This document discusses functional brain networks and network science approaches to studying the brain. It begins by defining complex systems and network science. It then outlines the main types of brain networks - anatomical and functional networks. Functional brain networks are constructed from time series data measuring brain activity and can be analyzed using network measures to study properties like segregation, integration and resilience.
Brain network modelling: connectivity metrics and group analysisGael Varoquaux
Slides of the course that I gave at the HBM 2012 connectome course on brain network modelling methods, with a focus on extracting connectivity graphs from correlation matrices and comparing them.
The document discusses the brain as a complex network and introduces the concept of the connectome. It describes how the brain exhibits both segregation into specialized areas and integration through connections between areas. Mapping the structural and functional connectivity between brain regions using tools from network science and graph theory provides a powerful way to quantitatively describe the topological organization of the brain. Analyzing the human connectome has revealed hierarchical modular organization and the presence of connector hubs and rich clubs that facilitate integration and efficient communication in the brain network. Understanding disruptions to functional and structural connectivity may help explain neurological and psychiatric disorders.
Artificial Intelligence in Neurology.pptxNeurologyKota
This document discusses the use of artificial intelligence and machine learning algorithms in neurology. It begins by introducing the topic and defining key terms like artificial intelligence, machine learning, and different types of machine learning algorithms. It then discusses how machine learning algorithms can be used for tasks like image classification in neurology, providing examples of analyzing retinal imaging, head CT scans, and MRI scans. The document also notes limitations of machine learning like bias, lack of generalizability, and the "black box" problem. It concludes by discussing specific applications of machine learning in areas like screening OCT images, predicting Alzheimer's progression, and detecting papilloedema and brain tumors.
The presentation focuses on one of the important aspects of Neurophysiology-- The sesnsorimotor integration for planning and execution of movement.
It highlights on the brain regions associated with motor functions, the crosstalk between association areas, hierarchical levels of movement execution and the diseases related to it.
The document discusses various current applications of electroencephalography (EEG) technology both within and outside of clinical settings. It outlines EEG's predominant use in epilepsy and sleep disorder diagnosis clinically. It also explores recent developments that enable portable and cheaper EEG units, allowing novel consumer and research applications. Specifically, the document examines EEG's role in investigating sleep disorders, assessing brain death, monitoring anesthesia depth, cognitive engagement, brain development, and more. It explores EEG's growing use in cognitive science, neuroscience, and other research domains. Finally, it discusses emerging areas like brain-computer interfaces, closed-loop systems, and neuromarketing.
Neurobiology of consciousness and its disordersNeurologyKota
1. Consciousness involves wakefulness, awareness of self and environment, and depends on complex interactions between brainstem, subcortical and cortical regions.
2. States of impaired consciousness include coma, vegetative state, minimally conscious state, and locked-in syndrome. Clinical assessment involves detailed history, examination, and tools like CRS-R to characterize awareness and functioning.
3. Imaging and electrophysiological techniques provide objective measures of brain activity, while sensory stimulation and pharmacologic agents may improve arousal or awareness in some patients. Prognosis depends on etiology, duration of impairment, and age.
The parietal lobe is located at the top of the brain and is involved in processing somatosensory information, spatial awareness, and language comprehension. It contains the primary somatosensory cortex and association areas important for functions like tactile perception, discrimination, localization, and stereognosis. Injuries or lesions to different areas of the parietal lobe can cause syndromes like Gerstmann's syndrome involving acalculia, finger agnosia, and right-left disorientation if the angular gyrus is affected. The supramarginal gyrus is involved in tasks like praxis, repetition, and constructional abilities.
MEG measures magnetic fields produced by electrical activity in the brain. It provides high spatial resolution to localize brain regions activated during specific cognitive tasks and can help localize epileptic seizures. While MEG was first developed in the 1970s, advances over decades now allow it to map brain rhythms, language processing, connectivity between regions, and development from prenatal periods to learning. Key applications include epilepsy evaluation, mapping functional areas near brain tumors to guide surgery, and monitoring stroke recovery and chronic pain.
Brain network modelling: connectivity metrics and group analysisGael Varoquaux
Slides of the course that I gave at the HBM 2012 connectome course on brain network modelling methods, with a focus on extracting connectivity graphs from correlation matrices and comparing them.
The document discusses the brain as a complex network and introduces the concept of the connectome. It describes how the brain exhibits both segregation into specialized areas and integration through connections between areas. Mapping the structural and functional connectivity between brain regions using tools from network science and graph theory provides a powerful way to quantitatively describe the topological organization of the brain. Analyzing the human connectome has revealed hierarchical modular organization and the presence of connector hubs and rich clubs that facilitate integration and efficient communication in the brain network. Understanding disruptions to functional and structural connectivity may help explain neurological and psychiatric disorders.
Artificial Intelligence in Neurology.pptxNeurologyKota
This document discusses the use of artificial intelligence and machine learning algorithms in neurology. It begins by introducing the topic and defining key terms like artificial intelligence, machine learning, and different types of machine learning algorithms. It then discusses how machine learning algorithms can be used for tasks like image classification in neurology, providing examples of analyzing retinal imaging, head CT scans, and MRI scans. The document also notes limitations of machine learning like bias, lack of generalizability, and the "black box" problem. It concludes by discussing specific applications of machine learning in areas like screening OCT images, predicting Alzheimer's progression, and detecting papilloedema and brain tumors.
The presentation focuses on one of the important aspects of Neurophysiology-- The sesnsorimotor integration for planning and execution of movement.
It highlights on the brain regions associated with motor functions, the crosstalk between association areas, hierarchical levels of movement execution and the diseases related to it.
The document discusses various current applications of electroencephalography (EEG) technology both within and outside of clinical settings. It outlines EEG's predominant use in epilepsy and sleep disorder diagnosis clinically. It also explores recent developments that enable portable and cheaper EEG units, allowing novel consumer and research applications. Specifically, the document examines EEG's role in investigating sleep disorders, assessing brain death, monitoring anesthesia depth, cognitive engagement, brain development, and more. It explores EEG's growing use in cognitive science, neuroscience, and other research domains. Finally, it discusses emerging areas like brain-computer interfaces, closed-loop systems, and neuromarketing.
Neurobiology of consciousness and its disordersNeurologyKota
1. Consciousness involves wakefulness, awareness of self and environment, and depends on complex interactions between brainstem, subcortical and cortical regions.
2. States of impaired consciousness include coma, vegetative state, minimally conscious state, and locked-in syndrome. Clinical assessment involves detailed history, examination, and tools like CRS-R to characterize awareness and functioning.
3. Imaging and electrophysiological techniques provide objective measures of brain activity, while sensory stimulation and pharmacologic agents may improve arousal or awareness in some patients. Prognosis depends on etiology, duration of impairment, and age.
The parietal lobe is located at the top of the brain and is involved in processing somatosensory information, spatial awareness, and language comprehension. It contains the primary somatosensory cortex and association areas important for functions like tactile perception, discrimination, localization, and stereognosis. Injuries or lesions to different areas of the parietal lobe can cause syndromes like Gerstmann's syndrome involving acalculia, finger agnosia, and right-left disorientation if the angular gyrus is affected. The supramarginal gyrus is involved in tasks like praxis, repetition, and constructional abilities.
MEG measures magnetic fields produced by electrical activity in the brain. It provides high spatial resolution to localize brain regions activated during specific cognitive tasks and can help localize epileptic seizures. While MEG was first developed in the 1970s, advances over decades now allow it to map brain rhythms, language processing, connectivity between regions, and development from prenatal periods to learning. Key applications include epilepsy evaluation, mapping functional areas near brain tumors to guide surgery, and monitoring stroke recovery and chronic pain.
1 basics of eeg and fundamentals of its measurementSwathy Ravi
The document discusses the basics and fundamentals of electroencephalography (EEG) and its measurement. It provides a timeline of EEG invention from 1875 to 1924. It describes cerebral generators of EEG potentials and how electrical signals propagate through neurons and are detected by EEG electrodes. The document outlines how EEG is recorded using a modern EEG machine and the 10-20 system for electrode placement. It discusses filters, amplifiers, polarity conventions, montages, artifacts, and clinical applications of EEG for monitoring brain activity and diagnosing conditions like epilepsy.
The nucleus accumbens is located at the base of the forebrain and plays an important role in motivation, reward, and addiction. It is divided into two subdivisions and interacts closely with the ventral tegmental area via the mesolimbic pathway. Research has shown that the release of neurotransmitters like dopamine in the nucleus accumbens is linked to addiction, reward processing, and the placebo effect. Studies also suggest the nucleus accumbens is involved in conditions like ADHD and Tourette syndrome.
The temporal lobe is involved in several important functions:
1) It processes auditory and visual information through distinct cortical areas.
2) The medial temporal lobe structures including the hippocampus and amygdala are critical for forming memories and regulating emotions.
3) Disorders of the temporal lobe can cause problems with memory, language processing, perception and personality changes depending on the area affected.
Artifacts in EEG - Recognition and differentiationRahul Kumar
This Presentation discusses the variously commonly seen artifacts in EEG, and how to recognize them. In EEG interpretation, it is often more important to identify an artifact than to identify true pathology. Once all the artifacts are ruled out, one is sure that what one is dealing with represents disease/abnormality
Event Related Potentials, Cognitive Evoked Potentials. These are stimulus unrelated potentials, which depend on the patient's ability to differentiate between a rare stimulus and a common stimulus.
Cerebral dominance and its pathophysiology.pptxMuyangaMark1
The document discusses cerebral dominance and its pathophysiology. It notes that in most people, language functions are lateralized to the left hemisphere. The left hemisphere is specialized for sequential-analytic processes while the right hemisphere is specialized for visuospatial relations. Lesions in the left hemisphere can cause language disorders while lesions in the right hemisphere can cause agnosias like astereognosis. Overall, the hemispheres show complementary specialization rather than one being simply dominant or nondominant.
MEG measures the magnetic fields generated by electric currents in the brain. It has very high temporal resolution and good spatial resolution when combined with MRI. MEG is more sensitive than EEG to superficial cortical activity due to the way magnetic fields propagate. It is useful for localizing epileptic foci prior to epilepsy surgery and mapping eloquent cortex. Source analysis is performed to estimate the location of cortical generators. MEG provides better spatial resolution than EEG for localizing interictal epileptic discharges.
This document provides an introduction to artificial neural networks. It discusses biological neurons and how artificial neurons are modeled. The key components of a neural network including the network architecture, learning approaches, and the backpropagation algorithm for supervised learning are described. Applications and advantages of neural networks are also mentioned. Neural networks are modeled after the human brain and learn by modifying connection weights between nodes based on examples.
Neuromodulation involves neurotransmitters regulating diverse neuron populations. Several neuromodulatory systems project to brain regions involved in cognition, including the prefrontal cortex. These systems include cholinergic, dopaminergic, serotonergic, and noradrenergic projections. Cholinergic modulation is important for attention, working memory, and cue detection through muscarinic and nicotinic receptors. Experimental evidence shows cholinergic systems are required for cognitive functions. Neuromodulators can alter neuron properties and influence cognitive processes by increasing signal-to-noise ratios and biasing cortical processing.
Brief overview of brain stimulation techniquesSujit Kumar Kar
This document discusses various neurostimulation techniques used to treat psychiatric and neurological conditions. It begins by outlining the history and milestones of different brain stimulation methods from the 18th century to present day. These include the first reported use of camphor-induced seizures in 1785 to treat conditions, and the development of electroconvulsive therapy (ECT) in the 1930s-1950s.
The document then provides an overview of current neurostimulation techniques like ECT, transcranial magnetic stimulation (TMS), deep brain stimulation (DBS), vagus nerve stimulation (VNS), and transcranial direct current stimulation (tDCS). It notes their effectiveness for treating various disorders such as depression, OCD, anxiety
Neurobionics and robotic neurorehabilitationsNeurologyKota
This document discusses neurobionics, robotic neurorehabilitation, and applications of neurobionics. It summarizes key areas including: (1) neurobionics aims to integrate electronics with the nervous system to repair or substitute impaired functions, (2) robotic neurorehabilitation uses robots to assist in rehabilitation processes, and (3) applications of neurobionics include motor interfaces like robotic arms, sensory interfaces like cochlear implants, and treating conditions like epilepsy and Parkinson's disease.
The document discusses artifact detection and removal in neural recordings. It defines artifacts as interfering signals originating from sources other than the brain that can obscure or distort the recorded neural signal. It describes common artifact sources like motion and electrode impedance changes. Artifact properties, detection techniques, and possible removal methods are examined, including filtering, slope measurement, and adaptive filtering. The document concludes some artifact removal methods are imperfect and loss of data can occur.
Evoked potentials are low amplitude electrical potentials recorded from the brain or peripheral nerves in response to sensory stimuli. They are used to evaluate the function of sensory and motor pathways. There are several types including sensory evoked potentials from visual, auditory and somatosensory stimulation as well as motor evoked potentials. Recording techniques involve signal averaging to detect the low amplitude signals. Evoked potentials provide objective measures for diagnosing various neurological disorders.
Basic MEP techniques and understanding for Intraoperative neuromonitoring of the motors tracts during Brain and Spinal surgeries to prevent postoperative complications.
The temporal lobe plays important roles in processing sensory input such as auditory and visual information. It is involved in functions such as memory formation, emotion processing, and language comprehension. Damage to temporal lobe structures can cause symptoms like auditory or visual processing issues, memory impairments, and changes in emotional behavior or personality. The superior, middle, and inferior temporal gyri and medial temporal structures each contribute to these various temporal lobe functions.
Frontal lobe functions and assessmeny 20th july 2013Shahnaz Syeda
The frontal lobes have several functional areas that control motor functions like movement as well as higher cognitive functions. The primary motor cortex directly controls muscle movement while areas like the premotor cortex plan movements. The prefrontal cortex is involved in executive functions, problem solving, emotion regulation, and decision making through areas like the dorsolateral prefrontal cortex. Damage to different frontal lobe areas can cause syndromes like difficulties with movement, language, behavior, personality and cognition depending on the location of the lesion. A neuropsychological assessment can evaluate these frontal lobe functions.
Magnetoencephalography (MEG) is a non-invasive technique that measures the magnetic fields generated by neuronal brain activity. MEG uses very sensitive magnetometers to record these natural magnetic fields produced by the brain's electrical currents. Though brain signals appear irregular, they may be generated by deterministic nonlinear systems. MEG provides both high temporal resolution and excellent spatial resolution of brain function without exposure to radiation or invasive procedures.
fMRI measures brain activity by detecting changes in blood oxygenation and flow related to neural activity. Machine learning can be applied to fMRI data to identify the cognitive state of a human subject based on their brain activity patterns over time. The process involves preprocessing the high-dimensional fMRI imaging data, then using classifiers like Gaussian Naive Bayes, k-Nearest Neighbor, or Support Vector Machines to learn patterns that distinguish different cognitive states from the multi-voxel activity patterns.
Functional magnetic resonance imaging-fMRIREMIX MAHARJAN
This document provides an overview of functional magnetic resonance imaging (fMRI) and the blood oxygen level dependent (BOLD) contrast mechanism. It discusses how BOLD fMRI works by measuring changes in oxygenated blood flow and volume in the brain during neural activation. The history and key discoveries are summarized, including how deoxyhemoglobin causes local magnetic field distortions that reduce the MRI signal. Experimental paradigms and considerations for optimizing BOLD pulse sequences and analysis are also briefly outlined.
This document provides an overview of neuroimaging techniques used in psychiatry. It discusses the types and principles of structural neuroimaging like CT and MRI. CT provides visualization of brain morphology while MRI also allows evaluation of biochemical processes through techniques like fMRI. The document outlines indications for neuroimaging in psychiatric evaluation and research to study clinically defined patient groups and brain activity during tasks. It provides details on the basic principles and anatomical images of CT and MRI to interpret neuroimaging findings.
1. Neural networks can be examined at multiple levels from individual axons between neurons to fibre tracts between brain areas.
2. Types of connectivity include structural revealed by DTI, functional from correlated activity, and effective showing causal relationships.
3. Network analysis examines topological properties like modular clusters, small-world organization with high clustering and short path lengths, as well as spatial organization of brain regions.
Spatial neural networks tend to connect adjacent neurons to minimize wiring costs. However, some long-distance connections exist that reduce path lengths and allow for faster processing. Deficits in long-distance connectivity are linked to cognitive impairments like Alzheimer's disease and lower IQ scores.
1 basics of eeg and fundamentals of its measurementSwathy Ravi
The document discusses the basics and fundamentals of electroencephalography (EEG) and its measurement. It provides a timeline of EEG invention from 1875 to 1924. It describes cerebral generators of EEG potentials and how electrical signals propagate through neurons and are detected by EEG electrodes. The document outlines how EEG is recorded using a modern EEG machine and the 10-20 system for electrode placement. It discusses filters, amplifiers, polarity conventions, montages, artifacts, and clinical applications of EEG for monitoring brain activity and diagnosing conditions like epilepsy.
The nucleus accumbens is located at the base of the forebrain and plays an important role in motivation, reward, and addiction. It is divided into two subdivisions and interacts closely with the ventral tegmental area via the mesolimbic pathway. Research has shown that the release of neurotransmitters like dopamine in the nucleus accumbens is linked to addiction, reward processing, and the placebo effect. Studies also suggest the nucleus accumbens is involved in conditions like ADHD and Tourette syndrome.
The temporal lobe is involved in several important functions:
1) It processes auditory and visual information through distinct cortical areas.
2) The medial temporal lobe structures including the hippocampus and amygdala are critical for forming memories and regulating emotions.
3) Disorders of the temporal lobe can cause problems with memory, language processing, perception and personality changes depending on the area affected.
Artifacts in EEG - Recognition and differentiationRahul Kumar
This Presentation discusses the variously commonly seen artifacts in EEG, and how to recognize them. In EEG interpretation, it is often more important to identify an artifact than to identify true pathology. Once all the artifacts are ruled out, one is sure that what one is dealing with represents disease/abnormality
Event Related Potentials, Cognitive Evoked Potentials. These are stimulus unrelated potentials, which depend on the patient's ability to differentiate between a rare stimulus and a common stimulus.
Cerebral dominance and its pathophysiology.pptxMuyangaMark1
The document discusses cerebral dominance and its pathophysiology. It notes that in most people, language functions are lateralized to the left hemisphere. The left hemisphere is specialized for sequential-analytic processes while the right hemisphere is specialized for visuospatial relations. Lesions in the left hemisphere can cause language disorders while lesions in the right hemisphere can cause agnosias like astereognosis. Overall, the hemispheres show complementary specialization rather than one being simply dominant or nondominant.
MEG measures the magnetic fields generated by electric currents in the brain. It has very high temporal resolution and good spatial resolution when combined with MRI. MEG is more sensitive than EEG to superficial cortical activity due to the way magnetic fields propagate. It is useful for localizing epileptic foci prior to epilepsy surgery and mapping eloquent cortex. Source analysis is performed to estimate the location of cortical generators. MEG provides better spatial resolution than EEG for localizing interictal epileptic discharges.
This document provides an introduction to artificial neural networks. It discusses biological neurons and how artificial neurons are modeled. The key components of a neural network including the network architecture, learning approaches, and the backpropagation algorithm for supervised learning are described. Applications and advantages of neural networks are also mentioned. Neural networks are modeled after the human brain and learn by modifying connection weights between nodes based on examples.
Neuromodulation involves neurotransmitters regulating diverse neuron populations. Several neuromodulatory systems project to brain regions involved in cognition, including the prefrontal cortex. These systems include cholinergic, dopaminergic, serotonergic, and noradrenergic projections. Cholinergic modulation is important for attention, working memory, and cue detection through muscarinic and nicotinic receptors. Experimental evidence shows cholinergic systems are required for cognitive functions. Neuromodulators can alter neuron properties and influence cognitive processes by increasing signal-to-noise ratios and biasing cortical processing.
Brief overview of brain stimulation techniquesSujit Kumar Kar
This document discusses various neurostimulation techniques used to treat psychiatric and neurological conditions. It begins by outlining the history and milestones of different brain stimulation methods from the 18th century to present day. These include the first reported use of camphor-induced seizures in 1785 to treat conditions, and the development of electroconvulsive therapy (ECT) in the 1930s-1950s.
The document then provides an overview of current neurostimulation techniques like ECT, transcranial magnetic stimulation (TMS), deep brain stimulation (DBS), vagus nerve stimulation (VNS), and transcranial direct current stimulation (tDCS). It notes their effectiveness for treating various disorders such as depression, OCD, anxiety
Neurobionics and robotic neurorehabilitationsNeurologyKota
This document discusses neurobionics, robotic neurorehabilitation, and applications of neurobionics. It summarizes key areas including: (1) neurobionics aims to integrate electronics with the nervous system to repair or substitute impaired functions, (2) robotic neurorehabilitation uses robots to assist in rehabilitation processes, and (3) applications of neurobionics include motor interfaces like robotic arms, sensory interfaces like cochlear implants, and treating conditions like epilepsy and Parkinson's disease.
The document discusses artifact detection and removal in neural recordings. It defines artifacts as interfering signals originating from sources other than the brain that can obscure or distort the recorded neural signal. It describes common artifact sources like motion and electrode impedance changes. Artifact properties, detection techniques, and possible removal methods are examined, including filtering, slope measurement, and adaptive filtering. The document concludes some artifact removal methods are imperfect and loss of data can occur.
Evoked potentials are low amplitude electrical potentials recorded from the brain or peripheral nerves in response to sensory stimuli. They are used to evaluate the function of sensory and motor pathways. There are several types including sensory evoked potentials from visual, auditory and somatosensory stimulation as well as motor evoked potentials. Recording techniques involve signal averaging to detect the low amplitude signals. Evoked potentials provide objective measures for diagnosing various neurological disorders.
Basic MEP techniques and understanding for Intraoperative neuromonitoring of the motors tracts during Brain and Spinal surgeries to prevent postoperative complications.
The temporal lobe plays important roles in processing sensory input such as auditory and visual information. It is involved in functions such as memory formation, emotion processing, and language comprehension. Damage to temporal lobe structures can cause symptoms like auditory or visual processing issues, memory impairments, and changes in emotional behavior or personality. The superior, middle, and inferior temporal gyri and medial temporal structures each contribute to these various temporal lobe functions.
Frontal lobe functions and assessmeny 20th july 2013Shahnaz Syeda
The frontal lobes have several functional areas that control motor functions like movement as well as higher cognitive functions. The primary motor cortex directly controls muscle movement while areas like the premotor cortex plan movements. The prefrontal cortex is involved in executive functions, problem solving, emotion regulation, and decision making through areas like the dorsolateral prefrontal cortex. Damage to different frontal lobe areas can cause syndromes like difficulties with movement, language, behavior, personality and cognition depending on the location of the lesion. A neuropsychological assessment can evaluate these frontal lobe functions.
Magnetoencephalography (MEG) is a non-invasive technique that measures the magnetic fields generated by neuronal brain activity. MEG uses very sensitive magnetometers to record these natural magnetic fields produced by the brain's electrical currents. Though brain signals appear irregular, they may be generated by deterministic nonlinear systems. MEG provides both high temporal resolution and excellent spatial resolution of brain function without exposure to radiation or invasive procedures.
fMRI measures brain activity by detecting changes in blood oxygenation and flow related to neural activity. Machine learning can be applied to fMRI data to identify the cognitive state of a human subject based on their brain activity patterns over time. The process involves preprocessing the high-dimensional fMRI imaging data, then using classifiers like Gaussian Naive Bayes, k-Nearest Neighbor, or Support Vector Machines to learn patterns that distinguish different cognitive states from the multi-voxel activity patterns.
Functional magnetic resonance imaging-fMRIREMIX MAHARJAN
This document provides an overview of functional magnetic resonance imaging (fMRI) and the blood oxygen level dependent (BOLD) contrast mechanism. It discusses how BOLD fMRI works by measuring changes in oxygenated blood flow and volume in the brain during neural activation. The history and key discoveries are summarized, including how deoxyhemoglobin causes local magnetic field distortions that reduce the MRI signal. Experimental paradigms and considerations for optimizing BOLD pulse sequences and analysis are also briefly outlined.
This document provides an overview of neuroimaging techniques used in psychiatry. It discusses the types and principles of structural neuroimaging like CT and MRI. CT provides visualization of brain morphology while MRI also allows evaluation of biochemical processes through techniques like fMRI. The document outlines indications for neuroimaging in psychiatric evaluation and research to study clinically defined patient groups and brain activity during tasks. It provides details on the basic principles and anatomical images of CT and MRI to interpret neuroimaging findings.
1. Neural networks can be examined at multiple levels from individual axons between neurons to fibre tracts between brain areas.
2. Types of connectivity include structural revealed by DTI, functional from correlated activity, and effective showing causal relationships.
3. Network analysis examines topological properties like modular clusters, small-world organization with high clustering and short path lengths, as well as spatial organization of brain regions.
Spatial neural networks tend to connect adjacent neurons to minimize wiring costs. However, some long-distance connections exist that reduce path lengths and allow for faster processing. Deficits in long-distance connectivity are linked to cognitive impairments like Alzheimer's disease and lower IQ scores.
This document discusses network analysis and measures of centrality and communicability in networks. It provides mathematical definitions and formulas for quantifying properties like betweenness centrality, clustering coefficient, communicability between nodes, and the number of walks and routes connecting nodes in a network. Examples of applying these metrics to real-world networks like social and biological networks are also mentioned.
This document provides an overview of a tutorial on connectome analysis given by Dr. Marcus Kaiser. The tutorial covers topics such as graph theory, spatial and topological properties of neural networks. It also discusses how brain structure is influenced by function and evolution. Computer simulations are presented that model brain dynamics and can predict the location of epileptic tissue or the effects of optogenetic stimulation. Dr. Kaiser's research group at Newcastle University studies brain connectivity across species using neuroimaging and modeling approaches.
This document summarizes Marc Barthelemy's presentation on spatial network theory and applications. The presentation covered various models of spatial networks including Voronoi tessellations, random geometric graphs, spatial generalizations of Erdos-Renyi and small-world networks, and growing network models. It also discussed optimal network design problems and models incorporating both network growth and optimization. Scaling relationships between network properties like total length and number of stations and socioeconomic factors like GDP and population were examined for subway and railway networks.
1. The document discusses using call detail record (CDR) data to study how mobile phone users manage their social contacts over time and characterize or predict social turnover.
2. By detecting new and old social relationships from CDRs that show communication patterns and frequencies between users, the author aims to analyze how users' social networks evolve and change.
3. The author proposes studying properties like the distribution of inter-event times between calls to the same contact and how this distribution depends on relationship longevity to provide insights into social turnover.
- Temporal networks are dynamic networks that change over time. They are commonly represented through temporal contact sequences or time-varying adjacency matrices.
- Key properties of temporal networks include distributions of contact durations and inter-contact times, measures of burstiness, and persistence/correlation of network structures over time.
- Analyzing temporal paths, centrality measures, motifs, and comparing empirical networks to temporal null models can provide insights into the structure and dynamics of temporal networks not evident from static representations.
1. The document discusses mesoscale network structures, which are middle-scale properties between microscale (individual nodes/edges) and macroscale (overall network properties). It focuses on community structure detection but notes there are other mesoscale structures like core-periphery and roles/positions.
2. Community detection algorithms aim to find densely connected groups of nodes but may return structure even in random networks. The document advocates a cautious approach and examining multiple possible structures.
3. Other mesoscale structures discussed include bipartite structures, block models representing roles of nodes, and stochastic block models providing a statistical framework.
This document provides an overview of spatial network theory and applications. It discusses how space impacts network structure and introduces several tools for analyzing spatial networks. These include indices to characterize street and transportation networks, typologies of planar graphs based on block shape and area statistics, and methods for studying the time evolution of networks using old map digitization. Specific examples analyzed include road, power grid, airline and neural networks.
This document discusses various topological and spatial features of brain networks, including small-world properties, motifs, clusters, degree distributions, and robustness. It provides examples of analyses conducted on structural and functional brain networks, such as detecting clusters in the cat cortex and examining the effects of simulated brain lesions. Modular organization is highlighted as important for local integration and global separation of processing. Developing brain networks are found to require less information to encode connectivity patterns compared to random networks.
This document discusses social and economic networks that can be analyzed using big data. It covers sources of social and geographic big data like mobile phone data, social media, financial transactions, and maps. It then discusses tools for analyzing this big data, including network analysis platforms, visualization libraries, and graph databases. Finally, it provides examples of applications of big data in domains like health, transportation, real estate, politics, and more.
This document discusses statistical inference of generative network models. It begins by discussing the problem of detecting modular structure in large-scale networks and different methods that produce different results. The document then advocates for a principled approach using generative models to formulate probabilistic models for network structure before devising algorithms. It discusses the exponential random graph model and the stochastic block model as examples. It covers maximum likelihood inference to estimate model parameters and efficient MCMC algorithms. Challenges discussed include broad degree distributions, overfitting due to unknown number of groups, and nonparametric Bayesian inference using minimum description length principle.
1. The document examines the relationship between brain anatomical networks and intelligence by analyzing structural, functional, and effective connectivity patterns.
2. It reviews concepts from graph theory and complex networks that are relevant for studying brain networks, including small-world networks and scale-free networks.
3. An experiment analyzed diffusion tensor images and other data from 79 subjects to construct and analyze anatomical brain networks and investigate their relationships with general and high intelligence.
The document discusses the default mode network (DMN), a network of brain regions that are active when an individual is not focused on tasks. The DMN is involved in daydreaming and predictive thinking based on past experiences and the current environment. There is ongoing research trying to understand what the DMN is doing and how it relates to behavior, beliefs, thoughts, and more. Coaches can help identify when a client's DMN is active and leverage it to achieve coaching goals by addressing negative patterns of thinking that may be hindering progress.
The study of the functional areas of our brain is important to understand the functions of left and right segments. Right brain activation is essential to be more creative
How the brain learns, formation of new neuronal networks, makiong your meory...Babu Appat
When you learn something new, a neuronal network in your brain is established. This networks conducts electric impulses and communication and processing of data and decision making happens as fast. So the strong network formation is can be conscientiously aided to improve the memory and processing speed of the brain.
This document discusses clinical assessment of developmental disorders. It introduces two main categories of developmental disorders - specific disorders like dyslexia and pervasive disorders like autism and intellectual disability. It proposes assessing developmental disorders via interviews, observation, psychometric tools and considering clinical variations in physical, emotional and social intelligence. Stages of development are also discussed from infancy through adulthood. Factors like immaturity, regression in illnesses and disorders like ADHD that can indirectly impact maturity are reviewed.
This document discusses how advances in neuroscience can inform new approaches to leadership. It covers key topics like the triune brain model consisting of the reptilian, mammalian, and human/neocortex parts. The social brain and neuroplasticity are also discussed, highlighting how the brain is hardwired for social connection and continues developing throughout life. The presentation argues that understanding these brain concepts can help leaders tap into the power of the brain and develop the whole person, moving beyond more mechanistic leadership models to systemic approaches suited for today's complex environment.
This document summarizes a presentation on exploring complex networks in the brain. It discusses defining the human connectome at multiple scales from neurons to brain regions. It outlines steps to map the structural and functional connectivity of the brain. It also describes using network measures and models to analyze topological properties of brain networks and detecting community structure. Detecting changes in network measures may help understand diseases.
This document discusses quantifying hierarchy in complex networks. It begins by providing examples of hierarchical structures in the brain, mental lexicon, gene regulation and food webs. It then outlines requirements for measuring hierarchy, such as being based on global topology. It introduces Random Walk Hierarchy as a measure that meets these requirements. Random Walk Hierarchy tracks how information spreads through random walks on the network. The more a network resembles a hierarchy, the more information will converge on root nodes. The measure is applied to different network structures and real-world examples.
Zhou Changsong presents a document discussing the brain as a complex dynamical network system subject to constraints of cost and function. It aims to reconcile irregular neuronal spiking with neural avalanches through a biologically plausible neuronal network model and statistical physics analysis. The key findings are that the model shows coexistence of irregular spiking, oscillations, and critical avalanches through a dynamical mechanism of Hopf bifurcation in the mean field model that explains critical neural avalanches corresponding to irregular spiking in the microscopic neuronal network model. This multiscale variability in brain activity reflects principles of cost-efficient neural representation and dynamics.
Networks in Space: Granular Force Networks and BeyondMason Porter
This is my talk for the Network Geometry Workshop (http://ginestra-bianconi-6flt.squarespace.com) at QMUL on 16 July 2015.
(A few of the slides are adapted from slides by my coauthors Dani Bassett and Karen Daniels.)
Some key models of social network generation are discussed, including random graph models, Watts-Strogatz models, and scale-free networks. Scale-free networks can generate networks with few components, small diameters, and heavy-tailed degree distributions, but do not capture high clustering. Biological networks like metabolic and protein interaction networks also tend to be scale-free.
FINE GRAIN PARALLEL CONSTRUCTION OF NEIGHBOUR-JOINING PHYLOGENETIC TREES WITH...ijdpsjournal
In biological research, scientists often need to use the information of the species to infer the evolutionary relationship among them. The evolutionary relationships are generally represented by a labeled binary tree, called the evolutionary tree (or phylogenetic tree). The phylogeny problem is computationally intensive, and thus it is suitable for parallel computing environment. In this paper, a fast algorithm for
constructing Neighbor-Joining phylogenetic trees has been developed. The CPU time is drastically reduced as compared with sequential algorithms. The new algorithm includes three techniques: Firstly, a linear array A[N] is introduced to store the sum of every row of the distance matrix (the same as SK),
which can eliminate many repeated (redundancy) computations, and the value of A[i] are computed only once at the beginning of the algorithm, and are updated by three elements in the iteration. Secondly, a very compact formula for the sum of all the branch lengths of OTUs (Operational Taxonomic Units) i and
j has been designed. Thirdly, multiple parallel threads are used for computation of nearest neighboring pair.
The Hidden Geometry of Multiplex Networks @ Next Generation Network Analytics Kolja Kleineberg
The document summarizes research on the hidden geometry of multiplex networks. It finds that real-world multiplex networks often have correlated geometric properties between network layers, with nodes maintaining similar radial and angular coordinates. This has implications like communities of nodes being similar across layers and hyperbolic distance in one layer predicting connections in another. A geometric multiplex model is introduced to generate realistic multiplex networks with tunable geometric correlations between layers.
Complex systems are characterized by constituents -- from neurons in the brain to individuals in a social network -- which exhibit special structural organization and nonlinear dynamics. As a consequence, a complex system cannot be understood by studying its units separately because their interactions lead to unexpected emerging phenomena, from collective behavior to phase transitions.
Recently, we have discovered that a new level of complexity characterizes a variety of natural and artificial systems, where units interact, simultaneously, in distinct ways. For instance, this is the case of multimodal transportation systems (e.g., metro, bus and train networks) or of biological molecules, whose interactions might be of different type (e.g. physical, chemical, genetic) or functionality (e.g., regulatory, inhibitory, etc.). The unprecedented newfound wealth of multivariate data allows to categorize system's interdependency by defining distinct "layers", each one encoding a different network representation of the system. The result is a multilayer network model.
Analyzing data from different domains -- including molecular biology, neuroscience, urban transport, telecommunications -- we will show that neglecting or disregarding multivariate information might lead to poor results. Conversely, multilayer models provide a suitable framework for complex data analytics, allowing to quantify the resilience of a system to perturbations (e.g., localized failures or targeted attacks), improving forecasting of spreading processes and accuracy in classification problems.
This document discusses using repeated simulations of a crisp neural network to obtain quasi-fuzzy weight sets (QFWS) that can be used to initialize fuzzy neural networks. The key points are:
1) A crisp neural network is repeatedly trained on input-output data to model an unknown function. The connection weights change with each simulation.
2) Recording the weights from multiple simulations produces quasi-fuzzy weight sets, where each weight is a fuzzy set rather than a single value.
3) These QFWS can provide initial solutions for training type-I fuzzy neural networks with reduced computational complexity compared to random initialization.
4) The QFWS follow fuzzy arithmetic and allow both numerical and linguistic data to
The document summarizes a study that mapped the rich-club organization of hub regions in the human connectome (structural brain network). Researchers used diffusion tensor imaging data from 21 subjects to reconstruct whole-brain structural networks and examine their connectivity profiles. They identified a group of 12 strongly interconnected bihemispheric hub regions, including the precuneus, frontal and parietal cortices, hippocampus, putamen, and thalamus. Importantly, these hub regions were found to be more densely interconnected than expected based on their degree alone, together forming a rich club in the human connectome.
This document discusses neural networks and their applications. It begins with an overview of neurons and the brain, then describes the basic components of neural networks including layers, nodes, weights, and learning algorithms. Examples are given of early neural network designs from the 1940s-1980s and their applications. The document also summarizes backpropagation learning in multi-layer networks and discusses common network architectures like perceptrons, Hopfield networks, and convolutional networks. In closing, it notes the strengths and limitations of neural networks along with domains where they have proven useful, such as recognition, control, prediction, and categorization tasks.
Self-Organizing Maps (SOM) are a type of neural network that can be used for clustering and visualizing complex, high-dimensional data. SOM reduces dimensionality while preserving topological relationships. It arranges nodes on a grid such that similar input vectors are mapped to nearby nodes. During training, the best matching node and its neighbors are adjusted to better match the input. This results in a 2D map where similar data clusters together. For example, a SOM was used to cluster countries based on quality of life indicators, grouping those with similar living standards. SOM can be useful for applications like data mining, pattern recognition, and more.
MODELING SOCIAL GAUSS-MARKOV MOBILITY FOR OPPORTUNISTIC NETWORK csandit
Mobility is attracting more and more interests due to its importance for data forwarding
mechanisms in many networks such as mobile opportunistic network. In everyday life mobile
nodes are often carried by human. Thus, mobile nodes’ mobility pattern is inevitable affected by
human social character. This paper presents a novel mobility model (HNGM) which combines
social character and Gauss-Markov process together. The performance analysis on this
mobility model is given and one famous and widely used mobility model (RWP) is chosen to
make comparison..
Elastic path2path (International Conference on Image Processing'18)TamalBatabyal
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Neural Networks with Anticipation: Problems and ProspectsSSA KPI
AACIMP 2010 Summer School lecture by Alexander Makarenko. "Applied Mathematics" stream. "General Tasks and Problems of Modelling of Social Systems. Problems and Models in Sustainable Development" course. Part 6.
More info at http://summerschool.ssa.org.ua
Spectral clustering with motifs and higher-order structuresDavid Gleich
I presented these slides at the #strathna meeting in Glasgow in June 2017. They are an updated and enhanced version of the earlier talks on the subject.
This document provides an introduction to networks. It discusses how networks are used to model relationships between entities in various domains, including social networks, protein interactions, and infrastructure networks. It also describes some key concepts in network analysis, such as degree distribution, shortest paths, centrality measures, and topological properties like the small-world and scale-free networks commonly seen in real-world systems.
Understanding Protein Function on a Genome-scale through the Analysis of Molecular Networks
Cornell Medical School, Physiology, Biophysics and Systems Biology (PBSB) graduate program, 2009.01.26, 16:00-17:00; [I:CORNELL-PBSB] (Long networks talk, incl. the following topics: why networks w. amsci*, funnygene*, net. prediction intro, memint*, tse*, essen*, sandy*, metagenomics*, netpossel*, tyna*+ topnet*, & pubnet* . Fits easily into 60’ w. 10’ questions. PPT works on mac & PC and has many photos w. EXIF tag kwcornellpbsb .)
Date Given: 01/26/2009
Interpretation of the biological knowledge using networks approachElena Sügis
This document discusses using biological networks to analyze and interpret biological knowledge. It begins with an overview of networks as tools to reduce complexity and integrate data. Key properties of networks are described, including nodes, edges, degree distribution, clustering coefficient, and centrality measures. Methods for analyzing networks like community detection and network motifs are also covered. The document emphasizes that biological networks must be analyzed and interpreted based on their properties and by mapping relevant biological data to provide meaningful insights.
Fuzzy Logic and Neuro-fuzzy Systems: A Systematic IntroductionWaqas Tariq
Fuzzy logic is a rigorous mathematical field, and it provides an effective vehicle for modeling the uncertainty in human reasoning. In fuzzy logic, the knowledge of experts is modeled by linguistic rules represented in the form of IF-THEN logic. Like neural network models such as the multilayer perceptron (MLP) and the radial basis function network (RBFN), some fuzzy inference systems (FISs) have the capability of universal approximation. Fuzzy logic can be used in most areas where neural networks are applicable. In this paper, we first give an introduction to fuzzy sets and logic. We then make a comparison between FISs and some neural network models. Rule extraction from trained neural networks or numerical data is then described. We finally introduce the synergy of neural and fuzzy systems, and describe some neuro-fuzzy models as well. Some circuits implementations of neuro-fuzzy systems are also introduced. Examples are given to illustrate the cocepts of neuro-fuzzy systems.
Soft computing is a set of computational techniques that aim to mimic human-like reasoning and decision making. The main techniques are fuzzy logic, neural networks, evolutionary computing, machine learning, and probabilistic reasoning. Each technique has strengths and weaknesses, but they complement each other. When used together, soft computing techniques can solve complex problems that are difficult for traditional mathematical methods. The paper reviews these soft computing techniques and explores how they could be applied to problems in various domains.
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Functional Brain Networks - Javier M. Buldù
1. FUNCTIONAL BRAIN NETWORKS
JAVIER M. BULDÚ
UNIVERSIDAD REY JUAN CARLOS (MÓSTOLES)
CENTRO DE TECNOLOGÍA BIOMÉDICA (POZUELO)
COMPLEJIMAD (MADRID)
(… A MINEFIELD!)
2. OUTLINE
❑ Functional Brain Networks
❑ Measuring Brain Activity
❑Time Series & Network Construction
❑ Network Analysis
❑ Risks & Challenges
❑ Functional Networks are alive
❑ Living in Hillsville
❑ Conclusions
❑ Brain Networks
❑ Anatomical Networks
❑ Functional Networks
4. COMPLEX SYSTEMS
A complex system is composed of interrelated parts which, as a whole, exhibit
properties and behaviors that can not be explained analyzing each of the individual parts
separately:
A neuron A brain
5. What if we apply network science to the most challenging
system we are facing?
APPLYING NETWORK SCIENCE TO THE BRAIN
6. APPLYING NETWORK SCIENCE TO THE BRAIN
In brief, (main) types of brain networks
From Bullmore & Sporns, Nature Rev. 10, 186 (2009)
anatomical functional
7. M. Rubinov and O. Sporns,
NeuroImage 52, 1059–1069 (2010)
Appendix B. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.neuroimage.2009.10.003.
References
Achard, S., Bullmore, E., 2007. Efficiency and cost of economical brain functional
networks. PLoS Comput. Biol. 3, e17.
Achard, S., Salvador, R., Whitcher, B., Suckling, J., Bullmore, E., 2006. A resilient, low-
frequency, small-world human brain functional network with highly connected
association cortical hubs. J. Neurosci. 26, 63–72.
Alstott, J., Breakspear, M., Hagmann, P., Cammoun, L., Sporns, O., 2009. Modeling the
impact of lesions in the human brain. PLoS Comput. Biol. 5, e1000408.
Barabasi, A.L., Albert, R., 1999. Emergence of scaling in random networks. Science 286,
509–512.
Barrat, A., Barthelemy, M., Pastor-Satorras, R., Vespignani, A., 2004. The architecture of
complex weighted networks. Proc. Natl. Acad. Sci. U. S. A. 101, 3747–3752.
Bassett, D.S., Bullmore, E., 2006. Small-world brain networks. Neuroscientist 12,
512–523.
Bassett, D.S., Bullmore, E.T., 2009. Human brain networks in health and disease. Curr.
Opin. Neurol. 22, 340–347.
Bassett, D.S., Meyer-Lindenberg, A., Achard, S., Duke, T., Bullmore, E., 2006. Adaptive
reconfiguration of fractal small-world human brain functional networks. Proc. Natl.
Acad. Sci. U. S. A. 103, 19518–19523.
Bassett, D.S., Bullmore, E., Verchinski, B.A.,Mattay,V.S.,Weinberger, D.R., Meyer-Lindenberg,
A., 2008. Hierarchical organization of human cortical networks in health and
schizophrenia. J. Neurosci. 28, 9239–9248.
Batagelj, V.,M
M., Mut
Blondel, V.D
commun
Boccaletti, S
Structur
Brandes, U.,
163–177
Bullmore, E.
structur
Butts, C.T., 2
Costa, L.d.F.
cortical
1, 16.
Costa, L.D.F.
complex
Damoiseaux
studies
ity. Brain
Danon, L., D
identific
Deuker, L., B
D.S., 200
NeuroIm
Estrada, E., H
Nonline
Fagiolo, G., 2
Soft Mat
Freeman, L.C
215–239
Table A1 (continued)
Measure Binary and undirected definitions W
Measures of resilience
Degree distribution Cumulative degree distribution of the network
(Barabasi and Albert, 1999),
P kð Þ =
X
kVzk
p kVð Þ;
where p(k′) is the probability of a node having degree k′.
C
C
C
Average neighbor
degree
Average degree of neighbors of node i (Pastor-Satorras et al., 2001),
knn;i =
P
jaN aijkj
ki
:
A
B
k
A
k
Assortativity coefficient Assortativity coefficient of the network (Newman, 2002),
r =
l
−1 P
i;jð ÞaL kikj − l
− 1 P
i;jð ÞaL
1
2 ki + kj
h i2
l−1
P
i;jð ÞaL
1
2 k2
i + k2
j
− l−1
P
i;jð ÞaL
1
2 ki + kj
h i2
:
W
L
r
D
r
Other concepts
Degree distribution
preserving network
randomization.
Degree-distribution preserving randomization is implemented by
iteratively choosing four distinct nodes i1, j1, i2, j2 ∈ N at random,
such that links (i1, j1), (i2, j2) ∈ L, while links (i1, j2), (i2, j1) ∉ L.
The links are then rewired such that (i1, j2), (i2, j1) ∈ L and (i1, j1),
(i2, j2) ∉ L, (Maslov and Sneppen, 2002).
“Latticization” (a lattice-like topology) results if an additional
constraint is imposed, |i1+j2| + |i2+j1| b |i1+j1| + |i2+j2|
(Sporns and Kotter, 2004).
T
In
li
p
to
sc
Measure `of network
small-worldness.
Network small-worldness (Humphries and Gurney, 2008),
S =
C = Crand
L = Lrand
;
where C and Crand are the clustering coefficients, and L and Lrand are
the characteristic path lengths of the respective tested network and
a random network. Small-world networks often have S ≫ 1.
W
D
In
All binary and undirected measures are accompanied by their weighted and directed generalizations. G
knowledge) are marked with an asterisk (⁎). The Brain Connectivity Toolbox contains Matlab functions
Table A1 (continued)
Measure Binary and undirected definitions Weighted and directed definitions
Modularity Modularity of the network (Newman, 2004b),
Q =
X
uaM
euu −
X
vaM
euv
!2
#
;
where the network is fully subdivided into a set of nonoverlapping
modules M, and euv is the proportion of all links that connect nodes
in module u with nodes in module v.
An equivalent alternative formulation of the modularity
(Newman, 2006) is given by Q = 1
l
P
i;jaN aij −
ki kj
l
δmi ;mj
,
where mi is the module containing node i, and δmi,mj = 1 if mi = mj,
and 0 otherwise.
Weighted modularity (Newman, 2004),
Qw
= 1
lw
P
i;jaN wij −
k
w
i k
w
j
l
w
!
δmi ;mj
:
Directed modularity (Leicht and Newman, 2008),
QY
= 1
l
P
i;jaN aij −
k
out
i k
in
i
l
!
δmi ;mj
:
Measures of centrality
Closeness centrality Closeness centrality of node i (e.g. Freeman, 1978),
L
−1
i =
n − 1
P
jaN;j≠i
dij
:
Weighted closeness centrality, Lw
i
À Á− 1
= n − 1P
jaN; j≠i
d
w
ij
.
Directed closeness centrality, LY
i
À Á−1
= n − 1P
jaN; j≠i
d
Y
ij
.
Betweenness centrality Betweenness centrality of node i (e.g., Freeman, 1978),
bi =
1
n − 1ð Þ n − 2ð Þ
P
h;jaN
h≠j;h≠i;j≠i;
ρ
hj ið Þ
ρ
hj
;
where ρhj is the number of shortest paths between h and j, and ρhj (i)
is the number of shortest paths between h and j that pass through i.
Betweenness centrality is computed equivalently on
weighted and directed networks, provided that path lengths
are computed on respective weighted or directed paths.
Within-module degree
z-score
Within-module degree z-score of node i
(Guimera and Amaral, 2005),
zi =
ki mið Þ − k mið Þ
σk mið Þ
;
where mi is the module containing node i, ki (mi) is the
within-module degree of i (the number of links between i and all
other nodes in mi), and k mið Þ and σk(mi)
are the respective mean
and standard deviation of the within-module mi degree distribution.
Weighted within-module degree z-score, zw
i =
k
w
i mið Þ − kw
mið Þ
σkw mið Þ
.
Within-module out-degree z-score, zout
i =
k
out
i mið Þ − kout
mið Þ
σ
kout mið Þ
.
Within-module in-degree z-score, zin
i =
k
in
i mið Þ − kin
mið Þ
σ
kin mið Þ
.
Participation coefficient Participation coefficient of node i (Guimera and Amaral, 2005),
yi = 1 −
X
maM
ki mð Þ
ki
2
;
where M is the set of modules (see modularity), and ki (m) is the
number of links between i and all nodes in module m.
Weighted participation coefficient, yw
i = 1 −
P
maM
kw
i
mð Þ
kw
i
2
.
Out-degree participation coefficient, yout
i = 1 −
P
maM
kout
i
mð Þ
kout
i
2
.
In-degree participation coefficient, yin
i = 1 −
P
maM
kin
i
ðmÞ
kin
i
2
.
Network motifs
Anatomical and
functional motifs
Jh is the number of occurrences of motif h in all subsets of the
network (subnetworks). h is an nh node, lh link, directed connected
pattern. h will occur as an anatomical motif in an nh node, lh link
subnetwork, if links in the subnetwork match links in h
(Milo et al., 2002). h will occur (possibly more than once) as a
functional motif in an nh node, lh′ ≥ lh link subnetwork, if at least one
combination of lh links in the subnetwork matches links in h
(Sporns and Kotter, 2004).
(Weighted) intensity of h (Onnela et al., 2005),
Ih =
P
u Π i;jð ÞaLhu
wij
1
lh ;
where the sum is over all occurrences of h in the network,
and L
hu
is the set of links in the uth occurrence of h.
Note that motifs are directed by definition.
Motif z-score z-Score of motif h (Milo et al., 2002),
zh =
Jh − h Jrand;hi
σ Jrand;h
;
where 〈Jrand,h〉 and σ Jrand,h
are the respective mean and standard
deviation for the number of occurrences of h in an ensemble of
random networks.
Intensity z-score of motif h (Onnela et al., 2005),
zI
h =
Ih − hIrand;h i
σ
Irand;h
;
where 〈Irand,h〉 and σ Irand,h
are the respective
mean and standard deviation for the intensity of h in an
ensemble of random networks.
Motif fingerprint nh node motif fingerprint of the network (Sporns and Kotter, 2004),
Fnh
hVð Þ =
X
iaN
Fnh;i hVð Þ =
X
iaN
JhV;i;
where h′ is any nh node motif, Fnh,i (h′) is the nh node motif
fingerprint for node i, and Jh′,i is the number of occurrences of
motif h′ around node i.
nh node motif intensity fingerprint of the network,
FI
nh
hVð Þ =
P
iaNFI
nh;i hV
À Á
=
P
iaN IhV; i,
where h′ is any nh node motif, FI
nh,i (h′) is the nh node motif
intensity fingerprint for node i, and Ih′,i is the intensity of
motif h′ around node i.
(continued on next page)
Mathematical definitions of complex network measures (see supplementary information for a self-contained version of this table).
Measure Binary and undirected definitions Weighted and directed definitions
Basic concepts and measures
Basic concepts and
notation
N is the set of all nodes in the network, and n is the number of nodes.
L is the set of all links in the network, and l is number of links.
(i, j) is a link between nodes i and j, (i, j ∈ N).
aij is the connection status between i and j: aij = 1 when link (i, j)
exists (when i and j are neighbors); aij = 0 otherwise (aii = 0 for all i).
We compute the number of links as l = ∑i,j∈N aij (to avoid
ambiguity with directed links we count each undirected link twice,
as aij and as aji).
Links (i, j) are associated with connection weights wij.
Henceforth, we assume that weights are normalized,
such that 0 ≤ wij ≤ 1 for all i and j.
lw
is the sum of all weights in the network, computed
as lw
= ∑i,j∈N wij.
Directed links (i, j) are ordered from i to j. Consequently,
in directed networks aij does not necessarily equal aji.
Degree: number of links
connected to a node
Degree of a node i,
ki =
X
jaN
aij:
Weighted degree of i, ki
w
= ∑j∈Nwij.
(Directed) out-degree of i, ki
out
= ∑j∈Naij.
(Directed) in-degree of i, ki
in
= ∑j∈Naji.
Shortest path length:
a basis for measuring
integration
Shortest path length (distance), between nodes i and j,
dij =
X
auv agi X j
auv;
where gi↔j is the shortest path (geodesic) between i and j. Note
that dij = ∞ for all disconnected pairs i, j.
Shortest weighted path length between i and j,
dij
w
= ∑auv∈gi↔j
w
f(wuv), where f is a map (e.g., an inverse)
from weight to length and gi↔j
w
is the shortest weighted
path between i and j.
Shortest directed path length from i to j, dij
→
= ∑aij∈gi→j
aij,
where gi→j is the directed shortest path from i to j.
Number of triangles: a
basis for measuring
segregation
Number of triangles around a node i,
ti =
1
2
X
j;haN
aijaihajh:
(Weighted) geometric mean of triangles around i,
tw
i = 1
2
P
j;haN wijwihwjh
À Á1=3
:
Number of directed triangles around i,
tY
i = 1
2
P
j;haN aij + aji
À Á
aih + ahið Þ ajh + ahj
À Á
.
Measures of integration
Characteristic path
length
Characteristic path length of the network
(e.g., Watts and Strogatz, 1998),
L =
1
n
X
iaN
Li =
1
n
X
iaN
P
jaN;j≠i dij
n − 1
;
where Li is the average distance between node i and all other nodes.
Weighted characteristic path length, Lw
= 1
n
P
iaN
P
jaN; j≠i
d
w
ij
n − 1 .
Directed characteristic path length, LY
= 1
n
P
iaN
P
jaN; j≠i
d
Y
ij
n − 1 .
Global efficiency Global efficiency of the network (Latora and Marchiori, 2001),
E =
1
n
X
iaN
Ei =
1
n
X
iaN
P
jaN;j≠i d
−1
ij
n − 1
;
where Ei is the efficiency of node i.
Weighted global efficiency, Ew
= 1
n
P
iaN
P
jaN; j≠i
dw
ij
− 1
n − 1 .
Directed global efficiency, EY
= 1
n
P
iaN
P
jaN; j≠i
dY
ij
− 1
n − 1 .
Measures of segregation
Clustering coefficient Clustering coefficient of the network (Watts and Strogatz, 1998),
C =
1
n
X
iaN
Ci =
1
n
X
iaN
2ti
ki ki − 1ð Þ
;
where Ci is the clustering coefficient of node i (Ci = 0 for ki b 2).
Weighted clustering coefficient (Onnela et al., 2005),
Cw
= 1
n
P
iaN
2tw
i
ki ki − 1ð Þ
. See Saramaki et al. (2007) for
other variants.
Directed clustering coefficient (Fagiolo, 2007),
CY
= 1
n
P
iaN
tY
i
kout
i
+ kin
ið Þ kout
i
+ kin
i
− 1ð Þ − 2
P
jaN
aijaji
:
Transitivity Transitivity of the network (e.g., Newman, 2003),
T =
P
iaN 2ti
P
iaN ki ki − 1ð Þ
:
Note that transitivity is not defined for individual nodes.
Weighted transitivity⁎, Tw
=
P
iaN
2tw
iP
iaN
ki ki − 1ð Þ
.
Directed transitivity⁎,
TY
=
P
iaN
tY
i
P
iaN
k
out
i + k
in
i
À Á
k
out
i + k
in
i − 1
À Á
− v2
P
jaN
aijaji
h i :
Local efficiency Local efficiency of the network (Latora and Marchiori, 2001),
Eloc =
1
n
X
iaN
Eloc;i =
1
n
X
iaN
P
j;haN;j≠i aijaih djh Nið Þ
h i−1
ki ki − 1ð Þ
;
where Eloc,i is the local efficiency of node i, and djh (Ni) is the
length of the shortest path between j and h, that contains only
neighbors of i.
Weighted local efficiency⁎,
Ew
loc = 1
2
P
iaN
P
j;haN; j≠i
wijwih d
w
jh Nið Þ½ Š
− 1
1 = 3
ki ki − 1ð Þ
:
Directed local efficiency⁎,
EY
loc = 1
2n
P
iaN
P
j;haN;j≠i
aij + ajið Þ aih + ahið Þ d
Y
jh Nið Þ
 Ã− 1
+ d
Y
hj Nið Þ
 Ã− 1
k
out
i + k
in
i
À Á
k
out
i + k
in
i − 1
À Á
− 2
P
jaN
aijaji
:
… and many more!!
8. ANATOMICAL BRAIN NETWORKS
The connectome is a comprehensive map of neural connections in the brain.The production
and study of connectomes, known as connectomics, may range in scale from a detailed map
of the full set of neurons and synapses of an organism to a macro scale description of
the structural connectivity between all cortical areas and subcortical structures.
9. Do we have a complete connectome?Yes, we do!
C. Elegans: connectivity matrix.
(O. Sporns,“The Networks of the Brain”)
• C. Elegans, a nematode.
• 302 neurons (hermaphrodite),
383 neurones (male).
• We now all neurons and
connections between them.
THE CONNECTOME: A NECESSARY SUBSTRATE
10. The wiring diagram is an starting point for making hypothesis but…
A) … it cannot reveal how neurons behave in real time, nor does it account
for the many “mysterious” ways that neurons regulate one another's behavior.
B) … the dynamics is quite unpredictable when studying complex movements.
C) … we don't have a comprehensive model of how the worm's nervous system
actually produces the behaviors.
D) … the strength of the synaptic connections changes due to dynamics, also
the amount of neurotransmitters…
THE CONNECTOME: A NECESSARY SUBSTRATE
11. Overall structure of PVX, a male-specific interneuron, showing distribution of synapses. (G) Detail
of individual synapses. Width of lines indicates synapse size. Edge weights are determined by
counting the number of 70- to 90-nm serial sections crossed by individual synapses and summing
over all the synapses.
onJuly26,2012www.sciencemag.orgDownloadedfrom
tween each pair of cells (16). (The resulting struc-
tural weight adjacency matrices for the chemical
S8 and S9). Individual presynaptic densities
varied in size over a 40-fold range, whereas
30-fold range (fig. S2). As a result of the vari-
ation in both number of synapses between pairs
onJuly26,2012www.sciencemag.orgDownloadedfrom
Fig. 1. Specializations of the C. elegans adult male tail for mating. (A) The
substeps of mating. (B) Ventral view of the adult male tail showing mating
structures with five types of sensilla. (C) Overall structure of the male ner-
vous system. (D) Ganglia in the tail containing the neuron cell bodies, con-
nected through commissures. Most synaptic connectivity occurs in the
preanal ganglion (PAG). DNC, dorsal nerve cord; VNC, ventral nerve cord;
DRG, dorsorectal ganglion; LG, lumbar ganglion (left and right); CG, cloacal
ganglion (left and right). (E) An example of a male-specific interneuron,
PVX, which has a cell body and extensive sensory input in the PAG, and a
pr
an
(d
ju
ch
si
po
(d
m
27 JULY 2012 VOL 337 SCIEN438
each module correlate well with experimental
evidence (21–26).
Sensory neurons are recurrently connected.
Whereas much of the information flow through the
network from sensory neurons to end organs—
either in monosynaptic pathways or through
type Ia interneurons in disynaptic pathways—
is feedforward, the 52 sensory neurons are ex-
tensively reciprocally and recurrently connected
by both chemical and gap junction synapses.
Forty-nine percent of the chemical synaptic out-
put of sensory neurons is onto other sensory
neurons, and this constitutes input to th
neurons that is seven times the feedb
type Ib and type Ic interneurons. Ninet
the 36 ray sensory neurons make auta
stituting 6.9% of their input from sen
rons. Fifty-eight percent of the gap
connectivity of the sensory neurons is
sensory neurons.
Only on the basis of the recurren
tivity of the sensory neurons and the
tions to the type Ib interneurons, the n
sensory neurons could be partitioned
DOI: 10.1126/science.1221762
, 437 (2012);337Science
et al.Travis A. Jarrell
The Connectome of a Decision-Making Neural Network
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THE CONNECTOME: A NECESSARY SUBSTRATE
13. BEFORE BEGINNING….
Functional networks are not functional networks!
Just a secret* only shared between scientists working on
functional networks…
* keep the secret, please.
14. IT’S A LONG ROAD… FULL OF TROUBLE!
Obtaining a functional brain network in three steps:
Measuring Brain Activity
STEP 1
Time Series Analysis
Network Construction
Network Analysis
STEP 2 STEP 3
15. OBTAINING FUNCTIONAL BRAIN NETWORKS
STEP 1: Measuring Brain Activity
Functional MRI (fMRI). The detection of changes in regional brain activity through their effects on
blood flow and blood oxygenation (which, in turn, affect magnetic susceptibility and tissue contrast in
magnetic resonance images). High spatial resolution (~mm3) but low temporal resolution
(~seconds).
Electroencephalography (EEG). A technique used to measure neural activity by monitoring
electrical signals from the brain, usually through scalp electrodes. EEG has good temporal resolution
but relatively poor spatial resolution.
Magnetoencephalography (MEG). A method of measuring brain activity by detecting
perturbations in the extracranial magnetic field that are generated by the electrical activity of
neuronal populations. Like EEG, it has good temporal resolution but relatively poor spatial resolution.
It has better resolution than EEG.
Others…
16. OBTAINING FUNCTIONAL BRAIN NETWORKS
STEP 1: Measuring Brain Activity
Functional MRI (fMRI). The detection of changes in regional brain activity through their effects on blood flow and blood
oxygenation (which, in turn, affect magnetic susceptibility and tissue contrast in magnetic resonance images). High spatial
resolution (~mm3) but low temporal resolution (~seconds).
Typical activation maps.Magnetic Resonance
18. OBTAINING FUNCTIONAL BRAIN NETWORKS
Electroencephalography (EEG). A technique used to measure neural activity by monitoring
electrical signals from the brain, usually through scalp electrodes. EEG has good temporal
resolution (up to kHz) but relatively poor spatial resolution (typically between 19-256
electrodes).
There are approximately 10 times more glial cells than neurons.
The general shape of neurons is longer and thinner than other cells of the body.
They transmit information and communicate with each other using a combination of
chemical and electrical signals. Figure 2.1 shows a simplified picture of communica-
tion between three neurons. Neuron 2 receives a chemical input from neuron 1, which
causes an electrical signal along its length and generates a chemical signal, which is
transmitted to neuron 3. The chemical signals are in the form of neurotransmitters,
which are released by one neuron and detected by another. The electrical signals are in
the form of action potentials, which travel along neuronal axons. While neurons have
a variety of shapes and sizes, the most general features are dendrites, which receive
input from other neurons, a soma or cell body, and the axon, which conveys electrical
information.
In the brain, each neuron influences and is influenced by many other neurons. An
action potential occurs when inputs at a neuron are summed and the threshold is ex-
ceeded. When the action potential reaches the axon terminal of the neuron, it results
in the release of neurotransmitter from the presynaptic membrane, which causes post-
synaptic potentials (PSP).
Two types of PSP’s can be classified. The Excitatory postsynaptic potential (E)PSP,
causes a depolarization of the cell due to the arrival of action potentials at a synapse.
Neuron 1
(Action potential)
Output
chemical
transmission
(Synapse)(Synapse)
Dendrites
Axon
Soma
Neuron 2 Neuron 3
Electrical
transmission
Input
chemical
transmission
Figure 2.1: A simple picture of signal transmission in neurons.
Oh my god! A syringe!
19. OBTAINING FUNCTIONAL BRAIN NETWORKS
The sample of human EEG with prominent resting state activity - alpha-rhythm. Left - EEG traces (horizontal
- time in seconds; vertical - amplitudes, scale 100uV). Right - power spectra of shown signals (vertical lines -
10 and 20 Hz, scale is linear).Alpha-rhythm consists of sinusoidal-like waves with frequencies in 8–12 Hz
range (11 Hz in this case) more prominent in posterior sites.Alpha range is red at power spectrum graph.
We are basically recording time series:
20. OBTAINING FUNCTIONAL BRAIN NETWORKS
The samples of main types of artifacts in human EEG. 1 - Electrooculographic artifact caused by the
excitation of eyeball's muscles (related to blinking, for example). Big amplitude, slow, positive wave
prominent in frontal electrodes. 2 - Electrode's artifact caused by bad contact (and thus bigger
impedance) between P3 electrode and skin. 3 - Swallowing artifact. 4 - Common reference electrode's
artifact caused by bad contact between reference electrode and skin. Huge wave similar in all channels.
Unavoidable artifacts:
21. OBTAINING FUNCTIONAL BRAIN NETWORKS
Magnetoencephalography (MEG). A method of measuring brain activity by detecting
perturbations in the extracranial magnetic field that are generated by the electrical activity of
neuronal populations. Like EEG, it has good temporal resolution but relatively poor spatial
resolution. It has better resolution than EEG.
EEG and MEG in brain research
+++
++++++
+ +
++++++
...
...
.
...
.....
..
..
.....
......
.
...
.....
...
Extracellular current
Volume
currents
Magnetic
field
lines
Electric
isopotential
lines
+
++++
+ + +
--
-
-
-
- --
c)
Propagation
+
a+
Dendrite
Na+
channels in the neuronal membrane open in response to a
of the membrane potential. The leading edge of the depolarization
y Na+
channels and a wave of depolarization spreads from the
ction potentials move in one direction. This is achieved because
iod of the Na+
channels. After activation Na+
channels do not
ures that the action potential is propagated in only one direction
intracellular current and oppositely directed extracellular current
rcuit. Within the relatively long time during, which the current
ically tens of milliseconds or more), it is reasonable to consider
femtoTeslas… yes: 10^(-15)…
… Earth doesn’t help (microTeslas)
23. STEP 1: Measuring Brain Activity
Low spatial resolution (we have ~10
11
neurons)
Measurements are overlapped
In EEG and MEG, we only measure cortical activity
Defining the nodes is a complex task
Brain is not an isolated system
High variability in the results
OBTAINING FUNCTIONAL BRAIN NETWORKS
25. Source reconstruction: inverse problem
Source reconstruction tries to identify the sources of the magnetic
field, but ….
… every inverse methods makes specific assumptions…
… (ideally) performs well if assumptions are met. …
… but there are no method that performs well in general.
OBTAINING FUNCTIONAL BRAIN NETWORKS
Inverse methods
MNE
MCE
WMNE
Loreta
sLORETA
eLORETA
Laura
Electra
WROP
DICS
LCMV-Beamformer
Nulling Beamformer
FOCUSS
Champagne
Minimum Entropy
Dipole Modeling
Multipole Modeling
MUSICRAP-MUSIC
S-FLEX
DCM
Different methodologies,
the majority are black
boxes for the user.
26. IT’S A LONG ROAD… FULL OF TROUBLE!
Obtaining a functional brain network in three steps:
Time Series Analysis
Network Construction
STEP 2
Measuring Brain Activity
STEP 1
Network Analysis
STEP 3
27. STEP 1I: Time Series Analysis Network Construction
How to measure coordination
between brain regions?
Cross-correlation
Wavelet coherence
Synchronization Likelihood
Generalized Synchronization
Phase Synchronization
Mutual Information
Granger Causality
Once coordination is evaluated, we
construct the functional network.
OBTAINING FUNCTIONAL BRAIN NETWORKS
* For a review: Pereda et al, Prog. Neurobiol, 77 (2005)
28. Linear: Evaluate correlation between time series.They are the simplest and,
sometimes, good enough.
OBTAINING FUNCTIONAL BRAIN NETWORKS
Two groups: MCI (21) and Control (21).
MEG. Memory task. Classification
algorithms: Multi-Layer Perceptron
(MLP), Probabilistic Neural Networks
(PNN), Decision Tree (DT), y K Nearest
Neighbours (KNN).M. Zanin, PhDThesis
29. OBTAINING FUNCTIONAL BRAIN NETWORKS
Non-Linear: Based on a nonlinear function between x(t) and y(t).They
also include phase synchronization indexes.
0 50 100 150
time [sec]
−5
0
5
10
15
ϕ1,1/2π
0 50 100 150
time [sec]
0 50 100 150
time [sec]
yx
(a) (b) (c)
0 50 100 150
time [sec]
−5
0
5
10
15
ϕ1,1/2π
0 50 100 150
time [sec]
0 50 100 150
time [sec]
yx
(a) (b) (c)
Fig. 7. Stabilograms of a neurological patient for EO (a), EC (b), and A
x(t)=f(y(t))
f(y(t))?
−5
0
5
10
15
ϕ1,1/2πy
(a) (b)
0 50 100 150
−5
0
5
10ϕ1,1/2π
0 50 100 150
yx
30. OBTAINING FUNCTIONAL BRAIN NETWORKS
Spectral: Based on the analysis of the spectrum of the time series. Also
include different linear/nonlinear ways of comparing spectra.
Spectra of EEG electrodes. M.G. Knyazeva et al., Journal of Neurophysiology
31. OBTAINING FUNCTIONAL BRAIN NETWORKS
And now, what matrix do I analyze?
“coordination” matrix adjacency matrix normalized matrix
32. OBTAINING FUNCTIONAL BRAIN NETWORKS
Percentage ThresholdWeighted
Basically, you can choose between three options:
33. OBTAINING FUNCTIONAL BRAIN NETWORKS
Binarize the matrix by selecting an adequate threshold:
Figure3. Effectsoftaskdifficultyonworkspaceconfigurationofbrainfunctionalnetworksatdifferentfrequencyintervalsoverarangeofnetworkconnectiondensities.A–E,Overallfrequencies
(A)andineachfrequencyinterval(B–E),meanbrainnetworkmetricswith95%confidenceinterval(dottedlines)forzero-back(redline),one-back(greenline),andtwo-back(blueline)taskstend
toconvergeontheirvaluesinsurrogatenetworks(grayline)asconnectiondensityisincreasedfrom2%to20%ofpossibleedges.Theverticaldottedlinesindicatestheconnectiondensityof10%
chosen for ANOVA modeling. Asterisks denote significant difference at p Ͻ 0.05 between two-back and surrogate networks.
Kitzbichler et al. • Workspace Configuration of MEG Networks J. Neurosci., June 1, 2011 • 31(22):8259–8270 • 8265
Kitzblicher et al., J. Neurosci. 2011
34. STEP 1I: Time Series Network Construction
It is difficult to evaluate weights and causality in the interactions
There is not a unique way of interacting
No clear way of defining the network (threshold problem spurious links)
Functional networks are not static
High variability in the results
OBTAINING FUNCTIONAL BRAIN NETWORKS
35. −5
0
5
10
15
ϕ1,1/2πy
(a)(b)(c)
OBTAINING FUNCTIONAL BRAIN NETWORKS
Example 1: Functional networks are virtual
REAL FUNCTIONAL
0 50 100 150
time [sec]
−5
0
5
10
15
ϕ1,1/2π
0 50 100 150
time [sec]
0 50 100 150
time [sec]
yx
(a) (b) (c)
0 50 100 150
time [sec]
0 50 100 150
time [sec]
(b) (c)
is it correct?
36. OBTAINING FUNCTIONAL BRAIN NETWORKS
1 4 7 10 13 16 19
40
50
60
70
80
Classificationscore(%)
Deleted node
0.775
0.7875
19 16 13 10 7 4
40
50
60
70
80
Classificationscore(%)
Number of nodes
F3
P8
T7
T8
P7
O2
FZ
FP1
F8
T7
FZ
O2
P8
T8
F3
F8
P7
FP1
Figure 14: Discarding nodes from the networks. (Top Left) Classification score as a function of the node discarded. The dashed
horizontal line represents the best classification score with the complete network (77.5%). (Top Right) Classification score as
a function of the number of surviving nodes. (Bottom) The networks of Fig. 5 when only the 9 most important nodes are
included.
these topological features yielded a rather low score (⇡ 60%). This suggests that these differences were not
as important as initially thought, possibly because the analysis (and specifically, its parameters) was not
properly tuned. The same data mining techniques were the instrument to increase the significance of the
networks, and to point us towards the synchronisation metrics and brain regions most relevant. The upshot
is that we end up with higher prognostic capabilities and better understanding of the pathology at hand,
EEG (19 electrodes), image recognition task. 40 controls alcoholic individuals. Discarding nodes from the networks. (Top
Left) Classification score as a function of the node discarded.The dashed horizontal line represents the best classification
score with the complete network (77.5%). (Top Right) Classification score as a function of the number of surviving nodes.
(Bottom)The networks with only the 9 most important nodes. (Zanin et al., Phys. Rep. 2016)
Example 1I: where to put the threshold?
37. IT’S A LONG ROAD… FULL OF TROUBLE!
Obtaining a functional brain network in three steps:
Time Series Analysis
Network Construction
STEP 2
Measuring Brain Activity
STEP 1
Network Analysis
STEP 3
39. A. Characterize the topology of brain functional networks and its
influence in the processes occurring in them.
B. Identify differences between healthy brains and those with a
certain pathology.
C. Develop models in order to explain the changes found in impaired
functional networks.
Network Analysis: Why?
ANALYZING FUNCTIONAL BRAIN NETWORKS
40. A. Characterize the topology of brain functional networks*
and its influence in the processes occurring in them:
• Heterogeneous - Crucial nodes.
• High clustering - Good local resilience?
• Small-world topology - High efficiency in information transmission?
• Modularity - Segregation integration of information?
• Others: Assortative, degree-degree correlations, rich-clubs, hierarchical
structure,…
ANALYZING FUNCTIONAL BRAIN NETWORKS
* “All generalizations are false, including this one”, MarkTwain (probably…)
41. Hubs unavoidably appear in functional networks:
❑ Two activities: music and finger tapping
❑ fMRI
❑ 36 x 64 x 64 regione (147456 voxels)
❑ Linear correlation between voxels:
❑ Matrix is thresholded
Music Finger tapping
FUNCTIONAL NETWORKS ARE HETEROGENEOUS
42. Highly (functionally) connected nodes:
Two different tasks (Eguíluz et al., PRL 2005)
FUNCTIONAL NETWORKS ARE HETEROGENEOUS
define the functional networks (rc 0:7). Our data were
also compared with values from a randomly rewired net-
work, where nodes keep their degree by permuting links
(i.e., the link connecting nodes i, jis permuted with that
connecting nodes k, l) [6] (see below). In this control the
degree of each node is maintained but all other correlations
(including clustering) are destroyed.
To test the generality of these findings the same analysis
10
0
10
1
10
2
10
3
Degree K
10
0
10
1
10
2
10
3
10
4
10
5
)k(stnuoC
rc
= 0.6
rc
= 0.7
rc
= 0.8
10
0
10
1
10
2
(mm)
10
-4
10
-3
10
-2
10
-1
10
0
k)(.borP
∆
∆
10
0
10
1
10
2
10
3
Degree K
10
0
10
1
10
2
10
3
10
4
Counts(k)
rc
= 0.5
rc
= 0.6
rc
= 0.7
700 800
Degree K
0
500
Counts(k)
FIG. 2 (color online). Degree distribution for three values of
the correlation threshold. The inset depicts the degree distribu-
tion for an equivalent randomly connected network.
PRL 94, 018102 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending
14 JANUARY 2005
fMRI, finger tapping, different thresholds
“…scale-free complex networks are known to
show resistance to failure, facility of
synchronization, and fast signal processing… ”
43. It is common to observe an exponential cut-off:
The degree distribution of all networks at all frequency bands
and both behavioral states was best described by a truncated
power law, given in the form P(k)∼Ak^(λ−1) e^(k/kc), where A is
the coefficient, λ describes the power law, and kc is the
exponential parameter.
Table 2. Parameters of exponentially
truncated power law degree distribution
A kc
Resting
1 0.8 ± 0.2 1.5 ± 0.4 8 ± 4
2 0.9 ± 0.3 1.6 ± 0.5 5 ± 3
3 0.9 ± 0.3 1.5 ± 0.5 8 ±15
4 0.9 ± 0.3 1.6 ± 0.6 6 ± 4
5 0.8 ± 0.2 1.6 ± 0.4 5 ± 2
6 1.0 ± 0.2 1.4 ± 0.3 8 ± 6
Tapping
1 0.9 ± 0.1 1.4 ± 0.2 9 ± 4
2 0.8 ± 0.2 1.7 ± 0.4 5 ± 1
3 0.8 ± 0.3 1.7 ± 0.5 5 ± 2
4 0.8 ± 0.3 1.7 ± 0.5 6 ± 4
5 0.9 ± 0.2 1.5 ± 0.5 10 ±14
6 1.0 ± 0.1 1.2 ± 0.3 14 ±20
The degree distribution of all networks at all fre-
quency bands and both behavioral states was best
described by a truncated power law, given in the
form P(k) ⇠ Ak 1
ek/kc
, where A is the coe cient,
describes the power law, and kc is the exponential
parameter. These three parameters are given here
along with their standard deviation and show a large
which reflects the distinctive topological properties (greater
density and clustering) of the ␥ network.
Spatial Configuration of Scale-Specific Networks. The spatial distri-
bution of network hubs was also broadly similar across scales and
states (see Fig. 2 and SI Fig. 5). See SI Fig. 6 for average hub
distributions across all scales in both states. However, there were
striking differences between scales and states in the physical
distance between functionally connected network nodes (see
Fig. 3).
In the resting state, long-range functional connectivity be-
tween brain regions was stronger at low frequencies. At higher
frequencies (, ␥), long-range connectivity was weaker, and most
of the edges in the graph represented high-density local con-
nections (see Figs. 1E and 4), shown by the increase in charac-
teristic length scale of network edges , going from high to low
frequency scales; and by the increasing number of connector
compared with provincial nodes at low frequencies (see SI Fig.
7 for a schematic and SI Fig. 8 for distributions of provincial and
connector hubs in both states and all frequency bands).
In the finger-tapping state, long-range functional connections
emerged more strongly at high frequencies (, ␥), shown by the
significant motor task-related increases in characteristic length
scale of edges in high-frequency motor networks. It is also
represented by the shift from resting-state ␥ networks dominated
by provincial hubs (predominantly connected to locally neigh-
boring regions of bilateral occipital, parietal, and central cortex)
to motor ␥ networks with a larger number of connector hubs in
medial premotor and bilateral prefrontal cortex. Some of the
new long-range connections engendered by task performance at
high frequencies link to topologically pivotal nodes in right
medial premotor and prefrontal cortex with high betweenness
scores (see Fig. 3; and see SI Fig. 9 for betweenness distributions
at all frequencies). This indicates that task performance is
associated with reconfiguration of high-frequency networks to
favor long-distance connections between prefrontal and premo-
Fig. 2. Self-similarity of spatial distribution of highly connected network nodes or ‘‘hubs’’ in the frequency range 2–38 Hz (64). Each column shows the surface
distribution of the degree of network nodes in frequency bands  to ␦: red represents nodes with high degree. The last column shows the spatial distribution
of degree averaged over these four frequency bands, which emphasizes the similarity of spatial configurations across scales. See SI Fig. 5 for the hub distributions
in both states at all frequency bands.
Fig. 3. State-related differences in spatial configuration of the highest frequency ␥ network. The top row shows the degree distribution and betweenness scores
for the resting state ␥ network; the middle row shows the same maps for the motor ␥ network; the bottom row shows the between-state differences in degree
and betweenness. It is clear that motor task performance is associated with emergence of greater connectivity in bilateral prefrontal and premotor nodes, and
appearance of topologically pivotal nodes (with high betweenness scores) in medial premotor, right prefrontal, and parietal areas. See SI Fig. 7 for the
betweenness distributions in both states at all frequency bands.
19520 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0606005103 Bassett et al.
MEG (275 channels), 11 resting and 11 finger tapping. Node
degree and betweenness. (Basset et al., PNAS 2006)
FUNCTIONAL NETWORKS ARE HETEROGENEOUS
47. Representation in the topological space. Left:Young adults (18-33); Right: Older adults (62-73)
The modular organization changes with age:
FUNCTIONAL NETWORKS ARE MODULAR
48. Assortativity in functional brain networks:
More (functionally) connected regions are prone
to be connected between them. (finger tapping)
music finger tapping
FUNCTIONAL NETWORKS ARE ASSORTATIVE
49. B. Identify differences between healthy brains and those
with a certain pathology:
• Identify differences with respect to a control group.
• Evaluate the effects of a certain disease in the functional network.
• Quantify evolution towards “impaired” topologies.
• Evaluate the loss of segregation/integration in the functional networks.
• Quantify the increase of energy expenses.
ANALYZING FUNCTIONAL BRAIN NETWORKS
50. Self-portrait of William Utermohlen (american painter (1993-2007)). In
1995 (62 years old) he began to suffer problems with memory and writing.
FROM A HEALTHY TO AN IMPAIRED FUNCTIONAL NETWORK
51. Fig. 5 Mean PLI averaged over all pairs of MEG sensors for
Alzheimer’s disease patients and controls in six frequency
bands. Error bars are SDs. The mean PLI was significantly lower
in Alzheimer’s disease patients compared to controls in the
lower alpha band (two-tailed t-test, P50.022) and the beta
band (two-tailed t-test, P = 0.036).
Fig. 4 Average weighted graphs of Alzheimer’s disease patients and controls in six frequency bands. The value of the PLI for all
individual pairs of MEG sensors is indicated in colour (blue: low PLI; red: high PLI).
Fig. 3 Damage modelling procedure. The mean PLI of a
control subject network is lowered by randomly weakening
edges in the network, until it reaches the same value as in a
Alzheimer’s disease patient network. The effect of this damage
is then examined by comparing the network characteristics of
the damaged network to the Alzheimer’s disease patient net-
work characteristics. RF = Random Failure, TA = Targeted
Attack, Cw = mean weighted clustering coefficient, Lw = mean
weighted path length.
byguestonApril7,2011brain.oxfordjournals.orgnloadedfrom
The non-parametric Mann–Whitney U-test for independent
samples revealed that Cw was lower in Alzheimer’s disease
subjects in the 8–10 Hz band (U = 89.5; P = 0.022), but not in
network in the Alzheimer’s disease group. Please note that, by
definition, the average PLI of both models is the same as the
average PLI of the Alzheimer’s disease data.
Further analysis of the model data compared with the real data
is shown in Fig. 8. For the Random Failure model the ^Cw was not
different from the control data, and significantly higher than ^Cw of
the Alzheimer’s disease group (Mann–Whitney U-test, U = 76.5;
P = 0.007). In contrast, ^Cw of the Targeted Attack model was
not significantly different from the Alzheimer’s disease group,
but significantly lower than ^Cw of the control group (U = 87.0;
P = 0.018). The weighted path length ^Lw showed a decreasing
trend going from controls to Random Failure, Targeted Failure
and controls (Fig. 8, right panel). ^Lw of both models did not
differ significantly from control data.
Correlation with MMSE
No significant correlations between MMSE and PLI or network
measures were found in the Alzheimer’s disease patient group
(Fig. 9). When correlation with MMSE was analysed for all subjects
(Alzheimer’s disease and control) put together in one group,
we found significant effects between MMSE and mean PLI in the
beta band (Spearman’s r = 0.570, P = 0.001) and between MMSE
and ^Cw in the lower alpha band (Spearman’s r = 0.475, P = 0.008).
Table 1 Results of weighted graph analysis for Alzheimer’s disease patients and controls in six frequency bands
Cw Lw
^Cw
^Lw
Alzheimer’s
disease
Control Alzheimer’s
disease
Control Alzheimer’s
disease
Control Alzheimer’s
disease
Control
0.5–4 Hz 0.12
(0.10–0.32)
0.12
(0.10–0.17)
4.05
(1.69–4.40)
3.92
(2.89–4.59)
1.04
(1.03–1.12)
1.04
(1.02–1.11)
1.09
(1.06–1.33)
1.08
(1.05–1.34)
4–8 Hz 0.11
(0.09–0.20)
0.10
(0.09–0.15)
4.23
(2.48–4.99)
4.44
(3.22–5.01)
1.05
(1.03–1.17)
1.04
(1.03–1.13)
1.14
(1.04–1.41)
1.15
(1.05–1.43)
8–10 Hz 0.15
(0.12–0.21)
0.17
(0.13–0.29)
3.27
(2.25–3.76)
2.69
(1.80–3.73)
1.04
(1.02–1.12)
1.07
(1.04–1.13)
1.08
(1.05–1.32)
1.19
(1.07–1.30)
10–13 Hz 0.12
(0.11–0.14)
0.13
(0.11–0.22)
3.83
(3.28–4.36)
3.72
(2.36–4.30)
1.04
(1.03–1.10)
1.04
(1.03–1.21)
1.10
(1.05–1.35)
1.12
(1.04–1.45)
13–30 Hz 0.06
(0.05–0.06)
0.06
(0.05–0.08)
7.97
(6.44–9.24)
7.61
(5.18–9.35)
1.04
(1.02–1.07)
1.04
(1.03–1.16)
1.11
(1.05–1.50)
1.12
(1.04–1.50)
30–45 Hz 0.05
(0.05–0.09)
0.05
(0.05–0.08)
8.70
(5.17–9.07)
8.54
(6.06–9.14)
1.02
(1.02–1.07)
1.02
(1.02–1.07)
1.09
(1.06–1.33)
1.04
(1.02–1.30)
Values are medians, with range printed between parentheses. Cw = mean weighted clustering coefficient; Lw = mean weighted path length; ^Cw = mean normalized
average weighted clustering coefficient (see Materials and Methods section), ^Lw = mean normalized average weighted path length. Significant differences between
Alzheimer’s disease and controls with non-parametric testing (Mann–Whitney U-test, P50.05) are given in bold.
Fig. 6 Schematic illustration of significant differences in long
distance (indicated by arrows) and short distance (indicated by
filled squares) PLI in the 8–10 Hz and 13–30 Hz band.
Alzheimer’s disease patients had lower left sided fronto-
temporal, fronto-parietal, temporo-occipital and parieto-
occipital PLI in the 8–10 Hz band. Local left frontal and tem-
poral, and right parietal PLI were also decreased in Alzheimer’s
disease patients (A). For the 13–30 Hz band, Alzheimer’s dis-
ease patients had lower inter hemispheric frontal, right fronto-
parietal and bilateral frontal PLI (B).
byguestonApril7,2011brain.oxfordjournals.orgDownloadedfrom
BRAINA JOURNAL OF NEUROLOGY
Graph theoretical analysis of
magnetoencephalographic functional
connectivity in Alzheimer’s disease
C. J. Stam,1
W. de Haan,2
A. Daffertshofer,3
B. F. Jones,4
I. Manshanden,1
A. M. van Cappellen van Walsum,5,6
T. Montez,7
J. P. A. Verbunt,1,8
J. C. de Munck,8
B. W. van Dijk,1,8
H. W. Berendse2
and P. Scheltens2
1 Department of Clinical Neurophysiology and MEG, Amsterdam, The Netherlands
2 Department of Neurology, Alzheimer Center, VU University Medical Center, Amsterdam, The Netherlands
3 Research Institute MOVE, VU University, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands
4 Dementia Research Centre, Institute of Neurology, UCL, London, UK
5 Department of Anatomy, Radboud University Nijmegen Medical Centre, Nijmegen, The Netherlands
6 Institute of Technical Medicine, University of Twente, Enschede, The Netherlands
7 Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Portugal
8 Department of Physics and Medical Technology, VU University Medical Center, Amsterdam, The Netherlands
Correspondence to: Willem de Haan,
Department of Neurology, Alzheimer Center,
VU University Medical Center, PO Box 7057,
1007 MB Amsterdam, the Netherlands
E-mail: w.dehaan@vumc.nl
In this study we examined changes in the large-scale structure of resting-state brain networks in patients with Alzheimer’s
disease compared with non-demented controls, using concepts from graph theory. Magneto-encephalograms (MEG) were
recorded in 18 Alzheimer’s disease patients and 18 non-demented control subjects in a no-task, eyes-closed condition. For
the main frequency bands, synchronization between all pairs of MEG channels was assessed using a phase lag index (PLI,
a synchronization measure insensitive to volume conduction). PLI-weighted connectivity networks were calculated, and char-
acterized by a mean clustering coefficient and path length. Alzheimer’s disease patients showed a decrease of mean PLI in the
lower alpha and beta band. In the lower alpha band, the clustering coefficient and path length were both decreased in
Alzheimer’s disease patients. Network changes in the lower alpha band were better explained by a ‘Targeted Attack’ model
than by a ‘Random Failure’ model. Thus, Alzheimer’s disease patients display a loss of resting-state functional connectivity
in lower alpha and beta bands even when a measure insensitive to volume conduction effects is used. Moreover, the large-scale
structure of lower alpha band functional networks in Alzheimer’s disease is more random. The modelling results suggest
that highly connected neural network ‘hubs’ may be especially at risk in Alzheimer’s disease.
Keywords: Alzheimer’s disease; functional connectivity; MEG; synchronization; small-world networks
Abbreviations: EEG = electro-encephalography; MEG = Magneto-encephalography; MMSE = mini mental state examination;
PLI = phase lag index; SL = synchronization likelihood
doi:10.1093/brain/awn262 Brain 2009: 132; 213–224 | 213
Received May 5, 2008. Revised September 12, 2008. Accepted September 18, 2008. Advance Access publication October 24, 2008
ß The Author (2008). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved.
For Permissions, please email: journals.permissions@oxfordjournals.org
byguestonApril7,2011brain.oxfordjournals.orgDownloadedfrom
MEG, resting state. 18 AD patients and 18 controls. (Phase Lag Index).Weighted Clustering coefficient (Cw) and
shortest path (Lw). Only one frequency band showed statistically significant differences (pval0.05)
FROM A HEALTHY TO AN IMPAIRED FUNCTIONAL NETWORK
52. Some general features of different brain diseases:
❑ Alzheimer’s Disease:
❑ The overall synchronization of the network is decreased.
❑The average path length increases (probably as a consequence of the reduction of
the synchronization).
❑The clustering coefficient is significantly reduced (the network evolves to random
topologies).
❑ Mild Cognitive Impairment:
❑ The average synchronization increases.
❑The network becomes more random.
❑ Network outreach increases as a consequence of an unbalanced increase of the
synchronization in the long-range connections.
FROM A HEALTHY TO AN IMPAIRED FUNCTIONAL NETWORK
53. ❑ Schizophrenia:
❑ The small-world properties of the network are impaired (specially at low-frequency
bands).
❑ Clustering and average path length are shifted to random configurations.
❑The hierarchical configuration of the network is also affected.
❑ Epilepsia:
❑ Synchronization increases during the epileptic episodes.
❑ As a consequence, clustering coefficient increases and average path length
decreases.
❑ Changes are more significant at delta, theta and alpha bands.
FROM A HEALTHY TO AN IMPAIRED FUNCTIONAL NETWORK
54. A brain disorder in which thinking abilities are mildly impaired.
Individuals with MCI are able to function in everyday activities but
have difficulty with memory, trouble remembering the names of
people they met recently, the flow of a conversation, and a tendency
to misplace things. Every year, around 10% of MCI patients develop
Alzheimer’s disease.
We perform magnetoencephalograms (MEG) to a group of 19 MCI's patients and 19 control
subjects during a memory task. By means of the synchronization likelihood (SL) we quantify the
interaction between the 148 channels of the MEG system and we obtained a weighted connectivity
matrix between cortical areas.
❑ What is Mild Cognitive Impairment (MCI)?
❑ The experiment
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
J.M. Buldú, R. Bajo, F. Maestú et al., Reorganization of Functional Networks in Mild Cognitive Impairment, PLoS ONE 6(5): e19584 (2011)
55. Topological analysis of the functional networks of both groups (Control and MCI):
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
56. Differences between the MCI and Control groups:
❑ Global Parameters:
❑The network strength K increases (+15.9%)
❑ Network outreach increases (+23.4%)
(and more than the increase in K)
❑The network modularity decreases (-13.5%)
❑ Normalized Parameters:
❑ Normalized clustering decreases (-13.6%):
CCONTROL =1.76 CMCI =1.52
❑ Normalized outreach increases (+6.7%):
OCONTROL =0.63 OMCI =0.67
CAUTION! The functional network is
becoming random
^ ^
^ ^
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
57. ❑ Intra-lobe synchronization:
❑The intra-lobe synchronization increases
❑The inter-lobe synchronization increases
(more than the intra-lobe sync.)
❑ Modularity decreases
CAUTION! The segregated operation of
the brain is decreasing
In-strengthOut-strengthModularity
Differences between the MCI and Control groups, Inter-lobe connections:
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
58. Within module degree Participation coefficient
From macroscopic (network) to microscopic (node) analysis:
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
59. Δ
Δ
Nodes increase their participation
From macroscopic (network) to microscopic (node) analysis:
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
60. MCI diagnostic must be done by analysing longitudinal recordings
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
Caution, GIGO is around...
61. Caution, GIGO is around...
“Lies, damned lies and statistics”
From :The Evolution of Adult Height in Europe: A Brief Note*
Jaume Garcia and Climent Quintana-Domeque
I’m Swedish!
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
62. ?
Randomness
Networkstrength
Control
Alzheimer
M.C.I.
We n e e d l o n g i t u d i n a l
experiments in order to
understand the emergence of
MCI
The evolution of MCI to
Alzheimer is still unknown …
despite there are some clues
❑ High Synchronization
❑ Low clustering
❑ Higher outreach
❑ Low modularity
❑ Higher Randomness
❑ Low Synchronization
❑ Low clustering
❑ Higher Randomness
Some conclusions:
EXAMPLE 1: MILD COGNITIVE IMPAIRMENT
63. Another good candidate:Trauma recovering therapy
Accident Head Trauma Cognitive Therapy
MEG recording
(after the accident)
MEG recording
(9-14 months of therapy)
Comparison
between both
networks
N.P. Castellanos, I. Leyva, J.M. Buldú, et al., “Principles of recovery from traumatic brain injury: reorganization of functional
networks, Neuroimage, 55, 1189-1199 (2011).
EXAMPLE 1I: TRAUMATIC BRAIN INJURY
64. Band δ [1-4 Hz]
Band α [8-13 Hz]
Network changes:
❑ The delta band is overconnected
❑ The alfa band is underconnected
❑ The cognitive therapy shifts network
parameters towards control values
Black bars:After the TBI
Grey bars:After the therapy
EXAMPLE 1I: TRAUMATIC BRAIN INJURY
Another good candidate:Trauma recovering therapy
65. C. Develop models in order to explain the changes found in
impaired functional networks:
• Identify what are the rules that determine the network distortion.
ANALYZING FUNCTIONAL BRAIN NETWORKS
66. Two specific applications of network modeling:
❑ Mild Cognitive Impairment
❑Traumatic Brain Injury
EVOLUTIONARY NETWORK MODELS
67. 1) We select a link randomly.
2) We change the weight of the link according to a certain function:
w'ij=wij [1+λ+η] ξ(dij)
3) We normalize and recalculate the network parameters.
4) We go back to step 1.
w'ij= modified link weight
wij = previous link weight
λ=degradation rate (λ 0)
η= noise term
ξ(dij)= length dependence function
dij= link length
EVOLUTIONARY NETWORK MODELS: MCI
Develop models in order to explain the changes found in impaired
functional networks:
68. Mild Cognitive Impairment: Real data versus evolutionary models
Real data
Models
EVOLUTIONARY NETWORK MODELS: MCI
69. Healthy brain
Impaired brain
Length dependent
Length independent
EVOLUTIONARY NETWORK MODELS: MCI
Develop models in order to explain the changes found in impaired
functional networks:
70. The goal of this model is enhancing those links with higher initial weights.
This leads to an increase of the relative difference between higher and
lower weights along the evolution.
Modeling network recovery inTraumatic Brain Injury:
Contrasting model (T+):
Unifying model (T-):
The global average strength of the matrix decreases and, in addition, the
relative differences between link weights are reduced at each time step.
EVOLUTIONARY NETWORK MODELS: TBI
71. Post (after therapy)
*Pre (before therapy) Control (healthy subject)
Alpha band
Contrasting model Unifying model
EVOLUTIONARY NETWORK MODELS: TBI
72. We are accumulating errors from the previous two steps
Functional networks are not static
High variability in the results
(Functional networks do not evaluate function)
But… above all…
STEP III: Network Analysis
ANALYZING FUNCTIONAL BRAIN NETWORKS
73. … NETWORK MEASURES ARE COMMONLY
MISINTERPRETED….
… SINCE WE NORMALLY FORGET THAT WE ARE
ANALYZINGTHE BRAIN!
ANALYZING FUNCTIONAL BRAIN NETWORKS
75. THE WHOLE PROCESS IS A MINELAND
2.4 The Brain as a Complex Network 39
0MROW
*MPXIVMRK1IXVMGW
7XEXMWXMGW
(ITIRHIRGMIW2SHIW
Brain
activity
Recorded
signals
Connectivity
Matrix
Graphs
Topological
properties
Neuromarkers
Healthy vs. Diseased
Rest vs. Task
Figure 2.5: The general framework of brain networks. Clockwise guideline. Nodes can be
regarded as sensor or electrodes recording the electromagnetic signals of the brain, which may
contain dependencies based on correlation or causality. These interdependencies, or link weights,
lead to a weighted connectivity matrix, which is the mathematical representation of a network. This
76. HOW CAN I COMPARE NETWORKS BETWEEN THEM?
Anatomical network (Hagmann et aI., 2008) and functional network (Honey et aI., 2009) of the
same group of individuals. 998 regions of interest (ROIs).The anatomical matrix is positive while
the functional one has both positive/negative values. RH: right hemisphere, LH: left hemisphere.
Anatomical Network (DTI) Functional Network (fMRI)
77. A SOCIAL ANALOGY:
Facebook: Four views of the
same Facebook network.
Respectively: friendship network,
profiles visited, unidirectional
c o m m u n i c a t i o n a n d
bidirectional communication.
Same network, different levels of information.
D. Easley J. Kleinberg, Networks, crowds and markets.
HOW CAN I COMPARE NETWORKS BETWEEN THEM?
78. fMRI in (A) resting state and (B) during a memory task. Functional relations between
the most active nodes. Node description: rMTL, right medial temporal lobe; IMTL, left medial
temporal lobe; dmPFC, dorsomedial prefrontal cortex; vmPFC, ventro medial prefrontal cortex; rTC,
right temporal cortex; lTC, left temporal cortex; rIPL, right inferior parietal lobe; lIPL, left inferior
parietal lobe. Fransson et al., Neuroimage (2008).
Functional networks adopt different configurations
depending on the task you are carrying out:
PROBLEM: FUNCTIONAL NETWORKS CHANGE
79. Functional network (fMRI) for groups of different ages.. In the picture, nodes are grouped following
a spring algorithm.The frontal region is depicted in blue. We can observe how it segregates with
the maturity of the functional network. Fair et al. PLoS Comp. Bio.(2009).
They also change with age:
PROBLEM: FUNCTIONAL NETWORKS CHANGE
80. The underlying anatomical network influences the dynamics but, in turn, the dynamics
influences the anatomical network. For example, hebbian learning reinforces
connexions between regions that are usually coordinated. Sporns, The networks of the Brain.
Functional networks do not evolve…. they co-evolve!
determina
afecta
evolución topológica
afecta
dinámica neuronal
topología
estado
determina
PROBLEM: TOPOLOGY AND DYNAMICS ARE INTERRELATED
81. FUNCTIONAL BRAIN NETWORKS: RISKS CHALLENGES
When projecting the brain activity into a network, we are
loosing a lot of information…
… and we may forget what is behind…
82. How to interpret the results of the network analysis?
FUNCTIONAL BRAIN NETWORKS: RISKS CHALLENGES
83. “…the analysis reported here looks at the
synchronizability from different perspective
and considers the synchronization properties
of the brain networks rather than looking for a
synchronous pattern in the original EEG signal…”
EXAMPLE 1: Synchronizability
M. Jalili, M.G. Knyazeva / Computers in Biology and Medicine 41 (2011)1184
compared to other bands), where the synchroniz
Fig. 7. Measure of synchronizability of brain functional netw
index, i.e., the eigenratio (the largest eigenvalue of the Laplac
patients and normal controls. Other designations are as Fig.
M. Jalili, M.G. Kny1184
compared to other bands), where the synchronization properties
of the SZ networks were worse than those of controls.
Ref. [43]), decreased cortic
increased cell packing dens
neurons [40], suggest the d
dysconnection hypothesis
Fig. 7. Measure of synchronizability of brain functional networks in SZ patients compared to normal controls. The graphs
index, i.e., the eigenratio (the largest eigenvalue of the Laplacian matrix of the connection graph divided by its second sma
patients and normal controls. Other designations are as Fig. 3.
M. Jalili, M.G. Knyazeva / Computers in Biology and Medicine 41 (2011) 1178–11184
Synchronizability parameter for the
control and patient (schizophrenia)
group in the alpha band.
Fig. 2. Whole-head difference maps of nod
in Eq. (4)) for delta, theta, alpha, beta, and
with strength values significantly higher in
gray regions.
Fig. 3. Functional segregation and integra
worldness index as a function of the thres
brain functional networks were based on
EEG-based functional networks in schizophrenia
Mahdi Jalili a,n
, Maria G. Knyazeva b,c
a
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
b
Department of Clinical Neuroscience, Centre Hospitalier Universitaire Vaudois (CHUV), and University of Lausanne, Lausanne, Switzerland
c
Department of Radiology, Centre Hospitalier Universitaire Vaudois and University of Lausanne, Switzerland
a r t i c l e i n f o
Keywords:
EEG
Schizophrenia
Functional connectivity
Graph theory
Unpartial cross-correlation
Partial cross-correlation
a b s t r a c t
Schizophrenia is often considered as a dysconnection syndrome in which, abnormal interactions between
large-scale functional brain networks result in cognitive and perceptual deficits. In this article we apply
the graph theoretic measures to brain functional networks based on the resting EEGs of fourteen
schizophrenic patients in comparison with those of fourteen matched control subjects. The networks were
extracted from common-average-referenced EEG time-series through partial and unpartial cross-correla-
tion methods. Unpartial correlation detects functional connectivity based on direct and/or indirect links,
while partial correlation allows one to ignore indirect links. We quantified the network properties with the
graph metrics, including mall-worldness, vulnerability, modularity, assortativity, and synchronizability.
The schizophrenic patients showed method-specific and frequency-specific changes especially pro-
nounced for modularity, assortativity, and synchronizability measures. However, the differences between
schizophrenia patients and normal controls in terms of graph theory metrics were stronger for the
unpartial correlation method.
2011 Elsevier Ltd. All rights reserved.
1. Introduction
Techniques from graph theory are increasingly being applied to
model the functional and/or structural networks of the brain [1,2].
The brain networks can be studied at different levels ranging from
micro-scale containing a number of interconnected neurons to
macro-scale containing distributed brain regions. To construct the
large-scale networks, signals recorded from the brain via methods
such as electroencephalography (EEG), magnetocephalography
(MEG), functional magnetic resonance imaging (fMRI), or diffusion
tensor imaging (DTI), are used [3–7]. Often, binary (directed or
undirected) adjacency matrices are analyzed [1,2], where binary
links represent the presence or absence of a connection. The first
step in analyzing brain networks is to extract its structure from
the time-series. Possible methods are cross-correlation, coherence,
and synchronization likelihood [3–6]. The next step is to represent
it in a number of biologically meaningful measures. To this end,
measures such as characteristic path length, efficiency of connec-
tions, clustering coefficient, modularity, node degree and central-
free properties [9,10]. Graph theoretical analysis on anatomical
and functional networks of the brain have revealed its economical
small-world structure characterized by high clustering (transitiv-
ity) and a short characteristic path length [11]. The brain func-
tional networks are cost-efficient in the sense that they provide
efficient parallel processing for low connection cost [12]. Brain
disorders influence the anatomical and functional brain networks.
Brain wirings may show abnormal patterns in schizophrenia
(SZ). SZ symptoms affect the patients by manifesting as auditory
hallucinations, paranoid or bizarre delusions and/or disorganized
speech and thinking in the context of significant social and/or
occupational dysfunction. About 1% of the population worldwide
suffers from different forms of SZ [13]. Additionally, another 3% of
the population has SZ-type personality disorders. SZ is the fourth
leading cause of disability in the developed counties for people at
the age of 15–44.
Schizophrenic patients show the abnormal patterns of brain
connectivity. MRI-based studies on a large group of SZ patients
revealed the reduced hierarchy of multimodal networks and
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Computers in Biology and Medicine
Computers in Biology and Medicine 41 (2011) 1178–1186
FUNCTIONAL BRAIN NETWORKS: RISKS CHALLENGES