Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia

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.

Altered cortical gyrification, sulcal depth, and fractal dimension in the autism spectrum disorder comorbid attention-deficit/hyperactivity disorder than the autism spectrum disorder

Autism spectrum disorder (ASD) frequently occurs accompanied by attention-deficit/hyperactivity disorder (ADHD), which catches increasing attention. The comorbid diagnosis of ASD with ADHD (ASD + ADHD) is permitted in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-V). However, compared to autism spectrum disorder without other symptoms (ASD-only), the special neural underpinnings in ASD+ADHD remain unclear. Therefore, this study aimed to uncover the differences in cortical complexity between ASD + ADHD and ASD-only patients. A total of 114 ASD participants (i.e. containing 40 ASD + ADHD and 74 ASD-only participants) with T1-weighted magnetic resonance images were collected from the Autism Brain Imaging Data Exchange II. Afterward, a surface-based morphometry method was carried out to compare the cortical complexity (i.e. gyrification index, fractal dimension, and sulcal depth) between the ASD + ADHD and ASD-only cohorts. Results showed the increased fractal dimension in the right fusiform gyrus of the ASD + ADHD cohort in comparison to the ASD-only cohort. Moreover, the ASD + ADHD cohort exhibited increased sulcal depth in the left middle temporal gyrus/inferior temporal gyrus and right middle temporal gyrus compared to the ASD-only cohort. Last but not least, the increased gyrification index in the insula/postcentral gyrus was observed in the ASD + ADHD cohort in comparison to the ASD-only cohort. Overall, the present study contributes to the delineation of particular structural abnormalities in ASD + ADHD than ASD-only, enriching the evidence of the combined phenotype of ASD + ADHD.

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.

Reduced cortical complexity in patients with thyroid-associated ophthalmopathy

Psychical and functional disturbances of thyroid-associated ophthalmopathy (TAO) patients are drawing increasingly attention, despite the characterized ophthalmic symptoms. We aimed to investigate the alterations of structural complexity using fractal dimension (FD) analysis in patients with TAO. Thirty-nine TAO patients and 25 healthy controls underwent high-resolution 3.0 T structural brain magnetic resonance imaging (MRI). FD values of brain regions were calculated by Computational Anatomy Toolbox (CAT12) and compared between groups. The associations between clinical variables and FD values were further estimated. We found that TAO patients exhibited significantly decreased FD values in right caudal anterior cingulate cortex, right lingual gyrus, right pars orbitalis and right cuneus cortex (FDR corrected p < 0.05). FD values of right cuneus cortex were positively correlated with visual acuity, and FD values of right caudal anterior cingulate cortex were also positively correlated with cognitive performance. Meanwhile, FD values of right lingual gyrus were found to be negatively correlated with emotional function. Our study indicated disturbed cortical complexity in brain regions corresponding to known functional deficits of vision, emotion and cognition in TAO. FD might be a potential marker for reflecting the underlying neurobiological basis of TAO.

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.

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.

Changes of cerebral cortical structure and cognitive dysfunction in "healthy hemisphere" after stroke: a study about cortical complexity and sulcus patterns in bilateral ischemic adult moyamoya disease

Background

Moyamoya disease (MMD) is an uncommon cerebrovascular disease which leads to progressive stenosis and occlusion of the bilateral internal carotid artery and main intracerebral arteries. Concerns are always on how the hemisphere with infarction affects cognitive function, while little attention is paid to the role that the non-infarcted hemisphere plays. Therefore, we aimed to detect cortical indexes, especially cortical complexity in the left or right hemisphere separately in patients with MMD after stroke.

Methods

28 patients with MMD (14 males, 14 females) and 14 healthy controls were included in this study. All participants underwent cognitive tests and magnetic resonance imaging (MRI) scan. The preprocessing of three-dimensional T1 weighted images were performed by standard surface-based morphometry. Surface-based morphometry statistical analysis was carried out with a threshold of False Discovery Rate (FDR) P < 0.05 and fractal dimension (FD) was used to provide a quantitative description of cerebral cortical complexity.

Results

Widespread cognitive dysfunctions were found in MMD patient with stroke. Extensive FD reduction in the left hemisphere with right-sided infarction, mainly in the superior temporal, inferior frontal, and insula, while the post central gyrus, superior parietal, and inferior parietal gyrus also showed a wide range of significant differences (FDR corrected P < 0.05). Meanwhile, FD changes in the right hemisphere with left-sided infarction are restricted to the precuneus and cingulate isthmus (FDR corrected P < 0.05).

Conclusions

Extensive cognitive impairment was reconfirmed in Moyamoya disease with stroke, while wild and asymmetrical decrease of cortical complexity is observed on both sides. These differences could be relative to unbalanced cognitive dysfunction, and may be the result of a long-term chronic ischemia and compensatory of the contralateral hemisphere to the infarction.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12868-021-00672-x.

Corneal Healing and Recovery of Ocular Crystallinity with a Dichloromethane Extract of Sedum dendroideum D.C. in a Novel Murine Model of Ocular Pterygium

Pterygium is a corneal alteration that can cause visual impairment, which has been traditionally treated with the sap of Sedum dendroideum D.C. The pharmacological effect of a dichloromethane extract of S. dendroideum was demonstrated and implemented in a pterygium model on the healing process of corneal damage caused by phorbol esters. In mice of the ICR strain, a corneal lesion was caused by intravitreal injection of tetradecanoylphorbol acetate (TPA). The evolution of the corneal scarring process was monitored with vehicle, dexamethasone, and dichloromethane extract of S. dendroideum treatments by daily ophthalmic administration for fifteen days. The lesions were evaluated in situ with highlighted images of fluorescence of the lesions. Following treatment levels in eyeballs of IL-1α, TNF-α, and IL-10 cytokines were measured. The effective dose of TPA to produce a pterygium-like lesion was determined. The follow-up of the evolution of the scarring process allowed us to define that the treatment with S. dendroideum improved the experimental pterygium and had an immunomodulatory effect by decreasing TNF-α, IL-1α, and maintaining the level of IL-10 expression, without difference with respect to the healthy control. Traditional medical use of S. dendroideum sap to treat pterygium is fully justified by its compound composition.

Cortical Complexity in Anorexia Nervosa: A Fractal Dimension Analysis

Fractal Dimension (FD) has shown to be a promising means to describe the morphology of cortical structures across different neurologic and psychiatric conditions, displaying a good sensitivity in capturing atrophy processes. In this study, we aimed at exploring the morphology of cortical areas by means of FD in 58 female patients with Anorexia Nervosa (AN) (38 currently underweight and 20 fully recovered) and 38 healthy controls (HC). All participants underwent high-resolution MRI. Surface extraction was completed using FreeSurfer, FD was computed using the calcFD toolbox. The whole cortex mean FD value was lower in acute AN patients compared to HC (p < 0.001). Recovered AN patients did not show differences in the global FD when compared to HC. However, some brain areas showed higher FD in patients than controls, while others showed the opposite pattern. Parietal regions showed lower FD in both AN groups. In acute AN patients, the FD correlated with age (p < 0.001), body mass index (p = 0.019) and duration of illness (p = 0.011). FD seems to represent a feasible method to explore cortical complexity in patients with AN since it demonstrated to be sensitive to the effects of both severity and duration of malnutrition.

Reduced Cortical Complexity in Cirrhotic Patients with Minimal Hepatic Encephalopathy

Purpose

Gray matter volume loss, regional cortical thinning, and local gyrification index alteration have been documented in minimal hepatic encephalopathy (MHE). Fractal dimension (FD), another morphological parameter, has been widely used to describe structural complexity alterations in neurological or psychiatric disease. Here, we conducted the first study to investigate FD alterations in MHE.

Methods and Materials

We performed high-resolution structural magnetic resonance imaging on cirrhotic patients with MHE (n = 20) and healthy controls (n = 21). We evaluated their cognitive performance using the psychometric hepatic encephalopathy score (PHES). The regional FD value was calculated by Computational Anatomy Toolbox (CAT12) and compared between groups. We further estimated the association between patients' cognitive performance and FD values.

Results

MHE patients presented significantly decreased FD values in the left precuneus, left supramarginal gyrus, right caudal anterior cingulate cortex, right isthmus cingulate cortex, right insula, bilateral pericalcarine cortex, and bilateral paracentral cortex compared to normal controls. In addition, the FD values in the right isthmus cingulate cortex and right insula were shown to be positively correlated with patients' cognitive performance.

Conclusion

Aberrant cortical complexity is an additional characteristic of MHE, and FD analysis may provide novel insight into the neurobiological basis of cognitive dysfunction in MHE.

Analysis of gear surface morphology based on gray level co-occurrence matrix and fractal dimension

To investigate morphological characteristics and generation mechanism of the machined gears surface, image characteristics of machined surface morphology including profile roughness, fractal and textural characteristics were studied. the change of profile curves for the surface image is subject to the normal probability density function and the W-M function. The orientation angle of surface texture is 0°, the surface profile curves are the smoothest and have the most uniform, regular textures. When the texture orientation is 45° or 135°, the surface profile curves show large fluctuations, while surface image textures present the deepest grooves and are shown to be distributed most irregularly. Additionally, the influence mechanism of different grinding parameters on the morphological characteristics of machined surface was investigated. The quality of machined surfaces increased with the grinding speed while deteriorated with increasing radial, or axial, feed speeds.

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.

Cortical surface architecture endophenotype and correlates of clinical diagnosis of autism spectrum disorder

AIM

Prior structural magnetic resonance imaging studies demonstrated atypical gray matter characteristics in siblings of individuals with autism spectrum disorder (ASD). However, they did not clarify which aspect of gray matter is related to the endophenotype (i.e., genetic vulnerability) of ASD. Further, because they did not enroll siblings of typically developing (TD) people, they may have underestimated the difference between individuals with ASD and their unaffected siblings. The current study aimed to address these gaps.

METHODS

We recruited 30 pairs of adult male siblings (15 pairs with an ASD endophenotype and 15 pairs without) and focused on four gray matter parameters: cortical volume and three surface-based parameters (cortical thickness, fractal dimension, and sulcal depth [SD]). First, we sought to identify a pattern of an ASD endophenotype, comparing the four parameters. Then, we compared individuals with ASD and their unaffected siblings in the cortical parameters to identify neural correlates for the clinical diagnosis accounting for the difference between TD siblings.

RESULTS

A sparse logistic regression with a leave-one-pair-out cross-validation showed the SD as having the highest accuracy for the identification of an ASD endophenotype (73.3%) compared with the other three parameters. A bootstrapping analysis accounting for the difference in the SD between TD siblings showed a significantly large difference between individuals with ASD and their unaffected siblings in six out of 68 regions of interest.

CONCLUSION

This proof-of-concept study suggests that an ASD endophenotype emerges in the SD and that neural bases for ASD diagnosis can be discerned from the endophenotype when accounting for the difference between TD siblings.

Quantitative analysis of grey matter degeneration in FTD patients using fractal dimension analysis

Fractal dimension (FD) is a quantitative parameter that can characterizes the complexity of human brain tissue. Extensive grey matter (GM) pathology has been previously identified in Frontotemporal dementia (FTD) and its variants. The aim of the present study was to investigate the GM morphometric abnormalities in the behavioral variant FTD (bvFTD) and primary progressive aphasia (PPA) using FD analysis. Twenty-seven bvFTD, 12 PPA and 20 controls were studied. SPM8 was used to segment the brain into GM tissue. Then the FD values were estimated for the GM skeleton, surface and general structure in patients and controls using our previously published algorithm. We found that patients with bvFTD had significant reduction in FD values of skeleton and general structure when compared to controls. In PPA, more significant decrease in FD was noted in the whole brain and left hemisphere skeleton along with left hemisphere general structure. Only the right hemisphere skeleton had a significant correlation with total score of Frontal Systems Behavior Scale (FrSBe). The results showed that the variants of FTD are associated with disease specific morphometric complexity patterns. These results indicate that FD can be used as a biomarker for the structural changes associated with neurodegenerative diseases.

Quantification of the detailed cardiac left ventricular trabecular morphogenesis in the mouse embryo

During embryogenesis, a mammalian heart develops from a simple tubular shape into a complex 4-chamber organ, going through four distinct phases: early primitive tubular heart, emergence of trabeculations, trabecular remodeling and development of the compact myocardium. In this paper we propose a framework for standardized and subject-independent 3D regional myocardial complexity analysis, applied to analysis of the development of the mouse left ventricle. We propose a standardized subdivision of the myocardium into 3D overlapping regions (in our case 361) and a novel visualization of myocardial complexity, whereupon we: 1) extend the fractal dimension, commonly applied to image slices, to 3D and 2) use volume occupied by the trabeculations in each region together with their surface area, in order to quantify myocardial complexity. The latter provides an intuitive characterization of the complexity, given that compact myocardium will tend to occupy a larger volume with little surface area while high surface area with low volume will correspond to highly trabeculated areas. Using 50 mouse embryo images at 5 different gestational ages (10 subjects per gestational age), we demonstrate how the proposed representation and complexity measures describe the development of LV myocardial complexity. The mouse embryo data was acquired using high resolution episcopic microscopy. The complexity analysis per region was carried out using: 3D fractal dimension, myocardial volume, myocardial surface area and ratio between the two. The analysis of gestational ages was performed on embryos of 14.5, 15.5, 16.5, 17.5 and 18.5 embryonic days, and demonstrated that the regional complexity of the trabeculations increases longitudinally from the base to the apex, with a maximum around the middle. The overall complexity decreases with gestational age, being most complex at 14.5. Circumferentially, at ages 14.5, 15.5 and 16.5, the trabeculations show similar complexity everywhere except for the anteroseptal and inferolateral area of the wall, where it is smaller. At 17.5 days, the regions of high complexity become more localized towards the inferoseptal and anterolateral parts of the wall. At 18.5 days, the high complexity area exhibits further localization at the inferoseptal and anterior part of the wall.

Reduced structural complexity of the right cerebellar cortex in male children with autism spectrum disorder

The cerebellum contains 80% of all neurons in the human brain and contributes prominently to implicit learning and predictive processing across motor, sensory, and cognitive domains. As morphological features of the cerebellum in atypically developing individuals remain unexplored in-vivo, this is the first study to use high-resolution 3D fractal analysis to estimate fractal dimension (FD), a measure of structural complexity of an object, of the left and right cerebellar cortex (automatically segmented from Magnetic Resonance Images using FreeSurfer), in male children with Autism Spectrum Disorders (ASD) (N = 20; mean age: 8.8 years old, range: 7.13-10.27) and sex, age, verbal-IQ, and cerebellar volume-matched typically developing (TD) boys (N = 18; mean age: 8.9 years old, range: 6.47-10.52). We focus on an age range within the 'middle and late childhood' period of brain development, between 6 and 12 years. A Mann-Whitney U test revealed a significant reduction in the FD of the right cerebellar cortex in ASD relative to TD boys (P = 0.0063, Bonferroni-corrected), indicating flatter and less regular surface protrusions in ASD relative to TD males. Consistent with the prediction that the cerebellum participates in implicit learning, those ASD boys with a higher (vs. lower) PIQ>VIQ difference showed higher, more normative complexity values, closer to TD children, providing new insight on our understanding of the neurological basis of differences in verbal and performance cognitive abilities that often characterize individuals with ASD.

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.

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.

Age-related differences in the structural complexity of subcortical and ventricular structures

It has been well established that the volume of several subcortical structures decreases in relation to age. Different metrics of cortical structure (e.g., volume, thickness, surface area, and gyrification) have been shown to index distinct characteristics of interindividual differences; thus, it is important to consider the relation of age to multiple structural measures. Here, we compare age-related differences in subcortical and ventricular volume to those differences revealed with a measure of structural complexity, quantified as fractal dimensionality. Across 3 large data sets, totaling nearly 900 individuals across the adult lifespan (aged 18-94 years), we found greater age-related differences in complexity than volume for the subcortical structures, particularly in the caudate and thalamus. The structural complexity of ventricular structures was not more strongly related to age than volume. These results demonstrate that considering shape-related characteristics improves sensitivity to detect age-related differences in subcortical structures.