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.

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 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.

Double pulsed field gradient diffusion MRI to assess skeletal muscle microstructure.

Purpose: Preliminary study to determine whether double pulsed field gradient (PFG) diffusion MRI is sensitive to key features of muscle microstructure related to function.

Methods: The restricted diffusion profile of molecules in models of muscle microstructure derived from histology were systematically simulated using a numerical simulation approach. Diffusion tensor subspace imaging analysis of the diffusion signal was performed, and spherical anisotropy (SA) was calculated for each model.

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.

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 [ 2, 023061 (2020); 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.

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.

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.

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.

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.

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.

Varying diffusion time to discriminate between simulated skeletal muscle injury models using stimulated echo diffusion tensor imaging.

Purpose: Evaluate the relationship between muscle microstructure, diffusion time (Δ), and the diffusion tensor (DT) to identify the optimal Δ where changes in muscle fiber size may be detected.

Methods: The DT was simulated in models with histology informed geometry over a range of Δ with a stimulated echo DT imaging (DTI) sequence using the numerical simulation application DifSim. The difference in the DT at each Δ between healthy and injured skeletal muscle models was calculated, to identify the optimal Δ at which changes in muscle fiber size may be detected.

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.

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.

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.

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.

Relationships between tissue microstructure and the diffusion tensor in simulated skeletal muscle.

Purpose: To establish a series of relationships defining how muscle microstructure and diffusion tensor imaging (DTI) are related.

Methods: The relationship among key microstructural features of skeletal muscle (fiber size, fibrosis, edema, and permeability) and the diffusion tensor were systematically simulated over physiologically relevant dimensions individually, and in combination, using a numerical simulation application. Stepwise multiple regression was used to identify which microstructural features of muscle significantly predict the diffusion tensor using single-echo and multi-echo DTI pulse sequences.

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.

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.

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.

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.

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.

The coelacanth rostral organ is a unique low-resolution electro-detector that facilitates the feeding strike.

The cartilaginous and non-neopterygian bony fishes have an electric sense typically comprised of hundreds or thousands of sensory canals distributed in broad clusters over the head. This morphology facilitates neural encoding of local electric field intensity, orientation, and polarity, used for determining the position of nearby prey. The coelacanth rostral organ electric sense, however, is unique in having only three paired sensory canals with distribution restricted to the dorsal snout, raising questions about its function.

Simultaneous multi-scale diffusion estimation and tractography guided by entropy spectrum pathways.

We have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi-dimensional and multi-modal diffusion field. Computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist, and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion. The intervoxel diffusion is sampled by multi b-shell multi q-angle diffusion weighted imaging data expanded in spherical waves.

Information pathways in a disordered lattice.

The maximum entropy random walk in a disordered lattice is obtained as a consequence of the principle of maximum entropy for a particular type of prior information without restriction on the number of steps. This novel result demonstrates that transition probabilities defining the random walk represent a general characterization of information on a defective lattice and does not necessarily reflect a physical process. The localization phenomenon is shown to be a consequence of solution of the Laplacian on the lattice-hence it contradicts the previous interpretation as a spherical Lifshitz state-and naturally generalizes to multiple modes, whose order reflects the significance of information.