FINSIG'05 25/8/2005

1Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Principal Component Regression Principal Component Regression Approach for Functional Connectivity Approach for Functional Connectivity of Neuronal Activation Measured by of Neuronal Activation Measured by

Functional MRIFunctional MRI

1University of Kuopio

Dept. of Applied Physics

P.O.Box 1627, FIN-70211 Kuopio

FINLAND

†E-mail: Eini.Niskanen@uku.fi

Eini I. Niskanen1,†, Mika P. Tarvainen1, Mervi Könönen2,

Hilkka Soininen3, and Pasi A. Karjalainen1

2Kuopio University HospitalDept. of Clinical NeurophysiologyP.O.Box 1777, FIN-70211 Kuopio

FINLAND

3University of KuopioDept. of Neuroscience and Neurology

P.O.Box 1627, FIN-70211 KuopioFINLAND

FINSIG'05 25/8/2005

2Eini Niskanen, Dept. of Applied Physics, University of Kuopio

functional Magnetic Resonance Imaging (fMRI)functional Magnetic Resonance Imaging (fMRI)

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3Eini Niskanen, Dept. of Applied Physics, University of Kuopio

fMRI signalfMRI 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

FINSIG'05 25/8/2005

4Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Blood Oxygenation Level Dependent (BOLD) Blood Oxygenation Level Dependent (BOLD) responseresponse

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

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5Eini Niskanen, Dept. of Applied Physics, University of Kuopio

BOLD responseBOLD 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

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6Eini Niskanen, Dept. of Applied Physics, University of Kuopio

0outf

Balloon modelBalloon model

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FINSIG'05 25/8/2005

7Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Functional connectivityFunctional connectivity

“the temporal correlations among neurophysiological events between spatially remote cortical areas”

Primary visual cortex, Brodmann area 17

Primary motor cortex, Brodmann area 4

?

Area 1 Area 2

How to detect the functional connectivity

from the fMRI data

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8Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Principal Component Regression (PCR)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

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9Eini Niskanen, Dept. of Applied Physics, University of Kuopio

SimulationsSimulations

• 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

FINSIG'05 25/8/2005

10Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Artificial activationsArtificial activations

• The artificial BOLD responses were generated using the Balloon model

• Response amplitude was scaled 5 % above the fMRI time series baseline

FINSIG'05 25/8/2005

11Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Artificial activationsArtificial 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

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12Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Artificial activationsArtificial 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

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13Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Artificial activationsArtificial activations

• A delay on response onset time effects on the sampled activation time series

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14Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Artificial activationsArtificial 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

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15Eini Niskanen, Dept. of Applied Physics, University of Kuopio

• The neuronal delays were assumed to be Χ2 distributed 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

Simulated data setsSimulated data sets

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16Eini Niskanen, Dept. of Applied Physics, University of Kuopio

ResultsResults

1. The voxel time series were divided into adequate BOLD responses and an augmented data matrix Z was formed

2. Data correlation matrix was estimated

and its eigenvectors and corresponding eigenvalues were solved

RZV = V λ

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17Eini Niskanen, Dept. of Applied Physics, University of Kuopio

ResultsResults

Independent data set Dependent data set

λi1 = 0.5968

λi2 = 0.1220

λi3 = 0.0850

λd1 = 0.6055

λd2 = 0.1390

λd3 = 0.0711

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18Eini Niskanen, Dept. of Applied Physics, University of Kuopio

Discussion and conclusionsDiscussion 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