Localizing Sources of Brain Disease Progression with Network Diffusion Model

Connectome-based biophysics models of Alzheimer's disease diagnosis and prognosis

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.

Graph Models of Pathology Spread in Alzheimer's Disease: An Alternative to Conventional Graph Theoretic Analysis

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.

Longitudinal predictive modeling of tau progression along the structural connectome

Tau neurofibrillary tangles, a pathophysiological hallmark of Alzheimer's disease (AD), exhibit a stereotypical spatiotemporal trajectory that is strongly correlated with disease progression and cognitive decline. Personalized prediction of tau progression is, therefore, vital for the early diagnosis and prognosis of AD. Evidence from both animal and human studies is suggestive of tau transmission along the brains preexisting neural connectivity conduits. We present here an analytic graph diffusion framework for individualized predictive modeling of tau progression along the structural connectome. To account for physiological processes that lead to active generation and clearance of tau alongside passive diffusion, our model uses an inhomogenous graph diffusion equation with a source term and provides closed-form solutions to this equation for linear and exponential source functionals. Longitudinal imaging data from two cohorts, the Harvard Aging Brain Study (HABS) and the Alzheimer's Disease Neuroimaging Initiative (ADNI), were used to validate the model. The clinical data used for developing and validating the model include regional tau measures extracted from longitudinal positron emission tomography (PET) scans based on the ¹⁸F-Flortaucipir radiotracer and individual structural connectivity maps computed from diffusion tensor imaging (DTI) by means of tractography and streamline counting. Two-timepoint tau PET scans were used to assess the goodness of model fit. Three-timepoint tau PET scans were used to assess predictive accuracy via comparison of predicted and observed tau measures at the third timepoint. Our results show high consistency between predicted and observed tau and differential tau from region-based analysis. While the prognostic value of this approach needs to be validated in a larger cohort, our preliminary results suggest that our longitudinal predictive model, which offers an in vivo macroscopic perspective on tau progression in the brain, is potentially promising as a personalizable predictive framework for AD.

Robust Bayesian Analysis of Early-Stage Parkinson's Disease Progression Using DaTscan Images

This paper proposes a mixture of linear dynamical systems model for quantifying the heterogeneous progress of Parkinson's disease from DaTscan Images. The model is fitted to longitudinal DaTscans from the Parkinson's Progression Marker Initiative. Fitting is accomplished using robust Bayesian inference with collapsed Gibbs sampling. Bayesian inference reveals three image-based progression subtypes which differ in progression speeds as well as progression trajectories. The model reveals characteristic spatial progression patterns in the brain, each pattern associated with a time constant. These patterns can serve as disease progression markers. The subtypes also have different progression rates of clinical symptoms measured by MDS-UPDRS Part III scores.

Deep Brain Stimulation for Alzheimer's Disease: Tackling Circuit Dysfunction

OBJECTIVES

Treatments for Alzheimer's disease are urgently needed given its enormous human and economic costs and disappointing results of clinical trials targeting the primary amyloid and tau pathology. On the other hand, deep brain stimulation (DBS) has demonstrated success in other neurological and psychiatric disorders leading to great interest in DBS as a treatment for Alzheimer's disease.

MATERIALS AND METHODS

We review the literature on 1) circuit dysfunction in Alzheimer's disease and 2) DBS for Alzheimer's disease. Human and animal studies are reviewed individually.

RESULTS

There is accumulating evidence of neural circuit dysfunction at the structural, functional, electrophysiological, and neurotransmitter level. Recent evidence from humans and animals indicate that DBS has the potential to restore circuit dysfunction in Alzheimer's disease, similarly to other movement and psychiatric disorders, and may even slow or reverse the underlying disease pathophysiology.

CONCLUSIONS

DBS is an intriguing potential treatment for Alzheimer's disease, targeting circuit dysfunction as a novel therapeutic target. However, further exploration of the basic disease pathology and underlying mechanisms of DBS is necessary to better understand how circuit dysfunction can be restored. Additionally, robust clinical data in the form of ongoing phase III clinical trials are needed to validate the efficacy of DBS as a viable treatment.

A physics-informed geometric learning model for pathological tau spread in Alzheimer's disease

Tau tangles are a pathophysiological hallmark of Alzheimer's disease (AD) and exhibit a stereotypical pattern of spatiotemporal spread which has strong links to disease progression and cognitive decline. Preclinical evidence suggests that tau spread depends on neuronal connectivity rather than physical proximity between different brain regions. Here, we present a novel physics-informed geometric learning model for predicting tau buildup and spread that learns patterns directly from longitudinal tau imaging data while receiving guidance from governing physical principles. Implemented as a graph neural network with physics-based regularization in latent space, the model enables effective training with smaller data sizes. For training and validation of the model, we used longitudinal tau measures from positron emission tomography (PET) and structural connectivity graphs from diffusion tensor imaging (DTI) from the Harvard Aging Brain Study. The model led to higher peak signal-to-noise ratio and lower mean squared error levels than both an unregularized graph neural network and a differential equation solver. The method was validated using both two-timepoint and three-timepoint tau PET measures. The effectiveness of the approach was further confirmed by a cross-validation study.

Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

A novel node-level structure embedding and alignment representation of structural networks for brain disease analysis

Brain networks based on various neuroimaging technologies, such as diffusion tensor image (DTI) and functional magnetic resonance imaging (fMRI), have been widely applied to brain disease analysis. Currently, there are several node-level structural measures (e.g., local clustering coefficients and node degrees) for representing and analyzing brain networks since they usually can reflect the topological structure of brain regions. However, these measures typically describe specific types of structural information, ignoring important network properties (i.e., small structural changes) that could further improve the performance of brain network analysis. To overcome this problem, in this paper, we first define a novel node-level structure embedding and alignment (nSEA) representation to accurately characterize the node-level structural information of the brain network. Different from existing measures that characterize a specific type of structural properties with a single value, our proposed nSEA method can learn a vector representation for each node, thus contain richer structure information to capture small structural changes. Furthermore, we develop an nSEA representation based learning (nSEAL) framework for brain disease analysis. Specifically, we first perform structural embedding to calculate node vector representations for each brain network and then align vector representations of all brain networks into the common space for two group-level network analyses, including a statistical analysis and brain disease classifications. Experiment results on a real schizophrenia dataset demonstrate that our proposed method not only discover disease-related brain regions that could help to better understand the pathology of brain diseases, but also improve the classification performance of brain diseases, compared with state-of-the-art methods.

Longitudinal progression of grey matter atrophy in non-amnestic Alzheimer's disease

Recent models of Alzheimer's disease progression propose that disease may be transmitted between brain areas either via local diffusion or long-distance transport via white matter fibre pathways. However, it is unclear whether such models are applicable in non-amnestic Alzheimer's disease, which is associated with domain-specific cognitive deficits and relatively spared episodic memory. To date, the anatomical progression of disease in non-amnestic patients remains understudied. We used longitudinal imaging to differentiate earlier atrophy and later disease spread in three non-amnestic variants, including logopenic-variant primary progressive aphasia (n = 25), posterior cortical atrophy (n = 20), and frontal-variant Alzheimer's disease (n = 12), as well as 17 amnestic Alzheimer's disease patients. Patients were compared to 37 matched controls. All patients had autopsy (n = 7) or CSF (n = 67) evidence of Alzheimer's disease pathology. We first assessed atrophy in suspected sites of disease origin, adjusting for age, sex, and severity of cognitive impairment; we then performed exploratory whole-brain analysis to investigate longitudinal disease spread both within and outside these regions. Additionally, we asked whether each phenotype exhibited more rapid change in its associated disease foci than other phenotypes. Finally, we investigated whether atrophy was related to structural brain connectivity. Each non-amnestic phenotype displayed unique patterns of initial atrophy and subsequent neocortical change that correlated with cognitive decline. Longitudinal atrophy included areas both proximal to and distant from sites of initial atrophy, suggesting heterogeneous mechanisms of disease spread. Moreover, regional rates of neocortical change differed by phenotype. Logopenic-variant patients exhibited greater initial atrophy and more rapid longitudinal change in left lateral temporal areas than other groups. Frontal-variant patients had pronounced atrophy in left insula and middle frontal gyrus, combined with more rapid atrophy of left insula than other non-amnestic patients. In the medial temporal lobes, non-amnestic patients had less atrophy at their initial scan than amnestic patients, but longitudinal rate of change did not differ between patient groups. Medial temporal sparing in non-amnestic Alzheimer's disease may thus be due in part to later onset of medial temporal degeneration than in amnestic patients rather than different rates of atrophy over time. Finally, the magnitude of longitudinal atrophy was predicted by structural connectivity, measured in terms of node degree; this result provides indirect support for the role of long-distance fibre pathways in the spread of neurodegenerative disease. 10.1093/brain/awz091_video1 awz091media1 6041544065001.

A method for inferring regional origins of neurodegeneration

Alzheimer's disease, the most common form of dementia, is characterized by the emergence and spread of senile plaques and neurofibrillary tangles, causing widespread neurodegeneration. Though the progression of Alzheimer's disease is considered to be stereotyped, the significant variability within clinical populations obscures this interpretation on the individual level. Of particular clinical importance is understanding where exactly pathology, e.g. tau, emerges in each patient and how the incipient atrophy pattern relates to future spread of disease. Here we demonstrate a newly developed graph theoretical method of inferring prior disease states in patients with Alzheimer's disease and mild cognitive impairment using an established network diffusion model and an L1-penalized optimization algorithm. Although the 'seeds' of origin using our inference method successfully reproduce known trends in Alzheimer's disease staging on a population level, we observed that the high degree of heterogeneity between patients at baseline is also reflected in their seeds. Additionally, the individualized seeds are significantly more predictive of future atrophy than a single seed placed at the hippocampus. Our findings illustrate that understanding where disease originates in individuals is critical to determining how it progresses and that our method allows us to infer early stages of disease from atrophy patterns observed at diagnosis.

A longitudinal model for tau aggregation in Alzheimer's disease based on structural connectivity

Tau tangles are a pathological hallmark of Alzheimer?s disease (AD) with strong correlations existing between tau aggregation and cognitive decline. Studies in mouse models have shown that the characteristic patterns of tau spatial spread associated with AD progression are determined by neural connectivity rather than physical proximity between different brain regions. We present here a network diffusion model for tau aggregation based on longitudinal tau measures from positron emission tomography (PET) and structural connectivity graphs from diffusion tensor imaging (DTI). White matter fiber bundles reconstructed via tractography from the DTI data were used to compute normalized graph Laplacians which served as graph diffusion kernels for tau spread. By linearizing this model and using sparse source localization, we were able to identify distinct patterns of propagative and generative buildup of tau at a population level. A gradient descent approach was used to solve the sparsity-constrained optimization problem. Model fitting was performed on subjects from the Harvard Aging Brain Study cohort. The fitted model parameters include a scalar factor controlling the network-based tau spread and a network-independent seed vector representing seeding in different regions-of-interest. This parametric model was validated on an independent group of subjects from the same cohort. We were able to predict with reasonably high accuracy the tau buildup at a future time-point. The network diffusion model, therefore, successfully identifies two distinct mechanisms for tau buildup in the aging brain and offers a macroscopic perspective on tau spread.

Diffusion MRI Indices and Their Relation to Cognitive Impairment in Brain Aging: The Updated Multi-protocol Approach in ADNI3

Brain imaging with diffusion-weighted MRI (dMRI) is sensitive to microstructural white matter (WM) changes associated with brain aging and neurodegeneration. In its third phase, the Alzheimer's Disease Neuroimaging Initiative (ADNI3) is collecting data across multiple sites and scanners using different dMRI acquisition protocols, to better understand disease effects. It is vital to understand when data can be pooled across scanners, and how the choice of dMRI protocol affects the sensitivity of extracted measures to differences in clinical impairment. Here, we analyzed ADNI3 data from 317 participants (mean age: 75.4 ± 7.9 years; 143 men/174 women), who were each scanned at one of 47 sites with one of six dMRI protocols using scanners from three different manufacturers. We computed four standard diffusion tensor imaging (DTI) indices including fractional anisotropy (FA^DTI) and mean, radial, and axial diffusivity, and one FA index based on the tensor distribution function (FA^TDF), in 24 bilaterally averaged WM regions of interest. We found that protocol differences significantly affected dMRI indices, in particular FA^DTI. We ranked the diffusion indices for their strength of association with four clinical assessments. In addition to diagnosis, we evaluated cognitive impairment as indexed by three commonly used screening tools for detecting dementia and AD: the AD Assessment Scale (ADAS-cog), the Mini-Mental State Examination (MMSE), and the Clinical Dementia Rating scale sum-of-boxes (CDR-sob). Using a nested random-effects regression model to account for protocol and site, we found that across all dMRI indices and clinical measures, the hippocampal-cingulum and fornix (crus)/stria terminalis regions most consistently showed strong associations with clinical impairment. Overall, the greatest effect sizes were detected in the hippocampal-cingulum (CGH) and uncinate fasciculus (UNC) for associations between axial or mean diffusivity and CDR-sob. FA^TDF detected robust widespread associations with clinical measures, while FA^DTI was the weakest of the five indices for detecting associations. Ultimately, we were able to successfully pool dMRI data from multiple acquisition protocols from ADNI3 and detect consistent and robust associations with clinical impairment and age.

Models of Network Spread and Network Degeneration in Brain Disorders

Network analysis can provide insight into key organizational principles of brain structure and help identify structural changes associated with brain disease. Though static differences between diseased and healthy networks are well characterized, the study of network dynamics, or how brain networks change over time, is increasingly central to understanding ongoing brain changes throughout disease. Accordingly, we present a short review of network models of spread, network dynamics, and network degeneration. Borrowing from recent suggestions, we divide this review into two processes by which brain networks can change: dynamics on networks, which are functional and pathological consequences taking place atop a static structural brain network; and dynamics of networks, which constitutes a changing structural brain network. We focus on diffusion magnetic resonance imaging-based structural or anatomic connectivity graphs. We address psychiatric disorders like schizophrenia; developmental disorders like epilepsy; stroke; and Alzheimer's disease and other neurodegenerative diseases.

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.