Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications

The brain is a system operating on multiple time scales, and characterisation of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry. However, currently there exists no established method for the study of brain dynamics using fractal geometry, due to the many challenges in the conceptual and technical understanding of the methods. We aim to highlight some of the practical challenges of applying fractal geometry to brain dynamics and propose solutions to enable its wider use in neuroscience. Using intracranially recorded EEG and simulated data, we compared monofractal and multifractal methods with regards to their sensitivity to signal variance. We found that both correlate closely with signal variance, thus not offering new information about the signal. However, after applying an epoch-wise standardisation procedure to the signal, we found that multifractal measures could offer non-redundant information compared to signal variance, power and other established EEG signal measures. We also compared different multifractal estimation methods and found that the Chhabra-Jensen algorithm performed best. Finally, we investigated the impact of sampling frequency and epoch length on multifractal properties. Using epileptic seizures as an example event in the EEG, we show that there may be an optimal time scale for detecting temporal changes in multifractal properties around seizures. The practical issues we highlighted and our suggested solutions should help in developing a robust method for the application of fractal geometry in EEG signals. Our analyses and observations also aid the theoretical understanding of the multifractal properties of the brain and might provide grounds for new discoveries in the study of brain signals. These could be crucial for understanding of neurological function and for the developments of new treatments.Comment: Final version published at Frontiers in Physiology. https://doi.org/10.3389/fphys.2018.0176

Multifractal organization of EEG signals in Multiple Sclerosis

Quantifying the complex/multifractal organization of the brain signals is crucial to fully understanding the brain processes and structure. In this contribution, we performed the multifractal analysis of the electroencephalographic (EEG) data obtained from a controlled multiple sclerosis (MS) study, focusing on the correlation between the degree of multifractality, disease duration, and disability level. Our results reveal a significant correspondence between the complexity of the time series and multiple sclerosis development, quantified respectively by scaling exponents and the Expanded Disability Status Scale (EDSS). Namely, for some brain regions, a well-developed multifractality and little persistence of the time series were identified in patients with a high level of disability, whereas the control group and patients with low EDSS were characterised by persistence and monofractality of the signals. The analysis of the cross-correlations between EEG signals supported these results, with the most significant differences identified for patients with EDSS $> 1$ and the combined group of patients with EDSS $\leq 1$ and controls. No association between the multifractality and disease duration was observed, indicating that the multifractal organisation of the data is a hallmark of developing the disease. The observed complexity/multifractality of EEG signals is hypothetically a result of neuronal compensation -- i.e., of optimizing neural processes in the presence of structural brain degeneration. The presented study is highly relevant due to the multifractal formalism used to quantify complexity and due to scarce resting-state EEG evidence for cortical reorganization associated with compensation.Comment: 39 pages, including supplementary materials (11 figures, 4 tables

Changes in surface electromyography characteristics and foot-tapping rate of force development as measures of spasticity in patients with multiple sclerosis

Spasticity is a common symptom experienced by individuals with upper motor neuron lesions such as those with stroke, spinal cord injury, traumatic brain injury, cerebral palsy, amyotrophic lateral sclerosis, and multiple sclerosis. Although the etiology and progression of spasticity differs between these clinical populations, it shares many of the same consequences: muscle pain, weakness, fatigue, increased disability, depression, medication side effects, and a reduced quality of life. For this reason, there has been increased interest in the measurement and treatment of spasticity symptoms. Subjective measures of spasticity like the Modified Ashworth Scale (MAS) and Tardieu Scale have shown questionable validity/reliability and poorly correlate to functional outcome measures but continue to be used in clinical and research settings. Objective measures like myotonometry, electrogoniometry, and inertial sensors on the other hand provide much more reliable measures but at the expense of increased costs, time, and equipment. Therefore, to properly assess and treat spasticity symptoms, a timelier and cost-effective objective measure of spasticity is needed. PURPOSE: To reexamine a previously collected dataset from a sample of patients with multiple sclerosis before and after dry-needling and functional electrically stimulated walking spasticity treatments. Specifically, we wished to know whether there were: 1.) Acute (within visit) and chronic (between visit) changes in sEMG and Foot-tapping rate of force development measures after treatment, 2.) Between leg differences before and after treatments, 3.) significant correlations between EMG, foot-tapping, and functional outcome measures. METHODS: 16 MS patients (10 relapsing-remitting and 6 progressive MS) participated in the original study. The study consisted of 14 visits: 2 pre/post visits, 4 visits of dry-needling + functional electrically stimulated walking (FESW), and 8 visits with FESW only. The more spastic leg (involved leg) was given the treatment, making the other the control. Dry-needling was performed on the involved leg’s gastrocnemius medial and lateral heads by inserting monofilament needles and electrically stimming the muscles until visible twitches occurred. Dry-needling was done 30 seconds on and 30 seconds off for a total of 90 seconds of treatment. FESW was performed on the involved leg by attaching electrodes to the tibialis anterior and gastrocnemius muscles. Patients walked 20-minutes at a self-selected pace while the involved leg was stimmed. sEMG was collected before and after each treatment by having the patient perform a single maximal heel raise. Foot-tapping ability was assessed using the 10-second foot-tapping test (FTT) and a small force plate. Functional measures also included the 25-foot walk test (25FWT) 6-minute walk test (6MWT), modified fatigue impact score (MFIS), and number of heel raises performed. RESULTS: No significant between leg differences were noted for any of the sEMG measures (p>0.05). No significant chronic changes occurred in any of the sEMG measures. For the Dry-needling + FESW visits, sEMG sample entropy was significantly increased in the involved leg at post-needling (p = 0.035) and post-FESW (p = 0.027). The non-involved leg’s sample entropy was significantly higher at post-FESW only (p = 0.017). The non-involved leg’s, mean frequency was significantly higher at post-FESW compared pre-needling (p = 0.033) and post-needling (p = 0.032). For the FESW only visits, there were no significant changes in the involved leg. The Non-involved leg’s mean frequency was significantly higher at Post-FESW (p = 0.006). Median frequency was significantly higher at Post-FESW (p = 0.009). The number of foot-taps was significantly increased from Pre to Post-intervention in both the Involved (p = 0.006) and Non-involved legs (p 0.002). There was a significantly higher number of foot-taps in the Non-involved leg compared to the Involved leg at both Pre (p =0.008) and Post (p = 0.015) timepoints. AUC was significantly higher in the Involved leg at Post-treatment (p = 0.030). Time to peak was found to be higher in the Involved leg compared to the Non-involved leg at both Pre (p = 0.037) and Post-intervention (p = 0.019). Time to base was higher in the Involved leg compared to the Non-involved leg at both Pre (p = 0.031) and Post-intervention (p = 0.004). Total tap time was higher in the Involved leg at both Pre (p = 0.010) and Post-intervention (p = 0.007). Percent time to peak was significantly lower in the involved limb at Pre-intervention (p = 0.026) and Post intervention (p = 0.037). Percent time to base was significantly higher in the Involved leg at Pre-intervention (p = 0.026) and Post intervention (p = 0.037). The sEMG measures tended to poorly or non-significantly correlate with the functional outcome measures. The foot-tapping measures, especially the involved leg, tended to exhibit stronger correlations with the functional outcome measures. CONCLUSION: sEMG Sample entropy and foot-tapping ability are significantly improved by dry-needling treatments and walking. sEMG measures did not tend to correlate well with functional outcome measures but the foot-tapping measures did. This suggests that foot-tapping rate and related measures may be a useful measure of spasticity and treatment effects

Aplicación de redes complejas a la descripción de la dinámica de contaminantes atmosféricos

Air pollution has been a major concern among environmental scientists due to its importance to public health. Among the different pollutants that can be found in the air, one can point out tropospheric ozone as one of the most studied ones in the recent years, due to the risk derived for living beings. As a result of the many factors involved in the creation and destruction of this gas, the analysis of its dynamics is quite complicated. Traditionally, conventional statistical methods have been employed, while in the last decades multifractal approaches have gained importance. This is due to their suitability describing systems with a great degree of variability. This thesis focuses on the evaluation and implementation of complex networks for the analysis of tropospheric O3 dynamics. The studies carried out are based on the Visibility Graph (VG) technique, which transforms time series into complex networks that inherit the properties of the first ones. In the first part, a combination of the VG and the multifractal Sand-Box (SB) algorithms is performed. By doing this, authors analyze the generalized fractal dimensions and the singularity spectra. Then, a comparison was made between these multifractal parameters and the quantities obtainable from the degree distribution of the resulting graphs. Regarding the second part of this thesis, the VG methodology was used on O3 time series from rural and urban stations, in order to retrieve the centrality parameters from the obtained networks. This way, degree, shortest path and betweenness are studied to support the use of this technique and find new information. Results show that this methodology can indeed differentiate between ozone measurements in urban and countryside environments, providing new insights about the dynamics. In the third and last part of this document, authors propose an alternative approach to the VG, called Sliding Visibility Graph (SVG). This new technique takes advantage of the fact that visibility adjacency matrices are mostly empty, since the bast majority of the nodes are not connected to each other. Thanks to this, it is possible to apply effectively a sliding window approach to lessen considerably the computation time, reducing one order the time efficiency (from O(N2) to O(N). This is especially convenient when dealing with very large time series. As the resulting network approximates the original VG, it has been evaluated how it converges to the VG case for different types of series, as there lies the actual interest of this tool. As expected, the SVG results converge quite rapidly to the exact values, especially for random and O3 concentration series.La contaminación atmosférica es uno de los principales problemas estudiados dentro de la ciencia ambiental, debido a su gran impacto en la salud pública. Entre los diferentes contaminantes que podemos encontrar en el aire, merece la pena destacar el ozono troposférico (O3) como uno de los más estudiados en los últimos años, debido al alto riesgo para los seres vivos. Como resultado de los numerosos factores implicados en la creación y destrucción de este gas, el análisis de sus dinámicas es bastante complejo. Tradicionalmente, se han usado métodos estadísticos convencionales, mientras que en las últimas décadas han ganado importancia las técnicas multifractales. Esto se debe a su adecuación para describir sistemas con un grado elevado de variabilidad. Esta tesis se centra en la evaluación e implementación de las redes complejas para el análisis de la dinámica del O3. Los estudios llevados a cabo se basan en el uso de la técnica del Grafo de Visibilidad (GV), que transforma series temporales en redes complejas que heredan propiedades de las primeras. En la primera parte, se utiliza una combinación del GV y del algoritmo multifractal Sand-Box (SB). Gracias a esto, es posible obtener las dimensiones fractales generalizadas y el espectro de singularidades. Por último, se ha realizado una comparación entre los parámetros multifractales y las cantidades obtenibles directamente a partir de la distribución del grado de los grafos resultantes. En cuanto a la segunda parte de esta tesis, el método del GV es usado en series temporales de O3 de estaciones rurales y urbanas, con la finalidad de obtener los parámetros de centralidad de las redes conseguidas. De este modo, el grado, el camino mínimo y la intermediación se estudian para refutar la aplicabilidad del GV y buscar nueva información. Los resultados muestran que en efecto esta metodología puede permitir diferenciar entre medidas de ozono en medios rurales y urbanos. En la tercera y última parte de este documento, los autores proponen un método alternativo al GV, llamado Grafo de Visibilidad Deslizante (GVD). Esta nueva técnica se aprovecha del hecho de que las matrices de adyacencia de los GV son prácticamente vacías, puesto que la mayoría de los vértices no están conectados entre sí. Gracias a ello, es posible aplicar de forma efectiva un algoritmo de ventana deslizante para reducir considerablemente el tiempo de cálculo, bajando en uno el orden de magnitud de la eficiencia (de O (N2) a O (N)). Esto es especialmente provechoso cuando se trata con series temporales muy grandes. Debido a que la red resultante aproxima al GV original, se ha evaluado cómo converge al segundo para diferentes tipos de series temporales, que es donde reside en interés real de esta herramienta. Como era de esperar, los resultados del GVD convergen rápidamente a los valores exactos, especialmente para series aleatorias y concentración de O3

Investigation of neural activity in Schizophrenia during resting-state MEG : using non-linear dynamics and machine-learning to shed light on information disruption in the brain

Environ 25% de la population mondiale est atteinte de troubles psychiatriques qui sont typiquement associés à des problèmes comportementaux, fonctionnels et/ou cognitifs et dont les corrélats neurophysiologiques sont encore très mal compris. Non seulement ces dysfonctionnements réduisent la qualité de vie des individus touchés, mais ils peuvent aussi devenir un fardeau pour les proches et peser lourd dans l’économie d’une société. Cibler les mécanismes responsables du fonctionnement atypique du cerveau en identifiant des biomarqueurs plus robustes permettrait le développement de traitements plus efficaces. Ainsi, le premier objectif de cette thèse est de contribuer à une meilleure caractérisation des changements dynamiques cérébraux impliqués dans les troubles mentaux, plus précisément dans la schizophrénie et les troubles d’humeur. Pour ce faire, les premiers chapitres de cette thèse présentent, en intégral, deux revues de littératures systématiques que nous avons menées sur les altérations de connectivité cérébrale, au repos, chez les patients schizophrènes, dépressifs et bipolaires. Ces revues révèlent que, malgré des avancées scientifiques considérables dans l’étude de l’altération de la connectivité cérébrale fonctionnelle, la dimension temporelle des mécanismes cérébraux à l’origine de l’atteinte de l’intégration de l’information dans ces maladies, particulièrement de la schizophrénie, est encore mal comprise. Par conséquent, le deuxième objectif de cette thèse est de caractériser les changements cérébraux associés à la schizophrénie dans le domaine temporel. Nous présentons deux études dans lesquelles nous testons l’hypothèse que la « disconnectivité temporelle » serait un biomarqueur important en schizophrénie. Ces études explorent les déficits d’intégration temporelle en schizophrénie, en quantifiant les changements de la dynamique neuronale dite invariante d’échelle à partir des données magnétoencéphalographiques (MEG) enregistrés au repos chez des patients et des sujets contrôles. En particulier, nous utilisons (1) la LRTCs (long-range temporal correlation, ou corrélation temporelle à longue-distance) calculée à partir des oscillations neuronales et (2) des analyses multifractales pour caractériser des modifications de l’activité cérébrale arythmique. Par ailleurs, nous développons des modèles de classification (en apprentissage-machine supervisé) pour mieux cerner les attributs corticaux et sous-corticaux permettant une distinction robuste entre les patients et les sujets sains. Vu que ces études se basent sur des données MEG spontanées enregistrées au repos soit avec les yeux ouvert, ou les yeux fermées, nous nous sommes par la suite intéressés à la possibilité de trouver un marqueur qui combinerait ces enregistrements. La troisième étude originale explore donc l’utilité des modulations de l’amplitude spectrale entre yeux ouverts et fermées comme prédicteur de schizophrénie. Les résultats de ces études démontrent des changements cérébraux importants chez les patients schizophrènes au niveau de la dynamique d’invariance d’échelle. Elles suggèrent une dégradation du traitement temporel de l’information chez les patients, qui pourrait être liée à leurs symptômes cognitifs et comportementaux. L’approche multimodale de cette thèse, combinant la magétoencéphalographie, analyses non-linéaires et apprentissage machine, permet de mieux caractériser l’organisation spatio-temporelle du signal cérébrale au repos chez les patients atteints de schizophrénie et chez des individus sains. Les résultats fournissent de nouvelles preuves supportant l’hypothèse d’une « disconnectivité temporelle » en schizophrénie, et étendent les recherches antérieures, en explorant la contribution des structures cérébrales profondes et en employant des mesures non-linéaires avancées encore sous-exploitées dans ce domaine. L’ensemble des résultats de cette thèse apporte une contribution significative à la quête de nouveaux biomarqueurs de la schizophrénie et démontre l’importance d’élucider les altérations des propriétés temporelles de l’activité cérébrales intrinsèque en psychiatrie. Les études présentées offrent également un cadre méthodologique pouvant être étendu à d’autres psychopathologie, telles que la dépression.Psychiatric disorders affect nearly a quarter of the world’s population. These typically bring about debilitating behavioural, functional and/or cognitive problems, for which the underlying neural mechanisms are poorly understood. These symptoms can significantly reduce the quality of life of affected individuals, impact those close to them, and bring on an economic burden on society. Hence, targeting the baseline neurophysiology associated with psychopathologies, by identifying more robust biomarkers, would improve the development of effective treatments. The first goal of this thesis is thus to contribute to a better characterization of neural dynamic alterations in mental health illnesses, specifically in schizophrenia and mood disorders. Accordingly, the first chapter of this thesis presents two systematic literature reviews, which investigate the resting-state changes in brain connectivity in schizophrenia, depression and bipolar disorder patients. Great strides have been made in neuroimaging research in identifying alterations in functional connectivity. However, these two reviews reveal a gap in the knowledge about the temporal basis of the neural mechanisms involved in the disruption of information integration in these pathologies, particularly in schizophrenia. Therefore, the second goal of this thesis is to characterize the baseline temporal neural alterations of schizophrenia. We present two studies for which we hypothesize that the resting temporal dysconnectivity could serve as a key biomarker in schizophrenia. These studies explore temporal integration deficits in schizophrenia by quantifying neural alterations of scale-free dynamics using resting-state magnetoencephalography (MEG) data. Specifically, we use (1) long-range temporal correlation (LRTC) analysis on oscillatory activity and (2) multifractal analysis on arrhythmic brain activity. In addition, we develop classification models (based on supervised machine-learning) to detect the cortical and sub-cortical features that allow for a robust division of patients and healthy controls. Given that these studies are based on MEG spontaneous brain activity, recorded at rest with either eyes-open or eyes-closed, we then explored the possibility of finding a distinctive feature that would combine both types of resting-state recordings. Thus, the third study investigates whether alterations in spectral amplitude between eyes-open and eyes-closed conditions can be used as a possible marker for schizophrenia. Overall, the three studies show changes in the scale-free dynamics of schizophrenia patients at rest that suggest a deterioration of the temporal processing of information in patients, which might relate to their cognitive and behavioural symptoms. The multimodal approach of this thesis, combining MEG, non-linear analyses and machine-learning, improves the characterization of the resting spatiotemporal neural organization of schizophrenia patients and healthy controls. Our findings provide new evidence for the temporal dysconnectivity hypothesis in schizophrenia. The results extend on previous studies by characterizing scale-free properties of deep brain structures and applying advanced non-linear metrics that are underused in the field of psychiatry. The results of this thesis contribute significantly to the identification of novel biomarkers in schizophrenia and show the importance of clarifying the temporal properties of altered intrinsic neural dynamics. Moreover, the presented studies offer a methodological framework that can be extended to other psychopathologies, such as depression