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Journal ArticleDOI

Tractography-Based Score for Learning Effective Connectivity From Multimodal Imaging Data Using Dynamic Bayesian Networks

01 May 2018-IEEE Transactions on Biomedical Engineering (IEEE)-Vol. 65, Iss: 5, pp 1057-1068

TL;DR: A novel anatomically informed (AI) score that evaluates fitness of a given connectivity structure to both DTI and fMRI data simultaneously is proposed that is employed in structure learning of DBN given the data.

AbstractObjective: Effective connectivity (EC) is the methodology for determining functional-integration among the functionally active segregated regions of the brain. By definition [1] EC is “the causal influence exerted by one neuronal group on another” which is constrained by anatomical connectivity (AC) (axonal connections). AC is necessary for EC but does not fully determine it, because synaptic communication occurs dynamically in a context-dependent fashion. Although there is a vast emerging evidence of structure–function relationship using multimodal imaging studies, till date only a few studies have done joint modeling of the two modalities: functional MRI (fMRI) and diffusion tensor imaging (DTI). We aim to propose a unified probabilistic framework that combines information from both sources to learn EC using dynamic Bayesian networks (DBNs). Method: DBNs are probabilistic graphical temporal models that learn EC in an exploratory fashion. Specifically, we propose a novel anatomically informed (AI) score that evaluates fitness of a given connectivity structure to both DTI and fMRI data simultaneously. The AI score is employed in structure learning of DBN given the data. Results: Experiments with synthetic-data demonstrate the face validity of structure learning with our AI score over anatomically uninformed counterpart. Moreover, real-data results are cross-validated by performing classification-experiments. Conclusion: EC inferred on real fMRI-DTI datasets is found to be consistent with previous literature and show promising results in light of the AC present as compared to other classically used techniques such as Granger-causality. Significance: Multimodal analyses provide a more reliable basis for differentiating brain under abnormal/diseased conditions than the single modality analysis.

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Citations
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Journal ArticleDOI
TL;DR: The presented methodology appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.
Abstract: In functional magnetic resonance imaging (fMRI), functional connectivity is conventionally characterized by correlations between fMRI time series, which are intrinsically undirected measures of connectivity. Yet, some information about the directionality of network connections can nevertheless be extracted from the matrix of pairwise temporal correlations between all considered time series, when expressed in the frequency-domain as a cross-spectral density matrix. Using a sparsity prior, it then becomes possible to determine a unique directed network topology that best explains the observed undirected correlations, without having to rely on temporal precedence relationships that may not be valid in fMRI. Applying this method on simulated data with 100 nodes yielded excellent retrieval of the underlying directed networks under a wide variety of conditions. Importantly, the method did not depend on temporal precedence to establish directionality, thus reducing susceptibility to hemodynamic variability. The computational efficiency of the algorithm was sufficient to enable whole-brain estimations, thus circumventing the problem of missing nodes that otherwise occurs in partial-brain analyses. Applying the method to real resting-state fMRI data acquired with a high temporal resolution, the inferred networks showed good consistency with structural connectivity obtained from diffusion tractography in the same subjects. Interestingly, this agreement could also be seen when considering high-frequency rather than low-frequency connectivity (average correlation: r = 0.26 for f < 0.3 Hz, r = 0.43 for 0.3 < f < 5 Hz). Moreover, this concordance was significantly better (p < 0.05) than for networks obtained with conventional functional connectivity based on correlations (average correlation r = 0.18). The presented methodology thus appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.

7 citations


Cites methods from "Tractography-Based Score for Learni..."

  • ...SC is commonly used to constrain the estimation (Gilson et al., 2016; Crimi et al., 2017; Dang et al., 2018), or may be used independently to validate the estimated EC (Uddin et al., 2011; Bringmann et al., 2013)....

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  • ...SC is commonly used to constrain the estimation (Gilson et al., 2016; Crimi et al., 2017; Dang et al., 2018), or may be used independently to validate the estimated EC (Uddin et al....

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Journal ArticleDOI
Long Chen1, Linqing Wang1, Zhongyang Han1, Jun Zhao1, Wei Wang1 
TL;DR: The experimental results indicate that the proposed variational inference method for the KDBN can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.
Abstract: Prediction intervals ( PIs ) for industrial time series can provide useful guidance for workers. Given that the failure of industrial sensors may cause the missing point in inputs, the existing kernel dynamic Bayesian networks ( KDBN ) , serving as an effective method for PIs construction, suffer from high computational load using the stochastic algorithm for inference. This study proposes a variational inference method for the KDBN for the purpose of fast inference, which avoids the time-consuming stochastic sampling. The proposed algorithm contains two stages. The first stage involves the inference of the missing inputs by using a local linearization based variational inference, and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices. To verify the effectiveness of the proposed method, a synthetic dataset and a practical dataset of generation flow of blast furnace gas ( BFG ) are employed with different ratios of missing inputs. The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.

5 citations


Cites methods from "Tractography-Based Score for Learni..."

  • ...To verify the performance of the proposed method, this study compares the experimental results of several other methods of PIs construction, including the KDBN with weighted likelihood inference (KDBN-WL) [25], the Bayesian multiple layer perceptron (Bayesian MLP) [13], and the bootstrap-based echo state networks (Bootstrap ESN) [20]....

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  • ...Besides, in [20], an ensemble model containing a number of reservoir computing networks was employed by using the bootstrap techniques, which was applied to the prediction of practical industrial data....

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  • ...Similarly, to further verify the performance of the proposed method for the BFG data, this study compares the experimental results of several other methods of PIs construction, including the KDBN-WL [25], the Bayesian MLP [13], and the bootstrap ESN [20]....

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Journal ArticleDOI
TL;DR: Four machine learning tools are applied to address the challenge in the IFDI of cutting arms and the experimental results show that the support vector machines based on dynamic cuckoo outperform the other methods.
Abstract: Incipient fault detection and identification (IFDI) of cutting arms is a crucial guarantee for the smooth operation of a roadheader. However, the shortage of fault samples restricts the application of the fault diagnosis technique, and the data analysis tools should be optimized efficiently. In this study, four machine learning tools (the back-propagation neural network based on genetic algorithm optimization, the naive Bayes based on genetic algorithm optimization, the support vector machines based on particle swarm optimization, and the support vector machines based on dynamic cuckoo) are applied to address the challenge in the IFDI of cutting arms. The commonly measured current and vibration data cutting arms are used in the IFDI. The experimental results show that the support vector machines based on dynamic cuckoo outperform the other methods. Besides, the performance of the four methods under different operating conditions is compared. The fault cause of cutting arms of the roadheader is analyzed and the design improvement scheme for cutting arms is provided. This study provides a reference for improving the fault diagnosis of the roadheader.

2 citations

Journal ArticleDOI
Abstract: The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

2 citations

Journal ArticleDOI
Abstract: Discrete Dynamic Bayesian Network (dDBN) is used in many challenging causal modelling applications, such as human brain connectivity, due to its multivariate, non-deterministic, and nonlinear capab...

1 citations


References
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Journal ArticleDOI
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

14,541 citations

Journal ArticleDOI
Abstract: SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi)/N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y{f(xj)p(x1)}/{q(xj)N}. This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1)/q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis

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Book ChapterDOI
01 Jan 2001
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.

10,077 citations


"Tractography-Based Score for Learni..." refers methods in this paper

  • ...Traditional Granger Causality (GC) [12] analysis for learning EC from fMRI is a model-based approach where model assumptions make GC vulnerable to violations for fMRI data, as shown in our previous work [13]....

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Journal ArticleDOI
TL;DR: Past observations are synthesized to provide strong evidence that the default network is a specific, anatomically defined brain system preferentially active when individuals are not focused on the external environment, and for understanding mental disorders including autism, schizophrenia, and Alzheimer's disease.
Abstract: Thirty years of brain imaging research has converged to define the brain’s default network—a novel and only recently appreciated brain system that participates in internal modes of cognition Here we synthesize past observations to provide strong evidence that the default network is a specific, anatomically defined brain system preferentially active when individuals are not focused on the external environment Analysis of connectional anatomy in the monkey supports the presence of an interconnected brain system Providing insight into function, the default network is active when individuals are engaged in internally focused tasks including autobiographical memory retrieval, envisioning the future, and conceiving the perspectives of others Probing the functional anatomy of the network in detail reveals that it is best understood as multiple interacting subsystems The medial temporal lobe subsystem provides information from prior experiences in the form of memories and associations that are the building blocks of mental simulation The medial prefrontal subsystem facilitates the flexible use of this information during the construction of self-relevant mental simulations These two subsystems converge on important nodes of integration including the posterior cingulate cortex The implications of these functional and anatomical observations are discussed in relation to possible adaptive roles of the default network for using past experiences to plan for the future, navigate social interactions, and maximize the utility of moments when we are not otherwise engaged by the external world We conclude by discussing the relevance of the default network for understanding mental disorders including autism, schizophrenia, and Alzheimer’s disease

7,504 citations


"Tractography-Based Score for Learni..." refers background in this paper

  • ...Previous studies [48]–[50] involving fMRI data have discussed...

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  • ...supports “self-referential” or “introspective” mental activity [48], [55], memory and emotion (including anxiety) [56], [57]....

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Journal ArticleDOI
TL;DR: It is suggested that both task-driven neuronal responses and behavior are reflections of this dynamic, ongoing, functional organization of the brain, featuring the presence of anticorrelated networks in the absence of overt task performance.
Abstract: During performance of attention-demanding cognitive tasks, certain regions of the brain routinely increase activity, whereas others routinely decrease activity. In this study, we investigate the extent to which this task-related dichotomy is represented intrinsically in the resting human brain through examination of spontaneous fluctuations in the functional MRI blood oxygen level-dependent signal. We identify two diametrically opposed, widely distributed brain networks on the basis of both spontaneous correlations within each network and anticorrelations between networks. One network consists of regions routinely exhibiting task-related activations and the other of regions routinely exhibiting task-related deactivations. This intrinsic organization, featuring the presence of anticorrelated networks in the absence of overt task performance, provides a critical context in which to understand brain function. We suggest that both task-driven neuronal responses and behavior are reflections of this dynamic, ongoing, functional organization of the brain.

6,962 citations


"Tractography-Based Score for Learni..." refers background in this paper

  • ...Default Mode Network has been identified as a group of regions which exhibit decreased neural activity during externally-generated task conditions [51]....

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