Tractography-Based Score for Learning Effective Connectivity From Multimodal Imaging Data Using Dynamic Bayesian Networks
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.
Abstract: Objective: 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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TL;DR: In this paper, the authors extended the matrix formalism representation to include permeable cell membranes and analyzed the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators.
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 tissue geometry 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. In a previous publication, we presented a simulation framework that we implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for biological cells subject to impermeable membrane boundary conditions. In this work, we extend our simulation framework to include geometries that contain permeable cell membranes. We describe the new computational techniques that allowed this generalization and we analyze the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.
TL;DR: The results show that the proposed algorithm can successfully learn the structure of Dynamic Bayesian Networks without prior knowledge, and balance solutions quality and computational effort.
Abstract: The temporal dimension makes it difficult and complex to learn the Dynamic Bayesian Networks structure for huge search space. We propose a new hybrid K2-Bat algorithm to learn the structure of Dyna...
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TL;DR: In this article, the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
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.
16,349 citations
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper 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.
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
14,965 citations
01 Jan 2001
TL;DR: In this article, it is 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, and measures of causal lag and causal strength can then be constructed.
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.
11,896 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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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
8,448 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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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.
7,741 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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