On the Emergent "Quantum" Theory in Complex Adaptive Systems.

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or "mock") quantum theory in the Lotka-Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton-Jacobi (HJ) equation and reduce it to an effective Schr\"odinger-type equation, with a (mock) Planck constant $\mockbar$, which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is cancelled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the "environment." We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we reframe the concept of decoherence into the concept of "quantum turbulence," i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.

Correspondence of mean apparent propagator MRI metrics with phosphorylated tau and astrogliosis in chronic traumatic encephalopathy.

Chronic traumatic encephalopathy is a neurodegenerative disease that is diagnosed and staged based on the localization and extent of phosphorylated tau pathology. Although its identification remains the primary diagnostic criteria to distinguish chronic traumatic encephalopathy from other tauopathies, the hyperphosphorylated tau that accumulates in neurofibrillary tangles in cortical grey matter and perivascular regions is often accompanied by concomitant pathology such as astrogliosis. Mean apparent propagator MRI is a clinically feasible diffusion MRI method that is suitable to characterize microstructure of complex biological media efficiently and comprehensively. We performed quantitative correlations between propagator metrics and underlying phosphorylated tau and astroglial pathology in a cross-sectional study of 10 ex vivo human tissue specimens with 'high chronic traumatic encephalopathy' at 0.25 mm isotropic voxels. Linear mixed effects analysis of regions of interest showed significant relationships of phosphorylated tau with propagator-estimated non-Gaussianity in cortical grey matter (P = 0.002) and of astrogliosis with propagator anisotropy in superficial cortical white matter (P = 0.0009). The positive correlation between phosphorylated tau and non-Gaussianity was found to be modest but significant (R2 = 0.44, P = 6.0 × 10-5) using linear regression. We developed an unsupervised clustering algorithm with non-Gaussianity and propagator anisotropy as inputs, which was able to identify voxels in superficial cortical white matter that corresponded to astrocytes that were accumulated at the grey-white matter interface. Our results suggest that mean apparent propagator MRI at high spatial resolution provides a means to not only identify phosphorylated tau pathology but also detect regions with astrocytic pathology and may therefore prove diagnostically valuable in the evaluation of concomitant pathology in cortical tissue with complex microstructure.

Parabolic avalanche scaling in the synchronization of cortical cell assemblies.

Neurons in the cerebral cortex fire coincident action potentials during ongoing activity and in response to sensory inputs. These synchronized cell assemblies are fundamental to cortex function, yet basic dynamical aspects of their size and duration are largely unknown. Using 2-photon imaging of neurons in the superficial cortex of awake mice, we show that synchronized cell assemblies organize as scale-invariant avalanches that quadratically grow with duration. The quadratic avalanche scaling was only found for correlated neurons, required temporal coarse-graining to compensate for spatial subsampling of the imaged cortex, and suggested cortical dynamics to be critical as demonstrated in simulations of balanced E/I-networks. The corresponding time course of an inverted parabola with exponent of χ = 2 described cortical avalanches of coincident firing for up to 5 s duration over an area of 1 mm2. These parabolic avalanches maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant temporal order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.

Oligodendrocyte-mediated myelin plasticity and its role in neural synchronization.

Temporal synchrony of signals arriving from different neurons or brain regions is essential for proper neural processing. Nevertheless, it is not well understood how such synchrony is achieved and maintained in a complex network of time-delayed neural interactions. Myelin plasticity, accomplished by oligodendrocytes (OLs), has been suggested as an efficient mechanism for controlling timing in brain communications through adaptive changes of axonal conduction velocity and consequently conduction time delays, or latencies; however, local rules and feedback mechanisms that OLs use to achieve synchronization are not known. We propose a mathematical model of oligodendrocyte-mediated myelin plasticity (OMP) in which OLs play an active role in providing such feedback. This is achieved without using arrival times at the synapse or modulatory signaling from astrocytes; instead, it relies on the presence of global and transient OL responses to local action potentials in the axons they myelinate. While inspired by OL morphology, we provide the theoretical underpinnings that motivated the model and explore its performance for a wide range of its parameters. Our results indicate that when the characteristic time of OL's transient intracellular responses to neural spikes is between 10 and 40 ms and the firing rates in individual axons are relatively low (10 Hz), the OMP model efficiently synchronizes correlated and time-locked signals while latencies in axons carrying independent signals are unaffected. This suggests a novel form of selective synchronization in the CNS in which oligodendrocytes play an active role by modulating the conduction delays of correlated spike trains as they traverse to their targets.

Identifying transcranial magnetic stimulation induced EEG signatures of different neuronal elements in primary motor cortex.

OBJECTIVE: To investigate the neuronal elements involved in the activation of corticospinal neurons in the primary motor cortex (M1). METHODS: We studied 10 healthy subjects. Cortical evoked potentials with different components induced by monophasic transcranial magnetic stimulation (TMS) in anterior-posterior and posterior-anterior currents recorded with electroencephalography (EEG) were analyzed. RESULTS: EEG signatures with P25 and N45 components recorded at the C3 electrode with posterior-anterior current were larger than those with anterior-posterior current, while the signatures with P180 and N280 components recorded at the FC1 electrode with anterior-posterior current were larger than those with posterior-anterior current. The source localization analysis revealed that the cortical evoked potential with anterior-posterior current distributed both in the M1 and premotor cortex while that with posterior-anterior current only located in the M1. CONCLUSIONS: We conclude that the activation of corticospinal pyramidal neurons in the M1 is affected by various neuronal elements including the local intracortical circuits in the M1 and inputs from premotor cortex with different sensitivities to TMS in opposite current directions. SIGNIFICANCE: Our finding helped answer a longstanding question about how the corticospinal pathway from the M1 is functionally organized and activated.

Long-term stability of avalanche scaling and integrative network organization in prefrontal and premotor cortex.

Ongoing neuronal activity in the brain establishes functional networks that reflect normal and pathological brain function. Most estimates of these functional networks suffer from low spatiotemporal resolution and indirect measures of neuronal population activity, limiting the accuracy and reliability in their reconstruction over time. Here, we studied the stability of neuronal avalanche dynamics and corresponding reconstructed functional networks in the adult brain. Using chronically implanted high-density microelectrode arrays, the local field potential (LFP) of resting-state activity was recorded in prefrontal and premotor cortex of awake nonhuman primates. Avalanche dynamics revealed stable scaling exhibiting an inverted parabolic profile and collapse exponent of 2 in line with a critical branching process over many days and weeks. Functional networks were based on a Bayesian-derived estimator and demonstrated stable integrative properties characterized by nontrivial high neighborhood overlap between strongly connected nodes and robustness to weak-link pruning. Entropy-based mixing analysis revealed significant changes in strong link weights over weeks. The long-term stability in avalanche scaling and integrative network organization in the face of individual link weight changes should support the development of noninvasive biomarkers to characterize normal and abnormal brain states in the adult brain.

A new framework for MR diffusion tensor distribution.

The ability to characterize heterogeneous and anisotropic water diffusion processes within macroscopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and efficient experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values while preserving the richness of diffusion tensor distribution (DTD) paradigm unlike existing models. We introduce a new Monte Carlo (MC) scheme to synthesize realistic 6D DTD numerical phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symmetries of the mean and covariance tensors of CNTVD. The robustness of the estimation pipeline is assessed by adding noise to calculated MR signals and compared with the ground truth. A family of invariant parameters and glyphs which characterize microscopic shape, size and orientation heterogeneity within a voxel are also presented.

Measuring latency distribution of transcallosal fibers using transcranial magnetic stimulation.

BACKGROUND: Neuroimaging technology is being developed to enable non-invasive mapping of the latency distribution of cortical projection pathways in white matter, and correlative clinical neurophysiological techniques would be valuable for mutual verification. Interhemispheric interaction through the corpus callosum can be measured with interhemispheric facilitation and inhibition using transcranial magnetic stimulation. OBJECTIVE: To develop a method for determining the latency distribution of the transcallosal fibers with transcranial magnetic stimulation. METHODS: We measured the precise time courses of interhemispheric facilitation and inhibition with a conditioning-test paired-pulse magnetic stimulation paradigm. The conditioning stimulus was applied to the right primary motor cortex and the test stimulus was applied to the left primary motor cortex. The interstimulus interval was set at 0.1 ms resolution. The proportions of transcallosal fibers with different conduction velocities were calculated by measuring the changes in magnitudes of interhemispheric facilitation and inhibition with interstimulus interval. RESULTS: Both interhemispheric facilitation and inhibition increased with increment in interstimulus interval. The magnitude of interhemispheric facilitation was correlated with that of interhemispheric inhibition. The latency distribution of transcallosal fibers measured with interhemispheric facilitation was also correlated with that measured with interhemispheric inhibition. CONCLUSIONS: The data can be interpreted as latency distribution of transcallosal fibers. Interhemispheric interaction measured with transcranial magnetic stimulation is a promising technique to determine the latency distribution of the transcallosal fibers. Similar techniques could be developed for other cortical pathways.

Measuring conduction velocity distributions in peripheral nerves using neurophysiological techniques.

OBJECTIVE: To determine how long it takes for neural impulses to travel along peripheral nerve fibers in living humans. METHODS: A collision test was performed to measure the conduction velocity distribution of the ulnar nerve. Two stimuli at the distal and proximal sites were used to produce the collision. Compound muscle or nerve action potentials were recorded to perform the measurements on the motor or mixed nerve, respectively. Interstimulus interval was set at 1-5 ms. A quadri-pulse technique was used to measure the refractory period and calibrate the conduction time. RESULTS: Compound muscle action potential produced by the proximal stimulation started to emerge at the interstimulus interval of about 1.5 ms and increased with the increment in interstimulus interval. Two groups of motor nerve fibers with different conduction velocities were identified. The mixed nerve showed a wider conduction velocity distribution with identification of more subgroups of nerve fibers than the motor nerve. CONCLUSIONS: The conduction velocity distributions in high resolution on a peripheral motor and mixed nerve are different and this can be measured with the collision test. SIGNIFICANCE: We provided ground truth data to verify the neuroimaging pipelines for the measurements of latency connectome in the peripheral nervous system.

Regulation of myelin structure and conduction velocity by perinodal astrocytes.

The speed of impulse transmission is critical for optimal neural circuit function, but it is unclear how the appropriate conduction velocity is established in individual axons. The velocity of impulse transmission is influenced by the thickness of the myelin sheath and the morphology of electrogenic nodes of Ranvier along axons. Here we show that myelin thickness and nodal gap length are reversibly altered by astrocytes, glial cells that contact nodes of Ranvier. Thrombin-dependent proteolysis of a cell adhesion molecule that attaches myelin to the axon (neurofascin 155) is inhibited by vesicular release of thrombin protease inhibitors from perinodal astrocytes. Transgenic mice expressing a dominant-negative fragment of VAMP2 in astrocytes, to reduce exocytosis by 50%, exhibited detachment of adjacent paranodal loops of myelin from the axon, increased nodal gap length, and thinning of the myelin sheath in the optic nerve. These morphological changes alter the passive cable properties of axons to reduce conduction velocity and spike-time arrival in the CNS in parallel with a decrease in visual acuity. All effects were reversed by the thrombin inhibitor Fondaparinux. Similar results were obtained by viral transfection of tetanus toxin into astrocytes of rat corpus callosum. Previously, it was unknown how the myelin sheath could be thinned and the functions of perinodal astrocytes were not well understood. These findings describe a form of nervous system plasticity in which myelin structure and conduction velocity are adjusted by astrocytes. The thrombin-dependent cleavage of neurofascin 155 may also have relevance to myelin disruption and repair.

Morphometric analysis and neuroanatomical mapping of the zebrafish brain.

Large-scale genomic studies have recently identified genetic variants causative for major neurodevelopmental disorders, such as intellectual disability and autism. However, determining how underlying developmental processes are affected by these mutations remains a significant challenge in the field. Zebrafish is an established model system in developmental neurogenetics that may be useful in uncovering the mechanisms of these mutations. Here we describe the use of voxel-intensity, deformation field, and volume-based morphometric techniques for the systematic and unbiased analysis of gene knock-down and environmental exposure-induced phenotypes in zebrafish. We first present a computational method for brain segmentation based on transgene expression patterns to create a comprehensive neuroanatomical map. This map allowed us to disclose statistically significant changes in brain microstructure and composition in neurodevelopmental models. We demonstrate the effectiveness of morphometric techniques in measuring changes in the relative size of neuroanatomical subdivisions in atoh7 morphant larvae and in identifying phenotypes in larvae treated with valproic acid, a chemical demonstrated to increase the risk of autism in humans. These tools enable rigorous evaluation of the effects of gene mutations and environmental exposures on neural development, providing an entry point for cellular and molecular analysis of basic developmental processes as well as neurodevelopmental and neurodegenerative disorders.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Emergent "Quantum" Theory in Complex Adaptive Systems.

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Simultaneous calcium fluorescence imaging and MR of ex vivo organotypic cortical cultures: a new test bed for functional MRI.

Recently, several new functional (f)MRI contrast mechanisms including diffusion, phase imaging, proton density, etc. have been proposed to measure neuronal activity more directly and accurately than blood-oxygen-level dependent (BOLD) fMRI. However, these approaches have proved difficult to reproduce, mainly because of the dearth of reliable and robust test systems to vet and validate them. Here we describe the development and testing of such a test bed for non-BOLD fMRI. Organotypic cortical cultures were used as a stable and reproducible biological model of neuronal activity that shows spontaneous activity similar to that of in vivo brain cortex without any hemodynamic confounds. An open-access, single-sided magnetic resonance (MR) "profiler" consisting of four permanent magnets with magnetic field of 0.32 T was used in this study to perform MR acquisition. A fluorescence microscope with long working distance objective was mounted on the top of a custom-designed chamber that keeps the organotypic culture vital, and the MR system was mounted on the bottom of the chamber to achieve real-time simultaneous calcium fluorescence optical imaging and MR acquisition on the same specimen. In this study, the reliability and performance of the proposed test bed were demonstrated by a conventional CPMG MR sequence acquired simultaneously with calcium imaging, which is a well-characterized measurement of neuronal activity. This experimental design will make it possible to correlate directly the other candidate functional MR signals to the optical indicia of neuronal activity in the future.

Opening bottlenecks on weighted networks by local adaptation to cascade failures.

Structure and dynamics of complex systems are often described using weighted networks in which the position, weight and direction of links quantify how activity propagates between system elements, or nodes. Nodes with only few outgoing links of low weight have low out-strength and thus form bottlenecks that hinder propagation. It is currently not well understood how systems can overcome limits imposed by such bottlenecks. Here, we simulate activity cascades on weighted networks and show that, for any cascade length, activity initially propagates towards high out-strength nodes before terminating in low out-strength bottlenecks. Increasing the weights of links that are active early in the cascade further enhances already strong pathways, but worsens the bottlenecks thereby limiting accessibility to other pathways in the network. In contrast, strengthening only links that propagated the activity just prior to cascade termination, i.e. links that point into bottlenecks, eventually removes these bottlenecks and increases the accessibility of all paths on the network. This local adaptation rule simply relies on the relative timing to a global failure signal and allows systems to overcome engrained structure to adapt to new challenges.

SCORHE: a novel and practical approach to video monitoring of laboratory mice housed in vivarium cage racks.

The System for Continuous Observation of Rodents in Home-cage Environment (SCORHE) was developed to demonstrate the viability of compact and scalable designs for quantifying activity levels and behavior patterns for mice housed within a commercial ventilated cage rack. The SCORHE in-rack design provides day- and night-time monitoring with the consistency and convenience of the home-cage environment. The dual-video camera custom hardware design makes efficient use of space, does not require home-cage modification, and is animal-facility user-friendly. Given the system's low cost and suitability for use in existing vivariums without modification to the animal husbandry procedures or housing setup, SCORHE opens up the potential for the wider use of automated video monitoring in animal facilities. SCORHE's potential uses include day-to-day health monitoring, as well as advanced behavioral screening and ethology experiments, ranging from the assessment of the short- and long-term effects of experimental cancer treatments to the evaluation of mouse models. When used for phenotyping and animal model studies, SCORHE aims to eliminate the concerns often associated with many mouse-monitoring methods, such as circadian rhythm disruption, acclimation periods, lack of night-time measurements, and short monitoring periods. Custom software integrates two video streams to extract several mouse activity and behavior measures. Studies comparing the activity levels of ABCB5 knockout and HMGN1 overexpresser mice with their respective C57BL parental strains demonstrate SCORHE's efficacy in characterizing the activity profiles for singly- and doubly-housed mice. Another study was conducted to demonstrate the ability of SCORHE to detect a change in activity resulting from administering a sedative.

An optimum principle predicts the distribution of axon diameters in normal white matter.

Many important functional properties affecting nerve conduction are influenced by axon diameter. It is also known that the axon diameter distribution (ADD) in normal nerve fascicles is heterogeneous and skewed. A recent attempt to model and explain the parametric form of these distributions was based on biomechanical principles. Here we explore a neurophysiologically-based hypothesis that the observed ADD can be obtained by optimizing the information flow through a fascicle subject to reasonable anatomical and metabolic constraints. Specifically, we use a variational framework to find an optimal distribution based on the fascicle's channel capacity and informative upper bound (IUB), subject to constraints of fixed available fascicle cross-sectional area and fixed number of axons, to derive two novel probability density functions, which we then compare to other previously used distributions. We show, using experimental histological data, that the distributions based on this optimum principle outperform other distributions. Moreover, the new distribution that optimizes the IUB is extremely robust in fitting ADD data obtained histologically, making it well-suited for use in MRI techniques to measure ADDs in vivo, e.g., AxCaliber MRI.

The organization of strong links in complex networks.

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium.

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the object being to estimate the position and lifetime of the fluorophore. Such information can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.