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Unifying integration and segregation in the brain has been a fundamental puzzle in neuroscience ever since the conception of the "binding problem." Here, we introduce a framework that places integration and segregation within a continuum based on a fundamental property of the brain-its structural connectivity graph Laplacian harmonics and a new feature we term the gap-spectrum. This framework organizes harmonics into three regimes-integrative, segregative, and degenerate-that together account for various group-level properties. Integrative and segregative harmonics occupy the ends of the continuum, and they share properties such as reproducibility across individuals, stability to perturbation, and involve "bottom-up" sensory networks. Degenerate harmonics are in the middle of the continuum, and they are subject-specific, flexible, and involve "top-down" networks. The proposed framework accommodates inter-subject variation, sensitivity to changes, and structure-function coupling in ways that offer promising avenues for studying cognition and consciousness in the brain.

BackgroundAlzheimer's disease (AD) is the most common form of dementia, progressively impairing cognitive abilities. While neuroimaging studies have revealed functional abnormalities in AD, how these relate to aberrant neuronal circuit mechanisms remains unclear. Using magnetoencephalography imaging we documented abnormal local neural synchrony patterns in patients with AD. To identify global abnormal biophysical mechanisms underlying the spatial and spectral electrophysiological patterns in AD, we estimated the parameters of a biophysical spectral graph model (SGM).MethodsSGM is an analytic neural mass model that describes how long-range fiber projections in the brain mediate the excitatory and inhibitory activity of local neuronal subpopulations. Unlike other coupled neuronal mass models, the SGM is linear, available in closed-form, and parameterized by a small set of biophysical interpretable global parameters. This facilitates their rapid and unambiguous inference which we performed here on a well-characterized clinical population of patients with AD (N = 88, age = 62.73 +/- 8.64 years) and a cohort of age-matched controls (N = 88, age = 65.07 +/- 9.92 years).ResultsPatients with AD showed significantly elevated long-range excitatory neuronal time scales, local excitatory neuronal time scales and local inhibitory neural synaptic strength. The long-range excitatory time scale had a larger effect size, compared to local excitatory time scale and inhibitory synaptic strength and contributed highest for the accurate classification of patients with AD from controls. Furthermore, increased long-range time scale was associated with greater deficits in global cognition.ConclusionsThese results demonstrate that long-range excitatory time scale of neuronal activity, despite being a global measure, is a key determinant in the local spectral signatures and cognition in the human brain, and how it might be a parsimonious factor underlying altered neuronal activity in AD. Our findings provide new insights into mechanistic links between abnormal local spectral signatures and global connectivity measures in AD.

Sleep is a highly stereotyped phenomenon, requiring robust spatiotemporal coordination of neural activity. Understanding how the brain coordinates neural activity with sleep onset can provide insights into the physiological functions subserved by sleep and the pathologic phenomena associated with sleep onset. We quantified whole-brain network changes in synchrony and information flow during the transition from wakefulness to light non-rapid eye movement (NREM) sleep, using MEG imaging in a convenient sample of 14 healthy human participants (11 female; mean 63.4 years [SD 11.8 years]). We furthermore performed computational modeling to infer excitatory and inhibitory properties of local neural activity. The transition from wakefulness to light NREM was identified to be encoded in spatially and temporally specific patterns of long-range synchrony. Within the delta band, there was a global increase in connectivity from wakefulness to light NREM, which was highest in frontoparietal regions. Within the theta band, there was an increase in connectivity in fronto-parieto-occipital regions and a decrease in temporal regions from wakefulness to Stage 1 sleep. Patterns of information flow revealed that mesial frontal regions receive hierarchically organized inputs from broad cortical regions upon sleep onset, including direct inflow from occipital regions and indirect inflow via parieto-temporal regions within the delta frequency band. Finally, biophysical neural mass modeling demonstrated changes in the anterior-to-posterior distribution of cortical excitation-to-inhibition with increased excitation-to-inhibition model parameters in anterior regions in light NREM compared with wakefulness. Together, these findings uncover whole-brain corticocortical structure and the orchestration of local and long-range, frequency-specific cortical interactions in the sleep-wake transition.SIGNIFICANCE STATEMENT Our work uncovers spatiotemporal cortical structure of neural synchrony and information flow upon the transition from wakefulness to light non-rapid eye movement sleep. Mesial frontal regions were identified to receive hierarchically organized inputs from broad cortical regions, including both direct inputs from occipital regions and indirect inputs via the parieto-temporal regions within the delta frequency range. Biophysical neural mass modeling revealed a spatially heterogeneous, anterior-posterior distribution of cortical excitation-to-inhibition. Our findings shed light on the orchestration of local and long-range cortical neural structure that is fundamental to sleep onset, and support an emerging view of cortically driven regulation of sleep homeostasis.

Dynamic resting state functional connectivity (RSFC) characterizes time-varying fluctuations of functional brain network activity. While many studies have investigated static functional connectivity, it has been unclear whether features of dynamic functional connectivity are associated with neurodegenerative diseases. Popular sliding-window and clustering methods for extracting dynamic RSFC have various limitations that prevent extracting reliable features to address this question. Here, we use a novel and robust time-varying dynamic network (TVDN) approach to extract the dynamic RSFC features from high resolution magnetoencephalography (MEG) data of participants with Alzheimer's disease (AD) and matched controls. The TVDN algorithm automatically and adaptively learns the low-dimensional spatiotemporal manifold of dynamic RSFC and detects dynamic state transitions in data. We show that amongst all the functional features we investigated, the dynamic manifold features are the most predictive of AD. These include: the temporal complexity of the brain network, given by the number of state transitions and their dwell times, and the spatial complexity of the brain network, given by the number of eigenmodes. These dynamic features have higher sensitivity and specificity in distinguishing AD from healthy subjects than the existing benchmarks do. Intriguingly, we found that AD patients generally have higher spatial complexity but lower temporal complexity compared with healthy controls. We also show that graph theoretic metrics of dynamic component of TVDN are significantly different in AD versus controls, while static graph metrics are not statistically different. These results indicate that dynamic RSFC features are impacted in neurodegenerative disease like Alzheimer's disease, and may be crucial to understanding the pathophysiological trajectory of these diseases.

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Understanding the connection between the brain's structural connectivity and its functional connectivity is of immense interest in computational neuroscience. Although some studies have suggested that whole brain functional connectivity is shaped by the underlying structure, the rule by which anatomy constraints brain dynamics remains an open question. In this work, we introduce a computational framework that identifies a joint subspace of eigenmodes for both functional and structural connectomes. We found that a small number of those eigenmodes are sufficient to reconstruct functional connectivity from the structural connectome, thus serving as low-dimensional basis function set. We then develop an algorithm that can estimate the functional eigen spectrum in this joint space from the structural eigen spectrum. By concurrently estimating the joint eigenmodes and the functional eigen spectrum, we can reconstruct a given subject's functional connectivity from their structural connectome. We perform elaborate experiments and demonstrate that the proposed algorithm for estimating functional connectivity from the structural connectome using joint space eigenmodes gives competitive performance as compared to the existing benchmark methods with better interpretability.

With the increasing prevalence of Alzheimer's disease (AD) among aging populations and the limited therapeutic options available to slow or reverse its progression, the need has never been greater for improved diagnostic tools for identifying patients in the preclinical and prodomal phases of AD. Biophysics models of the connectome-based spread of amyloid-beta (Aβ) and microtubule-associated protein tau (τ) have enjoyed recent success as tools for predicting the time course of AD-related pathological changes. However, given the complex etiology of AD, which involves not only connectome-based spread of protein pathology but also the interactions of many molecular and cellular players over multiple spatiotemporal scales, more robust, complete biophysics models are needed to better understand AD pathophysiology and ultimately provide accurate patient-specific diagnoses and prognoses. Here we discuss several areas of active research in AD whose insights can be used to enhance the mathematical modeling of AD pathology as well as recent attempts at developing improved connectome-based biophysics models. These efforts toward a comprehensive yet parsimonious mathematical description of AD hold great promise for improving both the diagnosis of patients at risk for AD and our mechanistic understanding of how AD progresses.

We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structural wiring of the brain. Previously, we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

BackgroundThe structural connectivity of neurons in the brain allows active neurons to impact the physiology of target neuron types with which they are functionally connected. While the structural connectome is at the basis of functional connectome, it is the functional connectivity measured through correlations between time series of individual neurophysiological events that underlies behavioral and mental states. However, in light of the diverse neuronal cell types populating the brain and their unique connectivity properties, both neuronal activity and functional connectivity are heterogeneous across the brain, and the nature of their relationship is not clear. Here, we employ brain-wide calcium imaging at cellular resolution in larval zebrafish to understand the principles of resting state functional connectivity.ResultsWe recorded the spontaneous activity of >12,000 neurons in the awake resting state forebrain. By classifying their activity (i.e., variances of ΔF/F across time) and functional connectivity into three levels (high, medium, low), we find that highly active neurons have low functional connections and highly connected neurons are of low activity. This finding holds true when neuronal activity and functional connectivity data are classified into five instead of three levels, and in whole brain spontaneous activity datasets. Moreover, such activity-connectivity relationship is not observed in randomly shuffled, noise-added, or simulated datasets, suggesting that it reflects an intrinsic brain network property. Intriguingly, deploying the same analytical tools on functional magnetic resonance imaging (fMRI) data from the resting state human brain, we uncover a similar relationship between activity (signal variance over time) and functional connectivity, that is, regions of high activity are non-overlapping with those of high connectivity.ConclusionsWe found a mutually exclusive relationship between high activity (signal variance over time) and high functional connectivity of neurons in zebrafish and human brains. These findings reveal a previously unknown and evolutionarily conserved brain organizational principle, which has implications for understanding disease states and designing artificial neuronal networks.

Dynamic resting state functional connectivity (RSFC) characterizes fluctuations that occur over time in functional brain networks. Existing methods to extract dynamic RSFCs, such as sliding-window and clustering methods that are inherently non-adaptive, have various limitations such as high-dimensionality, an inability to reconstruct brain signals, insufficiency of data for reliable estimation, insensitivity to rapid changes in dynamics, and a lack of generalizability across multiply functional imaging modalities. To overcome these deficiencies, we develop a novel and unifying time-varying dynamic network (TVDN) framework for examining dynamic resting state functional connectivity. TVDN includes a generative model that describes the relation between a low-dimensional dynamic RSFC and the brain signals, and an inference algorithm that automatically and adaptively learns the low-dimensional manifold of dynamic RSFC and detects dynamic state transitions in data. TVDN is applicable to multiple modalities of functional neuroimaging such as fMRI and MEG/EEG. The estimated low-dimensional dynamic RSFCs manifold directly links to the frequency content of brain signals. Hence we can evaluate TVDN performance by examining whether learnt features can reconstruct observed brain signals. We conduct comprehensive simulations to evaluate TVDN under hypothetical settings. We then demonstrate the application of TVDN with real fMRI and MEG data, and compare the results with existing benchmarks. Results demonstrate that TVDN is able to correctly capture the dynamics of brain activity and more robustly detect brain state switching both in resting state fMRI and MEG data.

The neurodegenerative disorder amyotrophic lateral sclerosis (ALS) is characterized by the progressive loss of upper and lower motor neurons, with pathological involvement of cerebral motor and extra-motor areas in a clinicopathological spectrum with frontotemporal dementia (FTD). A key unresolved issue is how the non-random distribution of pathology in ALS reflects differential network vulnerability, including molecular factors such as regional gene expression, or preferential spread of pathology via anatomical connections. A system of histopathological staging of ALS based on the regional burden of TDP-43 pathology observed in postmortem brains has been supported to some extent by analysis of distribution of in vivo structural MRI changes. In this paper, computational modeling using a Network Diffusion Model (NDM) was used to investigate whether a process of focal pathological 'seeding' followed by structural network-based spread recapitulated postmortem histopathological staging and, secondly, whether this had any correlation to the pattern of expression of a panel of genes implicated in ALS across the healthy brain. Regionally parcellated T1-weighted MRI data from ALS patients (baseline n=79) was studied in relation to a healthy control structural connectome and a database of associated regional cerebral gene expression. The NDM provided strong support for a structural network-based basis for regional pathological spread in ALS, but no simple relationship to the spatial distribution of ALS-related genes in the healthy brain. Interestingly, OPTN gene was identified as a significant but a weaker non-NDM contributor within the network-gene interaction model (LASSO). Intriguingly, the critical seed regions for spread within the model were not within the primary motor cortex but basal ganglia, thalamus and insula, where NDM recapitulated aspects of the postmortem histopathological staging system. Within the ALS-FTD clinicopathological spectrum, non-primary motor structures may be among the earliest sites of cerebral pathology.

The advent of increasingly sophisticated imaging platforms has allowed for the visualization of the murine nervous system at single-cell resolution. However, current experimental approaches have not yet produced whole-brain maps of a comprehensive set of neuronal and nonneuronal types that approaches the cellular diversity of the mammalian cortex. Here, we aim to fill in this gap in knowledge with an open-source computational pipeline, Matrix Inversion and Subset Selection (MISS), that can infer quantitatively validated distributions of diverse collections of neural cell types at 200-μm resolution using a combination of single-cell RNA sequencing (RNAseq) and in situ hybridization datasets. We rigorously demonstrate the accuracy of MISS against literature expectations. Importantly, we show that gene subset selection, a procedure by which we filter out low-information genes prior to performing deconvolution, is a critical preprocessing step that distinguishes MISS from its predecessors and facilitates the production of cell-type maps with significantly higher accuracy. We also show that MISS is generalizable by generating high-quality cell-type maps from a second independently curated single-cell RNAseq dataset. Together, our results illustrate the viability of computational approaches for determining the spatial distributions of a wide variety of cell types from genetic data alone.

Mathematical modeling of the relationship between the functional activity and the structural wiring of the brain has largely been undertaken using non-linear and biophysically detailed mathematical models with regionally varying parameters. While this approach provides us a rich repertoire of multistable dynamics that can be displayed by the brain, it is computationally demanding. Moreover, although neuronal dynamics at the microscopic level are nonlinear and chaotic, it is unclear if such detailed nonlinear models are required to capture the emergent meso-(regional population ensemble) and macro-scale (whole brain) behavior, which is largely deterministic and reproducible across individuals. Indeed, recent modeling effort based on spectral graph theory has shown that an analytical model without regionally varying parameters and without multistable dynamics can capture the empirical magnetoencephalography frequency spectra and the spatial patterns of the alpha and beta frequency bands accurately. In this work, we demonstrate an improved hierarchical, linearized, and analytic spectral graph theory-based model that can capture the frequency spectra obtained from magnetoencephalography recordings of resting healthy subjects. We reformulated the spectral graph theory model in line with classical neural mass models, therefore providing more biologically interpretable parameters, especially at the local scale. We demonstrated that this model performs better than the original model when comparing the spectral correlation of modeled frequency spectra and that obtained from the magnetoencephalography recordings. This model also performs equally well in predicting the spatial patterns of the empirical alpha and beta frequency bands.

The prion-like transsynaptic propagation of misfolded tau along the brain's connectome has previously been modeled using connectome-based network diffusion models. In addition to the connectome, interactions between the general neurological "milieu" in the neurodegenerative brain and proteinopathic species can also contribute to pathology propagation. Such a molecular nexopathy framework posits that the distinct characteristics of neurodegenerative disorders stem from interactions between the network and surrounding molecular players. However, the effects of these modulators remain unquantified. Here, we present Nexopathy in silico ("Nexis"), a quantitative model of tau progression augmenting earlier models by including parameters of pathology propagation defined by the molecular modulators of connectome-based spread. Our Nexis:microglia model provides the first quantitative characterization of this effect on the whole brain by expanding previous models of neuropathology progression by incorporating microglial influence. We show that Trem2, but not microglial homeostasis genes, significantly improved the model's predictive power. Trem2 appears to reduce tau accumulation rate while increasing its interregional spread from the hippocampal seed area, causing higher tau burden in the striatum, pallidum, and contralateral hippocampus. Nexis provides an improved understanding and quantification of microglial contribution to tau propagation and can be flexibly modified to include other modulators of progressive neurodegeneration.

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

BackgroundNeuronal- and circuit-level abnormalities of excitation and inhibition are shown to be associated with tau and amyloid-beta (Aβ) in preclinical models of Alzheimer's disease (AD). These relationships remain poorly understood in patients with AD.MethodsUsing empirical spectra from magnetoencephalography and computational modeling (neural mass model), we examined excitatory and inhibitory parameters of neuronal subpopulations and investigated their specific associations to regional tau and Aβ, measured by positron emission tomography, in patients with AD.ResultsPatients with AD showed abnormal excitatory and inhibitory time-constants and neural gains compared to age-matched controls. Increased excitatory time-constants distinctly correlated with higher tau depositions while increased inhibitory time-constants distinctly correlated with higher Aβ depositions.ConclusionsOur results provide critical insights about potential mechanistic links between abnormal neural oscillations and cellular correlates of impaired excitatory and inhibitory synaptic functions associated with tau and Aβ in patients with AD.FundingThis study was supported by the National Institutes of Health grants: K08AG058749 (KGR), F32AG050434-01A1 (KGR), K23 AG038357 (KAV), P50 AG023501, P01 AG19724 (BLM), P50-AG023501 (BLM and GDR), R01 AG045611 (GDR); AG034570, AG062542 (WJ); NS100440 (SSN), DC176960 (SSN), DC017091 (SSN), AG062196 (SSN); a grant from John Douglas French Alzheimer's Foundation (KAV); grants from Larry L. Hillblom Foundation: 2015-A-034-FEL (KGR), 2019-A-013-SUP (KGR); grants from the Alzheimer's Association: AARG-21-849773 (KGR); PCTRB-13-288476 (KAV), and made possible by Part the CloudTM (ETAC-09-133596); a grant from Tau Consortium (GDR and WJJ), and a gift from the S. D. Bechtel Jr. Foundation.

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by "computational model" is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Understanding how complex dynamic activity propagates over a static structural network is an overarching question in the field of neuroscience. Previous work has demonstrated that linear graph-theoretic models perform as well as non-linear neural simulations in predicting functional connectivity with the added benefits of low dimensionality and a closed-form solution which make them far less computationally expensive. Here we show a simple model relating the eigenvalues of the structural connectivity and functional networks using the Gamma function, producing a reliable prediction of functional connectivity with a single model parameter. We also investigate the impact of local activity diffusion and long-range interhemispheric connectivity on the structure-function model and show an improvement in functional connectivity prediction when accounting for such latent variables which are often excluded from traditional diffusion tensor imaging (DTI) methods.

Background: Graph theory and connectomics are new techniques for uncovering disease-induced changes in the brain's structural network. Most prior studied have focused on network statistics as biomarkers of disease. However, an emerging body of work involves exploring how the network serves as a conduit for the propagation of disease factors in the brain and has successfully mapped the functional and pathological consequences of disease propagation. In Alzheimer's disease (AD), progressive deposition of misfolded proteins amyloid and tau is well-known to follow fiber projections, under a "prion-like" trans-neuronal transmission mechanism, through which misfolded proteins cascade along neuronal pathways, giving rise to network spread. Methods: In this review, we survey the state of the art in mathematical modeling of connectome-mediated pathology spread in AD. Then we address several open questions that are amenable to mathematically precise parsimonious modeling of pathophysiological processes, extrapolated to the whole brain. We specifically identify current formal models of how misfolded proteins are produced, aggregate, and disseminate in brain circuits, and attempt to understand how this process leads to stereotyped progression in Alzheimer's and other related diseases. Conclusion: This review serves to unify current efforts in modeling of AD progression that together have the potential to explain observed phenomena and serve as a test-bed for future hypothesis generation and testing in silico. Impact statement Graph theory is a powerful new approach that is transforming the study of brain processes. There do not exist many focused reviews of the subfield of graph modeling of how Alzheimer's and other dementias propagate within the brain network, and how these processes can be mapped mathematically. By providing timely and topical review of this subfield, we fill a critical gap in the community and present a unified view that can serve as an in silico test-bed for future hypothesis generation and testing. We also point to several open and unaddressed questions and controversies that future practitioners can tackle.

Background: Alzheimer's disease involves widespread and progressive deposition of misfolded protein tau (τ), first appearing in the entorhinal cortex, coagulating in longer polymers and insoluble fibrils. There is mounting evidence for "prion-like" trans-neuronal transmission, whereby misfolded proteins cascade along neuronal pathways, giving rise to networked spread. However, the cause-effect mechanisms by which various oligomeric τ species are produced, aggregate, and disseminate are unknown. The question of how protein aggregation and subsequent spread lead to stereotyped progression in the Alzheimer brain remains unresolved. Materials and Methods: We address these questions by using mathematically precise parsimonious modeling of these pathophysiological processes, extrapolated to the whole brain. We model three key processes: τ monomer production; aggregation into oligomers and then into tangles; and the spatiotemporal progression of misfolded τ as it ramifies into neural circuits via the brain connectome. We model monomer seeding and production at the entorhinal cortex, aggregation using Smoluchowski equations; and networked spread using our prior Network-Diffusion model. Results: This combined aggregation-network-diffusion model exhibits all hallmarks of τ progression seen in human patients. Unlike previous theoretical studies of protein aggregation, we present here an empirical validation on in vivo imaging and fluid τ measurements from large datasets. The model accurately captures not just the spatial distribution of empirical regional τ and atrophy but also patients' cerebrospinal fluid phosphorylated τ profiles as a function of disease progression. Conclusion: This unified quantitative and testable model has the potential to explain observed phenomena and serve as a test-bed for future hypothesis generation and testing in silico. Impact statement The presented aggregation-network-diffusion model exhibits all hallmarks of tau progression in human patients; it accurately captures not just the spatial distribution of empirical regional tau and atrophy but also patients' cerebrospinal fluid phosphorylated tau profiles. Thus, it serves to fill a theoretical gap between microscopic biophysical processes and empirical macroscopic measurements of pathological patterns in Alzheimer's disease. This unified quantitative and testable model has the potential to explain observed phenomena and serve as a test-bed for future hypothesis generation and testing in silico.

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its "structural connectome". By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

Defects in axonal transport may partly underpin the differences between the observed pathophysiology of Alzheimer's disease (AD) and that of other non-amyloidogenic tauopathies. Particularly, pathological tau variants may have molecular properties that dysregulate motor proteins responsible for the anterograde-directed transport of tau in a disease-specific fashion. Here we develop the first computational model of tau-modified axonal transport that produces directional biases in the spread of tau pathology. We simulated the spatiotemporal profiles of soluble and insoluble tau species in a multicompartment, two-neuron system using biologically plausible parameters and time scales. Changes in the balance of tau transport feedback parameters can elicit anterograde and retrograde biases in the distributions of soluble and insoluble tau between compartments in the system. Aggregation and fragmentation parameters can also perturb this balance, suggesting a complex interplay between these distinct molecular processes. Critically, we show that the model faithfully recreates the characteristic network spread biases in both AD-like and non-AD-like mouse tauopathy models. Tau transport feedback may therefore help link microscopic differences in tau conformational states and the resulting variety in clinical presentations.

Current methods for measuring the chronic rates of cognitive decline and degeneration in Alzheimer's disease rely on the sensitivity of longitudinal neuropsychological batteries and clinical neuroimaging, particularly structural magnetic resonance imaging of brain atrophy, either at a global or regional scale. There is particular interest in approaches predictive of future disease progression and clinical outcomes using a single time point. If successful, such approaches could have great impact on differential diagnosis, therapeutic treatment and clinical trial inclusion. Unfortunately, it has proven quite challenging to accurately predict clinical and degeneration progression rates from baseline data. Specifically, a key limitation of the previously proposed approaches for disease progression based on the brain atrophy measures has been the limited incorporation of the knowledge from disease pathology progression models, which suggest a prion-like spread of disease pathology and hence the neurodegeneration. Here, we present a new metric for disease progression rate in Alzheimer that uses only MRI-derived atrophy data yet is able to infer the underlying rate of pathology transmission. This is enabled by imposing a spread process driven by the brain networks using a Network Diffusion Model. We first fit this model to each patient's longitudinal brain atrophy data defined on a brain network structure to estimate a patient-specific rate of pathology diffusion, called the pathology progression rate. Using machine learning algorithms, we then build a baseline data model and tested this rate metric on data from longitudinal Alzheimer's Disease Neuroimaging Initiative study including 810 subjects. Our measure of disease progression differed significantly across diagnostic groups as well as between groups with different genetic risk factors. Remarkably, hierarchical clustering revealed 3 distinct clusters based on CSF profiles with >90% accuracy. These pathological clusters exhibit progressive atrophy and clinical impairments that correspond to the proposed rate measure. We demonstrate that a subject's degeneration speed can be best predicted from baseline neuroimaging volumetrics and fluid biomarkers for subjects in the middle of their degenerative course, which may be a practical, inexpensive screening tool for future prognostic applications.

IntroductionQuantitative positron emission tomography (PET) studies of neurodegenerative diseases typically require the measurement of arterial input functions (AIF), an invasive and risky procedure. This study aims to assess the reproducibility of [11C]DPA-713 PET kinetic analysis using population-based input function (PBIF). The final goal is to possibly eliminate the need for AIF.Materials and methodsEighteen subjects including six healthy volunteers (HV) and twelve Parkinson disease (PD) subjects from two [11C]-DPA-713 PET studies were included. Each subject underwent 90 min of dynamic PET imaging. Five healthy volunteers underwent a test-retest scan within the same day to assess the repeatability of the kinetic parameters. Kinetic modeling was carried out using the Logan total volume of distribution (VT) model. For each data set, kinetic analysis was performed using a patient-specific AIF (PSAIF, ground-truth standard) and then repeated using the PBIF. PBIF was generated using the leave-one-out method for each subject from the remaining 17 subjects and after normalizing the PSAIFs by 3 techniques: (a) Weightsubject×DoseInjected, (b) area under AIF curve (AUC), and (c) Weightsubject×AUC. The variability in the VT measured with PSAIF, in the test-retest study, was determined for selected brain regions (white matter, cerebellum, thalamus, caudate, putamen, pallidum, brainstem, hippocampus, and amygdala) using the Bland-Altman analysis and for each of the 3 normalization techniques. Similarly, for all subjects, the variabilities due to the use of PBIF were assessed.ResultsBland-Altman analysis showed systematic bias between test and retest studies. The corresponding mean bias and 95% limits of agreement (LOA) for the studied brain regions were 30% and ± 70%. Comparing PBIF- and PSAIF-based VT estimate for all subjects and all brain regions, a significant difference between the results generated by the three normalization techniques existed for all brain structures except for the brainstem (P-value = 0.095). The mean % difference and 95% LOA is -10% and ±45% for Weightsubject×DoseInjected; +8% and ±50% for AUC; and +2% and ± 38% for Weightsubject×AUC. In all cases, normalizing by Weightsubject×AUC yielded the smallest % bias and variability (% bias = ±2%; LOA = ±38% for all brain regions). Estimating the reproducibility of PBIF-kinetics to PSAIF based on disease groups (HV/PD) and genotype (MAB/HAB), the average VT values for all regions obtained from PBIF is insignificantly higher than PSAIF (%difference = 4.53%, P-value = 0.73 for HAB; and %difference = 0.73%, P-value = 0.96 for MAB). PBIF also tends to overestimate the difference between PD and HV for HAB (% difference = 32.33% versus 13.28%) and underestimate it in MAB (%difference = 6.84% versus 20.92%).ConclusionsPSAIF kinetic results are reproducible with PBIF, with variability in VT within that obtained for the test-retest studies. Therefore, VT assessed using PBIF-based kinetic modeling is clinically feasible and can be an alternative to PSAIF.

PurposeCompressive sensing (CS)-based image reconstruction methods have proposed random undersampling schemes that produce incoherent, noise-like aliasing artifacts, which are easier to remove. The denoising process is critically assisted by imposing sparsity-enforcing priors. Sparsity is known to be induced if the prior is in the form of the Lp (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L1 norm, which may not exploit the full power of CS. An efficient, discrete optimization formulation is proposed, which works not only on arbitrary Lp -norm priors as some non-convex CS methods do, but also on highly non-convex truncated penalty functions, resulting in a specific type of edge-preserving prior. These advanced features make the minimization problem highly non-convex, and thus call for more sophisticated minimization routines.Theory and methodsThe work combines edge-preserving priors with random undersampling, and solves the resulting optimization using a set of discrete optimization methods called graph cuts. The resulting optimization problem is solved by applying graph cuts iteratively within a dictionary, defined here as an appropriately constructed set of vectors relevant to brain MRI data used here.ResultsExperimental results with in vivo data are presented.ConclusionThe proposed algorithm produces better results than regularized SENSE or standard CS for reconstruction of in vivo data.

The relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled nonlinear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30 Hz) activity estimated from source localized magnetoencephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics. .

There is enormous clinical value in inferring the brain regions initially atrophied in Parkinson disease for individual patients and understanding its relationship with clinical and genetic risk factors. The aim of this study is to leverage a new seed-inference algorithm demonstrated for Alzheimer's disease to the Parkinsonian context and to cluster patients in meaningful subgroups based on these incipient atrophy patterns. Instead of testing brain regions separately as the likely initiation site for each patient, we solve an L1-penalized optimization problem that can return a more predictive heterogeneous, multi-locus seed patterns. A cluster analysis of the individual seed patterns reveals two distinct subgroups (S1 versus S2). The S1 subgroup is characterized by the involvement of the brainstem and ventral nuclei, and S2 by cortex and striatum. Post hoc analysis in features not included in the clustering shows significant differences between subgroups regarding age of onset and local transcriptional patterns of Parkinson-related genes. Top genes associated with regional microglial abundance are strongly associated with subgroup S1 but not with S2. Our results suggest two distinct aetiological mechanisms operative in Parkinson disease. The interplay between immune-related genes, lysosomal genes, microglial abundance and atrophy initiation sites may explain why the age of onset for patients in S1 is on average 4.5 years later than for those in S2. We highlight and compare the most prominently affected brain regions for both subgroups. Altogether, our findings may improve current screening strategies for early Parkinson onsetters.

In Parkinson's disease, some of the first alpha-synuclein aggregates appear in the olfactory system and the dorsal motor nucleus of the vagus nerve before spreading to connected brain regions. We previously demonstrated that injection of alpha-synuclein fibrils unilaterally into the olfactory bulb of wild type mice leads to widespread synucleinopathy in brain regions directly and indirectly connected to the injection site, consistently, over the course of periods longer than 6 months. Our previously reported observations support the idea that alpha-synuclein inclusions propagates between brain region through neuronal networks. In the present study, we further defined the pattern of propagation of alpha-synuclein inclusions and developed a mathematical model based on known mouse brain connectivity. Using this model, we first predicted the pattern of alpha-synuclein inclusions propagation following an injection of fibrils into the olfactory bulb. We then analyzed the fitting of these predictions to our published histological data. Our results demonstrate that the pattern of propagation we observed in vivo is consistent with axonal transport of alpha-synuclein aggregate seeds, followed by transsynaptic transmission. By contrast, simple diffusion of alpha-synuclein fits very poorly our in vivo data. We also found that the spread of alpha-synuclein inclusions appeared to primarily follow neural connections retrogradely until 9 months after injection into the olfactory bulb. Thereafter, the pattern of spreading was consistent with anterograde propagation mathematical models. Finally, we applied our mathematical model to a different, previously published, dataset involving alpha-synuclein fibril injections into the striatum, instead of the olfactory bulb. We found that the mathematical model accurately predicts the reported progressive increase in alpha-synuclein neuropathology also in that paradigm. In conclusion, our findings support that the progressive spread of alpha-synuclein inclusions after injection of protein fibrils follows neural networks in the mouse connectome.

BackgroundThe release of a broad, longitudinal anatomical dataset by the Parkinson's Progression Markers Initiative promoted a surge of machine-learning studies aimed at predicting disease onset and progression. However, the excessive number of features used in these models often conceals their relationship to the Parkinsonian symptomatology.ObjectivesThe aim of this study is two-fold: (i) to predict future motor and cognitive impairments up to four years from brain features acquired at baseline; and (ii) to interpret the role of pivotal brain regions responsible for different symptoms from a neurological viewpoint.MethodsWe test several deep-learning neural network configurations, and report our best results obtained with an autoencoder deep-learning model, run on a 5-fold cross-validation set. Comparison with Existing Methods: Our approach improves upon results from standard regression and others. It also includes neuroimaging biomarkers as features.ResultsThe relative contributions of pivotal brain regions to each impairment change over time, suggesting a dynamical reordering of culprits as the disease progresses. Specifically, the Putamen is initially the most critical region accounting for the overall cognitive state, only being surpassed by the Substantia Nigra in later years. The Pallidum is the first region to influence motor scores, followed by the parahippocampal and ambient gyri, and the anterior orbital gyrus.ConclusionsWhile the causal link between regional brain atrophy and Parkinson symptomatology is poorly understood, our methods demonstrate that the contributions of pivotal regions to cognitive and motor impairments are more dynamical than generally appreciated.

The cat brain is a useful model for neuroscientific research and with the increasing use of advanced neuroimaging techniques there is a need for an open-source stereotaxic white matter brain atlas to accompany the cortical gray matter atlas, currently available. A stereotaxic white matter atlas would facilitate anatomic registration and segmentation of the white matter to aid in lesion localization or standardized regional analysis of specific regions of the white matter. In this article, we document the creation of a stereotaxic feline white matter atlas from diffusion tensor imaging (DTI) data obtained from a population of eight mesaticephalic felines. Deterministic tractography reconstructions were performed to create tract priors for the major white matter projections of Corpus callosum (CC), fornix, cingulum, uncinate, Corona Radiata (CR), Corticospinal tract (CST), inferior longitudinal fasciculus (ILF), Superior Longitudinal Fasciculus (SLF), and the cerebellar tracts. T1-weighted, fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD) and axial diffusivity (AD) population maps were generated. The volume, mean tract length and mean FA, MD, AD and RD values for each tract prior were documented. A structural connectome was then created using previously published cortical priors and the connectivity metrics for all cortical regions documented. The provided white matter atlas, diffusivity maps, tract priors and connectome will be a valuable resource for anatomical, pathological and translational neuroimaging research in the feline model. Multi-atlas population maps and segmentation priors are available at Cornell's digital repository: https://ecommons.cornell.edu/handle/1813/58775.2.

Sporadic Creutzfeldt-Jakob disease is a rare fatal rapidly progressive dementia caused by the accumulation and spread of pathologically misfolded prions. Evidence from animal models and in vitro experiments suggests that prion pathology propagates along neural connectivity pathways, with the transmission of misfolded prions initiating a corruptive templating process in newly encountered brain regions. Although particular regional patterns of disease have been recognized in humans, the underlying mechanistic basis of these patterns remains poorly understood. Here, we demonstrate that the spatial pattern of disease derived from publicly available human diffusion-weighted MRI data demonstrates stereotypical features across patient cohorts and can be largely explained by intrinsic connectivity properties of the human structural brain network. Regional diffusion-weighted MRI signal abnormalities are predicted by graph theoretical measures of centrality, with highly affected regions such as cingulate gyrus demonstrating strong structural connectivity to other brain regions. We employ network diffusion modelling to demonstrate that the spatial pattern of disease can be predicted by a diffusion process originating from a single regional pathology seed and operating on the structural connectome. The most likely seeds correspond to the most highly affected brain regions, suggesting that pathological prions could originate in a single brain region and spread throughout the brain to produce the regional distribution of pathology observed on MRI. Further investigation of top seed regions and associated connectivity pathways may be a useful strategy for developing therapeutic approaches.

Parkinson disease (PD) is the second most common neurodegenerative disorder, characterized by loss of nigrostriatal dopaminergic neurons. Impairment of the neurovascular unit (NVU) has been hypothesized to play a critical role in early PD pathophysiology, and to precede neurodegenerative mechanisms. [C-11]-PE2I (N-(3-iodoprop-2E-enyl)-2b-carbomethoxy-3b-(4-methyl-phenyl)nortropane) (PE2I) is a PET radiotracer targeting neuronal dopamine transporters (DaT) with high specificity, allowing for highly accurate and specific DaT quantification. We investigated NVU integrity using arterial spin labeling (ASL) MRI in a prospective cohort of 26 patients with PD, and correlated our findings with analysis of striatal DaT density using PE2I PET in a subcohort of 17 patients. Analysis was performed in FreeSurfer to obtain rCBF and mean standardized regional PET avidity. Pearson correlations and Mann-Whitney tests were performed. Significantly lower mean normalized striatal PE2I SUV values were seen in multiple regions in patients with greater disease duration (p < 0.05). PET uptake in the putamen correlated with disease duration independent of patient age. Stratifying patients based on Montreal Cognitive Assessment (MoCA) scores (stratified into ≥ 27 vs. < 27), there was statistically significantly lower PE2I PET avidity in the higher MoCA score group in both more and less affected sides of the caudate, putamen and pallidum (p < 0.05). A moderate negative correlation between MDS-UPDRS part 3 (motor) "off" and rCBF values was also seen in the L and R cerebellum WM (r = -0.43 and -0.47, p < 0.05). A statistically significant negative correlation was found between dominant hand pegboard test results and rCBF in the less affected pallidum (r = -0.41; p = 0.046). A statistically significant negative correlation of ASL MRI with [11C]-PE2I PET was also found (r = -0.53 to -0.58; p-value 0.017-0.033) between left cerebral WM rCBF and more and less affected striatal PET regions. Our ROI-based analyses suggest that longer disease duration is associated with lower rCBF and lower PE2I mean SUV, implying greater NVU dysfunction and dopaminergic neuronal loss, respectively. Combined ASL MRI and PE2I PET imaging could inform future prospective clinical trials providing an improved mechanistic understanding of the disease, laying the foundation for the development of early disease biomarkers and potential therapeutic targets.

Traumatic brain injury damages white matter pathways that connect brain regions, disrupting transmission of electrochemical signals and causing cognitive and emotional dysfunction. Connectome-level mechanisms for how the brain compensates for injury have not been fully characterized. Here, we collected serial MRI-based structural and functional connectome metrics and neuropsychological scores in 26 mild traumatic brain injury subjects (29.4 ± 8.0 years, 20 males) at 1 and 6 months postinjury. We quantified the relationship between functional and structural connectomes using network diffusion (ND) model propagation time, a measure that can be interpreted as how much of the structural connectome is being utilized for the spread of functional activation, as captured via the functional connectome. Overall cognition showed significant improvement from 1 to 6 months (t25 = -2.15, p = .04). None of the structural or functional global connectome metrics was significantly different between 1 and 6 months, or when compared to 34 age- and gender-matched controls (28.6 ± 8.8 years, 25 males). We predicted longitudinal changes in overall cognition from changes in global connectome measures using a partial least squares regression model (cross-validated R2 = .27). We observe that increased ND model propagation time, increased structural connectome segregation, and increased functional connectome integration were related to better cognitive recovery. We interpret these findings as suggesting two connectome-based postinjury recovery mechanisms: one of neuroplasticity that increases functional connectome integration and one of remote white matter degeneration that increases structural connectome segregation. We hypothesize that our inherently multimodal measure of ND model propagation time captures the interplay between these two mechanisms.

Although a significant genetic contribution to the risk of developing sporadic Parkinson's disease has been well described, the relationship between local genetic factors, pathogenesis, and subsequent spread of pathology throughout the brain has been largely unexplained in humans. To address this question, we use network diffusion modelling to infer probable pathology seed regions and patterns of disease spread from MRI atrophy maps derived from 232 de novo subjects in the Parkinson's Progression Markers Initiative study. Allen Brain Atlas regional transcriptional profiles of 67 Parkinson's disease risk factor genes were mapped to the inferred seed regions to determine the local influence of genetic risk factors. We used hierarchical clustering and L1 regularized regression analysis to show that transcriptional profiles of immune-related and lysosomal risk factor genes predict seed region location and the pattern of disease propagation from the most likely seed region, substantia nigra. By leveraging recent advances in transcriptomics, we show that regional microglial abundance quantified by high fidelity gene expression also predicts seed region location. These findings suggest that early disease sites are genetically susceptible to dysfunctional lysosomal α-synuclein processing and microglia-mediated neuroinflammation, which may initiate the disease process and contribute to spread of pathology along neural connectivity pathways.

It is well-known that the human visual system is adapted to the statistical structure of natural scenes. Yet there are important classes of images - for example, medical images - that are not natural scenes, and therefore, that are expected to have statistical properties that deviate from the class of images that shaped the evolution and development of human vision. Here, focusing on structural brain MRI images, we quantify and characterize these deviations in terms of a set of local image statistics to which human visual sensitivity has been well-characterized, and that has previously been used for natural image analysis. We analyzed MRI images in multiple databases including T1-weighted and FLAIR sequence types, and simulated MRI images based on a published image simulation procedure for T1 images, which we also modified to generate FLAIR images. We first computed the power spectra of MRI images; spectral slopes were in the range -2.6 to -3.1 for T1 sequences, and -2.2 to -2.7 for FLAIR sequences. Analysis of local image statistics was then carried out on whitened images. For all of the databases as well as for the simulated images, we found that the three-point correlations contributed substantially to the differences between the "texture" of randomly selected ROIs. The informative nature of three-point correlations for brain MRI was greater than for natural images, and also disproportionate to human visual sensitivity. As this finding was consistent across databases, it is likely to result from brain geometry at the scale of brain MRI resolution, rather than characteristics of specific imaging and reconstruction methods.