Fractal dimension and white matter changes in multiple sclerosis

Differing patterns of cortical grey matter pathology identified by multifractal analysis in UMN-predominant ALS patients with and without corticospinal tract hyperintensity

The pathological hallmarks of amyotrophic lateral sclerosis (ALS) are degeneration of the primary motor cortex grey matter (GM) and corticospinal tract (CST) resulting in upper motor neuron (UMN) dysfunction. Conventional brain magnetic resonance imaging (MRI) shows abnormal CST hyperintensity in some UMN-predominant ALS patients (ALS-CST+) but not in others (ALS-CST-). In addition to the CST differences, we aimed to determine whether GM degeneration differs between ALS-CST+ and ALS-CST- patients by cortical thickness (CT), voxel-based morphometry (VBM) and fractal dimension analyses. We hypothesized that MRI multifractal (MF) measures could differentiate between neurologic controls (n = 14) and UMN-predominant ALS patients as well as between patient subgroups (ALS-CST+, n = 21 vs ALS-CST-, n = 27). No significant differences were observed in CT or GM VBM in any brain regions between patients and controls or between ALS subgroups. MF analyses were performed separately on GM of the whole brain, of frontal, parietal, occipital, and temporal lobes as well as of cerebellum. Estimating MF measures D (Q = 0), D (Q = 1), D (Q = 2), Δf, Δα of frontal lobe GM classified neurologic controls, ALS-CST+ and ALS-CST- groups with 98% accuracy and > 95% in F1, recall, precision and specificity scores. Classification accuracy was only 74% when using whole brain MF measures and < 70% for other brain lobes. We demonstrate that MF analysis can distinguish UMN-predominant ALS subgroups based on GM changes, which the more commonly used quantitative approaches of CT and VBM cannot.

Fractal Analysis in Neurodegenerative Diseases

Neurodegenerative diseases are defined by progressive nervous system dysfunction and death of neurons. The abnormal conformation and assembly of proteins is suggested to be the most probable cause for many of these neurodegenerative disorders, leading to the accumulation of abnormally aggregated proteins, for example, amyloid β (Aβ) (Alzheimer's disease and vascular dementia), tau protein (Alzheimer's disease and frontotemporal lobar degeneration), α-synuclein (Parkinson's disease and Lewy body dementia), polyglutamine expansion diseases (Huntington disease), or prion proteins (Creutzfeldt-Jakob disease). An aberrant gain-of-function mechanism toward excessive intraparenchymal accumulation thus represents a common pathogenic denominator in all these proteinopathies. Moreover, depending upon the predominant brain area involvement, these different neurodegenerative diseases lead to either movement disorders or dementia syndromes, although the underlying mechanism(s) can sometimes be very similar, and on other occasions, clinically similar syndromes can have quite distinct pathologies. Non-Euclidean image analysis approaches such as fractal dimension (FD) analysis have been applied extensively in quantifying highly variable morphopathological patterns, as well as many other connected biological processes; however, their application to understand and link abnormal proteinaceous depositions to other clinical and pathological features composing these syndromes is yet to be clarified. Thus, this short review aims to present the most important applications of FD in investigating the clinical-pathological spectrum of neurodegenerative diseases.

Fractal Dimension Studies of the Brain Shape in Aging and Neurodegenerative Diseases

The fractal dimension is a morphometric measure that has been used to investigate the changes of brain shape complexity in aging and neurodegenerative diseases. This chapter reviews fractal dimension studies in aging and neurodegenerative disorders in the literature. Research has shown that the fractal dimension of the left cerebral hemisphere increases until adolescence and then decreases with aging, while the fractal dimension of the right hemisphere continues to increase until adulthood. Studies in neurodegenerative diseases demonstrated a decline in the fractal dimension of the gray matter and white matter in Alzheimer's disease, amyotrophic lateral sclerosis, and spinocerebellar ataxia. In multiple sclerosis, the white matter fractal dimension decreases, but conversely, the fractal dimension of the gray matter increases at specific stages of disease. There is also a decline in the gray matter fractal dimension in frontotemporal dementia and multiple system atrophy of the cerebellar type and in the white matter fractal dimension in epilepsy and stroke. Region-specific changes in fractal dimension have also been found in Huntington's disease and Parkinson's disease. Associations were found between the fractal dimension and clinical scores, showing the potential of the fractal dimension as a marker to monitor brain shape changes in normal or pathological processes and predict cognitive or motor function.

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.

ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research

To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration. With those notions in mind, this chapter's aim is threefold: (1) it introduces ImageJ, (2) it outlines ways this software tool has influenced fractal analysis in neuroscience and shaped the questions researchers devote time to, and (3) it reviews a few examples of ways investigators have developed and used ImageJ for pattern extraction in fractal analysis. Throughout this chapter, the focus is on fostering a collaborative and creative mindset for translating knowledge of the fractal geometry of the brain into clinical reality.

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.

Altered voxel-based and surface-based morphometry in inflammatory bowel disease

Inflammatory bowel disease (IBD), including Crohn's disease (CD) and ulcerative colitis (UC), is characterized by inflammation of the gastrointestinal tract and is a disorder of the brain-gut axis. Neuroimaging studies of brain function and structure have helped better understand the relationships between the brain, gut, and comorbidity in IBD. Studies of brain structure have primarily employed voxel-based morphometry to measure grey matter volume and surface-based morphometry to measure cortical thickness. Far fewer studies have employed other surface-based morphometry metrics such as gyrification, cortical complexity, and sulcal depth. In this study, brain structure differences between 72 adults with IBD and 90 healthy controls were assessed using all five metrics. Significant differences were found for cortical thickness with the IBD group showing extensive left-lateralized thinning, and for cortical complexity with the IBD group showing greater complexity in the left fusiform and right posterior cingulate. No significant differences were found in grey matter volume, gyrification, or sulcal depth. Within the IBD group, a post hoc analysis identified that disease duration is associated with cortical complexity of the right supramarginal gyrus, albeit with a more lenient threshold applied.

Structural brain morphology in young adult women who have been choked/strangled during sex: A whole-brain surface morphometry study

INTRODUCTION

Being choked/strangled during partnered sex is an emerging sexual behavior, particularly prevalent among young adult women. Using a multiparameter morphometric imaging approach, we aimed to characterize neuroanatomical differences between young adult women (18-30 years old) who were exposed to frequent sexual choking and their choking naïve controls.

METHODS

This cross-sectional study consisted of two groups (choking [≥4 times in the past 30 days] vs. choking-naïve group). Participants who reported being choked four or more times during sex in the past 30 days were enrolled in the choking group, whereas those without were assigned to the choking naïve group. High-resolution anatomical magnetic resonance imaging (MRI) data were analyzed using both volumetric features (cortical thickness) and geometric features (fractal dimensionality, gyrification, sulcal depth).

RESULTS

Forty-one participants (choking n = 20; choking-naïve n = 21) contributed to the final analysis. The choking group showed significantly increased cortical thickness across multiple regions (e.g., fusiform, lateral occipital, lingual gyri) compared to the choking-naïve group. Widespread reductions of the gyrification were observed in the choking group as opposed to the choking-naïve group. However, there was no group difference in sulcal depth. The fractal dimensionality showed bi-directional results, where the choking group exhibited increased dimensionality in areas including the postcentral gyrus, insula, and fusiform, whereas decreased dimensionality was observed in the bilateral superior frontal gyrus and pericalcarine cortex.

CONCLUSION

These data in cortical morphology suggest that sexual choking events may be associated with neuroanatomical alteration. A longitudinal study with multimodal assessment is needed to better understand the temporal ordering of sexual choking and neurological outcomes.

Fractal dimension: analyzing its potential as a neuroimaging biomarker for brain tumor diagnosis using machine learning

Purpose: The main purpose of this study was to comprehensively investigate the potential of fractal dimension (FD) measures in discriminating brain gliomas into low-grade glioma (LGG) and high-grade glioma (HGG) by examining tumor constituents and non-tumorous gray matter (GM) and white matter (WM) regions. Methods: Retrospective magnetic resonance imaging (MRI) data of 42 glioma patients (LGG, n = 27 and HGG, n = 15) were used in this study. Using MRI, we calculated different FD measures based on the general structure, boundary, and skeleton aspects of the tumorous and non-tumorous brain GM and WM regions. Texture features, namely, angular second moment, contrast, inverse difference moment, correlation, and entropy, were also measured in the tumorous and non-tumorous regions. The efficacy of FD features was assessed by comparing them with texture features. Statistical inference and machine learning approaches were used on the aforementioned measures to distinguish LGG and HGG patients. Results: FD measures from tumorous and non-tumorous regions were able to distinguish LGG and HGG patients. Among the 15 different FD measures, the general structure FD values of enhanced tumor regions yielded high accuracy (93%), sensitivity (97%), specificity (98%), and area under the receiver operating characteristic curve (AUC) score (98%). Non-tumorous GM skeleton FD values also yielded good accuracy (83.3%), sensitivity (100%), specificity (60%), and AUC score (80%) in classifying the tumor grades. These measures were also found to be significantly (p < 0.05) different between LGG and HGG patients. On the other hand, among the 25 texture features, enhanced tumor region features, namely, contrast, correlation, and entropy, revealed significant differences between LGG and HGG. In machine learning, the enhanced tumor region texture features yielded high accuracy, sensitivity, specificity, and AUC score. Conclusion: A comparison between texture and FD features revealed that FD analysis on different aspects of the tumorous and non-tumorous components not only distinguished LGG and HGG patients with high statistical significance and classification accuracy but also provided better insights into glioma grade classification. Therefore, FD features can serve as potential neuroimaging biomarkers for glioma.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Analyzing global features of magnetic resonance images in widespread neurodegenerative diseases: new hope to understand brain mechanism and robust neurodegenerative disease diagnosis

Neurodegenerative diseases are caused by progressive degeneration of the central nervous system (CNS)'s neuronal structure. Well-known diseases in this category include Alzheimer's disease (AD), Parkinson's disease (PD), and multiple sclerosis (MS), which are also addressed in this study. The CNS appears to be a complex dynamic system, whose parameters change during the disease due to neuronal damage, resulting in various symptoms. Since the change in dynamic behavior is due to the neurons' death and change in neurons' connectivity, brain images of the affected areas appear to provide a good understanding of this change. This work attempts to focus on brain magnetic resonance images (MRI) and examine the effect of neuronal loss on the images. To this end, the complex features of these images, including 2D and Higuchi's fractal dimensions (HFD), correlation dimension (CD), largest Lyapunov exponent (LLE), and approximate entropy (ApEn) were calculated. Despite small differences in numerical values (0.01-0.35), these values differ significantly. This shows that the brain dynamic system behaves and functions differently in the disease state, which is clear in the behavior of global features. These three diseases have the same functional pattern, and this study seems to have captured the roots of these seemingly variant diseases.

Hypometabolic and hypermetabolic brain regions in patients with ALS-FTD show distinct patterns of grey and white matter degeneration: A pilot multimodal neuroimaging study

BACKGROUND

Up to 50% of amyotrophic lateral sclerosis (ALS) patients develop some degree of cognitive dysfunction and a small proportion of these develop frontotemporal dementia (FTD). Non-invasive techniques of magnetic resonance imaging (MRI) and [¹⁸F]-fluoro-2-deoxy-d-glucose (¹⁸F-FDG) positron emission tomography (PET) have demonstrated structural and metabolic abnormalities, respectively, in the brains of such patients with ALS-FTD. Although initial ¹⁸F-FDG PET studies in ALS patients showed only hypometabolism of motor and extramotor brain regions, subsequent studies have demonstrated hypermetabolic changes as well. Such contrasting findings prompted us to hypothesize that hypo- and hypermetabolic brain regions in ALS-FTD patients are associated with divergent degeneration of structural grey matter (GM) and white matter (WM).

METHODS

Cerebral glucose metabolic rate (CMR_glc), cortical thickness (CT), fractal dimension (FD), and graph theory WM network analyses were performed on clinical MRI and ¹⁸F-FDG PET images from 8 ALS-FTD patients and 14 neurologic controls to explore the relationship between GM-WM degeneration and hypo- and hypermetabolic brain regions.

RESULTS

CMR_glc revealed significant hypometabolism in frontal and precentral gyrus brain regions, with hypermetabolism in temporal, occipital and cerebellar regions. Cortical thinning was noted in both hypo- and hypermetabolic brain areas. Unlike CT, FD did not reveal widespread GM degeneration in hypo- and hypermetabolic brain regions of ALS-FTD patients. Graph theory analysis showed severe WM degeneration in hypometabolic but not hypermetabolic areas, especially in the right hemisphere.

CONCLUSION

Our multimodal MRI-PET study provides insights into potentially differential pathophysiological mechanisms between hypo- and hypermetabolic brain regions of ALS-FTD patients.

Using fractal dimension analysis to assess the effects of normal aging and sex on subregional cortex alterations across the lifespan from a Chinese dataset

Fractal dimension (FD) is used to quantify brain structural complexity and is more sensitive to morphological variability than other cortical measures. However, the effects of normal aging and sex on FD are not fully understood. In this study, age- and sex-related differences in FD were investigated in a sample of 448 adults age of 19–80 years from a Chinese dataset. The FD was estimated with the surface-based morphometry (SBM) approach, sex differences were analyzed on a vertex level, and correlations between FD and age were examined. Generalized additive models (GAMs) were used to characterize the trajectories of age-related changes in 68 regions based on the Desikan–Killiany atlas. The SBM results showed sex differences in the entire sample and 3 subgroups defined by age. GAM results demonstrated that the FD values of 51 regions were significantly correlated with age. The trajectories of changes can be classified into 4 main patterns. Our results indicate that sex differences in FD are evident across developmental stages. Age-related trajectories in FD are not homogeneous across the cerebral cortex. Our results extend previous findings and provide a foundation for future investigation of the underlying mechanism.

Longitudinal Effects of Combination Antiretroviral Therapy on Cognition and Neuroimaging Biomarkers in Treatment-Naïve People with HIV

BACKGROUND AND OBJECTIVES

While combination antiretroviral therapy (cART) has dramatically increased the life expectancy of people with HIV (PWH), nearly 50% develop HIV-associated neurocognitive disorders (HAND)¹. This may be due to previously uncontrolled HIV viral replication, immune activation maintained by residual viral replication² or activation from other sources^{3, 4}, or cART-associated neurotoxicity⁵. The aim of this study was to determine the effect of cART on cognition and neuroimaging biomarkers markers in people with HIV (PWH) before and after initiation of cART compared to HIV negative controls (HC) and HIV elite controllers (EC) who remain untreated.

METHODS

We recruited three groups of participants from the University of Rochester, McGovern Medical School and SUNY Upstate Medical University: 1) ART-treatment-naïve PWH; 2) age-matched HC; and 3) EC. Participants underwent brain MRI and clinical and neuropsychological assessments at baseline, one year, and two years. PWH were also assessed 12 weeks after initiating cART. Volumetric analysis and fractal dimensionality (FD) were calculated for cortical and subcortical regions. Mixed effect regressions examined the effect of group and imaging variables on cognition.

RESULTS

We enrolled 47 PWH, 58 HC, and 10 EC. At baseline, PWH had worse cognition and lower cortical volumes than HC. Cognition improved following initiation of cART and remained stable over time. Greater cortical thickness was associated with better cognition at baseline; greater FD of parietal, temporal and occipital lobes was associated with better cognition at baseline and longitudinally. At baseline, EC had worse cognition, lower cortical thickness and lower FD in all four lobes and caudate than PWH and HC. Greater cortical thickness, hippocampal volumes and FD of frontal, temporal and occipital lobes were associated with better cognition longitudinally.

CONCLUSIONS

Initiation of cART in PWH is associated with improvement in brain structure and cognition. However, significant differences persist over time compared to HC. Similar trends in EC suggest that results are due to HIV infection rather than treatment. Stronger associations between cognition and FD suggest this imaging metric may be a more sensitive marker of neuronal injury than cortical thickness and volumetric 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.

Longitudinal study of the effect of a 5-year exercise intervention on structural brain complexity in older adults. A Generation 100 substudy

Physical inactivity has been identified as an important risk factor for dementia. High levels of cardiorespiratory fitness (CRF) have been shown to reduce the risk of dementia. However, the mechanism by which exercise affects brain health is still debated. Fractal dimension (FD) is an index that quantifies the structural complexity of the brain. The purpose of this study was to investigate the effects of a 5-year exercise intervention on the structural complexity of the brain, measured through the FD, in a subset of 105 healthy older adults participating in the randomized controlled trial Generation 100 Study. The subjects were randomized into control, moderate intensity continuous training, and high intensity interval training groups. Both brain MRI and CRF were acquired at baseline and at 1-, 3- and 5-years follow-ups. Cortical thickness and volume data were extracted with FreeSurfer, and FD of the cortical lobes, cerebral and cerebellar gray and white matter were computed. CRF was measured as peak oxygen uptake (VO_2peak) using ergospirometry during graded maximal exercise testing. Linear mixed models were used to investigate exercise group differences and possible CRF effects on the brain's structural complexity. Associations between change over time in CRF and FD were performed if there was a significant association between CRF and FD. There were no effects of group membership on the structural complexity. However, we found a positive association between CRF and the cerebral gray matter FD (p < 0.001) and the temporal lobe gray matter FD (p < 0.001). This effect was not present for cortical thickness, suggesting that FD is a more sensitive index of structural changes. The change over time in CRF was associated with the change in temporal lobe gray matter FD from baseline to 5-year follow-up (p < 0.05). No association of the change was found between CRF and cerebral gray matter FD. These results demonstrated that entering old age with high and preserved CRF levels protected against loss of structural complexity in areas sensitive to aging and age-related pathology.

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.

Cortical Complexity Analyses and Their Cognitive Correlate in Alzheimer's Disease and Frontotemporal Dementia

Background:

The changes of cortical structure in Alzheimer’s disease (AD) and frontotemporal dementia (FTD) are usually described in terms of atrophy. However, neurodegenerative diseases may also affect the complexity of cortical shape, such as the fractal dimension of the brain surface.

Objective:

In this study, we aimed at assessing the regional patterns of cortical thickness and fractal dimension changes in a cross-sectional cohort of patients with AD and FTD.

Methods:

Thirty-two people with symptomatic AD-pathology (clinically probable AD, n = 18, and amyloid-positive mild cognitive impairment, n = 14), 24 with FTD and 28 healthy controls underwent high-resolution 3T structural brain MRI. Using surface-based morphometry, we created vertex-wise cortical thickness and fractal dimension maps for group comparisons and correlations with cognitive measures in AD and FTD.

Results:

In addition to the well-established pattern of cortical thinning encompassing temporoparietal regions in AD and frontotemporal areas in FTD, we observed reductions of fractal dimension encompassing cingulate areas and insula for both conditions, but specifically involving orbitofrontal cortex and paracentral gyrus for FTD (FDR p < 0.05). Correlational analyses between fractal dimension and cognition showed that these regions were particularly vulnerable with regards to memory and language impairment, especially in FTD.

Conclusion:

While the present study demonstrates globally similar patterns of fractal dimension changes in AD and FTD, we observed distinct cortical complexity correlates of cognitive domains impairment. Further studies are required to assess cortical complexity measures at earlier disease stages (e.g., in prodromal/asymptomatic carriers of FTD-related gene mutations) and determine whether fractal dimension represents a sensitive imaging marker for prevention and diagnostic strategies.

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.

Corticospinal Tract and Related Grey Matter Morphometric Shape Analysis in ALS Phenotypes: A Fractal Dimension Study

A pathological hallmark of amyotrophic lateral sclerosis (ALS) is corticospinal tract (CST) degeneration resulting in upper motor neuron (UMN) dysfunction. No quantitative test is available to easily assess UMN pathways. Brain neuroimaging in ALS promises to potentially change this through identifying biomarkers of UMN dysfunction that may accelerate diagnosis and track disease progression. Fractal dimension (FD) has successfully been used to quantify brain grey matter (GM) and white matter (WM) shape complexity in various neurological disorders. Therefore, we investigated CST and whole brain GM and WM morphometric changes using FD analyses in ALS patients with different phenotypes. We hypothesized that FD would detect differences between ALS patients and neurologic controls and even between the ALS subgroups. Neuroimaging was performed in neurologic controls (n = 14), and ALS patients (n = 75). ALS patients were assigned into four groups based on their clinical or radiographic phenotypes. FD values were estimated for brain WM and GM structures. Patients with ALS and frontotemporal dementia (ALS-FTD) showed significantly higher CST FD values and lower primary motor and sensory cortex GM FD values compared to other ALS groups. No other group of ALS patients revealed significant FD value changes when compared to neurologic controls or with other ALS patient groups. These findings support a more severe disease process in ALS-FTD patients compared to other ALS patient groups. FD value measures may be a sensitive index to evaluate GM and WM (including CST) degeneration in ALS patients.

Using Fractal Dimension Analysis with the Desikan-Killiany Atlas to Assess the Effects of Normal Aging on Subregional Cortex Alterations in Adulthood

Normal aging is associated with functional and structural alterations in the human brain. The effects of normal aging and gender on morphological changes in specific regions of the brain are unknown. The fractal dimension (FD) can be a quantitative measure of cerebral folding. In this study, we used 3D-FD analysis with the Desikan–Killiany (DK) atlas to assess subregional morphological changes in adulthood. A total of 258 participants (112 women and 146 men) aged 30–85 years participated in this study. Participants in the middle-age group exhibited a decreased FD in the lateral frontal lobes, which then spread to the temporal and parietal lobes. Men exhibited an earlier and more significant decrease in FD values, mainly in the right frontal and left parietal lobes. Men exhibited more of a decrease in FD values in the subregions on the left than those in the right, whereas women exhibited more of a decrease in the lateral subregions. Older men were at a higher risk of developing mild cognitive impairment (MCI) and exhibited age-related memory decline earlier than women. Our FD analysis using the DK atlas-based prediagnosis may provide a suitable tool for assessing normal aging and neurodegeneration between groups or in individual patients.

Brain Cortical Complexity Alteration in Amyotrophic Lateral Sclerosis: A Preliminary Fractal Dimensionality Study

Objective

Fractal dimensionality (FD) analysis provides a quantitative description of brain structural complexity. The application of FD analysis has provided evidence of amyotrophic lateral sclerosis- (ALS-) related white matter degeneration. This study is aimed at evaluating, for the first time, FD alterations in a gray matter in ALS and determining its association with clinical parameters. Materials and Methods. This study included 22 patients diagnosed with ALS and 20 healthy subjects who underwent high-resolution T1-weighted imaging scanning. Disease severity was assessed using the revised ALS Functional Rating Scale (ALSFRS-R). The duration of symptoms and rate of disease progression were also assessed. The regional FD value was calculated by a computational anatomy toolbox and compared among groups. The relationship between cortical FD values and clinical parameters was evaluated by Spearman correlation analysis.

Results

ALS patients showed decreased FD values in the left precentral gyrus and central sulcus, left circular sulcus of insula (superior segment), left cingulate gyrus and sulcus (middle-posterior part), right precentral gyrus, and right postcentral gyrus. The FD values in the right precentral gyrus were positively correlated to ALSFRS-R scores (r = 0.44 and P = 0.023), whereas negatively correlated to the rate of disease progression (r = 0.44 and P = 0.023), whereas negatively correlated to the rate of disease progression (r = 0.44 and P = 0.023), whereas negatively correlated to the rate of disease progression (

Conclusions

Our results suggest an ALS-related reduction in structural complexity involving the gray matter. FD analysis may shed more light on the pathophysiology of ALS.

Classifyber, a robust streamline-based linear classifier for white matter bundle segmentation

Virtual delineation of white matter bundles in the human brain is of paramount importance for multiple applications, such as pre-surgical planning and connectomics. A substantial body of literature is related to methods that automatically segment bundles from diffusion Magnetic Resonance Imaging (dMRI) data indirectly, by exploiting either the idea of connectivity between regions or the geometry of fiber paths obtained with tractography techniques, or, directly, through the information in volumetric data. Despite the remarkable improvement in automatic segmentation methods over the years, their segmentation quality is not yet satisfactory, especially when dealing with datasets with very diverse characteristics, such as different tracking methods, bundle sizes or data quality. In this work, we propose a novel, supervised streamline-based segmentation method, called Classifyber, which combines information from atlases, connectivity patterns, and the geometry of fiber paths into a simple linear model. With a wide range of experiments on multiple datasets that span from research to clinical domains, we show that Classifyber substantially improves the quality of segmentation as compared to other state-of-the-art methods and, more importantly, that it is robust across very diverse settings. We provide an implementation of the proposed method as open source code, as well as web service.

Alteration of the Intra- and Inter-Lobe Connectivity of the Brain Structural Network in Normal Aging

The morphological changes in cortical parcellated regions during aging and whether these atrophies may cause brain structural network intra- and inter-lobe connectivity alterations are subjects that have been minimally explored. In this study, a novel fractal dimension-based structural network was proposed to measure atrophy of 68 parcellated cortical regions. Alterations of structural network parameters, including intra- and inter-lobe connectivity, were detected in a middle-aged group (30–45 years old) and an elderly group (50–65 years old). The elderly group exhibited significant lateralized atrophy in the left hemisphere, and most of these fractal dimension atrophied regions were included in the regions of the “last-in, first-out” model. Globally, the elderly group had lower modularity values, smaller component size modules, and fewer bilateral association fibers. They had lower intra-lobe connectivity in the frontal and parietal lobes, but higher intra-lobe connectivity in the temporal and occipital lobes. Both groups exhibited similar inter-lobe connecting pattern. The elderly group revealed separations, sparser long association fibers, commissural fibers, and lateral inter-lobe connectivity lost effect, mainly in the right hemisphere. New wiring and reconfiguring modules may have occurred within the brain structural network to compensate for connectivity, decreasing and preventing functional loss in cerebral intra- and inter-lobe connectivity.

Supratentorial and Infratentorial Lesions in Spinocerebellar Ataxia Type 3

Background: Spinocerebellar ataxia type 3 (SCA) is a cerebellum-dominant degenerative disorder that is characterized primarily by infratentorial damage, although less severe supratentorial involvement may contribute to the clinical manifestation. These impairments may result from the efferent loss of the cerebellar cortex and degeneration of the cerebral cortex. Method: We used the three-dimensional fractal dimension (3D-FD) method to quantify the morphological changes in the supratentorial regions and assessed atrophy in the relatively focal regions in patients with SCA3. A total of 48 patients with SCA3 and 50 sex- and age-matched healthy individuals, as the control group, participated in this study. The 3D-FD method was proposed to distinguish 97 automatic anatomical label regions of gray matter (left cerebrum: 45, right cerebrum: 45, cerebellum: 7) between healthy individuals and patients with SCA3. Results: Patients with SCA3 exhibited reduced brain complexity within both the traditional olivopontocerebellar atrophy (OPCA) pattern and specific supratentorial regions. The study results confirmed the extensive involvement of extracerebellar regions in SCA3. The atrophied regions of SCA3 in infratentorial and supratentorial cortex showed a wide range of overlapped areas as in two functional cortexes, namely cerebellum-related cortex and basal ganglia-related cortex. Conclusions: Our results found that the atrophy of the SCA3 are not only limited in the infratentorial regions. Both cerebellar related cortex and basal ganglia related cortex were affected in the disease process of SCA3. Our findings might correlate to the common symptoms of SCA3, such as ataxia, Parkinsonism, dysarthria, and dysmetria. SCA3 should no longer be considered a disease limited to the cerebellum and its connections; rather, it should be considered a pathology affecting the whole brain.

Fractal dimension brain morphometry: a novel approach to quantify white matter in traumatic brain injury

Traumatic brain injury (TBI) is the main cause of disability in people younger than 35 in the United States. The mechanisms of TBI are complex resulting in both focal and diffuse brain damage. Fractal dimension (FD) is a measure that can characterize morphometric complexity and variability of brain structure especially white matter (WM) structure and may provide novel insights into the injuries evident following TBI. FD-based brain morphometry may provide information on WM structural changes after TBI that is more sensitive to subtle structural changes post injury compared to conventional MRI measurements. Anatomical and diffusion tensor imaging (DTI) data were obtained using a 3 T MRI scanner in subjects with moderate to severe TBI and in healthy controls (HC). Whole brain WM volume, grey matter volume, cortical thickness, cortical area, FD and DTI metrics were evaluated globally and for the left and right hemispheres separately. A neuropsychological test battery sensitive to cognitive impairment associated with traumatic brain injury was performed. TBI group showed lower structural complexity (FD) bilaterally (p < 0.05). No significant difference in either grey matter volume, cortical thickness or cortical area was observed in any of the brain regions between TBI and healthy controls. No significant differences in whole brain WM volume or DTI metrics between TBI and HC groups were observed. Behavioral data analysis revealed that WM FD accounted for a significant amount of variance in executive functioning and processing speed beyond demographic and DTI variables. FD therefore, may serve as a sensitive marker of injury and may play a role in outcome prediction in TBI.

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.

Unbiased MRI Analyses Identify Micropathologic Differences Between Upper Motor Neuron-Predominant ALS Phenotypes

Amyotrophic lateral sclerosis (ALS) is an incurable and progressively fatal neurodegenerative disease that manifests with distinct clinical phenotypes, which are seen in neuroimaging, and clinical studies. T2- and proton density (PD)-weighted magnetic resonance imaging (MRI) displays hyperintense signal along the corticospinal tract (CST) in some ALS patients with upper motor neuron (UMN)-predominant signs. These patients tend to be younger and have significantly faster disease progression. We hypothesize that such ALS patients with CST hyperintensity (ALS-CST+) comprise a clinical subtype distinct from other ALS subtypes, namely patients with UMN-predominant ALS without CST hyperintensity, classic ALS, and ALS with frontotemporal dementia (FTD). Novel approaches such as fractal dimension analysis on conventional MRI (cMRI) and advanced MR techniques such as diffusion tensor imaging (DTI) reveal significant differences between ALS-CST+ and the aforementioned ALS subtypes. Our unbiased neuroimaging studies demonstrate that the ALS-CST+ group, which can be initially identified by T2-, PD-, and FLAIR-weighted cMRI, is distinctive and distinguishable from other ALS subtypes with possible differences in disease pathogenesis.

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.

Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension

The fractal dimension (FD) is calculated for seven species of the genus Quercus L. in Calabria region (southern Italy), five of which have a marcescent-deciduous and two a sclerophyllous character. The fractal analysis applied to the leaves reveals different FD values for the two groups. The difference between the means and medians is very small in the case of the marcescent-deciduous group and very large when these differences are established between both groups: all this highlights the distance between the two groups in terms of similarity. Specifically, Q.crenata, which is hybridogenic in origin and whose parental species are Q.cerris and Q.suber, is more closely related to Q.cerris than to Q.suber, as also expressed in the molecular analysis. We consider that, in combination with other morphological, physiological and genetic parameters, the fractal dimension is a useful tool for studying similarities amongst species.

Fractal Dimension Analysis of High-Resolution X-Ray Phase Contrast Micro-Tomography Images at Different Threshold Levels in a Mouse Spinal Cord

Fractal analysis is a powerful method for the morphological study of complex systems that is increasingly applied to biomedical images. Spatial resolution and image segmentation are crucial for the discrimination of tissue structures at the multiscale level. In this work, we have applied fractal analysis to high-resolution X-ray phase contrast micro-tomography (XrPCμT) images in both uninjured and injured tissue of a mouse spinal cord. We estimated the fractal dimension (FD) using the box-counting method on tomographic slices segmented at different threshold levels. We observed an increased FD in the ipsilateral injured hemicord compared with the contralateral uninjured tissue, which was almost independent of the chosen threshold. Moreover, we found that images exhibited the highest fractality close to the global histogram threshold level. Finally, we showed that the FD estimate largely depends on the image histogram regardless of tissue appearance. Our results demonstrate that the pre-processing of XrPCμT images is critical to fractal analysis and the estimation of FD.

Structural Complexity of the Cerebellum and Cerebral Cortex is Reduced in Spinocerebellar Ataxia Type 2

BACKGROUND AND PURPOSE

Fractal dimension (FD) is an index of structural complexity of cortical gray matter (GM) and white matter (WM). Application of FD to pontocerebellar degeneration has revealed cerebellar changes. However, so far, possible concurrent cerebral changes and progression of changes in brain complexity have not been investigated.

METHODS

We computed FD of cerebellar and cerebral cortex and WM derived from longitudinal brain MRI of patients with spinocerebellar ataxia type 2 (SCA2), which is an inherited cause of pontocerebellar degeneration. Nine SCA2 patients and 16 age-matched healthy controls were examined twice (3.6 ± .7 and 3.3 ± 1.0 years apart, respectively) on the same 1.5T MR scanner with T1-weighted imaging. Cortical GM and WM of the cerebrum and cerebellum were segmented using FreeSurfer and FD of these segmentations were computed.

RESULTS

At baseline, FD values of cerebellar GM and WM were significantly (P < .001) lower in SCA2 patients (2.48 ± .04 for GM and 1.74 ± .09 for WM) than in controls (2.56 ± .02 for GM and 2.22 ± .19 for WM). Also, FD values of cerebral GM were significantly (P < .05) lower in SCA2 patients (2.39 ± .03) than in controls (2.43 ± .02). No significant differences were observed for FD of the cerebral WM. The rate of change of FD values was not significantly different between SCA2 patients and controls.

CONCLUSIONS

The structural complexity of the cerebellum and cerebral cortex is reduced in SCA2 patients. Fractal analysis seems not to be able to demonstrate progression of changes associated with degeneration in SCA2.

Age is reflected in the Fractal Dimensionality of MRI Diffusion Based Tractography

Fractal analysis is a widely used tool to analyze the geometrical complexity of biological structures. The geometry of natural objects such as plants, clouds, cellular structures, blood vessel, and many others cannot be described sufficiently with Euclidian geometric properties, but can be represented by a parameter called the fractal dimension. Here we show that a specific estimate of fractal dimension, the correlation dimension, is able to describe changes in the structural complexity of the human brain, based on data from magnetic resonance diffusion imaging. White matter nerve fiber bundles, represented by tractograms, were analyzed with regards to geometrical complexity, using fractal geometry. The well-known age-related change of white matter tissue was used to verify changes by means of fractal dimension. Structural changes in the brain were successfully be observed and quantified by fractal dimension and compared with changes in fractional anisotropy.

Complexity analysis of cortical surface detects changes in future Alzheimer's disease converters

Alzheimer's disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study, we investigate spherical harmonic-based FD (SHFD), thickness, and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI converters and 29 MCI nonconverters), and 32 healthy controls (HC). SHFD, thickness, and LGI methodology allowed us to perform not only global level but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI converters compared to HC, and in MCI converters compared to MCI nonconverters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white-matter SHFD was significantly reduced in MCI converters compared to MCI nonconverters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next 4 years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD. Hum Brain Mapp 38:5905-5918, 2017. © 2017 Wiley Periodicals, Inc.

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.

Fractal dimension analysis of cerebellum in Chiari Malformation type I

Chiari Malformation type I (CM-I) is a serious neurological disorder that is characterized by hindbrain herniation. Our aim was to evaluate the usefulness of fractal analysis in CM-I patients. To examine the morphological complexity features of this disorder, fractal dimension (FD) of cerebellar regions were estimated from magnetic resonance images (MRI) of 17 patients with CM-I and 16 healthy control subjects in this study. The areas of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) were calculated and the corresponding FD values were computed using a 2D box-counting method in both groups. The results indicated that CM-I patients had significantly higher (p<0.05) FD values of GM, WM and CSF tissues compared to control group. According to the results of correlation analysis between FD values and the corresponding area values, FD and area values of GM tissues in the patients group were found to be correlated. The results of the present study suggest that FD values of cerebellar regions may be a discriminative feature and a useful marker for investigation of abnormalities in the cerebellum of CM-I patients. Further studies to explore the changes in cerebellar regions with the help of 3D FD analysis and volumetric calculations should be performed as a future work.

Change in the cortical complexity of spinocerebellar ataxia type 3 appears earlier than clinical symptoms

Patients with spinocerebellar ataxia type 3 (SCA3) have exhibited cerebral cortical involvement and various mental deficits in previous studies. Clinically, conventional measurements, such as the Mini-Mental State Examination (MMSE) and electroencephalography (EEG), are insensitive to cerebral cortical involvement and mental deficits associated with SCA3, particularly at the early stage of the disease. We applied a three-dimensional fractal dimension (3D-FD) method, which can be used to quantify the shape complexity of cortical folding, in assessing cortical degeneration. We evaluated 48 genetically confirmed SCA3 patients by employing clinical scales and magnetic resonance imaging and using 50 healthy participants as a control group. According to the Scale for the Assessment and Rating of Ataxia (SARA), the SCA3 patients were diagnosed with cortical dysfunction in the cerebellar cortex; however, no significant difference in the cerebral cortex was observed according to the patients’ MMSE ratings. Using the 3D-FD method, we determined that cortical involvement was more extensive than involvement of traditional olivopontocerebellar regions and the corticocerebellar system. Moreover, the significant correlation between decreased 3D-FD values and disease duration may indicate atrophy of the cerebellar cortex and cerebral cortex in SCA3 patients. The change of the cerebral complexity in the SCA3 patients can be detected throughout the disease duration, especially it becomes substantial at the late stage of the disease. Furthermore, we determined that atrophy of the cerebral cortex may occur earlier than changes in MMSE scores and EEG signals.

Fractals in the Neurosciences, Part II

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Application of fractal and grey level co-occurrence matrix analysis in evaluation of brain corpus callosum and cingulum architecture

This aim of this study was to assess the discriminatory value of fractal and grey level co-occurrence matrix (GLCM) analysis methods in standard microscopy analysis of two histologically similar brain white mass regions that have different nerve fiber orientation. A total of 160 digital micrographs of thionine-stained rat brain white mass were acquired using a Pro-MicroScan DEM-200 instrument. Eighty micrographs from the anterior corpus callosum and eighty from the anterior cingulum areas of the brain were analyzed. The micrographs were evaluated using the National Institutes of Health ImageJ software and its plugins. For each micrograph, seven parameters were calculated: angular second moment, inverse difference moment, GLCM contrast, GLCM correlation, GLCM variance, fractal dimension, and lacunarity. Using the Receiver operating characteristic analysis, the highest discriminatory value was determined for inverse difference moment (IDM) (area under the receiver operating characteristic (ROC) curve equaled 0.925, and for the criterion IDM≤0.610 the sensitivity and specificity were 82.5 and 87.5%, respectively). Most of the other parameters also showed good sensitivity and specificity. The results indicate that GLCM and fractal analysis methods, when applied together in brain histology analysis, are highly capable of discriminating white mass structures that have different axonal orientation.

Age- and sex-related variations in the brain white matter fractal dimension throughout adulthood: an MRI study

PURPOSE

To observe age- and sex-related differences in the complexity of the global and hemispheric white matter (WM) throughout adulthood by means of fractal dimension (FD).

METHODS

A box-counting algorithm was used to extract FD from the WM magnetic resonance images of 209 healthy adults from three structural layers, including general (gFD), skeleton (sFD), and boundaries (bFD). Model selection algorithms and statistical analyses, respectively, were used to examine the patterns and significance of the changes.

RESULTS

gFD and sFD showed inverse U-shape patterns with aging, with a slighter slope of increase from young to mid-age and a steeper decrease to the old. bFD was less affected by age. Sex differences were evident, specifically in gFD and sFD, with men showing higher FDs. Age × sex interaction was significant mainly in the hemispheric analysis, with men undergoing sharper age-related changes. After adjusting for the volume effect, age-related results remained approximately the same, but sex differences changed in most of the features, with women indicating higher values, specifically in the left hemisphere and boundaries. Right hemisphere was still more complex in men.

CONCLUSIONS

This study is the first that investigates the WM FD spanning adulthood, treating age both as a continuous and categorical variable. We found positive correlations between FD and volume, and our results show similarities with those investigating small-world properties of the brain networks, as well as those of functional complexity and WM integrity. These suggest that FD could yield a highly compact description of the structural changes and also might inform us about functional and cognitive variations.

Brain white matter shape changes in amyotrophic lateral sclerosis (ALS): a fractal dimension study

Amyotrophic lateral sclerosis (ALS) is a fatal progressive neurodegenerative disorder. Current diagnosis time is about 12-months due to lack of objective methods. Previous brain white matter voxel based morphometry (VBM) studies in ALS reported inconsistent results. Fractal dimension (FD) has successfully been used to quantify brain WM shape complexity in various neurological disorders and aging, but not yet studied in ALS. Therefore, we investigated WM morphometric changes using FD analyses in ALS patients with different clinical phenotypes. We hypothesized that FD would better capture clinical features of the WM morphometry in different ALS phenotypes than VBM analysis. High resolution MRI T1-weighted images were acquired in controls (n = 11), and ALS patients (n = 89). ALS patients were assigned into four subgroups based on their clinical phenotypes.VBM analysis was carried out using SPM8. FD values were estimated for brain WM skeleton, surface and general structure in both controls and ALS patients using our previously published algorithm. No significant VBM WM changes were observed between controls and ALS patients and among the ALS subgroups. In contrast, significant (p<0.05) FD reductions in skeleton and general structure were observed between ALS with dementia and other ALS subgroups. No significant differences in any of the FD measures were observed between control and ALS patients. FD correlated significantly with revised ALS functional rating scale (ALSFRS-R) score a clinical measure of function. Results suggest that brain WM shape complexity is more sensitive to ALS disease process when compared to volumetric VBM analysis and FD changes are dependent on the ALS phenotype. Correlation between FD and clinical measures suggests that FD could potentially serve as a biomarker of ALS pathophysiology, especially after confirmation by longitudinal studies.

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the gray matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9-0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies.

Relevance of magnetic resonance imaging for early detection and diagnosis of Alzheimer disease

Hippocampus volumetry currently is the best-established imaging biomarker for AD. However, the effect of multicenter acquisition on measurements of hippocampus volume needs to be explicitly considered when it is applied in large clinical trials, for example by using mixed-effects models to take the clustering of data within centers into account. The marker needs further validation in respect of the underlying neurobiological substrate and potential confounds such as vascular disease, inflammation, hydrocephalus, and alcoholism, and with regard to clinical outcomes such as cognition but also to demographic and socioeconomic outcomes such as mortality and institutionalization. The use of hippocampus volumetry for risk stratification of predementia study samples will further increase with the availability of automated measurement approaches. An important step in this respect will be the development of a standard hippocampus tracing protocol that harmonizes the large range of presently available manual protocols. In the near future, regionally differentiated automated methods will become available together with an appropriate statistical model, such as multivariate analysis of deformation fields, or techniques such as cortical-thickness measurements that yield a meaningful metrics for the detection of treatment effects. More advanced imaging protocols, including DTI, DSI, and functional MRI, are presently being used in monocenter and first multicenter studies. In the future these techniques will be relevant for the risk stratification in phase IIa type studies (small proof-of-concept trials). By contrast, the application of the broader established structural imaging biomarkers, such as hippocampus volume, for risk stratification and as surrogate end point is already today part of many clinical trial protocols. However, clinical care will also be affected by these new technologies. Radiologic expert centers already offer “dementia screening” for well-off middle-aged people who undergo an MRI scan with subsequent automated, typically VBM-based analysis, and determination of z-score deviation from a matched control cohort. Next-generation scanner software will likely include radiologic expert systems for automated segmentation, deformation-based morphometry, and multivariate analysis of anatomic MRI scans for the detection of a typical AD pattern. As these developments will start to change medical practice, first for selected subject groups that can afford this type of screening but later eventually also for other cohorts, clinicians must become aware of the potentials and limitations of these technologies. It is decidedly unclear to date how a middle-aged cognitively intact subject with a seemingly AD-positive MRI scan should be clinically advised. There is no evidence for individual risk prediction and even less for specific treatments. Thus, the development of preclinical diagnostic imaging poses not only technical but also ethical problems that must be critically discussed on the basis of profound knowledge. From a neurobiological point of view, the main determinants of cognitive impairment in AD are the density of synapses and neurons in distributed cortical and subcortical networks. MRI-based measures of regional gray matter volume and associated multivariate analysis techniques of regional interactions of gray matter densities provide insight into the onset and temporal dynamics of cortical atrophy as a close proxy for regional neuronal loss and a basis of functional impairment in specific neuronal networks. From the clinical point of view, clinicians must bear in mind that patients do not suffer from hippocampus atrophy or disconnection but from memory impairment, and that dementia screening in asymptomatic subjects should not be used outside of clinical studies.

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.