Cortical fractal dimension predicts disability worsening in Multiple Sclerosis patients

Development of a predictive model for predicting disability after optic neuritis: a secondary analysis of the Optic Neuritis Treatment Trial

Objective

The present study aimed to develop a prediction model for predicting developing debilities after optic neuritis.

Methods

The data for this research was obtained from the Optic Neuritis Treatment Trial (ONTT). The predictive model was built based on a Cox proportional hazards regression model. Model performance was assessed using Harrell's C-index for discrimination, calibration plots for calibration, and stratification of patients into low-risk and high-risk groups for utility evaluation.

Results

A total of 416 patients participated. Among them, 101 patients (24.3%) experienced disability, which was defined as achieving or surpassing a score of 3 on the expanded disability status scale. The median follow-up duration was 15.5 years (interquartile range, 7.0 to 16.8). Two predictors in the final predictive model included the classification of multiple sclerosis at baseline and the condition of the optic disk in the affected eye at baseline. Upon incorporating these two factors into the model, the model's C-index stood at 0.71 (95% CI, 0.66-0.76, with an optimism of 0.005) with a favorable alignment with the calibration curve. By utilizing this model, the ONTT cohort can be categorized into two risk categories, each having distinct rates of disability development within a 15-year timeframe (high-risk group, 41% [95% CI, 31-49%] and low-risk group, 13% [95% CI, 8.4-17%]; log-rank p-value of <0.001).

Conclusion

This predictive model has the potential to assist physicians in identifying individuals at a heightened risk of experiencing disability following optic neuritis, enabling timely intervention and treatment.

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 Analysis in Neurological Disorders: An Overview

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

Neuroimaging to monitor worsening of multiple sclerosis: advances supported by the grant for multiple sclerosis innovation

Key unmet needs in multiple sclerosis (MS) include detection of early pathology, disability worsening independent of relapses, and accurate monitoring of treatment response. Collaborative approaches to address these unmet needs have been driven in part by industry-academic networks and initiatives such as the Grant for Multiple Sclerosis Innovation (GMSI) and Multiple Sclerosis Leadership and Innovation Network (MS-LINK™) programs. We review the application of recent advances, supported by the GMSI and MS-LINK™ programs, in neuroimaging technology to quantify pathology related to central pathology and disease worsening, and potential for their translation into clinical practice/trials. GMSI-supported advances in neuroimaging methods and biomarkers include developments in magnetic resonance imaging, positron emission tomography, ocular imaging, and machine learning. However, longitudinal studies are required to facilitate translation of these measures to the clinic and to justify their inclusion as endpoints in clinical trials of new therapeutics for MS. Novel neuroimaging measures and other biomarkers, combined with artificial intelligence, may enable accurate prediction and monitoring of MS worsening in the clinic, and may also be used as endpoints in clinical trials of new therapies for MS targeting relapse-independent disease pathology.

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.

The complexity of cortical folding is reduced in chronic cocaine users

Cocaine use is a worldwide health problem with psychiatric, somatic and socioeconomic complications, being the second most widely used illicit drug in the world. Despite several structural neuroimaging studies, the alterations in cortical morphology associated with cocaine use and addiction are still poorly understood. In this study, we compared the complexity of cortical folding (CCF), a measure that aims to summarize the convoluted structure of the cortex between patients with cocaine addiction (n = 52) and controls (n = 36), and correlated it with characteristics of addiction and impulsivity. We found that patients with cocaine addiction had greater impulsivity and showed reduced CCF in a cluster that encompassed the left insula and the supramarginal gyrus (SMG) and in one in the left medial orbitofrontal cortex. Finally, the CCF in the left medial orbitofrontal cortex was correlated with the age of onset of cocaine addiction and with attentional impulsivity. Overall, our findings suggest that chronic cocaine use is associated with changes in the cortical surface in the fronto-parieto-limbic regions that underlie emotional regulation and these changes are associated with earlier cocaine use. Future longitudinal studies are warranted to unravel the association of these changes with the diathesis for the disorder and with the chronic use of this substance.

Toward an Automatic Assessment of Cognitive Dysfunction in Relapsing-Remitting Multiple Sclerosis Patients Using Eye Movement Analysis

Despite the importance of cognitive function in multiple sclerosis, it is poorly represented in the Expanded Disability Status Scale (EDSS), the commonly used clinical measure to assess disability, suggesting that an analysis of eye movement, which is generated by an extensive and well-coordinated functional network that is engaged in cognitive function, could have the potential to extend and complement this more conventional measure. We aimed to measure the eye movement of a case series of MS patients with relapsing−remitting MS to assess their cognitive status using a conventional gaze tracker. A total of 41 relapsing−remitting MS patients and 43 age-matched healthy controls were recruited for this study. Overall, we could not find a clear common pattern in the eye motor abnormalities. Vertical eye movement was more impaired in MS patients than horizontal movement. Increased latencies were found in the prosaccades and reflexive saccades of antisaccade tests. The smooth pursuit was impaired with more corrections (backup and catchup movements, p<0.01). No correlation was found between eye movement variables and EDSS or disease duration. Despite significant alterations in the behavior of the eye movements in MS patients, which are compatible with altered cognitive status, there is no common pattern of these alterations. We interpret this as a consequence of the patchy, heterogeneous distribution of white matter involvement in MS that provokes multiple combinations of impairment at different points in the different networks involved in eye motor control. Further studies are therefore required.

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.

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.

Estimation of Rice Biomass at Different Growth Stages by Using Fractal Dimension in Image Processing

Rice has long served as the staple food in Asia, and the cultivation of high-yield rice crops draws increasing attention from academic researchers. The prediction of rice growth condition by image features realizes nondestructive prediction and it has great implications for smart agriculture. We found a special image parameter called the fractal dimension that can improve the effect of the prediction model. As an important geometric feature, the fractal dimension could be calculated from the image, but it is rarely used in the field of rice growth prediction. In this paper, we attempt to combine the fractal dimension with traditional rice image features to improve the effect of the model. The thresholding method is used to transform the cropped rice image into binary image, and the box-counting method is used to calculate the fractal dimension of the image. The correlation coefficients are calculated to select the characteristics with a strong correlation with biomass. The prediction models of dry weight, fresh weight and plant height of rice are established by using random forest, support vector regression and linear regression. By evaluating the prediction effect of the model, it can be concluded that the fractal dimension can improve the prediction effect of the model. Among the models obtained by the three methods, the multiple linear regression model has the best comprehensive effect, with the dry weight prediction model R2 reaching 0.8697, the fresh weight prediction model R2 reaching 0.8631 and the plant height prediction model R2 reaching 0.9196. The model established in this paper has a fine effect and has a certain guiding significance in rice research.