The wiring economy principle: connectivity determines anatomy in the human brain

Minimization of the wiring cost of white matter fibers in the human brain appears to be an organizational principle. We investigate this aspect in the human brain using whole brain connectivity networks extracted from high resolution diffusion MRI data of 14 normal volunteers. We specifically address the question of whether brain anatomy determines its connectivity or vice versa. Unlike previous studies we use weighted networks, where connections between cortical nodes are real-valued rather than binary off-on connections. In one set of analyses we found that the connectivity structure of the brain has near optimal wiring cost compared to random networks with the same number of edges, degree distribution and edge weight distribution. A specifically designed minimization routine could not find cheaper wiring without significantly degrading network performance. In another set of analyses we kept the observed brain network topology and connectivity but allowed nodes to freely move on a 3D manifold topologically identical to the brain. An efficient minimization routine was written to find the lowest wiring cost configuration. We found that beginning from any random configuration, the nodes invariably arrange themselves in a configuration with a striking resemblance to the brain. This confirms the widely held but poorly tested claim that wiring economy is a driving principle of the brain. Intriguingly, our results also suggest that the brain mainly optimizes for the most desirable network connectivity, and the observed brain anatomy is merely a result of this optimization.     

Structural Synaptic Plasticity Has High Memory Capacity and Can Explain Graded Amnesia,Catastrophic Forgetting,and the Spacing Effect

Although already William James and, more explicitly, Donald Hebb''s theory of cell assemblies have suggested that activity-dependent rewiring of neuronal networks is the substrate of learning and memory, over the last six decades most theoretical work on memory has focused on plasticity of existing synapses in prewired networks. Research in the last decade has emphasized that structural modification of synaptic connectivity is common in the adult brain and tightly correlated with learning and memory. Here we present a parsimonious computational model for learning by structural plasticity. The basic modeling units are “potential synapses” defined as locations in the network where synapses can potentially grow to connect two neurons. This model generalizes well-known previous models for associative learning based on weight plasticity. Therefore, existing theory can be applied to analyze how many memories and how much information structural plasticity can store in a synapse. Surprisingly, we find that structural plasticity largely outperforms weight plasticity and can achieve a much higher storage capacity per synapse. The effect of structural plasticity on the structure of sparsely connected networks is quite intuitive: Structural plasticity increases the “effectual network connectivity”, that is, the network wiring that specifically supports storage and recall of the memories. Further, this model of structural plasticity produces gradients of effectual connectivity in the course of learning, thereby explaining various cognitive phenomena including graded amnesia, catastrophic forgetting, and the spacing effect.     

Interplay between Short- and Long-Term Plasticity in Cell-Assembly Formation

Various hippocampal and neocortical synapses of mammalian brain show both short-term plasticity and long-term plasticity, which are considered to underlie learning and memory by the brain. According to Hebb’s postulate, synaptic plasticity encodes memory traces of past experiences into cell assemblies in cortical circuits. However, it remains unclear how the various forms of long-term and short-term synaptic plasticity cooperatively create and reorganize such cell assemblies. Here, we investigate the mechanism in which the three forms of synaptic plasticity known in cortical circuits, i.e., spike-timing-dependent plasticity (STDP), short-term depression (STD) and homeostatic plasticity, cooperatively generate, retain and reorganize cell assemblies in a recurrent neuronal network model. We show that multiple cell assemblies generated by external stimuli can survive noisy spontaneous network activity for an adequate range of the strength of STD. Furthermore, our model predicts that a symmetric temporal window of STDP, such as observed in dopaminergic modulations on hippocampal neurons, is crucial for the retention and integration of multiple cell assemblies. These results may have implications for the understanding of cortical memory processes.     

Default Mode Network Connectivity in Stroke Patients

The pathophysiology of episodic memory dysfunction after infarction is not completely understood. It has been suggested that infarctions located anywhere in the brain can induce widespread effects causing disruption of functional networks of the cortical regions. The default mode network, which includes the medial temporal lobe, is a functional network that is associated with episodic memory processing. We investigated whether the default mode network activity is reduced in stroke patients compared to healthy control subjects in the resting state condition. We assessed the whole brain network properties during resting state functional MRI in 21 control subjects and 20 ‘first-ever’ stroke patients. Patients were scanned 9–12 weeks after stroke onset. Stroke lesions were located in various parts of the brain. Independent component analyses were conducted to identify the default mode network and to compare the group differences of the default mode network. Furthermore, region-of-interest based analysis was performed to explore the functional connectivity between the regions of the default mode network. Stroke patients performed significantly worse than control subjects on the delayed recall score on California verbal learning test. We found decreased functional connectivity in the left medial temporal lobe, posterior cingulate and medial prefrontal cortical areas within the default mode network and reduced functional connectivity between these regions in stroke patients compared with controls. There were no significant volumetric differences between the groups. These results demonstrate that connectivity within the default mode network is reduced in ‘first-ever’ stroke patients compared to control subjects. This phenomenon might explain the occurrence of post-stroke cognitive dysfunction in stroke patients.     

Mapping connectivity damage in the case of Phineas Gage

White matter (WM) mapping of the human brain using neuroimaging techniques has gained considerable interest in the neuroscience community. Using diffusion weighted (DWI) and magnetic resonance imaging (MRI), WM fiber pathways between brain regions may be systematically assessed to make inferences concerning their role in normal brain function, influence on behavior, as well as concerning the consequences of network-level brain damage. In this paper, we investigate the detailed connectomics in a noted example of severe traumatic brain injury (TBI) which has proved important to and controversial in the history of neuroscience. We model the WM damage in the notable case of Phineas P. Gage, in whom a "tamping iron" was accidentally shot through his skull and brain, resulting in profound behavioral changes. The specific effects of this injury on Mr. Gage's WM connectivity have not previously been considered in detail. Using computed tomography (CT) image data of the Gage skull in conjunction with modern anatomical MRI and diffusion imaging data obtained in contemporary right handed male subjects (aged 25-36), we computationally simulate the passage of the iron through the skull on the basis of reported and observed skull fiducial landmarks and assess the extent of cortical gray matter (GM) and WM damage. Specifically, we find that while considerable damage was, indeed, localized to the left frontal cortex, the impact on measures of network connectedness between directly affected and other brain areas was profound, widespread, and a probable contributor to both the reported acute as well as long-term behavioral changes. Yet, while significantly affecting several likely network hubs, damage to Mr. Gage's WM network may not have been more severe than expected from that of a similarly sized "average" brain lesion. These results provide new insight into the remarkable brain injury experienced by this noteworthy patient.     

Axon-glial disruption: the link between vascular disease and Alzheimer's disease?

Vascular risk factors play a critical role in the development of cognitive decline and AD (Alzheimer's disease), during aging, and often result in chronic cerebral hypoperfusion. The neurobiological link between hypoperfusion and cognitive decline is not yet defined, but is proposed to involve damage to the brain's white matter. In a newly developed mouse model, hypoperfusion, in isolation, produces a slowly developing and diffuse damage to myelinated axons, which is widespread in the brain, and is associated with a selective impairment in working memory. Cerebral hypoperfusion, an early event in AD, has also been shown to be associated with white matter damage and notably an accumulation of amyloid. The present review highlights some of the published data linking white matter disruption to aging and AD as a result of vascular dysfunction. A model is proposed by which chronic cerebral hypoperfusion, as a result of vascular factors, results in both the generation and accumulation of amyloid and injury to white matter integrity, resulting in cognitive impairment. The generation of amyloid and accumulation in the vasculature may act to perpetuate further vascular dysfunction and accelerate white matter pathology, and as a consequence grey matter pathology and cognitive decline.     

Acetylcholine and associative memory in the piriform cortex

The significance of cholinergic modulation for associative memory performance in the piriform cortex was examined in a study combining cellular neurophysiology in brain slices with realistic biophysical network simulations. Three different physiological effects of acetylcholine were identified at the single-cell level: suppression of neuronal adaptation, suppression of synaptic transmission in the intrinsic fibers layer, and activity-dependent increase in synaptic strength. Biophysical simulations show how these three effects are joined together to enhance learning and recall performance of the cortical network. Furthermore, our data suggest that activity-dependent synaptic decay during learning is a crucial factor in determining learning capability of the cortical network. Accordingly, it is predicted that acetylcholine should also enhance long-term depression in the piriform cortex.     

Modeling the Impact of Lesions in the Human Brain

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous (“resting-state”) neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions.     

Differences in regional brain activation patterns assessed by functional magnetic resonance imaging in patients with systemic lupus erythematosus stratified by disease duration

The mediators of tissue damage in systemic lupus erythematosus (SLE) such as antibodies, cytokines and activated immune cells have direct access to most organs in the body but must penetrate the blood-brain barrier (BBB) to gain access to brain tissue. We hypothesized that compromise of the BBB occurs episodically such that the brain will acquire tissue damage slowly and not at the same rate as other organs. On the basis of these assumptions, we wished to determine if duration of disease correlated with brain injury, as measured with functional magnetic resonance imaging (fMRI), and if this was independent of degree of tissue damage in other organs. We investigated differences in brain activation patterns using fMRI in 13 SLE patients stratified by disease duration of ≤2 years (short-term [ST]) or ≥10 years (long-term [LT]). Two fMRI paradigms were selected to measure working memory and emotional response (fearful faces task). Performance in the working memory task was significantly better in the ST group for one and two shape recall; however, both groups did poorly with three shape recall. Imaging studies demonstrated significantly increased cortical activation in the ST group in regions associated with cognition during the two shape retention phase of the working memory task (P < 0.001) and increased amygdala (P < 0.05) and superior parietal (P < 0.01) activation in response to the fearful faces paradigm. In conclusion, analysis of activation patterns stratified by performance accuracy, differences in co-morbid disease, corticosteroid doses or disease activity suggests that these observed differences are attributable to SLE effects on the central nervous system exclusive of vascular disease or other confounding influences. Our hypothesis is further supported by the lack of correlation between regional brain abnormalities on fMRI and the Systemic Lupus International Collaborating Clinics (SLICC) damage index.     

Mechanical role of a growing solid tumor on cortical folding

Cortical folding, or convolution of the brain, is a vital process in mammals that causes the brain to have a wrinkled appearance. The existence of different types of prenatal solid tumors may alter this complex phenomenon and cause severe brain disorders. Here we interpret the effects of a growing solid tumor on the cortical folding in the fetal brain by virtue of theoretical analyses and computational modeling. The developing fetal brain is modeled as a simple, double-layered, and soft structure with an outer cortex and an inner core, in combination with a circular tumor model imbedded in the structure to investigate the developmental mechanism of cortical convolution. Analytical approaches offer introductory insight into the deformation field and stress distribution of a developing brain. After the onset of instability, analytical approaches fail to capture complex secondary evolution patterns, therefore a series of non-linear finite element simulations are carried out to study the crease formation and the influence from a growing solid tumor inside the structure. Parametric studies show the dependency of the cortical folding pattern on the size, location, and growth speed of a solid tumor in fetal brain. It is noteworthy to mention that there is a critical distance from the cortex/core interface where the growing tumor shows its pronounced effect on the cortical convolution, and that a growing tumor decreases the gyrification index of cortical convolution while its stiffness does not have a profound effect on the gyrification process.     

How Does Connectivity Between Cortical Areas Depend on Brain Size? Implications for Efficient Computation

A formula for an average connectivity between cortical areas in mammals is derived. Based on comparative neuroanatomical data, it is found, surprisingly, that this connectivity is either only weakly dependent or independent of brain size. It is discussed how this formula can be used to estimate the average length of axons in white matter. Other allometric relations, such as cortical patches and area sizes vs. brain size, are also provided. Finally, some functional implications, with an emphasis on efficient cortical computation, are discussed as well.     

White Matter Hyperintensities among Older Adults Are Associated with Futile Increase in Frontal Activation and Functional Connectivity during Spatial Search

The mechanisms by which aging and other processes can affect the structure and function of brain networks are important to understanding normal age-related cognitive decline. Advancing age is known to be associated with various disease processes, including clinically asymptomatic vascular and inflammation processes that contribute to white matter structural alteration and potential injury. The effects of these processes on the function of distributed cognitive networks, however, are poorly understood. We hypothesized that the extent of magnetic resonance imaging white matter hyperintensities would be associated with visual attentional control in healthy aging, measured using a functional magnetic resonance imaging search task. We assessed cognitively healthy older adults with search tasks indexing processing speed and attentional control. Expanding upon previous research, older adults demonstrate activation across a frontal-parietal attentional control network. Further, greater white matter hyperintensity volume was associated with increased activation of a frontal network node independent of chronological age. Also consistent with previous research, greater white matter hyperintensity volume was associated with anatomically specific reductions in functional magnetic resonance imaging functional connectivity during search among attentional control regions. White matter hyperintensities may lead to subtle attentional network dysfunction, potentially through impaired frontal-parietal and frontal interhemispheric connectivity, suggesting that clinically silent white matter biomarkers of vascular and inflammatory injury can contribute to differences in search performance and brain function in aging, and likely contribute to advanced age-related impairments in cognitive control.     

Brain networks of explicit and implicit learning

Are explicit versus implicit learning mechanisms reflected in the brain as distinct neural structures, as previous research indicates, or are they distinguished by brain networks that involve overlapping systems with differential connectivity? In this functional MRI study we examined the neural correlates of explicit and implicit learning of artificial grammar sequences. Using effective connectivity analyses we found that brain networks of different connectivity underlie the two types of learning: while both processes involve activation in a set of cortical and subcortical structures, explicit learners engage a network that uses the insula as a key mediator whereas implicit learners evoke a direct frontal-striatal network. Individual differences in working memory also differentially impact the two types of sequence learning.     

Age-Related Changes in Task Related Functional Network Connectivity

Aging has a multi-faceted impact on brain structure, brain function and cognitive task performance, but the interaction of these different age-related changes is largely unexplored. We hypothesize that age-related structural changes alter the functional connectivity within the brain, resulting in altered task performance during cognitive challenges. In this neuroimaging study, we used independent components analysis to identify spatial patterns of coordinated functional activity involved in the performance of a verbal delayed item recognition task from 75 healthy young and 37 healthy old adults. Strength of functional connectivity between spatial components was assessed for age group differences and related to speeded task performance. We then assessed whether age-related differences in global brain volume were associated with age-related differences in functional network connectivity. Both age groups used a series of spatial components during the verbal working memory task and the strength and distribution of functional network connectivity between these components differed across the age groups. Poorer task performance, i.e. slower speed with increasing memory load, in the old adults was associated with decreases in functional network connectivity between components comprised of the supplementary motor area and the middle cingulate and between the precuneus and the middle/superior frontal cortex. Advancing age also led to decreased brain volume; however, there was no evidence to support the hypothesis that age-related alterations in functional network connectivity were the result of global brain volume changes. These results suggest that age-related differences in the coordination of neural activity between brain regions partially underlie differences in cognitive performance.     

Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain

Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors—the “recruitment” of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells—in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of “white matter disease,” where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.     

Identification of a Functional Connectome for Long-Term Fear Memory in Mice

Long-term memories are thought to depend upon the coordinated activation of a broad network of cortical and subcortical brain regions. However, the distributed nature of this representation has made it challenging to define the neural elements of the memory trace, and lesion and electrophysiological approaches provide only a narrow window into what is appreciated a much more global network. Here we used a global mapping approach to identify networks of brain regions activated following recall of long-term fear memories in mice. Analysis of Fos expression across 84 brain regions allowed us to identify regions that were co-active following memory recall. These analyses revealed that the functional organization of long-term fear memories depends on memory age and is altered in mutant mice that exhibit premature forgetting. Most importantly, these analyses indicate that long-term memory recall engages a network that has a distinct thalamic-hippocampal-cortical signature. This network is concurrently integrated and segregated and therefore has small-world properties, and contains hub-like regions in the prefrontal cortex and thalamus that may play privileged roles in memory expression.     

A Biomechanical Model of Tumor-Induced Intracranial Pressure and Edema in Brain Tissue

Brain tumor growth and tumor-induced edema result in increased intracranial pressure (ICP), which, in turn, is responsible for conditions as benign as headaches and vomiting or as severe as seizures, neurological damage, or even death. Therefore, it has been hypothesized that tracking ICP dynamics may offer improved prognostic potential in terms of early detection of brain cancer and better delimitation of the tumor boundary. However, translating such theory into clinical practice remains a challenge, in part because of an incomplete understanding of how ICP correlates with tumor grade. Here, we propose a multiphase mixture model that describes the biomechanical response of healthy brain tissue—in terms of changes in ICP and edema—to a growing tumor. The model captures ICP dynamics within the diseased brain and accounts for the ability/inability of healthy tissue to compensate for this pressure. We propose parameter regimes that distinguish brain tumors by grade, thereby providing critical insight into how ICP dynamics vary by severity of disease. In particular, we offer an explanation for clinically observed phenomena, such as a lack of symptoms in low-grade glioma patients versus a rapid onset of symptoms in those with malignant tumors. Our model also takes into account the effects tumor-derived proteases may have on ICP levels and the extent of tumor invasion. This work represents an important first step toward understanding the mechanisms that underlie the onset of edema and ICP in cancer-afflicted brains. Continued modeling effort in this direction has the potential to make an impact in the field of brain cancer diagnostics.     

Segregation of the brain into gray and white matter: a design minimizing conduction delays

A ubiquitous feature of the vertebrate anatomy is the segregation of the brain into white and gray matter. Assuming that evolution maximized brain functionality, what is the reason for such segregation? To answer this question, we posit that brain functionality requires high interconnectivity and short conduction delays. Based on this assumption we searched for the optimal brain architecture by comparing different candidate designs. We found that the optimal design depends on the number of neurons, interneuronal connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into white and gray matter. These results provide a possible explanation for the structure of various regions of the vertebrate brain, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.     

Network Self-Organization Explains the Statistics and Dynamics of Synaptic Connection Strengths in Cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.