Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system

It is shown how to compute both direct and total effective connection matrices (deCMs and teCMs), which embody the strengths of neural connections between regions, from correlation-based functional CMs using propagator-based interferometry, a method that stems from geophysics and acoustics, coupled with the recent identification of deCMs and teCMs with bare and dressed propagators, respectively. The approach incorporates excitatory and inhibitory connections, multiple structures and populations, and measurement effects. The propagator is found for a generalized scalar wave equation derived from neural field theory, and expressed in terms of neural activity correlations and covariances, and wave damping rates. It is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain. The results are illustrated in analytically tractable test cases.

Determination of effective brain connectivity from functional connectivity with application to resting state connectivities

Neural field theory insights are used to derive effective brain connectivity matrices from the functional connectivity matrix defined by activity covariances. The symmetric case is exactly solved for a resting state system driven by white noise, in which strengths of connections, often termed effective connectivities, are inferred from functional data; these include strengths of connections that are underestimated or not detected by anatomical imaging. Proximity to criticality is calculated and found to be consistent with estimates obtainable from other methods. Links between anatomical, effective, and functional connectivity and resting state activity are quantified, with applicability to other complex networks. Proof-of-principle results are illustrated using published experimental data on anatomical connectivity and resting state functional connectivity. In particular, it is shown that functional connection matrices can be used to uncover the existence and strength of connections that are missed from anatomical connection matrices, including interhemispheric connections that are difficult to track with techniques such as diffusion spectrum imaging.

Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG

OBJECTIVE

To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain.

METHODS

Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling.

RESULTS

All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation.

CONCLUSIONS

The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon.

SIGNIFICANCE

Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain.

Spectral Characterization of Hierarchical Modularity in Product Architectures

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

Prediction and verification of nonlinear sleep spindle harmonic oscillations

This paper examines nonlinear effects in a neural field model of the corticothalamic system to predict the EEG power spectrum of sleep spindles. Nonlinearity in the thalamic relay nuclei gives rise to a spindle harmonic visible in the cortical EEG. By deriving an analytic expression for nonlinear spectrum, the power in the spindle harmonic is predicted to scale quadratically with the power in the spindle oscillation. By isolating sleep spindles from background sleep in experimental EEG data, the spindle harmonic is directly observed.

Discrete-network versus modal representations of brain activity: why a sparse regions-of-interest approach can work for analysis of continuous dynamics

The efficacy of the common practice of tracking brain dynamics using a few key regions of interest is explained via the fact that these regions are sensitive to underlying extended modes of activity, not just local dynamics. This underlines the inseparable interplay between modes and regions and reflects the reality that brain functions range from highly localized to highly extended.

Electrostatic decay in a weakly magnetized plasma

The kinematics of the electrostatic (ES) decay of a Langmuir wave into a Langmuir wave and an ion sound wave are generalized to a weakly magnetized plasma. Unlike the unmagnetized case, ES decay in a magnetized plasma is always kinematically permitted and can produce daughter Langmuir waves with very small wave numbers, which we demonstrate by quasilinear simulations. The simulations further show that ES decay in magnetized plasmas is consistent with STEREO spacecraft observations of transversely polarized Langmuir waves in the solar wind.

Cortical information flow in Parkinson's disease: a composite network/field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main “input” layer of the cortex (layer 4) to the main “output” layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

A minimal physiologically based model of the HPA axis under influence of the sleep-wake cycles

The hypothalamic-pituitary-adrenal axis (also called the HPA or stress axis) exhibits distinct circadian and ultradian rhythms in cortisol release that cannot be explained solely by the feedback loops from cortisol to the control systems in the paraventricular nucleus (PVN) and pituitary gland. The HPA axis is intimately connected with other brain functions. In particular, it is strongly affected by the sleep-wake cycles via direct and indirect effects of the circadian and homeostatic mechanisms. For example, the HPA axis has direct inputs from the master circadian clock in the suprachiasmatic nuclei (SCN), and from the various sleep-wake related neuronal populations, which themselves are under the effects of the circadian and homeostatic processes. In this paper a first step towards a physiologically based mathematical model of the HPA-axis under effects of the sleep-wake cycles is presented. This model accounts for 3 major characteristics of daily cortisol profile in the blood: i) abrupt increase of cortisol concentration in response to awakening, the so-called cortisol-awakening response (CAR); ii) reduced cortisol levels during daytime with underlying ultradian oscillations; and iii) suppression of cortisol release during sleep.

Relationships between Electroencephalographic Spectral Peaks Across Frequency Bands

The degree to which electroencephalographic spectral peaks are independent, and the relationships between their frequencies have been debated. A novel fitting method was used to determine peak parameters in the range 2-35 Hz from a large sample of eyes-closed spectra, and their interrelationships were investigated. Findings were compared with a mean-field model of thalamocortical activity, which predicts near-harmonic relationships between peaks. The subject set consisted of 1424 healthy subjects from the Brain Resource International Database. Peaks in the theta range occurred on average near half the alpha peak frequency, while peaks in the beta range tended to occur near twice and three times the alpha peak frequency on an individual-subject basis. Moreover, for the majority of subjects, alpha peak frequencies were significantly positively correlated with frequencies of peaks in the theta and low and high beta ranges. Such a harmonic progression agrees semiquantitatively with theoretical predictions from the mean-field model. These findings indicate a common or analogous source for different rhythms, and help to define appropriate individual frequency bands for peak identification.

Spatiotemporal pattern formation in two-dimensional neural circuits: roles of refractoriness and noise

Refractoriness is one of the most fundamental states of neural firing activity, in which neurons that have just fired are unable to produce another spike, regardless of the strength of afferent stimuli. Another essential and unavoidable feature of neural systems is the existence of noise. To study the role of these essential factors in spatiotemporal pattern formation in neural systems, a spatially expended neural network model is constructed, with the dynamics of its individual neurons capturing the three most essential states of the neural firing behavior: firing, refractory and resting, and the network topology consistent with the widely observed center-surround coupling manner in the real brain. By changing the refractory period with and without noise in a systematic way in the network, it is shown numerically and analytically that without refractoriness, or when the refractory period is smaller than a certain value, the collective activity pattern of the system consists of localized, oscillating patterns. However, when the refractory period is greater than a certain value, crescent-shaped, localized propagating patterns emerge in the presence of noise. It is further illustrated that the formation of the dynamical spiking patterns is due to a symmetry breaking mechanism, refractoriness-induced symmetry breaking; that is generated by the interplay of noise and refractoriness in the network model. This refractoriness-induced symmetry breaking provides a novel perspective on the emergence of localized, spiking wave patterns or spike timing sequences as ubiquitously observed in real neural systems; it therefore suggests that refractoriness may benefit neural systems in their temporal information processing, rather than limiting the performance of neurons, as has been conventionally thought. Our results also highlight the importance of considering noise in studying spatially extended neural systems, where it may facilitate the formation of spatiotemporal order.

Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos

Responding to various stimuli, some neurons either remain resting or can fire several distinct patterns of action potentials, such as spiking, bursting, subthreshold oscillations, and chaotic firing. In particular, Wilson's conductance-based neocortical neuron model, derived from the Hodgkin-Huxley model, is explored to understand underlying mechanisms of the firing patterns. Phase diagrams describing boundaries between the domains of different firing patterns are obtained via extensive numerical computations. The boundaries are further studied by standard instability analyses, which demonstrates that the chaotic neural firing could develop via period-doubling and/or period- adding cascades. Sequences of the firing patterns often observed in many neural experiments are also discussed in the phase diagram framework developed. Our results lay the groundwork for wider use of the model, especially for incorporating it into neural field modeling of the brain.

Abstract P1-12-04: Carboplatin, nab-paclitaxel and bevacizumab as first-line treatment for metastatic breast cancer

Background: Bevacizumab added to weekly paclitaxel resulted in improved progression free survival (PFS) and objective response rates (ORR) compared to weekly paclitaxel alone. Nab-paclitaxel and the platins are active in MBC. We conducted an efficacy and safety study of carboplatin, nab-paclitaxel and bevacizumab.

Methods: A phase II open label prospective multi-site study enrolled patients (pts) who had measurable MBC according to RECIST 1.1 criteria and no prior chemotherapy for advanced disease. The primary endpoint was PFS with secondary endpoints of overall survival (OS), ORR, and safety. Pts initially received carboplatin AUC 6 day 1, 22,43, plus weekly nab-paclitaxel 100mg/m2 and bevacizumab 15mg/m2 day 1,22,43 of a 56 day cycle. This was later changed to carboplatin AUC 6 day 1, nab-paclitaxel 100mg/m2 day 1,8,15, and bevacizumab 10mg/m2 day 1,15 of a 28 day cycle. Thirty-two pts were required to detect an increase in median PFS from 6.7 to 10.5 mo with 80% power based on a one-sided p = 0.05. Kaplan–Meier analyses estimated PFS and OS. The log rank test was used for the comparison of survival curves between pts with triple negative MBC (TNBC) and pts with non-TNBC.

Results: Thirty-two pts were enrolled between 2/2008 and 11/2011 by 1 academic and 5 community oncology practices. Two pts were ineligible due to non-measurable disease and not included in the response analyses. The median age was 58 years (range 35–81), 22 pts (69%) had an ECOG PS 0, 9 (28%) had a PS 1, 1 (3%) PS 2. Twenty-four (75%) pts had ER+ disease, 7 (22%) had TNBC, 1 (3%) had ER-HER2+ disease not eligible for trastuzumab-based therapy. Metastatic sites were bone (26%), liver (18%), loco-regional (16%), and lung (12%). One pt (3%) had bone and loco-regional disease only, 19 (59%) had visceral dominant disease. The median number of weeks on treatment was 28.9 (range 5–131). The median PFS in all pts was 13.6 months (mo) (95% CI 11.2–21.9), with a median OS of 26.8 mo (95% CI 13.3–41.2). The ORR (2 CR and 18 PR) was 66.7% (CI 47.2–82.7). There also were 6 (20%) unconfirmed PR and 3 (10%) stable disease, resulting in a clinical benefit rate of 96.7% (CI 82.78–99.92). There was no significant difference in PFS (median 13.6 vs 16.1mo, p = 0.37) or OS (median 13.6 vs 26.8mo, p = 0.32) in pts with TNBC versus non-TNBC disease. The most common toxicities of any grade (gr) include neutropenia and thrombocytopenia in 24 pts (75%) each, leukopenia and fatigue in 17 pts (53%) each, anemia in 15 (47%), and neuropathy in 10 (31%). Gr 4 neutropenia was seen in 7 pts (22%) without febrile neutropenia, and gr 4 thrombocytopenia occurred in 6 (19%). There were no pts with gr 4 sensory neuropathy. All pts required chemotherapy dose delays, 15 (47%) had chemotherapy dose reductions.

Conclusions: The carboplatin, nab-paclitaxel and bevacizumab combination is highly effective with good tolerance in first line MBC. As the role of anti-angiogenic therapy in first line metastatic breast cancer is being clarified, this would be an attractive regimen to test in the (neo)adjuvant setting and together with novel molecular targeted agents.

Citation Information: Cancer Res 2012;72(24 Suppl):Abstract nr P1-12-04.

Arousal state feedback as a potential physiological generator of the ultradian REM/NREM sleep cycle

Human sleep episodes are characterized by an approximately 90-min ultradian oscillation between rapid eye movement (REM) and non-REM (NREM) sleep stages. The source of this oscillation is not known. Pacemaker mechanisms for this rhythm have been proposed, such as a reciprocal interaction network, but these fail to account for documented homeostatic regulation of both sleep stages. Here, two candidate mechanisms are investigated using a simple model that has stable states corresponding to Wake, REM sleep, and NREM sleep. Unlike other models of the ultradian rhythm, this model of sleep dynamics does not include an ultradian pacemaker, nor does it invoke a hypothetical homeostatic process that exists purely to drive ultradian rhythms. Instead, only two inputs are included: the homeostatic drive for Sleep and the circadian drive for Wake. These two inputs have been the basis for the most influential Sleep/Wake models, but have not previously been identified as possible ultradian rhythm generators. Using the model, realistic ultradian rhythms are generated by arousal state feedback to either the homeostatic or circadian drive. For the proposed 'homeostatic mechanism', homeostatic pressure increases in Wake and REM sleep, and decreases in NREM sleep. For the proposed 'circadian mechanism', the circadian drive is up-regulated in Wake and REM sleep, and is down-regulated in NREM sleep. The two mechanisms are complementary in the features they capture. The homeostatic mechanism reproduces experimentally observed rebounds in NREM sleep duration and intensity following total sleep deprivation, and rebounds in both NREM sleep intensity and REM sleep duration following selective REM sleep deprivation. The circadian mechanism does not reproduce sleep state rebounds, but more accurately reproduces the temporal patterns observed in a normal night of sleep. These findings have important implications in terms of sleep physiology and they provide a parsimonious explanation for the observed ultradian rhythm of REM/NREM sleep.

Neural field theory of plasticity in the cerebral cortex

A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle-node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.

Complementarity of spike- and rate-based dynamics of neural systems

Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other.

Neural field theory with variance dynamics

Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation.

Hemodynamic traveling waves in human visual cortex

Functional MRI (fMRI) experiments rely on precise characterization of the blood oxygen level dependent (BOLD) signal. As the spatial resolution of fMRI reaches the sub-millimeter range, the need for quantitative modelling of spatiotemporal properties of this hemodynamic signal has become pressing. Here, we find that a detailed physiologically-based model of spatiotemporal BOLD responses predicts traveling waves with velocities and spatial ranges in empirically observable ranges. Two measurable parameters, related to physiology, characterize these waves: wave velocity and damping rate. To test these predictions, high-resolution fMRI data are acquired from subjects viewing discrete visual stimuli. Predictions and experiment show strong agreement, in particular confirming BOLD waves propagating for at least 5–10 mm across the cortical surface at speeds of 2–12 mm s-1. These observations enable fundamentally new approaches to fMRI analysis, crucial for fMRI data acquired at high spatial resolution.

Functional magnetic resonance imaging (fMRI) experiments have advanced our understanding of the structure and function of the human brain. Dynamic changes in the flow and concentration of oxygen in blood are observed experimentally in fMRI data via the blood oxygen level dependent (BOLD) signal. Since neuronal activity induces this hemodynamic response, the BOLD signal provides a noninvasive measure of neuronal activity. Understanding the mechanisms that drive this BOLD response is fundamental for accurately inferring the underlying neuronal activity. The goal of this study is to systematically predict spatiotemporal hemodynamics from a biophysical model, then test these in a high resolution fMRI study of the visual cortex. Using this theory, we predict and empirically confirm the existence of hemodynamic waves in cortex – a striking and novel finding.

Spike, rate, field, and hybrid methods for treating neuronal dynamics and interactions

Spike-, rate-, and field-based approaches to neural dynamics are adapted and hybridized to provide new methods of analyzing dynamics of single neurons and large neuronal systems, to elucidate the relationships and intermediate forms between these limiting cases, and to enable faster simulations with reduced memory requirements. At the single-neuron level, the new approaches involve reformulation of dynamics in synapses, dendrites, cell bodies, and axons to enable new types of analysis, longer numerical timesteps, and demonstration that rate-based methods can predict spike times. In multineuron systems, hybrids and intermediates between spike-based and field-based coupling between neurons are used to provide stepping stones between descriptions based on pairwise spike-based interactions between neurons and ones based on neural field-based interactions within and between populations, including arbitrary spatial structure and temporal delays in the connections in general. In particular, a new neuron-in-cell approach is introduced that is a hybrid between neural field theory and spiking-neuron models in analogy to particle-in-cell methods in plasma physics. This approach enables large speedups in computations while preserving spike shapes and times. Various approaches are illustrated numerically for specific cases.

Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model

Linear instabilities are analyzed in a physiologically based mean-field corticothalamic model and a reduced-parameter model derived from it. In both models, the stable zone corresponding to normal arousal states is bounded by a series of surfaces demarcating the onsets of instabilities. The stable zone is found to depend on delay and rate parameters, whose values have a simple relationship to the number of instabilities and dominant frequencies on the stable zone's boundary. The dominant frequencies of linear activity inside the stable zone are found to lie in clearly delineated regions, each corresponding to an instability surface on its boundary and having approximately the same dominant frequency. These regions are ordered in parameter space according to their dominant frequencies, and an instability associated with the intrathalamic loop is shown to have the highest frequency that can become unstable. This reveals an important role for the thalamus in controlling the stability and bandwidth of dynamics in the corticothalamic system as a whole. The reduced model is found to agree well with the full model in a wide region of parameter space and, thus, is a useful guide to the full model's dynamics.

Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory

It is shown how to compute effective and functional connection matrices (eCMs and fCMs) from anatomical CMs (aCMs) and corresponding strength-of-connection matrices (sCMs) using propagator methods in which neural interactions play the role of scatterings. This analysis demonstrates how network effects dress the bare propagators (the sCMs) to yield effective propagators (the eCMs) that can be used to compute the covariances customarily used to define fCMs. The results incorporate excitatory and inhibitory connections, multiple structures and populations, asymmetries, time delays, and measurement effects. They can also be postprocessed in the same manner as experimental measurements for direct comparison with data and thereby give insights into the role of coarse-graining, thresholding, and other effects in determining the structure of CMs. The spatiotemporal results show how to generalize CMs to include time delays and how natural network modes give rise to long-range coherence at resonant frequencies. The results are demonstrated using tractable analytic cases via neural field theory of cortical and corticothalamic systems. These also demonstrate close connections between the structure of CMs and proximity to critical points of the system, highlight the importance of indirect links between brain regions and raise the possibility of imaging specific levels of indirect connectivity. Aside from the results presented explicitly here, the expression of the connections among aCMs, sCMs, eCMs, and fCMs in terms of propagators opens the way for propagator theory to be further applied to analysis of connectivity.

Quantitative modelling of sleep dynamics

Arousal is largely controlled by the ascending arousal system of the hypothalamus and brainstem, which projects to the corticothalamic system responsible for electroencephalographic (EEG) signatures of sleep. Quantitative physiologically based modelling of brainstem dynamics theory is described here, using realistic parameters, and links to EEG are outlined. Verification against a wide range of experimental data is described, including arousal dynamics under normal conditions, sleep deprivation, stimuli, stimulants and jetlag, plus key features of wake and sleep EEGs.

Neural field theory of synaptic plasticity

Plasticity is crucial to neural development, learning, and memory. In the common in vivo situation where postsynaptic neural activity results from multiple presynaptic inputs, it is shown that a widely used class of correlation-dependent and spike-timing dependent plasticity rules can be written in a form that can be incorporated into neural field theory, which enables their system-level dynamics to be investigated. It is shown that the resulting plasticity dynamics depends strongly on the stimulus spectrum via overall system frequency responses. In the case of perturbations that are approximately linear, explicit formulas are found for the dynamics in terms of stimulus spectra via system transfer functions. The resulting theory is applied to a simple model system to reveal how collective effects, especially resonances, can drastically modify system-level plasticity dynamics from that implied by single-neuron analyses. The simplified model illustrates the potential relevance of these effects in applications to brain stimulation, synaptic homeostasis, and epilepsy.

Geometric effects on complex network structure in the cortex

It is shown that homogeneous, short-range, two-dimensional (2D) cortical connectivity, without modularity, hierarchy, or other specialized structure, reproduces key observed properties of cortical networks, including low path length, high clustering and modularity index, and apparent hierarchical block-diagonal structure in connection matrices. Geometry strongly influences connection matrices, implying that simple interpretations of connectivity measures as reflecting specialized structure can be misleading: Such apparent structure is seen in strictly uniform, locally connected architectures in 2D. Geometry is thus a proxy for function, modularity, and hierarchy and must be accounted for when structural inferences are made.