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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

Example of random hemodynamic response functions (HRFs) used in the experiment. The HRFs are generated from canonical HRFs where the parameters are drawn from a uniform distribution such that positions of the positive and the negative peaks lie in the intervals [2.5s, 6.5s] and [15s, 16.7s], respectively. The bold dashed line shows the default HRF with peaks at 5 and 15.75 s.
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Figure 6: Example of random hemodynamic response functions (HRFs) used in the experiment. The HRFs are generated from canonical HRFs where the parameters are drawn from a uniform distribution such that positions of the positive and the negative peaks lie in the intervals [2.5s, 6.5s] and [15s, 16.7s], respectively. The bold dashed line shows the default HRF with peaks at 5 and 15.75 s.

Mentions: As processing at the neuronal level occurs at temporal scales which are orders of magnitudes faster than the sampling interval of the MRI scanner, it is important to analyze how the performance of causality based methods is affected by the low sampling rate. Another important question is the effect of HRF variability on the performance. In this experiment we analyze the influence of these effects on the estimated causality. In order to do so, we generate s(t) for two regions and a single connection according to Equation (1) with zero-mean, i.i.d., Gaussian innovations, i.e., η (t) ~ (0, I). The simulated sampling rate at the neuronal level is 1 kHz and we generate a total of 240 s of data. We use a11,1 = a12,2 = 0.95 to simulate a degree of autocorrelation within each time series. To simulate connection with a certain neuronal delay, depending of the direction of the influence we draw the value of either ad1,2 or ad2,1 from a uniform distribution on the interval [0.4, 0.9]. The lag parameter d is used to simulate the neuronal delay, e.g., d = 10 corresponds to a delay of 10 ms. Next, we convolve the obtained neuronal time series with an HRF for each region. In the first simulation we use the same canonical HRF with peaks at 5 and 15.75 s for both regions, whereas in the second simulation we use a randomly generated HRF for each region. To generate a random HRF, we use the HRF generation function provided in SPM8 (http://www.fil.ion.ucl.ac.uk/spm/). The parameter controlling the time-to-peak is drawn from a uniform distribution, such that the positions of the positive peak lies between 2.5 and 6.5 s, which is the range of peak positions reported in Handwerker et al. (2004). The parameter controlling the position of the negative peak (“undershoot”) is held constant at 16 s. Due the implementation in SPM8, the negative peak of the generated HRF lies between 15 and 16.7 s, depending on the position of the positive peak. An example of HRFs used in our experiment is depicted in Figure 6. After each time series has been convolved with a HRF, the data is downsampled to simulate a certain TR value. Finally we add zero-mean, i.i.d., Gaussian noise such that the resulting SNR is 0 dB. To study both the influence of downsampling and the neuronal delay, we linearly vary the simulated TR between 50 ms and 2 s using a step size of 50 ms (40 points) and the delay using 40 linearly spaced values between 5 and 300 ms, resulting in a total of 1600 TR/delay combinations.


Variational Bayesian causal connectivity analysis for fMRI.

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

Example of random hemodynamic response functions (HRFs) used in the experiment. The HRFs are generated from canonical HRFs where the parameters are drawn from a uniform distribution such that positions of the positive and the negative peaks lie in the intervals [2.5s, 6.5s] and [15s, 16.7s], respectively. The bold dashed line shows the default HRF with peaks at 5 and 15.75 s.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Example of random hemodynamic response functions (HRFs) used in the experiment. The HRFs are generated from canonical HRFs where the parameters are drawn from a uniform distribution such that positions of the positive and the negative peaks lie in the intervals [2.5s, 6.5s] and [15s, 16.7s], respectively. The bold dashed line shows the default HRF with peaks at 5 and 15.75 s.
Mentions: As processing at the neuronal level occurs at temporal scales which are orders of magnitudes faster than the sampling interval of the MRI scanner, it is important to analyze how the performance of causality based methods is affected by the low sampling rate. Another important question is the effect of HRF variability on the performance. In this experiment we analyze the influence of these effects on the estimated causality. In order to do so, we generate s(t) for two regions and a single connection according to Equation (1) with zero-mean, i.i.d., Gaussian innovations, i.e., η (t) ~ (0, I). The simulated sampling rate at the neuronal level is 1 kHz and we generate a total of 240 s of data. We use a11,1 = a12,2 = 0.95 to simulate a degree of autocorrelation within each time series. To simulate connection with a certain neuronal delay, depending of the direction of the influence we draw the value of either ad1,2 or ad2,1 from a uniform distribution on the interval [0.4, 0.9]. The lag parameter d is used to simulate the neuronal delay, e.g., d = 10 corresponds to a delay of 10 ms. Next, we convolve the obtained neuronal time series with an HRF for each region. In the first simulation we use the same canonical HRF with peaks at 5 and 15.75 s for both regions, whereas in the second simulation we use a randomly generated HRF for each region. To generate a random HRF, we use the HRF generation function provided in SPM8 (http://www.fil.ion.ucl.ac.uk/spm/). The parameter controlling the time-to-peak is drawn from a uniform distribution, such that the positions of the positive peak lies between 2.5 and 6.5 s, which is the range of peak positions reported in Handwerker et al. (2004). The parameter controlling the position of the negative peak (“undershoot”) is held constant at 16 s. Due the implementation in SPM8, the negative peak of the generated HRF lies between 15 and 16.7 s, depending on the position of the positive peak. An example of HRFs used in our experiment is depicted in Figure 6. After each time series has been convolved with a HRF, the data is downsampled to simulate a certain TR value. Finally we add zero-mean, i.i.d., Gaussian noise such that the resulting SNR is 0 dB. To study both the influence of downsampling and the neuronal delay, we linearly vary the simulated TR between 50 ms and 2 s using a step size of 50 ms (40 points) and the delay using 40 linearly spaced values between 5 and 300 ms, resulting in a total of 1600 TR/delay combinations.

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