1 University of Kuopio Dept. of Applied Physics P.O.Box 1627, FIN-70211 Kuopio FINLAND

1. Principal Component Regression Approach for Functional Connectivity of Neuronal Activation Measured by Functional MRI Eini I. Niskanen1,†,Mika P. Tarvainen1, Mervi Könönen2, Hilkka Soininen3, and Pasi A. Karjalainen1 1University of Kuopio Dept. of Applied Physics P.O.Box 1627, FIN-70211 Kuopio FINLAND †E-mail: Eini.Niskanen@uku.fi 2Kuopio University Hospital Dept. of Clinical Neurophysiology P.O.Box 1777, FIN-70211 Kuopio FINLAND 3University of Kuopio Dept. of Neuroscience and Neurology P.O.Box 1627, FIN-70211 Kuopio FINLAND Eini Niskanen, Dept. of Applied Physics, University of Kuopio

2. functional Magnetic Resonance Imaging (fMRI) Eini Niskanen, Dept. of Applied Physics, University of Kuopio

3. fMRI signal • Each fMRI study contains a huge number of voxel time series (70 000 – 100 000 or more) depending on the imaging parameters • Typical interscan interval is ~ 1-3 seconds ⇒ low sampling frequency • A lot of noise from head motion, cardiac and respiratory cycles, and hardware-related signal drifts Eini Niskanen, Dept. of Applied Physics, University of Kuopio

4. Blood Oxygenation Level Dependent (BOLD) response • Paramagnetic deoxyhemoglobin causes local inhomogeneities in transversal magnetization • ⇒ signal decrease in T2*-weighted images • Stimulus increases the need of oxygen in active cortical areas • Blood flow and blood volume increase • concentration of oxygenated hemoglobin increases • relative concentration of deoxygenated hemoglobin decreases • in T2*-weighted images this is seen as a signal increase = BOLD response Eini Niskanen, Dept. of Applied Physics, University of Kuopio

5. BOLD response • BOLD response is slow: time to peak ~3-5 s, total duration over 10 s • The signal change due to functional activation is small ~ 0.5 – 5 % • The shape of the BOLD response varies across subjects and also within subject depending on the type of the stimulus and active cortical area • The summation of the consecutive responses for short interstimulus intervals is highly nonlinear Eini Niskanen, Dept. of Applied Physics, University of Kuopio

6. BOLD signal εu s Balloon model volume v ′ Inflow f ′ Stimulus u signal s′ deoxyHb q′ Buxton et al. 1998, MRM39:855-864 Obata et al. 2004, NeuroImage21:144-153 Friston et al. 2000, NeuroImage 12:466-477 Eini Niskanen, Dept. of Applied Physics, University of Kuopio

7. Functional connectivity “the temporal correlations among neurophysiological events between spatially remote cortical areas” Area 1 Area 2 How to detect the functional connectivity from the fMRI data ? Primary visual cortex, Brodmann area 17 Primary motor cortex, Brodmann area 4 Eini Niskanen, Dept. of Applied Physics, University of Kuopio

8. Principal Component Regression (PCR) • The data is presented as a weighted sum of orthogonal basis functions • The basis functions are selected to be the eigenvectors of either covariance or correlation matrix of the data • The eigenvectors are obtained from eigenvalue decomposition • The first eigenvector is the best mean square fit to the ensemble of the data, thus, often similar to the mean. • The significance of each eigenvector is described by the corresponding eigenvalue Eini Niskanen, Dept. of Applied Physics, University of Kuopio

9. Simulations • A young healthy volunteer was scanned in the Department of Clinical Radiology in the Kuopio University Hospital with a Siemens Magnetom Vision 1.5 T MRI scanner • ~700 T2*-weighted gradient-echo echo-planar (EP) images were acquired with interscan interval of 2.5 seconds • Each EP image comprised of 16 slices, slice thickness 5 mm, in-plane resolution 4×4 mm • A voxel from primary visual cortex (area 1) and primary motor cortex (area2) were selected for analysis and 70 artificial BOLD-responses were added to both voxel time series • Two data sets were created: one set where the response in area 2 was independent on the neuronal delay in area 1, and the other where the response in area 2 was dependent on the neuronal delay in area 1 Eini Niskanen, Dept. of Applied Physics, University of Kuopio

10. Artificial activations • The artificial BOLD responses were generated using the Balloon model • Response amplitude was scaled 5 % above the fMRI time series baseline Eini Niskanen, Dept. of Applied Physics, University of Kuopio

11. Artificial activations • The artificial BOLD responses were generated using the Balloon model • Response amplitude was scaled 5 % above the fMRI time series baseline • Sampling interval was 2.5 seconds = used interscan interval Eini Niskanen, Dept. of Applied Physics, University of Kuopio

12. Artificial activations • The artificial BOLD responses were generated using the Balloon model • Response amplitude was scaled 5 % above the fMRI time series baseline • Sampling interval was 2.5 seconds = used interscan interval • 70 artificial BOLD responses with variable delay were added to both time series Eini Niskanen, Dept. of Applied Physics, University of Kuopio

13. Artificial activations • A delay on response onset time effects on the sampled activation time series Eini Niskanen, Dept. of Applied Physics, University of Kuopio

14. Artificial activations • A delay on response onset time effects on the sampled activation time series • Small delays are seen as change on amplitude in sampled response • Larger delays may change the shape of the sampled response Eini Niskanen, Dept. of Applied Physics, University of Kuopio

15. Simulated data sets • The neuronal delays were assumed to be Χ2distributed in both areas • Two data sets were created: in the dependent case the delay in area 1 was a part of the total delay in area 2, and in the independent case the delay in area 2 did not depend on the delay in area 1 • A constant delay of 300 ms between the responses in area 1 and area 2 was assumed in both data sets Eini Niskanen, Dept. of Applied Physics, University of Kuopio

16. Results • The voxel time series were divided into adequate BOLD responses and an augmented data matrix Z was formed • Data correlation matrix was estimated and its eigenvectors and corresponding eigenvalues were solved RZV = V λ Eini Niskanen, Dept. of Applied Physics, University of Kuopio

17. Results Independent data set Dependent data set λi1 = 0.5968 λi2 = 0.1220 λi3 = 0.0850 λd1 = 0.6055 λd2 = 0.1390 λd3 = 0.0711 Eini Niskanen, Dept. of Applied Physics, University of Kuopio

18. Discussion and conclusions • A PCR based method for studying functional connectivity in fMRI data was presented • Using the method the dependency between two cortical areas can be determined from the second and the third eigenvectors • In case of independent responses, the second and third eigenvectors are required to cover the time variations of the BOLD responses • In case of dependent responses, this time variation can be mainly covered by one eigenvector • The second and third eigenvalues in the independent case are somewhat closer to each other than in the dependent case (Δλi23 = 0.0370 vs. Δλd23 = 0.0679) ⇒ the third eigenvector is not so significant in the dependent case as in the independent case • In the future the method will be tested with real fMRI data and the trial-to-trial information of the BOLD responses is further estimated from the principal components Eini Niskanen, Dept. of Applied Physics, University of Kuopio