Diffusion MRI tractography of the locus coeruleus-transentorhinal cortex connections using GO-ESP.

PURPOSE: The locus coeruleus (LC) is implicated as an early site of protein pathogenesis in Alzheimer's disease (AD). Tau pathology is hypothesized to propagate in a prion-like manner along the LC-transentorhinal cortex (TEC) white matter (WM) pathway, leading to atrophy of the entorhinal cortex and adjacent cortical regions in a progressive and stereotypical manner. However, WM damage along the LC-TEC pathway may be an earlier observable change that can improve detection of preclinical AD. THEORY AND METHODS: Diffusion-weighted MRI (dMRI) allows reconstruction of WM pathways in vivo, offering promising potential to examine this pathway and enhance our understanding of neural mechanisms underlying the preclinical phase of AD. However, standard dMRI analysis tools have generally been unable to reliably reconstruct this pathway. We apply a novel method, geometric-optics based entropy spectrum pathways (GO-ESP) and produce a new measure of connectivity: the equilibrium probability (EP). RESULTS: We demonstrated reliable reconstruction of LC-TEC pathways in 50 cognitively normal older adults and showed a negative association between LC-TEC EP and cerebrospinal fluid tau. Using Human Connectome Project data, we demonstrated replicability of the method across acquisition schemes and scanners. Finally, we compared our findings with the only other existing LC-TEC tractography template, and replicated their pathway as well as investigated the source of these discrepant findings. CONCLUSIONS: AD-related tau pathology may be detectable within GO-ESP-identified LC-TEC pathways. Furthermore, there may be multiple possible routes from LC to TEC, raising important questions for future research on the LC-TEC connectome and its role in AD pathogenesis.

Collective Synchronous Spiking in a Brain Network of Coupled Nonlinear Oscillators.

A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into account. The nonlinear behavior of the modes participating in the network are the result of the nonresonant dynamics of weakly evanescent cortical waves that, as shown recently, adhere to an inverse frequency-wave number dispersion relation when propagating through an inhomogeneous anisotropic media characteristic of the brain cortex. This description provides a missing link between simplistic models of synchronization in networks of small amplitude phase coupled oscillators and in networks built with various empirically fitted models of pulse or amplitude coupled spiking neurons. Overall the phase-amplitude coupling mechanism presented in the Letter shows significantly more efficient synchronization compared to current standard approaches and demonstrates an emergence of collective synchronized spiking from subthreshold oscillations that neither phase nor amplitude coupling alone are capable of explaining.

Brain Waves: Emergence of Localized, Persistent, Weakly Evanescent Cortical Loops.

An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of nonevanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full-brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the commonly agreed paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation because of the cortex wave modes in the highly folded areas will exhibit no apparent correlation with the fiber directions. Nonlinear coupling of those linear weakly evanescent wave modes then provides a universal mechanism for the emergence of synchronized brain wave field activity. The resonant and nonresonant terms of nonlinear coupling between multiple modes produce both synchronous spiking-like high-frequency wave activity as well as low-frequency wave rhythms. Numerical simulation of forced multiple-mode dynamics shows that, as forcing increases, there is a transition from damped to oscillatory regime that can then transition quickly to a nonoscillatory state when a critical excitation threshold is reached. The resonant nonlinear coupling results in the emergence of low-frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these weakly evanescent cortical wave modes have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and magnetoencephalography, and for the understanding of brain activity in general, including mechanisms of memory.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties.

PURPOSE: A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented. METHODS: This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods. RESULTS: Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition. CONCLUSIONS: The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Symplectomorphic registration with phase space regularization by entropy spectrum pathways.

PURPOSE: The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies. However, in spite of the abundance of literature on the subject and the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods. METHODS: A new registration method is presented that utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization. For validation of the framework a panel of deformations expressed in analytical form is developed that includes deformations based on known physical processes in MRI and reproduces various distortions and artifacts typically present in images collected using these different MRI modalities. RESULTS: The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW-MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes. CONCLUSIONS: The method has shown an excellent performance and the panel of deformations was instrumental to quantify its repeatability and reproducibility in comparison to several available alternative approaches.

Joint Estimation of Effective Brain Wave Activation Modes Using EEG/MEG Sensor Arrays and Multimodal MRI Volumes.

In this letter, we present a new method for integration of sensor-based multifrequency bands of electroencephalography and magnetoencephalography data sets into a voxel-based structural-temporal magnetic resonance imaging analysis by utilizing the general joint estimation using entropy regularization (JESTER) framework. This allows enhancement of the spatial-temporal localization of brain function and the ability to relate it to morphological features and structural connectivity. This method has broad implications for both basic neuroscience research and clinical neuroscience focused on identifying disease-relevant biomarkers by enhancing the spatial-temporal resolution of the estimates derived from current neuroimaging modalities, thereby providing a better picture of the normal human brain in basic neuroimaging experiments and variations associated with disease states.

A Unified Theory of Neuro-MRI Data Shows Scale-Free Nature of Connectivity Modes.

A primary goal of many neuroimaging studies that use magnetic resonance imaging (MRI) is to deduce the structure-function relationships in the human brain using data from the three major neuro-MRI modalities: high-resolution anatomical, diffusion tensor imaging, and functional MRI. To date, the general procedure for analyzing these data is to combine the results derived independently from each of these modalities. In this article, we develop a new theoretical and computational approach for combining these different MRI modalities into a powerful and versatile framework that combines our recently developed methods for morphological shape analysis and segmentation, simultaneous local diffusion estimation and global tractography, and nonlinear and nongaussian spatial-temporal activation pattern classification and ranking, as well as our fast and accurate approach for nonlinear registration between modalities. This joint analysis method is capable of extracting new levels of information that is not achievable from any of those single modalities alone. A theoretical probabilistic framework based on a reformulation of prior information and available interdependencies between modalities through a joint coupling matrix and an efficient computational implementation allows construction of quantitative functional, structural, and effective brain connectivity modes and parcellation. This new method provides an overall increase of resolution, accuracy, level of detail, and information content and has the potential to be instrumental in the clinical adaptation of neuro-MRI modalities, which, when jointly analyzed, provide a more comprehensive view of a subject's structure-function relations, while the current standard, wherein single-modality methods are analyzed separately, leaves a critical gap in an integrated view of a subject's neuorphysiological state. As one example of this increased sensitivity, we demonstrate that the jointly estimated structural and functional dependencies of mode power follow the same power law decay with the same exponent.

The Lamellar Structure of the Brain Fiber Pathways.

We present a quantitative statistical analysis of pairwise crossings for all fibers obtained from whole brain tractography that confirms with high confidence that the brain grid theory (Wedeen et al., 2012a ) is not supported by the evidence. The overall fiber tracts structure appears to be more consistent with small angle treelike branching of tracts rather than with near-orthogonal gridlike crossing of fiber sheets. The analysis uses our new method for high-resolution whole brain tractography that is capable of resolving fibers crossing of less than 10 degrees and correctly following a continuous angular distribution of fibers even when the individual fiber directions are not resolved. This analysis also allows us to demonstrate that the whole brain fiber pathway system is very well approximated by a lamellar vector field, providing a concise and quantitative mathematical characterization of the structural connectivity of the human brain.

Dynamic Multiscale Modes of Resting State Brain Activity Detected by Entropy Field Decomposition.

The ability of functional magnetic resonance imaging (FMRI) to noninvasively measure fluctuations in brain activity in the absence of an applied stimulus offers the possibility of discerning functional networks in the resting state of the brain. However, the reconstruction of brain networks from these signal fluctuations poses a significant challenge because they are generally nonlinear and nongaussian and can overlap in both their spatial and temporal extent. Moreover, because there is no explicit input stimulus, there is no signal model with which to compare the brain responses. A variety of techniques have been devised to address this problem, but the predominant approaches are based on the presupposition of statistical properties of complex brain signal parameters, which are unprovable but facilitate the analysis. In this article, we address this problem with a new method, entropy field decomposition, for estimating structure within spatiotemporal data. This method is based on a general information field-theoretic formulation of Bayesian probability theory incorporating prior coupling information that allows the enumeration of the most probable parameter configurations without the need for unjustified statistical assumptions. This approach facilitates the construction of brain activation modes directly from the spatial-temporal correlation structure of the data. These modes and their associated spatial-temporal correlation structure can then be used to generate space-time activity probability trajectories, called functional connectivity pathways, which provide a characterization of functional brain networks.

Quantitative Classification of Cerebellar Foliation in Cartilaginous Fishes (Class: Chondrichthyes) Using Three-Dimensional Shape Analysis and Its Implications for Evolutionary Biology.

A true cerebellum appeared at the onset of the chondrichthyan (sharks, batoids, and chimaerids) radiation and is known to be essential for executing fast, accurate, and efficient movement. In addition to a high degree of variation in size, the corpus cerebellum in this group has a high degree of variation in convolution (or foliation) and symmetry, which ranges from a smooth cerebellar surface to deep, branched convexities and folds, although the functional significance of this trait is unclear. As variation in the degree of foliation similarly exists throughout vertebrate evolution, it becomes critical to understand this evolutionary process in a wide variety of species. However, current methods are either qualitative and lack numerical rigor or they are restricted to two dimensions. In this paper, a recently developed method for the characterization of shapes embedded within noisy, three-dimensional data called spherical wave decomposition (SWD) is applied to the problem of characterizing cerebellar foliation in cartilaginous fishes. The SWD method provides a quantitative characterization of shapes in terms of well-defined mathematical functions. An additional feature of the SWD method is the construction of a statistical criterion for the optimal fit, which represents the most parsimonious choice of parameters that fits to the data without overfitting to background noise. We propose that this optimal fit can replace a previously described qualitative visual foliation index (VFI) in cartilaginous fishes with a quantitative analog, i.e. the cerebellar foliation index (CFI). The capability of the SWD method is demonstrated in a series of volumetric images of brains from different chondrichthyan species that span the range of foliation gradings currently described for this group. The CFI is consistent with the qualitative grading provided by the VFI, delivers a robust measure of cerebellar foliation, and can provide a quantitative basis for brain shape characterization across taxa.

Automated segmentation and shape characterization of volumetric data.

Characterization of complex shapes embedded within volumetric data is an important step in a wide range of applications. Standard approaches to this problem employ surface-based methods that require inefficient, time consuming, and error prone steps of surface segmentation and inflation to satisfy the uniqueness or stability of subsequent surface fitting algorithms. Here we present a novel method based on a spherical wave decomposition (SWD) of the data that overcomes several of these limitations by directly analyzing the entire data volume, obviating the segmentation, inflation, and surface fitting steps, significantly reducing the computational time and eliminating topological errors while providing a more detailed quantitative description based upon a more complete theoretical framework of volumetric data. The method is demonstrated and compared to the current state-of-the-art neuroimaging methods for segmentation and characterization of volumetric magnetic resonance imaging data of the human brain.

The Nature of the Action Potential.

We demonstrate that our recently developed theory of electric field wave propagation in anisotropic and inhomogeneous brain tissues, which has been shown to explain a broad range of observed coherent synchronous brain electrical processes, also explains the spiking behavior of single neurons, thus bridging the gap between the fundamental element of brain electrical activity (the neuron) and large-scale coherent synchronous electrical activity. Our analysis indicates that the membrane interface of the axonal cellular system can be mathematically described by a nonlinear system with several small parameters. This allows for the rigorous derivation of an accurate yet simpler nonlinear model following the formal small parameter expansion. The resulting action potential model exhibits a smooth, continuous transition from the linear wave oscillatory regime to the nonlinear spiking regime, as well as a critical transition to a non-oscillatory regime. These transitions occur with changes in the criticality parameter and include several different bifurcation types, representative of the various experimentally detected neuron types. This new theory overcomes the limitations of the Hodgkin-Huxley model, such as the inability to explain extracellular spiking, efficient brain synchronization, saltatory conduction along myelinated axons, and a variety of other observed coherent macroscopic brain electrical phenomena. We also show that the standard cable axon theory can be recovered by our approach, using the very crude assumptions of piece-wise homogeneity and isotropy. However, the diffusion process described by the cable equation is not capable of supporting action potential propagation across a wide range of experimentally reported axon parameters.

Characterizing the dynamics of multi-scale global high impact weather events.

The quantitative characterization and prediction of localized severe weather events that emerge as coherences generated by the highly non-linear interacting multivariate dynamics of global weather systems poses a significant challenge whose solution is increasingly important in the face of climate change where weather extremes are on the rise. As weather measurement systems (multiband satellite, radar, etc) continue to dramatically improve, increasingly complex time-dependent multivariate 3D datasets offer the potential to inform such problems but pose an increasingly daunting computational challenge. Here we describe the application to global weather systems of a novel computational method called the Entropy Field Decomposition (EFD) capable of efficiently characterizing coherent spatiotemporal structures in non-linear multivariate interacting physical systems. Using the EFD derived system configurations, we demonstrate the application of a second novel computational method called Space-Time Information Trajectories (STITs) that reveal how spatiotemporal coherences are dynamically connected. The method is demonstrated on the specific phenomenon known as atmospheric rivers (ARs) which are a prime example of a highly coherent, in both space and time, severe weather phenomenon whose generation and persistence are influenced by weather dynamics on a wide range of spatial and temporal scales. The EFD reveals how the interacting wind vector field and humidity scalar field couple to produce ARs, while the resulting STITS reveal the linkage between ARs and large-scale planetary circulations. The focus on ARs is also motivated by their devastating social and economic effects that have made them the subject of increasing scientific investigation to which the EFD may offer new insights. The application of EFD and STITs to the broader range of severe weather events is discussed.

Imaging of brain electric field networks.

We present a method for direct imaging of the electric field networks in the human brain from electroencephalography (EEG) data with much higher temporal and spatial resolution than functional MRI (fMRI), without the concomitant distortions. The method is validated using simultaneous EEG/fMRI data in healthy subjects, intracranial EEG data in epilepsy patients, and in a direct comparison with standard EEG analysis in a well-established attention paradigm. The method is then demonstrated on a very large cohort of subjects performing a standard gambling task designed to activate the brain's 'reward circuit'. The technique uses the output from standard EEG systems and thus has potential for immediate benefit to a broad range of important basic scientific and clinical questions concerning brain electrical activity, but also provides an inexpensive and portable alternative to function MRI (fMRI).

Neuronal avalanches: Sandpiles of self-organized criticality or critical dynamics of brain waves?

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics [Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Critically synchronized brain waves form an effective, robust and flexible basis for human memory and learning.

The effectiveness, robustness, and flexibility of memory and learning constitute the very essence of human natural intelligence, cognition, and consciousness. However, currently accepted views on these subjects have, to date, been put forth without any basis on a true physical theory of how the brain communicates internally via its electrical signals. This lack of a solid theoretical framework has implications not only for our understanding of how the brain works, but also for wide range of computational models developed from the standard orthodox view of brain neuronal organization and brain network derived functioning based on the Hodgkin-Huxley ad-hoc circuit analogies that have produced a multitude of Artificial, Recurrent, Convolution, Spiking, etc., Neural Networks (ARCSe NNs) that have in turn led to the standard algorithms that form the basis of artificial intelligence (AI) and machine learning (ML) methods. Our hypothesis, based upon our recently developed physical model of weakly evanescent brain wave propagation (WETCOW) is that, contrary to the current orthodox model that brain neurons just integrate and fire under accompaniment of slow leaking, they can instead perform much more sophisticated tasks of efficient coherent synchronization/desynchronization guided by the collective influence of propagating nonlinear near critical brain waves, the waves that currently assumed to be nothing but inconsequential subthreshold noise. In this paper we highlight the learning and memory capabilities of our WETCOW framework and then apply it to the specific application of AI/ML and Neural Networks. We demonstrate that the learning inspired by these critically synchronized brain waves is shallow, yet its timing and accuracy outperforms deep ARCSe counterparts on standard test datasets. These results have implications for both our understanding of brain function and for the wide range of AI/ML applications.

Critical brain wave dynamics of neuronal avalanches.

Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Unveiling the third dimension in morphometry with automated quantitative volumetric computations.

As computed tomography and related technologies have become mainstream tools across a broad range of scientific applications, each new generation of instrumentation produces larger volumes of more-complex 3D data. Lagging behind are step-wise improvements in computational methods to rapidly analyze these new large, complex datasets. Here we describe novel computational methods to capture and quantify volumetric information, and to efficiently characterize and compare shape volumes. It is based on innovative theoretical and computational reformulation of volumetric computing. It consists of two theoretical constructs and their numerical implementation: the spherical wave decomposition (SWD), that provides fast, accurate automated characterization of shapes embedded within complex 3D datasets; and symplectomorphic registration with phase space regularization by entropy spectrum pathways (SYMREG), that is a non-linear volumetric registration method that allows homologous structures to be correctly warped to each other or a common template for comparison. Together, these constitute the Shape Analysis for Phenomics from Imaging Data (SAPID) method. We demonstrate its ability to automatically provide rapid quantitative segmentation and characterization of single unique datasets, and both inter-and intra-specific comparative analyses. We go beyond pairwise comparisons and analyze collections of samples from 3D data repositories, highlighting the magnified potential our method has when applied to data collections. We discuss the potential of SAPID in the broader context of generating normative morphologies required for meaningfully quantifying and comparing variations in complex 3D anatomical structures and systems.

Universal theory of brain waves: from linear loops to nonlinear synchronized spiking and collective brain rhythms.

An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non-evanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and to the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the standard paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation due to the cortex wave modes in highly folded areas will exhibit no apparent correlation with the fiber directions. The results are consistent with numerous recent experimental animal and human brain studies demonstrating the existence of electrostatic field activity in the form of traveling waves (including studies where neuronal connections were severed) and with wave loop induced peaks observed in EEG spectra. In addition, we demonstrate that the resonant and non-resonant terms of the nonlinear coupling between multiple modes produce both synchronous spiking-like high frequency wave activity as well as low frequency wave rhythms as a result of their unique dispersion properties. Numerical simulation of forced multiple mode dynamics shows that as forcing increases there is a transition from damped to oscillatory regime that subsequently decays away as over-excitation is reached. The resonant nonlinear coupling results in the emergence of low frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these cortical wave modes, and this new mechanism for understanding the nature of spiking behavior, have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and MEG, and in general for the understanding of brain activity, including mechanisms of memory.

Detecting Spatio-Temporal Modes in Multivariate Data by Entropy Field Decomposition.

A new data analysis method that addresses a general problem of detecting spatio-temporal variations in multivariate data is presented. The method utilizes two recent and complimentary general approaches to data analysis, information field theory (IFT) and entropy spectrum pathways (ESP). Both methods reformulate and incorporate Bayesian theory, thus use prior information to uncover underlying structure of the unknown signal. Unification of ESP and IFT creates an approach that is non-Gaussian and non-linear by construction and is found to produce unique spatio-temporal modes of signal behavior that can be ranked according to their significance, from which space-time trajectories of parameter variations can be constructed and quantified. Two brief examples of real world applications of the theory to the analysis of data bearing completely different, unrelated nature, lacking any underlying similarity, are also presented. The first example provides an analysis of resting state functional magnetic resonance imaging (rsFMRI) data that allowed us to create an efficient and accurate computational method for assessing and categorizing brain activity. The second example demonstrates the potential of the method in the application to the analysis of a strong atmospheric storm circulation system during the complicated stage of tornado development and formation using data recorded by a mobile Doppler radar. Reference implementation of the method will be made available as a part of the QUEST toolkit that is currently under development at the Center for Scientific Computation in Imaging.