The human brain exhibits a remarkable network organization. Although sparsely connected, each neuron is within a few synaptic connections of any other neuron [1
]. This remarkable connectivity is achieved by a kind of hierarchical organization that is not fully understood in the brain, but is ubiquitous in nature and is called a scale-free network [2
] that changes with development. Complex networks are characterized by dense local connectivity and sparser long-range connectivity [2
] that are fractal or self-similar at all scales. Modules or clusters can be identified on multiple scales. A comparison of network properties using functional magnetic resonance imaging showed that children and young adults' brains had similar "small-world" or scale-free organization at the global level, but differed significantly in hierarchical organization and interregional connectivity [5
]. White matter fiber tracking has revealed that brain development in children involves changes in both short-range and long-range wiring, with synaptogenesis and pruning occurring at both the local (neuronal) level and the systems level [5
]. Abnormal network connectivity may be a key to understanding developmental disabilities.
Autism is a complex and heterogeneous developmental disorder that affects the developmental trajectory in several key behavioral domains, including social, cognitive and language abilities. The underlying brain dysfunction that results in the behavioral characteristics is not well understood. Complex mental disorders such as autism cannot easily be described as being associated with underconnectivity or overconnectivity, but may involve some form of abnormal connectivity that varies between different brain regions [6
]. Normal and abnormal connectivity may also change during development, so that, for example, a condition may not exist at age 3 months but may emerge by age 24 months. A key to understanding neurodevelopmental disorders is the relationship between functional brain connectivity and cognitive development [7
]. Measuring functional brain development is difficult both because the brain is a complex, hierarchical system and because few methods are available for noninvasive measurements of brain function in infants. New nonlinear methods for analyzing brain electrical activity measured using scalp electrodes may enable differences in infant brain connectivity to be detected. For example, coarse-grained entropy synchronization between electroencephalography (EEG) electrodes revealed that synchronization was significantly lower in children with autism than in a group of typically developing children [8
], supporting the theory that autistic brains exhibit low functional connectivity. In the autistic brain, high local connectivity and low long-range connectivity may develop concurrently because of problems with synapse pruning or formation [9
]. Estimation of changes in neural connectivity might be an effective diagnostic marker for atypical connectivity development.
EEG signals are believed to derive from pyramidal cells aligned in parallel in the cerebral cortex and the hippocampus [11
], which act as many interacting nonlinear oscillators [12
]. As a consequence of the scale-free network organization of neurons, EEG signals carry nonlinear, complex system information reflecting the underlying network topology, including transient synchronization between frequencies, short- and long-range correlations and cross-modulation of amplitudes and frequencies [13
]. The mathematical relationship between network structure and time series is a subject of current research and may eventually shed further light on the relationship between neural networks and EEG signals.
A great deal of information about interrelationships in the nervous system likely remains undiscovered because the linear analysis techniques currently in use fail even to detect them [14
]. If brain function and behavior are mirrors of each other as is commonly accepted [15
], then biomarkers of complex developmental disorders may be hidden in complex, nonlinear patterns of EEG data. The dynamics of the brain are inherently nonlinear, exhibiting emergent dynamics such as chaotic and transiently synchronized behavior that may be central to understanding the mind-brain relationship [19
] or the "dynamic core" [20
]. Methods for chaotic signal analysis originally arose from a need to rigorously describe physical phenomena that exhibited what was formerly thought to be purely stochastic behavior, but was then discovered to represent complex, aperiodic yet organized behavior, referred to as self-organized dynamics [21
]. The analysis of signal complexity on multiple scales may reveal information about neural connectivity that is diagnostically useful [1
One interpretation of biological complexity is that it reflects a system's ability to adapt quickly and function in a changing environment [23
]. The complexity of EEG signals was found in one study to be associated with the ability to attend to a task and adapt to new cognitive tasks; a significant difference in complexity was found between controls and patients diagnosed with schizophrenia [24
]. Patients with schizophrenia were found to have lower complexity than controls in some EEG channels and significantly higher interhemispheric and intrahemispheric cross-mutual information values than controls [25
]. A study of the correlation dimension (another measure of signal complexity) of EEG signals in healthy individuals showed an increase with aging, interpreted as an increase in the number of independent synchronous networks in the brain [22
Several different methods for computing complex or nonlinear time series features have been defined and used successfully to analyze biological signals [26
]. Sample entropy, a measure of time series complexity, was significantly higher in certain regions of the right hemisphere in preterm neonates who received skin-to-skin contact than in those who did not, indicating faster brain maturation [28
]. Sample entropy has also been used as a marker of brain maturation in neonates [29
] and was found to increase prenatally until maturation at about 42 weeks, then decreased after newborns reached full term [30
Living systems exhibit a fundamental propensity to move forward in time. This property also describes physical systems that are far from an equilibrium state. For example, heat moves in only one direction, from hot to cold areas. In thermodynamics, this property is related to the requirement that all systems must move in the direction of higher entropy. Time irreversibility is a common characteristic of living biosignals. It was found to be a characteristic of healthy human heart electrocardiographic (ECG) recordings and was shown to be a reliable way to distinguish between actual ECG recordings and model ECG simulations [31
]. ECG signals from patients with congestive heart disease were found to have lower time irreversibility indices than healthy patients [32
]. Interestingly, the time irreversibility of EEG signals has been associated with epileptic regions of the brain, and this measure has been proposed as a biomarker for seizure foci [33
]. Time irreversibility may be used as a practical test for nonlinearity in a time series.
This study is a preliminary investigation of the difference in multiscale entropy between two groups of infants between 6 and 24 months of age. The groups include typically developing infants and infants who have an older sibling with a confirmed diagnosis of autism spectrum disorder (ASD) and who are thus at higher risk for developing autism. ASD is a developmental disorder in which symptoms emerge during the second year of life. Behavioral indicators are not evident at 6 months of age [34
]; however, on the basis of the use of a novel observational scale to assess ASD characteristics in infants, distinguishing characteristics were seen at 12 months [35
]. Another study compared behavioral measures such as frequency of gaze at faces and shared smiles in infants. Again, group differences between those who later developed an ASD and typically developing controls were apparent at age 12 months, but not at age 6 months [34
]. Only one study has investigated behavioral differences at age 9 months: infants at risk for ASD showed distinct differences in visual orientation from those with no family history of autism [37
]. These behavioral observations suggest that important developmental differences are occurring in the brains of typically developing infants and those who will later develop an ASD. Although there have been no other published studies on brain development during the first year of life, one of the most replicated findings, based on a retrospective review of medical records, is accelerated growth in head circumference (a valid and reliable proxy for brain growth), which begins at around 6 to 9 months of age [38
]. If multiscale entropy is a measure of functional brain complexity, then it may be a useful marker for distinguishing differences in brain activity between at-risk and typical infants.