Application of a multifractal analysis to study brain white matter abnormalities of schizophrenia on T2-weighted magnetic resonance imaging

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

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

Fractal Structure of Brain Electrical Activity of Patients With Mental Disorders

This work was aimed at a comparative analysis of the degree of multifractality of electroencephalographic time series obtained from a group of healthy subjects and from patients with mental disorders. We analyzed long-term records of patients with paranoid schizophrenia and patients with depression. To evaluate the properties of multifractal scaling of various electroencephalographic time series, the method of maximum modulus of the wavelet transform and multifractal analysis of fluctuations without a trend were used. The stability of the width and position of the singularity spectrum for each of the test groups was revealed, and a relationship was established between the correlation and anticorrelation dynamics of successive values of the electroencephalographic time series and the type of mental disorders. It was shown that the main differences between the multifractal properties of brain activity in normal and pathological conditions lie in the different width of the multifractality spectrum and its location associated with the correlated or anticorrelated dynamics of the values of successive time series. It was found that the schizophrenia group is characterized by a greater degree of multifractality compared to the depression group. Thus, the degree of multifractality can be included in a set of tests for differential diagnosis and research of mental disorders.

Altered Brain Criticality in Schizophrenia: New Insights From Magnetoencephalography

Schizophrenia has a complex etiology and symptomatology that is difficult to untangle. After decades of research, important advancements toward a central biomarker are still lacking. One of the missing pieces is a better understanding of how non-linear neural dynamics are altered in this patient population. In this study, the resting-state neuromagnetic signals of schizophrenia patients and healthy controls were analyzed in the framework of criticality. When biological systems like the brain are in a state of criticality, they are thought to be functioning at maximum efficiency (e.g., optimal communication and storage of information) and with maximum adaptability to incoming information. Here, we assessed the self-similarity and multifractality of resting-state brain signals recorded with magnetoencephalography in patients with schizophrenia patients and in matched controls. Schizophrenia patients had similar, although attenuated, patterns of self-similarity and multifractality values. Statistical tests showed that patients had higher values of self-similarity than controls in fronto-temporal regions, indicative of more regularity and memory in the signal. In contrast, patients had less multifractality than controls in the parietal and occipital regions, indicative of less diverse singularities and reduced variability in the signal. In addition, supervised machine-learning, based on logistic regression, successfully discriminated the two groups using measures of self-similarity and multifractality as features. Our results provide new insights into the baseline cognitive functioning of schizophrenia patients by identifying key alterations of criticality properties in their resting-state brain data.

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.

Fourier transform infrared spectroscopy microscopic imaging classification based on multifractal methods

Multifractal analysis (MFA) based on generalized concepts of fractals has been applied to biological tissues composed of complex structures. In this paper, a new MFA methodology based on the neighborhood spatial correlation (NSC) is proposed for an extracting texture feature. NSC is used to extract spatial features, and the obtained spatial features are combined with spectral features of characteristic absorption peaks (CAPs) to promote more feature information. This spatial-spectral structure is used as a feature to differentiate cholesterol from Fourier transform infrared spectroscopy microscopic imaging of a rabbit artery by a support vector machine classifier. The dataset was collected between 4000 and 720  cm^-1 on rabbit arteries as research objects. The experimental results show that the accuracy of the proposed spatial-spectral structure is higher than that of other multivariate analysis methods (PCA and 2DPCA). The NSC method, compared to the bottom interface method, new bottom interface method, variance method multi-weight method, and neighborhood spatial correlation method, could effectively reduce the influence of speckle noise, and the convergence rate of the weight factor q is not increased.

Reduced white matter fractional anisotropy and clinical symptoms in schizophrenia: a voxel-based diffusion tensor imaging study

Although not consistently replicated, diffusion tensor imaging (DTI) studies in schizophrenia have revealed lower fractional anisotropy (FA) in various white matter regions, a finding consistent with the disruption of white matter integrity. In this study, we used voxel-based DTI to investigate possible whole-brain differences in the white matter FA values between 58 schizophrenia patients and 58 healthy controls. We also explored the association between FA values and clinical symptoms in schizophrenia. Compared with the controls, the schizophrenia patients showed significant FA reductions in bilateral superior longitudinal fasciculus, bilateral inferior fronto-occipital fasciculus, and genu of right internal capsule. Furthermore, in the patient group, the FA value of the anterior part of the corpus callosum was negatively correlated with the avolition score on the Scale for the Assessment of Negative Symptoms. These findings suggest widespread disruption of white matter integrity in schizophrenia, which could partly explain the severity of negative symptomatology.