Fractal dimension in human cerebellum measured by magnetic resonance imaging

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.

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.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

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.

BrainFD: Measuring the Intracranial Brain Volume With Fractal Dimension

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

Left Cerebral Cortex Complexity in Patients with Major Depression Disorder: A Small-Sample Pilot Study

Objective

To investigate cerebral cortical complexity (CCC) in patients with first-episode, drug-naive major depressive disorder (MDD) with source-based morphometry (SBM) analyses.

Methods

We used the SBM parameters gyrification index (GI) and fractal dimension (FD) to evaluate CCC in 14 first-episode, drug-naive patients diagnosed with MDD. The severity of depression symptoms was assessed with the 17-item Hamilton Depression Scale (HAMD-17). GI and FD alterations in the MDD group, relative to healthy controls (HCs), were correlated with depression symptom severity with GI/FD.

Results

Increased GIs in the MDD group, relative to HCs, were found mainly in the left postcentral gyrus, whereas GI reductions were found in the left angular gyrus, left lingual gyrus, left superior temporal gyrus, and left insular cortex. Increased FDs in the MDD group, relative to HCs, were located in the superior frontal gyrus. In contrast, decreased FDs were located in the left superior temporal gyrus and left superior frontal gyrus.

Conclusion

Although the group differences in GI and FD values obtained did not withstand family-wise error (FWE) correction, the results show a consistent trend of alterations in left-hemisphere CCC in first-episode, drug-naive patients diagnosed with MDD. These findings support the hypothesis that there is a pattern of subtle neocortical aberrations in early-stage MDD.

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

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

Atherosclerotic Plaque Tissue Characterization: An OCT-Based Machine Learning Algorithm With ex vivo Validation

There is a need to develop a validated algorithm for plaque characterization which can help to facilitate the standardization of optical coherence tomography (OCT) image interpretation of plaque morphology, and improve the efficiency and accuracy in the application of OCT imaging for the quantitative assessment of plaque vulnerability. In this study, a machine learning algorithm was implemented for characterization of atherosclerotic plaque components by intravascular OCT using ex vivo carotid plaque tissue samples. A total of 31 patients underwent carotid endarterectomy and the ex vivo carotid plaques were imaged with OCT. Optical parameter, texture features and relative position of pixels were extracted within the region of interest and then used to quantify the tissue characterization of plaque components. The potential of individual and combined feature set to discriminate tissue components was quantified using sensitivity, specificity, accuracy. The results show there was a lower classification accuracy in the calcified tissue than the fibrous tissue and lipid tissue. The pixel-wise classification accuracy obtained by the developed method, to characterize the fibrous, calcified and lipid tissue by comparing with histology, were 80.0, 62.0, and 83.1, respectively. The developed algorithm was capable of characterizing plaque components with an excellent accuracy using the combined feature set.

Nonlinear correlations in multifractals: Visibility graphs of magnitude and sign series

Correlations in a multifractal series have been investigated extensively. Almost all approaches try to find scaling features of a given time series. However, the scaling analysis has always been encountered with some difficulties. Of particular importance is finding a proper scaling region and removing the impact of the probability distribution function of the series on the correlation extraction methods. In this article, we apply the horizontal visibility graph algorithm to map a stochastic time series into networks. By investigating the magnitude and sign of a multifractal time series, we show that one can detect linear as well as nonlinear correlations, even for situations that have been considered as uncorrelated noises by typical approaches such as the multifractal detrended fluctuation analysis. Furthermore, we introduce a topological parameter that can well measure the strength of nonlinear correlations. This parameter is independent of the probability distribution function and calculated without the need to find any scaling region. Our findings may provide new insights about the multifractal analysis of a time series in a variety of complex systems.

A Model of Brain Folding Based on Strong Local and Weak Long-Range Connectivity Requirements

Throughout the animal kingdom, the structure of the central nervous system varies widely from distributed ganglia in worms to compact brains with varying degrees of folding in mammals. The differences in structure may indicate a fundamentally different circuit organization. However, the folded brain most likely is a direct result of mechanical forces when considering that a larger surface area of cortex packs into the restricted volume provided by the skull. Here, we introduce a computational model that instead of modeling mechanical forces relies on dimension reduction methods to place neurons according to specific connectivity requirements. For a simplified connectivity with strong local and weak long-range connections, our model predicts a transition from separate ganglia through smooth brain structures to heavily folded brains as the number of cortical columns increases. The model reproduces experimentally determined relationships between metrics of cortical folding and its pathological phenotypes in lissencephaly, polymicrogyria, microcephaly, autism, and schizophrenia. This suggests that mechanical forces that are known to lead to cortical folding may synergistically contribute to arrangements that reduce wiring. Our model provides a unified conceptual understanding of gyrification linking cellular connectivity and macroscopic structures in large-scale neural network models of the brain.

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.

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.

Alpha shapes: determining 3D shape complexity across morphologically diverse structures

Background

Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To use this data to address evolutionary and ecological questions, an array of tools has been developed to conduct shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose a new ‘alpha-shapes’ method for quantifying 3D shape complexity.

Methods

We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute size differences, a suite of alpha-shapes was fitted per specimen. An alpha shape is formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall ‘complexity’.

Results

Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall ‘complexity’. Alpha-shapes agrees with other measures of complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as being most complex, contrasting with other shape metrics. 3D fractal dimension is identified as an inappropriate metric of complexity when applied to bacula.

Conclusions

Alpha-shapes is used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. We interpret alpha-shapes as being particularly sensitive to concavities in surface topology, potentially distinguishing it from other shape complexity metrics. Beyond genital shape, the alpha-shapes technique holds considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.

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.

Comparison of Classical Kinematics, Entropy, and Fractal Properties As Measures of Complexity of the Motor System in Swimming

The aim of this study was to compare the non-linear properties of the four competitive swim strokes. Sixty-eight swimmers performed a set of maximal 4 × 25 m using the four competitive swim strokes. The hip's speed-data as a function of time was collected with a speedo-meter. The speed fluctuation (dv), approximate entropy (ApEn) and the fractal dimension by Higuchi's method (D) were computed. Swimming data exhibited non-linear properties that were different among the four strokes (14.048 ≤ dv ≤ 39.722; 0.682 ≤ ApEn ≤ 1.025; 1.823 ≤ D ≤ 1.919). The ApEn showed the lowest value for front-crawl, followed by breaststroke, butterfly, and backstroke (P < 0.001). Fractal dimension and dv had the lowest values for front-crawl and backstroke, followed by butterfly and breaststroke (P < 0.001). It can be concluded that swimming data exhibits non-linear properties, which are different among the four competitive swimming strokes.

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.

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.

A Web platform for the interactive visualization and analysis of the 3D fractal dimension of MRI data

This study presents a Web platform (http://3dfd.ujaen.es) for computing and analyzing the 3D fractal dimension (3DFD) from volumetric data in an efficient, visual and interactive way. The Web platform is specially designed for working with magnetic resonance images (MRIs) of the brain. The program estimates the 3DFD by calculating the 3D box-counting of the entire volume of the brain, and also of its 3D skeleton. All of this is done in a graphical, fast and optimized way by using novel technologies like CUDA and WebGL. The usefulness of the Web platform presented is demonstrated by its application in a case study where an analysis and characterization of groups of 3D MR images is performed for three neurodegenerative diseases: Multiple Sclerosis, Intrauterine Growth Restriction and Alzheimer's disease. To the best of our knowledge, this is the first Web platform that allows the users to calculate, visualize, analyze and compare the 3DFD from MRI images in the cloud.

Spatial fuzzy c-means algorithm with adaptive fuzzy exponent selection for robust vermilion border detection in healthy and diseased lower lips

INTRODUCTION

Accurate lip contour identification is demanding since variations in color, form and surface texture, even in normal lips, introduce artifacts in non-adapted segmentation algorithms. Herein, a method for vermilion border detection and quantification in healthy and diseased lower lips is presented.

AIM

To quantify the morphological irregularities of lower lip border, to validate its discriminative power in solar cheilosis diagnosis and to provide supportive tools toward, cost effective, non invasive, disease monitoring.

MATERIALS

Segmentation algorithm for lower lip border was based on spatial fuzzy c-means clustering algorithm with adaptive selection of fuzzy exponent m. Lip features measuring morphological lip border deviations were estimated. The method of lip border extraction and quantitative description was evaluated in a gold standard set of 25 young volunteers without onset of lip diseases. Quantitative descriptors were evaluated in terms of correct classification rates in differentiating 30 healthy control cases from 41 patients with solar cheilosis and were further applied to quantify the therapeutic outcome after immunocryosurgery in eight patients with solar cheilosis.

RESULTS

Adaptive estimation of fuzzy exponent m substantially boosted the segmentation quality in gold standard cases yielding quite smooth lip contours and uniformly low values of lip irregularity features. Discriminant analysis highlighted the distance between the extracted and modeled vermilion border as a feature with excellent diagnostic accuracy (sensitivity and specificity 98% and 93% respectively). Results on patients with solar cheilosis followed up after treatment with immunocryosurgery showed that proposed quantitative lip marker was able to trace the improvement of disease after treatment.

CONCLUSION

Correct lip border recognition is the prerequisite for extracting essential morphological descriptors from lips with epithelial diseases like solar cheilosis. In this paper we presented an efficient method for the automatic identification and quantitative description of lower lip vermilion border morphology in health and disease using digital photography and image analysis techniques.

The impact of Platelet Rich Plasma (PRP) in osseointegration of oral implants in dental panoramic radiography: texture based evaluation

PURPOSE

In this study the temporal texture differentiation associated with the bone formation properties, around loaded oral implants after Platelet Rich Plasma (PRP) employment, was investigated in Panoramic Radiographs.

MATERIALS AND METHODS

Thirty eligible patients are randomly assigned to two groups. The test group received PRP application around new implants, while in the control group no PRP treatment was made. The bone-to-implant contact region was analyzed in a clinical sample of 60 Digitized Panoramic Radiographs, 30 corresponding to immediate implant loading (Class-I) and 30 after an 8 month follow-up period (Class-II). This region was sampled by 1146 circular Regions-of-Interest (ROIs), resulting from a specifically designed segmentation scheme based on Markov-Random-Fields (MRF). From each ROI, 41 textural features were extracted, then reduced to a subset of 4 features due to redundancy and employed as input to Receiver-Operating-Characteristic (ROC) analysis, to assess the textural differentiation between two classes.

RESULTS

The selected subset, achieved Area-Under-Curve (AUC) values ranging from 0.77-0.81 in the PRP group, indicating the significant temporal textural differentiation has been made. In the control group, the AUC values ranged from 0.56-0.68 demonstrating lesser osseo integration activity.

CONCLUSION

This study provides evidences that PRP application may favor bone formation around loaded dental implants that could modify the dental treatment planning.

Adsorption kinetics of DPPG liposome layers: a quantitative analysis of surface roughness

Roughness of a positively charged poly(allylamine hydrochloride) (PAH) polyelectrolyte surface was shown to strongly influence the adsorption of 1.2-dipalmitoyl-sn-3-glycero-[phosphorrac-(1-glycerol)] (DPPG) liposomes on it. The adsorption kinetic curves of DPPG liposomes onto a low-roughness PAH layer reveal an adsorbed amount of 5 mg/m², pointing to liposome rupture, whereas a high-roughness surface leads to adsorbed amounts of 51 mg/m², signifying adsorption of intact liposomes. The adsorption kinetic parameters calculated from adsorption kinetic curves allow us to conclude that the adsorption process is due to electrostatic interactions and also depends on processes such as diffusion and reorganization of lipids on the surface. Analysis of the roughness kinetics enabled us to calculate a growth exponent of 0.19 ± 0.07 and a roughness exponent of around 0.84, revealing that DPPG liposomes adsorbed onto rough surfaces follow the Villain self-affine model. By relating self-affine surfaces with hydrophobicity, the liposome integrity was explained by the reduction in the number of water molecules on the PAH surface, contributing to counterion anchorage near PAH ionic groups, reducing the liposome/PAH layer electrostatic forces and, consequently, avoiding liposome rupture.

Coercively adjusted auto regression model for forecasting in epilepsy EEG

Recently, data with complex characteristics such as epilepsy electroencephalography (EEG) time series has emerged. Epilepsy EEG data has special characteristics including nonlinearity, nonnormality, and nonperiodicity. Therefore, it is important to find a suitable forecasting method that covers these special characteristics. In this paper, we propose a coercively adjusted autoregression (CA-AR) method that forecasts future values from a multivariable epilepsy EEG time series. We use the technique of random coefficients, which forcefully adjusts the coefficients with −1 and 1. The fractal dimension is used to determine the order of the CA-AR model. We applied the CA-AR method reflecting special characteristics of data to forecast the future value of epilepsy EEG data. Experimental results show that when compared to previous methods, the proposed method can forecast faster and accurately.

Fast box-counting algorithm on GPU

The box-counting algorithm is one of the most widely used methods for calculating the fractal dimension (FD). The FD has many image analysis applications in the biomedical field, where it has been used extensively to characterize a wide range of medical signals. However, computing the FD for large images, especially in 3D, is a time consuming process. In this paper we present a fast parallel version of the box-counting algorithm, which has been coded in CUDA for execution on the Graphic Processing Unit (GPU). The optimized GPU implementation achieved an average speedup of 28 times (28×) compared to a mono-threaded CPU implementation, and an average speedup of 7 times (7×) compared to a multi-threaded CPU implementation. The performance of our improved box-counting algorithm has been tested with 3D models with different complexity, features and sizes. The validity and accuracy of the algorithm has been confirmed using models with well-known FD values. As a case study, a 3D FD analysis of several brain tissues has been performed using our GPU box-counting algorithm.

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.

UJA-3DFD: a program to compute the 3D fractal dimension from MRI data

This work presents a computer program for computing the 3D fractal dimension (3DFD) from magnetic-resonance images of the brain. The program is based on an algorithm that calculates the 3D box counting of the entire volume of the brain, and also of its 3D skeletonization. The validity and accuracy of the software has been confirmed using solids with well-known 3DFD values. The usefulness of the program developed is demonstrated by its successful characterization of several neurodegenerative diseases.

Fractal dimension analysis of the cortical ribbon in mild Alzheimer's disease

Fractal analysis methods are used to quantify the complexity of the human cerebral cortex. Many recent studies have focused on high resolution three-dimensional reconstructions of either the outer (pial) surface of the brain or the junction between the gray and white matter, but ignore the structure between these surfaces. This study uses a new method to incorporate the entire cortical thickness. Data were obtained from the Alzheimer's Disease (AD) Neuroimaging Initiative database (Control N=35, Mild AD N=35). Image segmentation was performed using a semi-automated analysis program. The fractal dimension of three cortical models (the pial surface, gray/white surface and entire cortical ribbon) were calculated using a custom cube-counting triangle-intersection algorithm. The fractal dimension of the cortical ribbon showed highly significant differences between control and AD subjects (p<0.001). The inner surface analysis also found smaller but significant differences (p<0.05). The pial surface dimensionality was not significantly different between the two groups. All three models had a significant positive correlation with the cortical gyrification index (r>0.55, p<0.001). Only the cortical ribbon had a significant correlation with cortical thickness (r=0.832, p<0.001) and the Alzheimer's Disease Assessment Scale cognitive battery (r=-0.513, p=0.002). The cortical ribbon dimensionality showed a larger effect size (d=1.12) in separating control and mild AD subjects than cortical thickness (d=1.01) or gyrification index (d=0.84). The methodological change shown in this paper may allow for further clinical application of cortical fractal dimension as a biomarker for structural changes that accrue with neurodegenerative diseases.

Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro

Neurons and glial cells in the brain are surrounded by a fractal environment. A fractal alkylketene dimmer (AKD) surface was shown to provide such a biomimetic environment for glial cell culture. However, little is known about the effects of fractal surface on the complexity of cell morphology. In particular, whether fractal surface induces glial cell differentiation remains to be elucidated. The present work, thus determined the fractal dimension (FD) of cell complexity with a geometrically calculational parameter, the expressions of GFAP gene and protein in C6 glioma cells on fractal AKD, non-fractal AKD and PLL-coated surfaces. Fractal surface suppressed the proliferation of glioma cell, and significantly increased the length and number of cell process. Furthermore, the enhanced values of FD were accompanied with the expressions of GFAP gene and protein, especially that of gene. However, cells on non-fractal and PLL surface proliferated gradually along with the culture time, showing the fibroblast-like morphology, and accompanied with the consistent expressions of GFAP gene and protein. These results suggested that C6 glioma cell differentiation can be induced by fractal AKD surface.

Fractal dimension analysis for quantifying cerebellar morphological change of multiple system atrophy of the cerebellar type (MSA-C)

Multiple system atrophy of the cerebellar type (MSA-C) is a degenerative neurological disease of the central nervous system. This study aims to demonstrate that the morphological changes of cerebellar structure, specifically, the cerebellum white matter (CBWM) and cerebellum gray matter (CBGM) from T1-weighted magnetic resonance (MR) images, can be quantified by three-dimensional (3D) fractal dimension (FD) analysis, which is a measure of complexity. Twenty-three MSA-C patients and twenty-one normal subjects participated in this study. The results of this study show that MSA-C patients presented significantly lower FD values compared to the control group, and that morphological change in the CBWM dominates the cerebellar degeneration. In addition, the FD analysis method is superior to conventional volumetric methods in quantifying the structural changes of WM and GM because it exhibits smaller variances and less gender effect. Since a decrease of cerebellar FD value indicates degeneration of the cerebellar structure, this study further suggests that the morphological changes of cerebellar structures (CBGM and CBWM) can be characterized by FD analysis.

Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis

The purpose of this project is to apply a modified fractal analysis technique to high-resolution T1 weighted magnetic resonance images in order to quantify the alterations in the shape of the cerebral cortex that occur in patients with Alzheimer's disease. Images were selected from the Alzheimer's Disease Neuroimaging Initiative database (Control N=15, Mild-Moderate AD N=15). The images were segmented using a semi-automated analysis program. Four coronal and three axial profiles of the cerebral cortical ribbon were created. The fractal dimensions (D(f)) of the cortical ribbons were then computed using a box-counting algorithm. The mean D(f) of the cortical ribbons from AD patients were lower than age-matched controls on six of seven profiles. The fractal measure has regional variability which reflects local differences in brain structure. Fractal dimension is complementary to volumetric measures and may assist in identifying disease state or disease progression.

Quantifying degeneration of white matter in normal aging using fractal dimension

Although degeneration of brain white matter (WM) in aging is a well-recognized problem, its quantification has mainly relied on volumetric measurements, which lack detail in describing the degenerative adaptation. In this study, WM structural complexity was evaluated in healthy old and young adults by analyzing the three-dimensional fractal dimension (FD) of WM segmented from magnetic resonance images of brain. FDs detected in the old were significantly smaller than in the young subjects. Specifically, WM interior structure complexity degenerated in the left hemisphere in old men but in the right hemisphere in old women. Men showed more complex WM patterns than women. An asymmetrical (right-greater-than-left-hemisphere) complexity pattern was observed in the interior and general structures of WM, yet the surface complexity was symmetrical across WM structures of the two hemispheres. WM volumes were also measured, but no significant decline was found with aging. These results suggest that the deterioration of WM complexity is not uniformly distributed between the genders and across brain hemispheres.

Fractal dimension and white matter changes in multiple sclerosis

The brain white matter (WM) in multiple sclerosis (MS) suffers visible and non-visible (normal-appearing WM (NAWM)) changes in conventional magnetic resonance (MR) images. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Our aim was to assess the usefulness of FD analysis in the measurement of WM abnormalities in conventional MR images in patients with MS, particularly to detect NAWM changes. First, we took on a voxel-based morphometry approach optimized for MS to obtain the segmented brain. Then, the FD of the whole grey-white matter interface (WM border) and skeletonized WM was calculated in patients with MS and healthy controls. To assess the FD of the NAWM, we focused our analysis on single sections without lesions at the centrum semiovale level. We found that patients with MS had a significant decrease in the FD of the entire brain WM compared with healthy controls. Such a decrease of the FD was detected not only on MR image sections with MS lesions but also on single sections with NAWM. Taken together, the results showed that FD identifies changes in the brain of patients with MS, including in NAWM, even at an early phase of the disease. Thus, FD might become a useful marker of diffuse damage of the central nervous system in MS.

Fractal dimension in human cortical surface: multiple regression analysis with cortical thickness, sulcal depth, and folding area

Fractal dimension (FD) has been widely used to provide a quantitative description of structural complexity in the cerebral cortex. FD is an extremely compact measure of shape complexity, condensing all details into a single numeric value. We interpreted the variation of the FD in the cortical surface of normal controls through multiple regression analysis with cortical thickness, sulcal depth, and folding area related to cortical complexity. We used a cortical surface showing a reliable representation of folded gyri and manually parcellated it into frontal, parietal, temporal, and occipital regions for regional analysis. In both hemispheres the mean cortical thickness and folding area showed significant combination effects on cortical complexity and accounted for about 50% of its variance. The folding area was significant in accounting for the FD of the cortical surface, with positive coefficients in both hemispheres and several lobe regions, while sulcal depth was significant only in the left temporal region. The results may suggest that human cortex develops a complex structure through the thinning of cortical thickness and by increasing the frequency of folds and the convolution of gyral shape rather than by deepening sulcal regions. Through correlation analysis of FD with IQ and the number of years of education, the results showed that a complex shape of the cortical surface has a significant relationship with intelligence and education. Our findings may indicate the structural characteristics that are revealed in the cerebral cortex when the FD in human brain is increased, and provide important information about brain development.

Quantitative morphologic evaluation of white matter in survivors of childhood medulloblastoma

In survivors of pediatric brain tumors, cranial radiation therapy can cause a debilitating cognitive decline associated with decreased volume in normal-appearing white matter (NAWM). We applied fractal geometry to quantify white matter (WM) integrity in the brain of medulloblastoma survivors. Fractal features of WM were evaluated by indices of fractal dimensions (FDs) of WM intensity and boundary on T1-weighted magnetic resonance images. The FD index of WM intensity was calculated by using a fractional Brownian motion model, and the FD index of WM boundary was calculated by using a box-counting method. Fractal features of WM on 116 magnetic resonance images of 58 patients with medulloblastoma were investigated at the start of therapy (Start TX) and approximately 2 years later (After TX). Patients were assigned to one of two groups based on change in NAWM volumes. Fractal features in patients with decreased NAWM volume were significantly greater After TX, whereas those in patients with increased NAWM volumes were not. Multiple linear regression analysis showed that fractal features were strongly correlated with NAWM volumes After TX in patients with decreased NAWM volume. These results demonstrated significant deficit in NAWM integrity and WM density changes in children treated for medulloblastoma. Multiple regression analysis illustrated that deficits in NAWM integrity in these children may partly explain the decrease in NAWM volume. We conclude that fractal geometry can be used to monitor the morphologic effects of neurotoxicity in brain tumor survivors.