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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

Average d-Accuracy calculated over 50 simulations for a network with two nodes and a single connection for varying neuronal delays (40 steps between 5 and 300 ms) and TR values of the fMRI scanner (40 steps between 50 ms and 2 s). Random HRFs are used with a time-to-peak uniformly distributed between 2.5 and 6.5 s, as shown in Figure 6, the signal-to-noise ratio is 0 dB. The proposed method is denoted VBCCA and we use P = 1, VBCCA(true HRF) denotes the proposed method with P = 1 and the HRF assumed in the algorithm is the same as the HRF that was used to generate the data. WGCA(P) denotes the Wiener–Granger causality method, for which we use AR model orders of 1 and an order between 1 and 20 selected using the Bayesian information criterion (BIC).
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Figure 8: Average d-Accuracy calculated over 50 simulations for a network with two nodes and a single connection for varying neuronal delays (40 steps between 5 and 300 ms) and TR values of the fMRI scanner (40 steps between 50 ms and 2 s). Random HRFs are used with a time-to-peak uniformly distributed between 2.5 and 6.5 s, as shown in Figure 6, the signal-to-noise ratio is 0 dB. The proposed method is denoted VBCCA and we use P = 1, VBCCA(true HRF) denotes the proposed method with P = 1 and the HRF assumed in the algorithm is the same as the HRF that was used to generate the data. WGCA(P) denotes the Wiener–Granger causality method, for which we use AR model orders of 1 and an order between 1 and 20 selected using the Bayesian information criterion (BIC).

Mentions: In the second simulation, we additionally introduce HRF variations. Results are shown in Figure 8. In this case, the proposed method performs poorly, even for low TR values, unless the method is provided with the true HRF for each region, in which case it can mitigate the effects of HRF variability. Somewhat surprisingly, WGCA(1) performs similarly as before when the same HRF was used for each region. However, when the BIC is used to determine the model order, the WGCA method exhibits low estimation performance for all TR and delay values. A possible explanation for this behavior is that due to the HRF convolution, the selected model order is higher than the true order and the order also depends on the HRF used (Seth et al., 2013), which results in spurious causality inversions and hence poor performance.


Variational Bayesian causal connectivity analysis for fMRI.

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

Average d-Accuracy calculated over 50 simulations for a network with two nodes and a single connection for varying neuronal delays (40 steps between 5 and 300 ms) and TR values of the fMRI scanner (40 steps between 50 ms and 2 s). Random HRFs are used with a time-to-peak uniformly distributed between 2.5 and 6.5 s, as shown in Figure 6, the signal-to-noise ratio is 0 dB. The proposed method is denoted VBCCA and we use P = 1, VBCCA(true HRF) denotes the proposed method with P = 1 and the HRF assumed in the algorithm is the same as the HRF that was used to generate the data. WGCA(P) denotes the Wiener–Granger causality method, for which we use AR model orders of 1 and an order between 1 and 20 selected using the Bayesian information criterion (BIC).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Average d-Accuracy calculated over 50 simulations for a network with two nodes and a single connection for varying neuronal delays (40 steps between 5 and 300 ms) and TR values of the fMRI scanner (40 steps between 50 ms and 2 s). Random HRFs are used with a time-to-peak uniformly distributed between 2.5 and 6.5 s, as shown in Figure 6, the signal-to-noise ratio is 0 dB. The proposed method is denoted VBCCA and we use P = 1, VBCCA(true HRF) denotes the proposed method with P = 1 and the HRF assumed in the algorithm is the same as the HRF that was used to generate the data. WGCA(P) denotes the Wiener–Granger causality method, for which we use AR model orders of 1 and an order between 1 and 20 selected using the Bayesian information criterion (BIC).
Mentions: In the second simulation, we additionally introduce HRF variations. Results are shown in Figure 8. In this case, the proposed method performs poorly, even for low TR values, unless the method is provided with the true HRF for each region, in which case it can mitigate the effects of HRF variability. Somewhat surprisingly, WGCA(1) performs similarly as before when the same HRF was used for each region. However, when the BIC is used to determine the model order, the WGCA method exhibits low estimation performance for all TR and delay values. A possible explanation for this behavior is that due to the HRF convolution, the selected model order is higher than the true order and the order also depends on the HRF used (Seth et al., 2013), which results in spurious causality inversions and hence poor performance.

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