Network Diffusion Model Research Articles

Hypergraph-Based Influence Maximization in Online Social Networks

Influence maximization in online social networks is used to select a set of influential seed nodes to maximize the influence spread under a given diffusion model. However, most existing proposals have huge computational costs and only consider the dyadic influence relationship between two nodes, ignoring the higher-order influence relationships among multiple nodes. It limits the applicability and accuracy of existing influence diffusion models in real complex online social networks. To this end, in this paper, we present a novel information diffusion model by introducing hypergraph theory to determine the most influential nodes by jointly considering adjacent influence and higher-order influence relationships to improve diffusion efficiency. We mathematically formulate the influence maximization problem under higher-order influence relationships in online social networks. We further propose a hypergraph sampling greedy algorithm (HSGA) to effectively select the most influential seed nodes. In the HSGA, a random walk-based influence diffusion method and a Monte Carlo-based influence approximation method are devised to achieve fast approximation and calculation of node influences. We conduct simulation experiments on six real datasets for performance evaluations. Simulation results demonstrate the effectiveness and efficiency of the HSGA, and the HSGA has a lower computational cost and higher seed selection accuracy than comparison mechanisms.

Integrated Somatic Mutation Network Diffusion Model for Stratification of Breast Cancer into Different Metabolic Mutation Subtypes

Background: Mutations in metabolism-related genes in somatic cells potentially lead to disruption of metabolic pathways, which results in patients exhibiting different molecular and pathological features. background: Mutations in metabolism-related genes in somatic cells potentially lead to disruption of metabolic pathways, which results in patients exhibiting different molecular and pathological features. Objective: In this study, we focused on somatic mutation data to investigate the significance of metabolic mutation typing in guiding the prognosis and treatment of breast cancer patients. objective: In this study, we focused on somatic mutation data to investigate the significance of metabolic mutation typing in guiding the prognosis and treatment of breast cancer patients. Methods: The somatic mutation profile of breast cancer patients was analyzed and smoothed by utilizing a network diffusion model within the protein-protein interaction network to construct a comprehensive somatic mutation network diffusion profile. Subsequently, a deep clustering approach was employed to explore metabolic mutation typing in breast cancer based on integrated metabolic pathway information and the somatic mutation network diffusion profile. In addition, we employed deep neural networks and machine learning prediction models to assess the feasibility of predicting drug responses through somatic mutation network diffusion profiles. Results: Significant differences in prognosis and metabolic heterogeneity were observed among the different metabolic mutation subtypes, characterized by distinct alterations in metabolic pathways and genetic mutations, and these mutational features offered potential targets for subtype-specific therapies. Furthermore, there was a strong consistency between the results of the drug response prediction model constructed on the somatic mutation network diffusion profile and the actual observed drug responses. Conclusion: Metabolic mutation typing of cancer assists in guiding patient prognosis and treatment.

Combining multimodal connectivity information improves modelling of pathology spread in Alzheimer's disease.

Cortical atrophy and aggregates of misfolded tau proteins are key hallmarks of Alzheimer's disease. Computational models that simulate the propagation of pathogens between connected brain regions have been used to elucidate mechanistic information about the spread of these disease biomarkers, such as disease epicentres and spreading rates. However, the connectomes that are used as substrates for these models are known to contain modality-specific false positive and false negative connections, influenced by the biases inherent to the different methods for estimating connections in the brain. In this work, we compare five types of connectomes for modelling both tau and atrophy patterns with the network diffusion model, which are validated against tau PET and structural MRI data from individuals with either mild cognitive impairment or dementia. We then test the hypothesis that a joint connectome, with combined information from different modalities, provides an improved substrate for the model. We find that a combination of multimodal information helps the model to capture observed patterns of tau deposition and atrophy better than any single modality. This is validated with data from independent datasets. Overall, our findings suggest that combining connectivity measures into a single connectome can mitigate some of the biases inherent to each modality and facilitate more accurate models of pathology spread, thus aiding our ability to understand disease mechanisms, and providing insight into the complementary information contained in different measures of brain connectivity.

Predictive spread of obsessive-compulsive disorder pathology using the network diffusion model

An increasing body of studies propose that structural abnormalities begin with focal brain regions then propagate to other regions following the architecture of healthy brain network in neuropsychiatric disorders. However, these findings are untested in obsessive-compulsive disorder (OCD), also showing widespread structural brain abnormalities. In this study, we aimed to investigate whether healthy functional brain network contributed to structural brain abnormalities in OCD. The gray matter morphological abnormalities were obtained in 98 patients with OCD in relative to matched healthy controls (n = 130, HCs). The network diffusion model (NDM) was conducted to identify putative seed regions and patterns of disease propagation from seed regions to other brain regions along the functional network in OCD. The NDM has been proved to succeeded in capturing the trans-neuronal propagation of pathology and even in predicting future longitudinal progression of pathology in neurodegenerative diseases. In this study, when seeding at the right anterior cingulate cortex, the NDM best recapitulated the patterns of gray matter morphological abnormalities, suggesting this region was the most likely seed region. Further analyses revealed that pathology preferentially propagated to higher order brain systems from seed region. For non-seed regions, the arrival time of pathology was negatively correlated with their shortest functional paths to the seed (r = −0.46, p < 0.001). These results suggest that gray matter morphological abnormalities are constrained by healthy brain network and reveal temporal sequencing of pathology progression in OCD.

Modeling pathological spread through the structural connectome in the FTLD spectrum

AbstractBackgroundTo explore the relationship between network vulnerability and longitudinal atrophy progression in FTLD spectrum, using Network Diffusion Model (NDM) of pathology spread.MethodThirty‐four behavioural‐variant frontotemporal dementia (bvFTD), 11 semantic‐variant primary progressive aphasia (svPPA) and 11 nonfluent/agrammatic‐variant primary progressive aphasia (nfvPPA) patients underwent longitudinal T1‐weighted MRI. Forty‐eight young controls underwent multi‐shell diffusion MRI scan. NDM was developed to assess the progression of FTLD pathology originating from a seed (right orbitofrontal cortex [bvFTD], left inferior temporal gyrus [svPPA], and left supplementary motor area [nfvPPA]) and proceeding through the healthy connectome. The connectivity measures were fractional anisotropy (FA) and intra‐cellular volume fraction (ICVF). Correlations were tested between atrophy estimated by NDM and those empirically obtained in FTLD patients over a follow‐up of 24 months.ResultIn bvFTD, NDM showed an early spread to frontal lobe and basal‐ganglia and to right sensorimotor, parietal, temporal and occipital lobes, with a subsequent involvement of the left hemisphere. In svPPA, NDM suggested an early spread of pathology to the left occipital and frontal lobes, while parietal lobe was reached later. In nfvPPA, NDM‐predicted spread through all brain regions, except for occipital lobe. NDM‐predicted atrophy of each region was positively correlated to longitudinal atrophy empirically observed in all three FTLD variants. Overall, NDM with ICVF connectome provided higher correlation values relative to NDM with FA maps.ConclusionThe NDM implementation to cross‐sectional structural connectome is a valuable tool to predict atrophy patterns and pathology spreading in FTLD variants.Supported‐by: European‐Research‐Council (StG‐2016_714388_NeuroTRACK); Foundation Research on Alzheimer’s Disease.

Network diffusion model reveals recovery multipliers and heterogeneous spatial effects in post-disaster community recovery

Community recovery from hazards occurs through various diffusion processes within social and spatial networks of communities. Existing knowledge regarding the diffusion of recovery in community socio-spatial networks, however, is rather limited. To bridge this gap, we created a network diffusion model to characterize the unfolding of population activity recovery in spatial networks of communities. In particular, this study aims to answer the research question “To what extent can the diffusion model capture the spatial patterns of recovery?” Using population activity recovery data derived from location-based information associated with 2017 Hurricane Harvey in the Houston area, we parameterized the threshold-based network diffusion model using the genetic algorithm and then simulated the recovery diffusion process. The results show that the spatial effects of recovery are rather heterogeneous across different areas; some spatial areas demonstrate a greater spatial effect in their recovery. Also, the results show that low-income and minority areas are community recovery multipliers; with faster recovery in these areas corresponding to accelerated recovery for the entire community. Hence, prioritizing these areas in resource allocation during recovery has the potential to accelerate could expedite the recovery of the entire community’s recovery process while promoting recovery equality and equity.

Network-Based Spreading of Gray Matter Changes Across Different Stages of Psychosis

Psychotic illness is associated with anatomically distributed gray matter reductions that can worsen with illness progression, but the mechanisms underlying the specific spatial patterning of these changes is unknown. To test the hypothesis that brain network architecture constrains cross-sectional and longitudinal gray matter alterations across different stages of psychotic illness and to identify whether certain brain regions act as putative epicenters from which volume loss spreads. This case-control study included 534 individuals from 4 cohorts, spanning early and late stages of psychotic illness. Early-stage cohorts included patients with antipsychotic-naive first-episode psychosis (n = 59) and a group of patients receiving medications within 3 years of psychosis onset (n = 121). Late-stage cohorts comprised 2 independent samples of people with established schizophrenia (n = 136). Each patient group had a corresponding matched control group (n = 218). A sample of healthy adults (n = 356) was used to derive representative structural and functional brain networks for modeling of network-based spreading processes. Longitudinal illness-related and antipsychotic-related gray matter changes over 3 and 12 months were examined using a triple-blind randomized placebo-control magnetic resonance imaging study of the antipsychotic-naive patients. All data were collected between April 29, 2008, and January 15, 2020, and analyses were performed between March 1, 2021, and January 14, 2023. Coordinated deformation models were used to estimate the extent of gray matter volume (GMV) change in each of 332 parcellated areas by the volume changes observed in areas to which they were structurally or functionally coupled. To identify putative epicenters of volume loss, a network diffusion model was used to simulate the spread of pathology from different seed regions. Correlations between estimated and empirical spatial patterns of GMV alterations were used to quantify model performance. Of 534 included individuals, 354 (66.3%) were men, and the mean (SD) age was 28.4 (7.4) years. In both early and late stages of illness, spatial patterns of cross-sectional volume differences between patients and controls were more accurately estimated by coordinated deformation models constrained by structural, rather than functional, network architecture (r range, >0.46 to <0.57; P < .01). The same model also robustly estimated longitudinal volume changes related to illness (r ≥ 0.52; P < .001) and antipsychotic exposure (r ≥ 0.50; P < .004). Network diffusion modeling consistently identified, across all 4 data sets, the anterior hippocampus as a putative epicenter of pathological spread in psychosis. Epicenters of longitudinal GMV loss were apparent in posterior cortex early in the illness and shifted to the prefrontal cortex with illness progression. These findings highlight a central role for white matter fibers as conduits for the spread of pathology across different stages of psychotic illness, mirroring findings reported in neurodegenerative conditions. The structural connectome thus represents a fundamental constraint on brain changes in psychosis, regardless of whether these changes are caused by illness or medication. Moreover, the anterior hippocampus represents a putative epicenter of early brain pathology from which dysfunction may spread to affect connected areas.

Cooperation and Competition Coupled Diffusion of Multi-Feature on Multiplex Networks and Its Control

Cooperation and competition widely exist in various kinds of network diffusions which however are usually studied separately. Recently, a novel network diffusion model, called multi-feature diffusion (MFD), attracts considerable attentions. The existing works usually assume that each feature diffuses independently and neglects the possible complex interplay between different features. In this paper, we introduce the cooperation and competition into the MFD and propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ooperation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ompetition coupled diffusion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> ulti- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> eature on multiplex network (CCMF). An unified framework and mathematical analytic theory regarding CCMF are then presented which are applicable and computationally efficient for any number of features and their own different sub-diffusion dynamics. In addition, an interesting finding is obtained in CCMF: compared with the high intensity competition, performing lower intensity competition under weak competition ability is more easier to result in positive effect. Due to the great importance of controlling network diffusion in many diverse contexts, we also propose an optimal allocation strategy of control resource for CCMF which first realizes the promotion and suppression of network diffusion simultaneously under one optimization framework and is also verified to be very efficient.

Prediction of the spread of African swine fever through pig and carcass movements in Thailand using a network analysis and diffusion model.

African swine fever (ASF) is a serious contagious viral disease of pigs that affects the pig industry. This study aimed to evaluate the possible African swine fever (ASF) distribution using network analysis and a diffusion model through live pig, carcass, and pig product movement data. Empirical movement data from Thailand for the year 2019 were used, and expert opinions were sought to evaluate network properties and the diffusion model. The networks were presented as live pig movement and carcass movement data at the provincial and district levels. For network analysis, a descriptive network analysis was performed using outdegree, indegree, betweenness, fragmentation, and power law distribution, and cutpoints were used to describe movement patterns. For the diffusion model, we simulated each network using spatially different infected locations, patterns, and initial infection sites. Based on expert opinions, the initial infection site, the probability of ASF occurrence, and the probability of the initial infected adopter were selected for the appropriated network. In this study, we also simulated networks under varying network parameters to predict the infection speed. The total number of movements recorded was 2,594,364. These were divided into 403,408 (403,408/2,594,364; 15.55%) for live pigs and 2,190,956 (2,190,956/2,594,364; 84.45%) for carcasses. We found that carcass movement at the provincial level showed the highest outdegree (mean = 342.554, standard deviation (SD) = 900.528) and indegree values (mean = 342.554, SD = 665.509). In addition, the outdegree and indegree presented similar mean values and the degree distributions of both district networks followed a power-law function. The network of live pigs at provincial level showed the highest value for betweenness (mean = 0.011, SD = 0.017), and the network of live pigs at provincial level showed the highest value for fragmentation (mean = 0.027, SD = 0.005). Our simulation data indicated that the disease occurred randomly due to live pig and carcass movements along the central and western regions of Thailand, causing the rapid spread of ASF. Without control measures, it could spread to all provinces within 5- and 3-time units and in all districts within 21- and 30-time units for the network of live pigs and carcasses, respectively. This study assists the authorities to plan control and preventive measures and limit economic losses caused by ASF.

Competition-based generalized self-profit maximization in dual-attribute network

Profit Maximization in social advertising aims at selecting some users of social network as initial adopters and information sources to trigger the spread of promotion information such that the profit generated by all the adopters reaches maximum when the dissemination terminates. A lot of related works mainly study this problem under three assumptions: pure network, single product and one-dimension diffusion model. However, in real advertising activities conducted in social networks, advertisement of competitive products may spread almost at the same time. And there are many factors that can influence the probability with which a potential consumer makes an adoption. For the purpose of approximating real social advertising, we propose the Dual-Attribute Compete (DAC) model where attributes of both potential consumers and competitive products are taken into consideration and the information about competitive products can spread simultaneously. Therefore, it can capture not only the competition between different products but also the reaction of potential consumers to products. Under DAC model, we study the Competition-based Generalized Self-profit Maximization (CGSM) problem whose purpose is selecting at most k individuals to form an optimal seed set as the source of information diffusion to maximize the profit related to adopters. Given that the objective function of CGSM problem is generally nonsubmodular, we design R-CGSM algorithm to tackle it. Based on the analysis of martingale and the concept of Shapley value, this algorithm uses sandwich method to get a pretty good solution of CGSM problem. We evaluate the R-CGSM algorithm by conducting experiments on four different data sets representing a synthetic network and three social networks in real world, respectively. Results of experiments validate the effectiveness and accuracy of R-CGSM algorithm.

Network diffusion model predicts neurodegeneration in limb-onset Amyotrophic Lateral Sclerosis.

ObjectiveEmerging evidences suggest that the trans-neural propagation of phosphorylated 43-kDa transactive response DNA-binding protein (pTDP-43) contributes to neurodegeneration in Amyotrophic Lateral Sclerosis (ALS). We investigated whether Network Diffusion Model (NDM), a biophysical model of spread of pathology via the brain connectome, could capture the severity and progression of neurodegeneration (atrophy) in ALS.MethodsWe measured degeneration in limb-onset ALS patients (n = 14 at baseline, 12 at 6-months, and 9 at 12 months) and controls (n = 12 at baseline) using FreeSurfer analysis on the structural T1-weighted Magnetic Resonance Imaging (MRI) data. The NDM was simulated on the canonical structural connectome from the IIT Human Brain Atlas. To determine whether NDM could predict the atrophy pattern in ALS, the accumulation of pathology modelled by NDM was correlated against atrophy measured using MRI. In order to investigate whether network spread on the brain connectome derived from healthy individuals were significant findings, we compared our findings against network spread simulated on random networks.ResultsThe cross-sectional analyses revealed that the network diffusion seeded from the inferior frontal gyrus (pars triangularis and pars orbitalis) significantly predicts the atrophy pattern in ALS compared to controls. Whereas, atrophy over time with-in the ALS group was best predicted by seeding the network diffusion process from the inferior temporal gyrus at 6-month and caudal middle frontal gyrus at 12-month. Network spread simulated on the random networks showed that the findings using healthy brain connectomes are significantly different from null models.InterpretationOur findings suggest the involvement of extra-motor regions in seeding the spread of pathology in ALS. Importantly, NDM was able to recapitulate the dynamics of pathological progression in ALS. Understanding the spatial shifts in the seeds of degeneration over time can potentially inform further research in the design of disease modifying therapeutic interventions in ALS.

Modeling seeding and neuroanatomic spread of pathology in amyotrophic lateral sclerosis

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 effect of microglial genes on network diffusion of pathology in mouse models of tauopathy

AbstractBackgroundMisfolded tau and amyloid, the hallmark pathologies of Alzheimer’s disease, undergo “prion‐like” trans‐synaptic transmission along the brain’s anatomic connectivity network (Frost, et al,2010). Our lab has previously shown that Alzheimer’s neuropathology progression is well‐approximated by a network diffusion model (NDM) (Raj, et al,2012). However, other processes in the brain may affect the neuropathology progression by mediating intraregional clearance/amplification and interregional spread. For instance, microglial activation is a common pathological feature of Alzheimer’s disease, with TREM2‐expressing microglia being integral to the inflammatory response. We show here that the NDM can be extended to include effects of microglial mediation of pathology.MethodWe modified the NDM to an extended NDM (eNDM) with additional model parameters related to microglia‐mediated spread/clearance and applied it to the 426×426 region mouse connectome. The eNDM included datasets of longitudinal spatiotemporal tau pathology in PS19 mice, expression levels of five microglial homeostatic signature genes (Cx3Cr1, C1qa, P2ry12, Fcrls, Olfml3) as well as TREM2 and CD33, microglial surface‐markers and phagocytosis regulators (Li, et al,2018). We compared the fits of the NDM to those of the eNDM using each gene individually as well as the first two principal components of spatial gene expression (Lein, et al,2007) after optimizing model parameters using a constrained nonlinear optimization algorithm.ResultsInclusion of microglial gene expression improved the predictive power of the model beyond that of the NDM (R2=0.46). Using the principal components of gene expression generally provided better model fits than individual genes. Notably, exclusion of TREM2 before performing PCA had a significant effect on model fit (p&lt;0.001, R2=0.5) (Table 1, Figure 1), increasing the values of the optimal diffusion and spread parameters.ConclusionAlthough network spread models capture well the spread of pathology between brain regions, there are other factors that mediate this process. We demonstrated that an eNDM with microglial genes had an improved model fit even after accounting for differences in model parsimony. We also showed that exclusion of TREM2 from the model resulted in higher diffusivity parameter values, thus supporting the biological observation of TREM2‐knockout resulting in increased spread of pathology, putatively by affecting microglial phagocytic potential (Griciuc, et al, 2019).

Combining network spread with protein aggregation correctly recapitulates empirical spatio-temporal progression of Alzheimer's tau pathology.

Alzheimer's disease involves widespread and progressive deposition of misfolded protein tau, likely via "prion-like" trans-neuronal transmission along the brain's structural connectome. It is not well understood how tau aggregation and spread leads to stereotypical progression in the Alzheimer brain. Here we extend our previous Network Diffusion Model (NDM, [1]) to include these critical processes (see Figure 1): a) Tau monomer seeding and production in the entorhinal cortex; b) aggregation of monomers into larger oligomers and then tangles using well-known Smoluchowski equations that were previously successful for amyloid beta and prions [2]. c) These processes were integrated into NDM, whereby anatomic connections govern the transmission of tau between two distant but connected brain regions. This extended model, which we call Aggregation-Network-Diffusion (AND), was then thoroughly tested on empirical data (Table 1): MRI-derived atrophy, AV1451-PET and CSF biomarkers (Ab42, pTau) from ADNI and Korea cohort [3]. AND model exhibits key hallmarks of AD, accurately capturing the spatial distribution of empirical tau (Korea cohort) as well as regional atrophy of ADNI cohort (Figure 2). R values shown in figure are all highly significant (p<0.0001). Next we interrogated different regions serving as seeding site; the best cortical seeding site was entorhinal cortex, while the best subcortical seeding was in amygdala followed by hippocampus. We also fitted the AND model's total tau PET against patients' cerebrospinal fluid phosphorylated tau (p-tau181) profiles as a function of disease progression; we obtained R = 0.37, p < 1e-36. Sensitivity analysis suggests that diffusion rate is far more important than monomer production rate in governing long-term pathology accumulation (Figure 3). This unified quantitative and testable model has the potential to explain observed phenomena. It may also serve as a test-bed for future hypothesis generation and testing in silico, e.g. to mathematically test whether monomer production, aggregation or diffusion is the key bottleneck.

New applications of diffusion model based prediction of pathological brain alterations: Introducing amyloid‐tau interactions

AbstractBackgroundAlzheimer’s disease involves widespread and progressive deposition of misfolded protein tau. There is mounting evidence for “prion‐like” trans‐neuronal transmission, whereby proteins misfold, triggering subsequent misfolding of adjacent same‐species proteins, which spread along white matter projections. It is not well understood how tau and amyloid beta interact, and how their subsequent spread lead to stereotypical progression in the Alzheimer brain.MethodHere we present a major advancement of our previously established Network Diffusion Model (Raj et al. Neuron 2012) that includes three key processes: a) Tau monomer seeding and production in the entorhinal cortex, and Ab monomer seeding in metabolically active areas. b) Interaction between Ab and tau, whereby Ab facilitates production of tau, or both facilitate each other. c) Both species then undergo network spread via our prior Network‐Diffusion model, whereby anatomic connections govern the rate at which two distant but connected brain regions can transfer pathologic species. This extended joint Ab‐tau model was thoroughly tested on empirical group‐averaged regional data (MRI‐derived atrophy, AV45‐PET for Ab and AV1451‐PET for tau) from ADNI‐3 (Table 1).ResultThe extended NDM model exhibits all hallmarks of tau and amyloid progression seen in human patients (Figure 1), accurately capturing the spatial distribution of empirical regional atrophy, Ab and tau (Table 2). Figure 1 shows evolution of the joint model with (middle column) and without amyloid‐facilitation of tau (right). Remarkably, the introduction of a 1‐way directed Aβ to tau influence recapitulated the concept of amyloid‐facilitated tauopathy, and was critical to the models’ success. In comparison, the non‐interacting model was significantly worse, while the 2‐way interaction model (bidirectional influence between tau and Ab) was essentially the same (see Table 2).ConclusionThis in silico exposition of the “pas de deux” of co‐evolving proteins supports a key role for an amyloid‐facilitated‐tau rather than the classic amyloid‐cascade or pure‐tau hypotheses, and helps explain known but poorly understood aspects of AD (Figure 2).

The Spreading of Shocks in the North America Production Network and Its Relation to the Properties of the Network

We evaluate the short-run effect of a shock in the manufacturing sector in the North America Production Network. We use input–output data for Canada, Mexico, the USA, and the North America region. With this data we represent the economies as networks and apply a network diffusion model and execute computer simulations according to different escenarios. We then study the relation between the effects of the shock and the structure of the networks by computing structural properties of sectors. Results show the limited effects of a shock on the manufacturing sector, and thus shed light on the heterogeneous impacts of the trade agreement of the region. They provide useful information to design an industrial policy focused on the development of the production network. In particular, we focus on recommendations for the Mexican economy.

Bayesian Physics-Based Modeling of Tau Propagation in Alzheimer's Disease.

Amyloid-β and hyperphosphorylated tau protein are known drivers of neuropathology in Alzheimer's disease. Tau in particular spreads in the brains of patients following a spatiotemporal pattern that is highly sterotypical and correlated with subsequent neurodegeneration. Novel medical imaging techniques can now visualize the distribution of tau in the brain in vivo, allowing for new insights to the dynamics of this biomarker. Here we personalize a network diffusion model with global spreading and local production terms to longitudinal tau positron emission tomography data of 76 subjects from the Alzheimer's Disease Neuroimaging Initiative. We use Bayesian inference with a hierarchical prior structure to infer means and credible intervals for our model parameters on group and subject levels. Our results show that the group average protein production rate for amyloid positive subjects is significantly higher with 0.019±0.27/yr, than that for amyloid negative subjects with −0.143±0.21/yr (p = 0.0075). These results support the hypothesis that amyloid pathology drives tau pathology. The calibrated model could serve as a valuable clinical tool to identify optimal time points for follow-up scans and predict the timeline of disease progression.

Combined Model of Aggregation and Network Diffusion Recapitulates Alzheimer's Regional Tau-Positron Emission Tomography.

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.

Network-constrained technique to characterize pathology progression rate in Alzheimer's disease.

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.

Policy diffusion through leadership transfer networks: Direct or indirect connections?

AbstractChange agents play important roles in the diffusion of policy innovation. Scholars argue that the career paths of change agents could facilitate the diffusion of innovation through network‐based mechanisms of portable innovation or policy wormholes, but have not fully distinguished between direct and indirect connections inherently important in a leadership transfer network. This study proposes an indirect portable innovation hypothesis and an indirect policy wormhole hypothesis to highlight the effects of leadership transfer networks through indirect network connections, extending the agent network diffusion (AND) model. We test the hypotheses empirically with the diffusion of local financial subsidy policies for new energy vehicles (NEVs) among cities in China from 2009 to 2016. The results confirm the effects of direct and indirect portable innovation and policy wormholes.