with three-dimensional shapes. Nonsphericity index and undulation index (UI) were used to validate the data against previously reported parameters associated with rupture status.

RESULTS

Nineteen ruptured and 10 unruptured aneurysms were analyzed. Through logistic regression analysis, lower FD was found to be significantly associated with rupture status (P = 0.035; odds ratio, 0.64; 95% confidence interval, 0.42-0.97 per FD increment of 0.05).

CONCLUSIONS

In this proof-of-concept study, we present a novel approach to quantify the geometric complexity of intracranial aneurysms through FD. These data suggest an association between FD and patient-specific aneurysm rupture status.

A new strategy for the early detection of alzheimer disease stages using multifractal geometry analysis based on K-Nearest Neighbor algorithm

Alzheimer's Disease (AD) is considered one of the most diseases that much prevalent among elderly people all over the world. AD is an incurable neurodegenerative disease affecting cognitive functions and were characterized by progressive and collective functions deteriorating. Remarkably, early detection of AD is essential for the development of new and invented treatment strategies. As Dementia causes irreversible damage to the brain neurons and leads to changes in its structure that can be described adequately within the framework of multifractals. Hence, the present work focus on developing a promising and efficient computing technique to pre-process and classify the AD disease especially in the early stages using multifractal geometry to extract the most changeable features due to AD. Then, A machine learning classification algorithm (K-Nearest Neighbor) has been implemented in order to classify and detect the main four early stages of AD. Two datasets have been used to ensure the validation of the proposed methodology. The proposed technique has achieved 99.4% accuracy and 100% sensitivity. The comparative results show that the proposed classification technique outperforms is recent techniques in terms of performance measures.

Fractal dimension of the brain in neurodegenerative disease and dementia: A systematic review

Sensitive and specific antemortem biomarkers of neurodegenerative disease and dementia are crucial to the pursuit of effective treatments, required both to reliably identify disease and to track its progression. Atrophy is the structural magnetic resonance imaging (MRI) hallmark of neurodegeneration. However in most cases it likely indicates a relatively advanced stage of disease less susceptible to treatment as some disease processes begin decades prior to clinical onset. Among emerging metrics that characterise brain shape rather than volume, fractal dimension (FD) quantifies shape complexity. FD has been applied in diverse fields of science to measure subtle changes in elaborate structures. We review its application thus far to structural MRI of the brain in neurodegenerative disease and dementia. We identified studies involving subjects who met criteria for mild cognitive impairment, Alzheimer's Disease, Vascular Dementia, Lewy Body Dementia, Frontotemporal Dementia, Amyotrophic Lateral Sclerosis, Parkinson's Disease, Huntington's Disease, Multiple Systems Atrophy, Spinocerebellar Ataxia and Multiple Sclerosis. The early literature suggests that neurodegenerative disease processes are usually associated with a decline in FD of the brain. The literature includes examples of disease-related change in FD occurring independently of atrophy, which if substantiated would represent a valuable advantage over other structural imaging metrics. However, it is likely to be non-specific and to exhibit complex spatial and temporal patterns. A more harmonious methodological approach across a larger number of studies as well as careful attention to technical factors associated with image processing and FD measurement will help to better elucidate the metric's utility.

Biocompatible Chitosan-Based Hydrogels for Bioabsorbable Wound Dressings

Supramolecular hydrogels based on chitosan and monoaldehydes are biomaterials with high potential for a multitude of bioapplications. This is due to the proper choice of the monoaldehyde that can tune the hydrogel properties for specific practices. In this conceptual framework, the present paper deals with the investigation of a hydrogel as bioabsorbable wound dressing. To this aim, chitosan was cross-linked with 2-formylphenylboronic acid to yield a hydrogel with antimicrobial activity. FTIR, NMR, and POM procedures have characterized the hydrogel from a structural and supramolecular point of view. At the same time, its biocompatibility and antimicrobial properties were also determined in vitro. Furthermore, in order to assess the bioabsorbable character, its biodegradation was investigated in vitro in the presence of lysosome in media of different pH, mimicking the wound exudate at different stages of healing. The biodegradation was monitored by gravimetrical measurements, SEM microscopy and fractal analyses of the images. The fractal dimension values and the lacunarity of SEM pictures were accurately calculated. All these successful investigations led to the conclusion that the tested materials are at the expected high standards.

Fractal characterization of retinal microvascular network morphology during diabetic retinopathy progression

OBJECTIVE

The study aimed to characterize morphological changes of the retinal microvascular network during the progression of diabetic retinopathy.

METHODS

Publicly available retinal images captured by a digital fundus camera from DIARETDB1 and STARE databases were used. The retinal microvessels were segmented using the automatic method, and vascular network morphology was analyzed by fractal parametrization such as box-counting dimension, lacunarity, and multifractals.

RESULTS

The results of the analysis were affected by the ability of the segmentation method to include smaller vessels with more branching generations. In cases where the segmentation was more detailed and included a higher number of vessel branching generations, increased severity of diabetic retinopathy was associated with increased complexity of microvascular network as measured by box-counting and multifractal dimensions, and decreased gappiness of retinal microvascular network as measured by lacunarity parameter. This association was not observed if the segmentation method included only 3-4 vessel branching generations.

CONCLUSIONS

Severe stages of diabetic retinopathy could be detected noninvasively by using high resolution fundus photography and automatic microvascular segmentation to the high number of branching generations, followed by fractal analysis parametrization. This approach could improve risk stratification for the development of microvascular complications, cardiovascular disease, and dementia in diabetes.

Pigmented macrophages and related aggregates in the spleen of european sea bass dosed with heavy metals: Ultrastructure and explorative morphometric analysis

The ultrastructure and morphometrics of pigmented macrophages (PMs) were assessed in the spleen of European sea bass experimentally dosed with Cd and Hg. PMs occurred either as solitary cells or as variably structured aggregations, defined as macrophage aggregates (MAs). Light microscopy revealed a high degree of morphological heterogeneity amongst MAs of all experimental groups. At the ultrastructural level, MAs showed a heterogeneous pigment content that was not influenced by the treatment. Cytoplasm rarefaction/vacuolation and euchromatic nuclei, were observed in PMs of dosed fish. Undosed and Cd-dosed samples differ significantly with regard to the following morphometric features: the Minor axis of the best fitting ellipse, Aspect Ratio, and Roundness. In Cd-dosed fish, MAs showed reduced size and complexity. Lacunarity showed significant differences between undosed and both Cd and Hg-dosed samples. These results suggest that heavy metals, and especially Cd, may influence the dynamics of PM aggregation/disaggregation. Variability in splenic MAs was observed both by light and electron microscopy. However, only the morphometric techniques adequately and objectively described the phenomenon, allowing a quantitative/statistical comparison of morphology among experimental groups. These morphometric analyses could be usefully applied in toxicological and ecotoxicological, as well as morpho-functional studies.