Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple-acquisition MRI

Classifying breast cancer and fibroadenoma tissue biopsies from paraffined stain-free slides by fractal biomarkers in Fourier Ptychographic Microscopy

Breast cancer is one of the most spread and monitored pathologies in high-income countries. After breast biopsy, histological tissue is stored in paraffin, sectioned and mounted. Conventional inspection of tissue slides under benchtop light microscopes involves paraffin removal and staining, typically with H&E. Then, expert pathologists are called to judge the stained slides. However, paraffin removal and staining are operator-dependent, time and resources consuming processes that can generate ambiguities due to non-uniform staining. Here we propose a novel method that can work directly on paraffined stain-free slides. We use Fourier Ptychography as a quantitative phase-contrast microscopy method, which allows accessing a very wide field of view (i.e., mm2) in one single image while guaranteeing high lateral resolution (i.e., 0.5 µm). This imaging method is multi-scale, since it enables looking at the big picture, i.e. the complex tissue structure and connections, with the possibility to zoom-in up to the single-cell level. To handle this informative image content, we introduce elements of fractal geometry as multi-scale analysis method. We show the effectiveness of fractal features in describing and classifying fibroadenoma and breast cancer tissue slides from ten patients with very high accuracy. We reach 94.0 ± 4.2% test accuracy in classifying single images. Above all, we show that combining the decisions of the single images, each patient's slide can be classified with no error. Besides, fractal geometry returns a guide map to help pathologist to judge the different tissue portions based on the likelihood these can be associated to a breast cancer or fibroadenoma biomarker. The proposed automatic method could significantly simplify the steps of tissue analysis and make it independent from the sample preparation, the skills of the lab operator and the pathologist.

Accurate identification of individuals with subjective cognitive decline using 3D regional fractal dimensions on structural magnetic resonance imaging

BACKGROUND AND OBJECTIVE

Accurate identification of individuals with subjective cognitive decline (SCD) is crucial for early intervention and prevention of neurodegenerative diseases. Fractal dimensionality (FD) has emerged as a robust and replicable measure, surpassing traditional geometric metrics, in characterizing the intricate fractal geometrical properties of brain structure. Nevertheless, the effectiveness of FD in identifying individuals with SCD remains largely unclear. A 3D regional FD method can be suggested to characterize and quantify the spatial complexity of the precise gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD.

METHODS

This study introduces a novel integer ratio based 3D box-counting fractal analysis (IRBCFA) to quantify regional fractal dimensions (FDs) in structural magnetic resonance imaging (MRI) data. The innovative method overcomes limitations of conventional box-counting techniques by accommodating arbitrary box sizes, thereby enhancing the precision of FD estimation in small, yet neurologically significant, brain regions.

RESULTS

The application of IRBCFA to two publicly available datasets, OASIS-3 and ADNI, consisting of 520 and 180 subjects, respectively. The method identified discriminative regions of interest (ROIs) predominantly within the limbic system, fronto-parietal region, occipito-temporal region, and basal ganglia-thalamus region. These ROIs exhibited significant correlations with cognitive functions, including executive functioning, memory, social cognition, and sensory perception, suggesting their potential as neuroimaging markers for SCD. The identification model trained on these ROIs demonstrated exceptional performance achieving over 93 % accuracy on the discovery dataset and exceeding 87 % on the independent testing dataset. Furthermore, an exchange experiment between datasets revealed a substantial overlap in discriminative ROIs, highlighting the robustness of our method across diverse populations.

CONCLUSION

Our findings indicate that IRBCFA can serve as a valuable tool for quantifying the spatial complexity of gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD. The demonstrated generalizability and robustness of this method position it as a promising tool for neurodegenerative disease research and offer potential for clinical applications.

Multi-scale fractal Fourier Ptychographic microscopy to assess the dose-dependent impact of copper pollution on living diatoms

Accumulation of bioavailable heavy metals in aquatic environment poses a serious threat to marine communities and human health due to possible trophic transfers through the food chain of toxic, non-degradable, exogenous pollutants. Copper (Cu) is one of the most spread heavy metals in water, and can severely affect primary producers at high doses. Here we show a novel imaging test to assay the dose-dependent effects of Cu on live microalgae identifying stress conditions when they are still capable of sustaining a positive growth. The method relies on Fourier Ptychographic Microscopy (FPM), capable to image large field of view in label-free phase-contrast mode attaining submicron lateral resolution. We uniquely combine FPM with a new multi-scale analysis method based on fractal geometry. The system is able to provide ensemble measurements of thousands of diatoms in the liquid sample simultaneously, while ensuring at same time single-cell imaging and analysis for each diatom. Through new image descriptors, we demonstrate that fractal analysis is suitable for handling the complexity and informative power of such multiscale FPM modality. We successfully tested this new approach by measuring how different concentrations of Cu impact on Skeletonema pseudocostatum diatom populations isolated from the Sarno River mouth.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens

Introduction

Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks.

Methods

In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach.

Results

The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05).

Conclusions

The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

Fractal Dimension Analysis in Neurological Disorders: An Overview

Fractal analysis has emerged as a powerful tool for characterizing irregular and complex patterns found in the nervous system. This characterization is typically applied by estimating the fractal dimension (FD), a scalar index that describes the topological complexity of the irregular components of the nervous system, both at the macroscopic and microscopic levels, that may be viewed as geometric fractals. Moreover, temporal properties of neurophysiological signals can also be interpreted as dynamic fractals. Given its sensitivity for detecting changes in brain morphology, FD has been explored as a clinically relevant marker of brain damage in several neuropsychiatric conditions as well as in normal and pathological cerebral aging. In this sense, evidence is accumulating for decreases in FD in Alzheimer's disease, frontotemporal dementia, Parkinson's disease, multiple sclerosis, and many other neurological disorders. In addition, it is becoming increasingly clear that fractal analysis in the field of clinical neurology opens the possibility of detecting structural alterations in the early stages of the disease, which highlights FD as a potential diagnostic and prognostic tool in clinical practice.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Age-associated sex and asymmetry differentiation in hemispheric and lobar cortical ribbon complexity across adulthood: A UK Biobank imaging study

Cortical morphology changes with ageing and age-related neurodegenerative diseases. Previous studies suggest that the age effect is more pronounced in the frontal lobe. However, our knowledge of structural complexity changes in male and female brains is still limited. We measured cortical ribbon complexity through fractal dimension (FD) analysis at the hemisphere and lobe level in 7010 individuals from the UK Biobank imaging cohort to study age-related sex differences (3332 males, age ranged 45-79 years). FD decreases significantly with age and sexual dimorphism exists. With correction for brain size, females showed higher complexity in the left hemisphere and left and right parietal lobes whereas males showed higher complexity in the right temporal and left and right occipital lobes. A nonlinear age effect was observed in the left and right frontal, and right temporal lobes. Differential patterns of age effects were observed in both sexes with relatively more age-affected regions in males. Significantly higher rightward asymmetries at hemisphere, frontal, parietal, and occipital lobe level and higher leftward asymmetry in temporal lobe were observed. There was no age-by-sex-by asymmetry interaction in any region. When controlling for brain size, the leftward hemispheric, and temporal lobe asymmetry decreased with age. Males had significantly lower asymmetry between hemispheres and higher asymmetry in the parietal and occipital lobes than females. This work provides distinct patterns of age-related sex and asymmetry differences that can aid in the future development of sex-specific models of the normal brain to ascribe cognitive functional significance of these patterns in ageing.

Structural Correlates of Overt Sentence Reading in Mild Cognitive Impairment and Mild-to-Moderate Alzheimer's Disease

BACKGROUND

Overt sentence reading in mild cognitive impairment (MCI) and mild-tomoderate Alzheimer's disease (AD) has been associated with slowness of speech, characterized by a higher number of pauses, shorter speech units and slower speech rate and attributed to reduced working memory/ attention and language capacity.

OBJECTIVE

This preliminary case-control study investigates whether the temporal organization of speech is associated with the volume of brain regions involved in overt sentence reading and explores the discriminative ability of temporal speech parameters and standard volumetric MRI measures for the classification of MCI and AD.

METHODS

Individuals with MCI, mild-to-moderate AD, and healthy controls (HC) had a structural MRI scan and read aloud sentences varying in cognitive-linguistic demand (length). The association between speech features and regional brain volumes was examined by linear mixed-effect modeling. Genetic programming was used to explore the discriminative ability of temporal and MRI features.

RESULTS

Longer sentences, slower speech rate, and a higher number of pauses and shorter interpausal units were associated with reduced volumes of the reading network. Speech-based classifiers performed similarly to the MRI-based classifiers for MCI-HC (67% vs. 68%) and slightly better for AD-HC (80% vs. 64%) and AD-MCI (82% vs. 59%). Adding the speech features to the MRI features slightly improved the performance of MRI-based classification for AD-HC and MCI-HC but not HC-MCI.

CONCLUSION

The temporal organization of speech in overt sentence reading reflects underlying volume reductions. It may represent a sensitive marker for early assessment of structural changes and cognitive- linguistic deficits associated with healthy aging, MCI, and AD.

Prospects of Structural Similarity Index for Medical Image Analysis

An image quality matrix provides a significant principle for objectively observing an image based on an alteration between the original and distorted images. During the past two decades, a novel universal image quality assessment has been developed with the ability of adaptation with human visual perception for measuring the difference of a degraded image from the reference image, namely a structural similarity index. Structural similarity has since been widely used in various sectors, including medical image evaluation. Although numerous studies have reported the use of structural similarity as an evaluation strategy for computer-based medical images, reviews on the prospects of using structural similarity for medical imaging applications have been rare. This paper presents previous studies implementing structural similarity in analyzing medical images from various imaging modalities. In addition, this review describes structural similarity from the perspective of a family’s historical background, as well as progress made from the original to the recent structural similarity, and its strengths and drawbacks. Additionally, potential research directions in applying such similarities related to medical image analyses are described. This review will be beneficial in guiding researchers toward the discovery of potential medical image examination methods that can be improved through structural similarity index.

Cortical Complexity Estimation Using Fractal Dimension: A Systematic Review of the Literature on Clinical and Nonclinical Samples

Fractal geometry has recently been proposed as a useful tool for characterizing the complexity of the brain cortex, which is likely to derive from the recurrence of sulci–gyri convolution patterns. The index used to describe the cortical complexity is called fractal dimensional (FD) and was employed by different research exploring the neurobiological correlates of distinct pathological and nonpathological conditions. This review aims to describe the literature on the application of this index, summarize the heterogeneities between studies and inform future research on this topic. Sixty‐two studies were included in the systematic review. The main research lines concern neurodevelopment, aging and the neurobiology of specific psychiatric and neurological disorders. Overall, the included papers indicate that cortical complexity is likely to reduce during aging and in various pathological processes affecting the brain. Nevertheless, the high heterogeneity between studies strongly prevents the possibility of drawing conclusions. Further research considering this index besides other morphological values is needed to better clarify the role of FD in characterizing the cortical structure.

Fractal dimension (FD) is a useful tool for the assessment of cortical complexity. In healthy controls, FD is associated with development, aging and cognition. Alterations in FD have been observed in different neurological and psychiatric disorders.

BrainFD: Measuring the Intracranial Brain Volume With Fractal Dimension

A few methods and tools are available for the quantitative measurement of the brain volume targeting mainly brain volume loss. However, several factors, such as the clinical conditions, the time of the day, the type of MRI machine, the brain volume artifacts, the pseudoatrophy, and the variations among the protocols, produce extreme variations leading to misdiagnosis of brain atrophy. While brain white matter loss is a characteristic lesion during neurodegeneration, the main objective of this study was to create a computational tool for high precision measuring structural brain changes using the fractal dimension (FD) definition. The validation of the BrainFD software is based on T1-weighted MRI images from the Open Access Series of Imaging Studies (OASIS)-3 brain database, where each participant has multiple MRI scan sessions. The software is based on the Python and JAVA programming languages with the main functionality of the FD calculation using the box-counting algorithm, for different subjects on the same brain regions, with high accuracy and resolution, offering the ability to compare brain data regions from different subjects and on multiple sessions, creating different imaging profiles based on the Clinical Dementia Rating (CDR) scores of the participants. Two experiments were executed. The first was a cross-sectional study where the data were separated into two CDR classes. In the second experiment, a model on multiple heterogeneous data was trained, and the FD calculation for each participant of the OASIS-3 database through multiple sessions was evaluated. The results suggest that the FD variation efficiently describes the structural complexity of the brain and the related cognitive decline. Additionally, the FD efficiently discriminates the two classes achieving 100% accuracy. It is shown that this classification outperforms the currently existing methods in terms of accuracy and the size of the dataset. Therefore, the FD calculation for identifying intracranial brain volume loss could be applied as a potential low-cost personalized imaging biomarker. Furthermore, the possibilities measuring different brain areas and subregions could give robust evidence of the slightest variations to imaging data obtained from repetitive measurements to Physicians and Radiologists.

Cortical complexity in world trade center responders with chronic posttraumatic stress disorder

Approximately 23% of World Trade Center (WTC) responders are experiencing chronic posttraumatic stress disorder (PTSD) associated with their exposures at the WTC following the terrorist attacks of 9/11/2001, which has been demonstrated to be a risk factor for cognitive impairment raising concerns regarding their brain health. Cortical complexity, as measured by analyzing Fractal Dimension (FD) from T1 MRI brain images, has been reported to be reduced in a variety of psychiatric and neurological conditions. In this report, we hypothesized that FD would be also reduced in a case-control sample of 99 WTC responders as a result of WTC-related PTSD. The results of our surface-based morphometry cluster analysis found alterations in vertex clusters of complexity in WTC responders with PTSD, with marked reductions in regions within the frontal, parietal, and temporal cortices, in addition to whole-brain absolute bilateral and unilateral complexity. Furthermore, region of interest analysis identified that the magnitude of changes in regional FD severity was associated with increased PTSD symptoms (reexperiencing, avoidance, hyperarousal, negative affect) severity. This study confirms prior findings on FD and psychiatric disorders and extends our understanding of FD associations with posttraumatic symptom severity. The complex and traumatic experiences that led to WTC-related PTSD were associated with reductions in cortical complexity. Future work is needed to determine whether reduced cortical complexity arose prior to, or concurrently with, onset of PTSD.

Novel Volumetric and Surface-Based Magnetic Resonance Indices of the Aging Brain - Does Male and Female Brain Age in the Same Way?

Introduction: Novel post-processing methods allow not only for assessment of brain volumetry or cortical thickness based on magnetic resonance imaging (MRI) but also for more detailed analysis of cortical shape and complexity using parameters such as sulcal depth, gyrification index, or fractal dimension. The aim of this study was to analyze changes in brain volumetry and other cortical indices during aging in men and women.

Material and Methods: Material consisted of 697 healthy volunteers (aged 38–80 years; M/F, 264/443) who underwent brain MRI using a 1.5-T scanner. Voxel-based volumetry of total gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) was performed followed by assessment of cortical parameters [cortical thickness (CT), sulcal depth (SD), gyrification index (GI), and fractal dimension (FD)] in 150 atlas locations using surface-based morphometry with a region-based approach. All parameters were compared among seven age groups (grouped every 5 years) separately for men and women. Additionally, percentile curves for men and women were provided for total volumes of GM, WM, and CSF.

Results: In men and women, a decrease in GM and WM volumes and an increase in CSF volume seem to progress slowly since the age of 45. In men, significant GM and WM loss as well as CSF increase start above 55 years of age, while in women, significant GM loss starts above 50 and significant WM loss as well as CSF increase above 60. CT was found to significantly decrease with aging in 39% of locations in women and in 36% of locations in men, SD was found to increase in 13.5% of locations in women and in 1.3% of locations in men, GI was decreased in 3.4% of locations in women and in 2.0% of locations in men, and FD was changed in 2.7% of locations in women compared to 2.0% in men.

Conclusions: Male and female brains start aging at the similar age of 45. Compared to men, in women, the cortex is affected earlier and in the more complex pattern regarding not only cortical loss but also other alterations within the cortical shape, with relatively longer sparing of WM volume.

Brain volumetric and fractal analysis of synthetic MRI: A comparative study with conventional 3D T1-weighted images

PURPOSE

The estimation of brain volumetric measurements based on Synthetic MRI (SyMRI) is easy and fast, however, the consistency of brain volumetric and morphologic measurements based on SyMRI and 3D T1WI should be further addressed. The current study evaluated the impact of spatial resolution on brain volumetric and morphologic measurements using SyMRI, and test whether the brain measurements derived from SyMRI were consistent with those resulted from 3D T1WI.

METHOD

Brain volumetric and fractal analysis were applied to thirty healthy subjects, each underwent four SyMRI acquisitions with different spatial resolutions (1 × 1 × 2 mm, 1 × 1x3mm, 1 × 1 × 4 mm, 2 × 2 × 2 mm) and a 3D T1WI (1 × 1 × 1 mm isotropic). The consistency of the SyMRI measurements was tested using one-way non-parametric Kruskal-Wallis test and post hoc Dwass-Steel-Critchlow-Fligner test. The association between SyMRI and 3D T1WI derived measurements was evaluated using linear regression models.

RESULTS

Our results demonstrated that both in- and through-plane resolutions show an impact on brain volumetric measurements, while brain parenchymal volume showed high consistency across the SyMRI acquisitions, and high association with the measurements from 3D T1WI. In addition, SyMRI with 1 × 1 × 4 mm resolution showed the strongest association with 3D T1WI compared to other SyMRI acquisitions in both volumetric and fractal analyses. Moreover, substantial differences were found in fractal dimension of both gray and white matter between the SyMRI and 3D T1WI tissue segmentations.

CONCLUSIONS

Our results suggested that the measurements from SyMRI with relatively higher in-plane and lower through-plane resolution (1 × 1 × 4 mm) are much closer to 3D T1WI.

On the quantitative effects of compression of retinal fundus images on morphometric vascular measurements in VAMPIRE

BACKGROUND AND OBJECTIVES

This paper reports a quantitative analysis of the effects of joint photographic experts group (JPEG) image compression of retinal fundus camera images on automatic vessel segmentation and on morphometric vascular measurements derived from it, including vessel width, tortuosity and fractal dimension.

METHODS

Measurements are computed with vascular assessment and measurement platform for images of the retina (VAMPIRE), a specialized software application adopted in many international studies on retinal biomarkers. For reproducibility, we use three public archives of fundus images (digital retinal images for vessel extraction (DRIVE), automated retinal image analyzer (ARIA), high-resolution fundus (HRF)). We generate compressed versions of original images in a range of representative levels.

RESULTS

We compare the resulting vessel segmentations with ground truth maps and morphological measurements of the vascular network with those obtained from the original (uncompressed) images. We assess the segmentation quality with sensitivity, specificity, accuracy, area under the curve and Dice coefficient. We assess the agreement between VAMPIRE measurements from compressed and uncompressed images with correlation, intra-class correlation and Bland-Altman analysis.

CONCLUSIONS

Results suggest that VAMPIRE width-related measurements (central retinal artery equivalent (CRAE), central retinal vein equivalent (CRVE), arteriolar-venular width ratio (AVR)), the fractal dimension (FD) and arteriolar tortuosity have excellent agreement with those from the original images, remaining substantially stable even for strong loss of quality (20% of the original), suggesting the suitability of VAMPIRE in association studies with compressed images.

Cortical fractal dimension predicts disability worsening in Multiple Sclerosis patients

BACKGROUND

Fractal geometry measures the morphology of the brain and detects CNS damage. We aimed to assess the longitudinal changes on brain's fractal geometry and its predictive value for disease worsening in patients with Multiple Sclerosis (MS).

METHODS

We prospectively analyzed 146 consecutive patients with relapsing-remitting MS with up to 5 years of clinical and brain MRI (3 T) assessments. The fractal dimension and lacunarity were calculated for brain regions using box-counting methods. Longitudinal changes were analyzed in mixed-effect models and the risk of disability accumulation were assessed using Cox Proportional Hazard regression analysis.

RESULTS

There was a significant decrease in the fractal dimension and increases of lacunarity in different brain regions over the 5-year follow-up. Lower cortical fractal dimension increased the risk of disability accumulation for the Expanded Disability Status Scale [HR 0.9734, CI 0.8420-0.9125; Harrell C 0.59; Wald p 0.038], 9-hole peg test [HR 0.9734, CI 0.8420-0.9125; Harrell C 0.59; Wald p 0.0083], 2.5% low contrast vision [HR 0.4311, CI 0.2035-0.9133; Harrell C 0.58; Wald p 0.0403], symbol digit modality test [HR 2.215, CI 1.043-4.705; Harrell C 0.65; Wald p 0.0384] and MS Functional Composite-4 [HR 0.55, CI 0.317-0.955; Harrell C 0.59; Wald p 0.0029].

CONCLUSIONS

Fractal geometry analysis of brain MRI identified patients at risk of increasing their disability in the next five years.

Investigation of associations between retinal microvascular parameters and albuminuria in UK Biobank: a cross-sectional case-control study

Background

Associations between microvascular variation and chronic kidney disease (CKD) have been reported previously. Non-invasive retinal fundus imaging enables evaluation of the microvascular network and may offer insight to systemic risk associated with CKD.

Methods

Retinal microvascular parameters (fractal dimension [FD] – a measure of the complexity of the vascular network, tortuosity, and retinal arteriolar and venular calibre) were quantified from macula-centred fundus images using the Vessel Assessment and Measurement Platform for Images of the REtina (VAMPIRE) version 3.1 (VAMPIRE group, Universities of Dundee and Edinburgh, Scotland) and assessed for associations with renal damage in a case-control study nested within the multi-centre UK Biobank cohort study. Participants were designated cases or controls based on urinary albumin to creatinine ratio (ACR) thresholds. Participants with ACR ≥ 3 mg/mmol (ACR stages A2-A3) were characterised as cases, and those with an ACR < 3 mg/mmol (ACR stage A1) were categorised as controls. Participants were matched on age, sex and ethnic background.

Results

Lower FD (less extensive microvascular branching) was associated with a small increase in odds of albuminuria independent of blood pressure, diabetes and other potential confounding variables (odds ratio [OR] 1.18, 95% confidence interval [CI] 1.03–1.34 for arterioles and OR 1.24, CI 1.05–1.47 for venules). Measures of tortuosity or retinal arteriolar and venular calibre were not significantly associated with ACR.

Conclusions

This study supports previously reported associations between retinal microvascular FD and other metabolic disturbances affecting the systemic vasculature. The association between retinal microvascular FD and albuminuria, independent of diabetes and blood pressure, may represent a useful indicator of systemic vascular damage associated with albuminuria.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12882-021-02273-6.

Toward a more reliable characterization of fractal properties of the cerebral cortex of healthy subjects during the lifespan

The cerebral cortex manifests an inherent structural complexity of folding. The fractal geometry describes the complexity of structures which show self-similarity in a proper interval of spatial scales. In this study, we aimed at evaluating in-vivo the effect of different criteria for selecting the interval of spatial scales in the estimation of the fractal dimension (FD) of the cerebral cortex in T₁-weighted magnetic resonance imaging (MRI). We compared four different strategies, including two a priori selections of the interval of spatial scales, an automated selection of the spatial scales within which the cerebral cortex manifests the highest statistical self-similarity, and an improved approach, based on the search of the interval of spatial scales which presents the highest rounded R²_adj coefficient and, in case of equal rounded R²_adj coefficient, preferring the widest interval in the log–log plot. We employed two public and international datasets of in-vivo MRI scans for a total of 159 healthy subjects (age range 6–85 years). The improved approach showed strong associations of FD with age and yielded the most accurate machine learning models for individual age prediction in both datasets. Our results indicate that the selection of the interval of spatial scales of the cerebral cortex is thus critical in the estimation of FD.

Haemodynamic activity characterization of resting state networks by fractal analysis and thalamocortical morphofunctional integrity in chronic migraine

BACKGROUND

Chronic migraine (CM) can be associated with aberrant long-range connectivity of MRI-derived resting-state networks (RSNs). Here, we investigated how the fractal dimension (FD) of blood oxygenation level dependent (BOLD) activity may be used to estimate the complexity of RSNs, reflecting flexibility and/or efficiency in information processing in CM patients respect to healthy controls (HC).

METHODS

Resting-state MRI data were collected from 20 untreated CM without history of medication overuse and 20 HC. On both groups, we estimated the Higuchi's FD. On the same subjects, fractional anisotropy (FA) and mean diffusivity (MD) values of bilateral thalami were retrieved from diffusion tensor imaging and correlated with the FD values.

RESULTS

CM showed higher FD values within dorsal attention system (DAS) and the anterior part of default-mode network (DMN), and lower FD values within the posterior DMN compared to HC. Although FA and MD were within the range of normality, both correlated with the FD values of DAS.

CONCLUSIONS

FD of DAS and DMN may reflect disruption of cognitive control of pain in CM. Since the normal microstructure of the thalamus and its positive connectivity with the cortical networking found in our CM patients reminds similar results obtained assessing the same structures but with the methods of neurophysiology, in episodic migraine during an attack, this may be yet another evidence in supporting CM as a never-ending migraine attack.

Differential longitudinal changes in structural complexity and volumetric measures in community-dwelling older individuals

Fractal geometry provides a method of analyzing natural and especially biological morphologies. To investigate the relationship between the complexity measure, which is indexed as fractal dimensionality (FD), and the traditional Euclidean metrics, such as the volume and thickness, of the brain in older age, we analyzed 483 MRI scans of 161 community-dwelling, nondemented individuals aged 70-90 years at the baseline and their 2-year and 6-year follow-ups. We quantified changes in neuroimaging metrics in cortical lobes and subcortical structures and investigated the effects of age, sex, hemisphere, and education on FD. We also analyzed the mediating effects of these metrics for further investigation. FD showed significant age-related decline in all structures, and its trajectory was best modeled quadratically in the bilateral frontal, parietal, and occipital lobes, as well as in the bilateral caudate, putamen, hippocampus, amygdala, and accumbens. FD showed specific mediating effects on aging and cognitive decline in some regions. Our findings suggest that FD is reliable yet shows a different pattern of decline compared with volumetric measures.

Quantitative measurements of enlarged perivascular spaces in the brain are associated with retinal microvascular parameters in older community-dwelling subjects

BACKGROUND

Perivascular Spaces (PVS) become increasingly visible with advancing age on brain MRI, yet their relationship to morphological changes in the underlying microvessels remains poorly understood. Retinal and cerebral microvessels share morphological and physiological properties. We compared computationally-derived PVS morphologies with retinal vessel morphologies in older people.

METHODS

We analysed data from community-dwelling individuals who underwent multimodal brain MRI and retinal fundus camera imaging at mean age 72.55 years (SD=0.71). We assessed centrum semiovale PVS computationally to determine PVS total volume and count, and mean per-subject individual PVS length, width and size. We analysed retinal images using the VAMPIRE software suite, obtaining the Central Retinal Artery and Vein Equivalents (CRVE and CRAE), Arteriole-to-Venule ratio (AVR), and fractal dimension (FD) of both eyes. We investigated associations using general linear models, adjusted for age, gender, and major vascular risk factors.

RESULTS

In 381 subjects with all measures, increasing total PVS volume and count were associated with decreased CRAE in the left eye (volume β=-0.170, count β=-0.184, p<0.001). No associations of PVS with CRVE were found. The PVS total volume, individual width and size increased with decreasing FD of the arterioles (a) and venules (v) of the left eye (total volume: FDa β=-0.137, FDv β=-0.139, p<0.01; width: FDa β=-0.144, FDv β=-0.158, p<0.01; size: FDa β=-0.157, FDv β=-0.162, p<0.01).

CONCLUSIONS

Increase in PVS number and size visible on MRI reflect arteriolar narrowing and lower retinal arteriole and venule branching complexity, both markers of impaired microvascular health. Computationally-derived PVS metrics may be an early indicator of failing vascular health and should be tested in longitudinal studies.

Fractal dimension of cerebral white matter: A consistent feature for prediction of the cognitive performance in patients with small vessel disease and mild cognitive impairment

Patients with cerebral small vessel disease (SVD) frequently show decline in cognitive performance. However, neuroimaging in SVD patients discloses a wide range of brain lesions and alterations so that it is often difficult to understand which of these changes are the most relevant for cognitive decline. It has also become evident that visually-rated alterations do not fully explain the neuroimaging correlates of cognitive decline in SVD. Fractal dimension (FD), a unitless feature of structural complexity that can be computed from high-resolution T₁-weighted images, has been recently applied to the neuroimaging evaluation of the human brain. Indeed, white matter (WM) and cortical gray matter (GM) exhibit an inherent structural complexity that can be measured through the FD.

In our study, we included 64 patients (mean age ± standard deviation, 74.6 ± 6.9, education 7.9 ± 4.2 years, 53% males) with SVD and mild cognitive impairment (MCI), and a control group of 24 healthy subjects (mean age ± standard deviation, 72.3 ± 4.4 years, 50% males). With the aim of assessing whether the FD values of cerebral WM (WM FD) and cortical GM (GM FD) could be valuable structural predictors of cognitive performance in patients with SVD and MCI, we employed a machine learning strategy based on LASSO (least absolute shrinkage and selection operator) regression applied on a set of standard and advanced neuroimaging features in a nested cross-validation (CV) loop. This approach was aimed at 1) choosing the best predictive models, able to reliably predict the individual neuropsychological scores sensitive to attention and executive dysfunctions (prominent features of subcortical vascular cognitive impairment) and 2) identifying a features ranking according to their importance in the model through the assessment of the out-of-sample error.

For each neuropsychological test, using 1000 repetitions of LASSO regression and 5000 random permutations, we found that the statistically significant models were those for the Montreal Cognitive Assessment scores (p-value = .039), Symbol Digit Modalities Test scores (p-value = .039), and Trail Making Test Part A scores (p-value = .025). Significant prediction of these scores was obtained using different sets of neuroimaging features in which the WM FD was the most frequently selected feature.

In conclusion, we showed that a machine learning approach could be useful in SVD research field using standard and advanced neuroimaging features. Our study results raise the possibility that FD may represent a consistent feature in predicting cognitive decline in SVD that can complement standard imaging.

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White matter fractal dimension is altered in small vessel disease patients with MCI.

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White matter complexity's decrease consistently predicts worse cognitive performance.

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Fractal dimension may be a new marker of white matter damage in small vessel disease.

Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple-acquisition MRI

Fractal analysis represents a promising new approach to structural neuroimaging data, yet systematic evaluation of the fractal dimension (FD) as a marker of structural brain complexity is scarce. Here we present in-depth methodological assessment of FD estimation in structural brain MRI. On the computational side, we show that spatial scale optimization can significantly improve FD estimation accuracy, as suggested by simulation studies with known FD values. For empirical evaluation, we analyzed two recent open-access neuroimaging data sets (MASSIVE and Midnight Scan Club), stratified by fundamental image characteristics including registration, sequence weighting, spatial resolution, segmentation procedures, tissue type, and image complexity. Deviation analyses showed high repeated-acquisition stability of the FD estimates across both data sets, with differential deviation susceptibility according to image characteristics. While less frequently studied in the literature, FD estimation in T2-weighted images yielded robust outcomes. Importantly, we observed a significant impact of image registration on absolute FD estimates. Applying different registration schemes, we found that unbalanced registration induced (a) repeated-measurement deviation clusters around the registration target, (b) strong bidirectional correlations among image analysis groups, and (c) spurious associations between the FD and an index of structural similarity, and these effects were strongly attenuated by reregistration in both data sets. Indeed, differences in FD between scans did not simply track differences in structure per se, suggesting that structural complexity and structural similarity represent distinct aspects of structural brain MRI. In conclusion, scale optimization can improve FD estimation accuracy, and empirical FD estimates are reliable yet sensitive to image characteristics.