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Variational Bayesian causal connectivity analysis for fMRI.

Luessi M, Babacan SD, Molina R, Booth JR, Katsaggelos AK - Front Neuroinform (2014)

Bottom Line: The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience.We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data.Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm.

View Article: PubMed Central - PubMed

Affiliation: Athinoula A. Martinos Center for Biomedical Imaging, Harvard Medical School, Massachusetts General Hospital Charlestown, MA, USA ; Department of Electrical Engineering and Computer Science, Northwestern University Evanston, IL, USA.

ABSTRACT
The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

No MeSH data available.


Related in: MedlinePlus

AUC, d-Accuracy, and mean squared error (MSE) scores for the proposed method with and without using the approximate time series z (t). The method are denoted by VBCCA (z (t) used) and VBCCA-D (z (t) not used). The simulation parameters are the same as in the first experiment, i.e., N = {5,10}, T = 500, P = 2, SNR = 0 dB. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
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Figure 4: AUC, d-Accuracy, and mean squared error (MSE) scores for the proposed method with and without using the approximate time series z (t). The method are denoted by VBCCA (z (t) used) and VBCCA-D (z (t) not used). The simulation parameters are the same as in the first experiment, i.e., N = {5,10}, T = 500, P = 2, SNR = 0 dB. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.

Mentions: As discussed in previous sections, the proposed method employs a hierarchical Bayesian model with an approximation to the neuronal time series. The approximate time series is denoted by z(t) and is a key part of the proposed method as it enables the method to be computationally efficient through a reduction of the state space dimension used in the Kalman smoother. In addition, the time series z(t) can be efficiently estimated in the frequency domain using fast Fourier transform algorithms. While the introduction of this approximation improves the computational efficiency, some reduction in the estimation performance may be caused. To quantify the influence of this approximation, we have implemented a modified version of the proposed method where z(t) is not used, i.e., we increase the dimension of x(t) to D = NL and model the observation process using Equation (42). This part of the modified model exactly corresponds to what is used in Smith et al. (2010) and Ryali et al. (2011). Due to the excessive memory requirements, the modified version of the proposed method, which we denote by “VBCCA-D,” can only be used for networks with small numbers of regions and HRFs consisting of a small number of time samples. We apply the method to the same data that is used in the first experiment, with N = {5, 10}, SNR = 0 dB. The resulting connectivity scores, as well as, the mean squared error (MSE) of the neuronal signal are shown in Figure 4. The MSE is calculated as follows


Variational Bayesian causal connectivity analysis for fMRI.

Luessi M, Babacan SD, Molina R, Booth JR, Katsaggelos AK - Front Neuroinform (2014)

AUC, d-Accuracy, and mean squared error (MSE) scores for the proposed method with and without using the approximate time series z (t). The method are denoted by VBCCA (z (t) used) and VBCCA-D (z (t) not used). The simulation parameters are the same as in the first experiment, i.e., N = {5,10}, T = 500, P = 2, SNR = 0 dB. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4017144&req=5

Figure 4: AUC, d-Accuracy, and mean squared error (MSE) scores for the proposed method with and without using the approximate time series z (t). The method are denoted by VBCCA (z (t) used) and VBCCA-D (z (t) not used). The simulation parameters are the same as in the first experiment, i.e., N = {5,10}, T = 500, P = 2, SNR = 0 dB. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
Mentions: As discussed in previous sections, the proposed method employs a hierarchical Bayesian model with an approximation to the neuronal time series. The approximate time series is denoted by z(t) and is a key part of the proposed method as it enables the method to be computationally efficient through a reduction of the state space dimension used in the Kalman smoother. In addition, the time series z(t) can be efficiently estimated in the frequency domain using fast Fourier transform algorithms. While the introduction of this approximation improves the computational efficiency, some reduction in the estimation performance may be caused. To quantify the influence of this approximation, we have implemented a modified version of the proposed method where z(t) is not used, i.e., we increase the dimension of x(t) to D = NL and model the observation process using Equation (42). This part of the modified model exactly corresponds to what is used in Smith et al. (2010) and Ryali et al. (2011). Due to the excessive memory requirements, the modified version of the proposed method, which we denote by “VBCCA-D,” can only be used for networks with small numbers of regions and HRFs consisting of a small number of time samples. We apply the method to the same data that is used in the first experiment, with N = {5, 10}, SNR = 0 dB. The resulting connectivity scores, as well as, the mean squared error (MSE) of the neuronal signal are shown in Figure 4. The MSE is calculated as follows

Bottom Line: The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience.We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data.Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm.

View Article: PubMed Central - PubMed

Affiliation: Athinoula A. Martinos Center for Biomedical Imaging, Harvard Medical School, Massachusetts General Hospital Charlestown, MA, USA ; Department of Electrical Engineering and Computer Science, Northwestern University Evanston, IL, USA.

ABSTRACT
The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

No MeSH data available.


Related in: MedlinePlus