Principal Component Regression Approach for Functional Connectivity of Neuronal Activation Measured

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_at_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
2
functional Magnetic Resonance Imaging (fMRI)
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

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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

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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

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Balloon model
volume v '
Inflow f '
Stimulus u
signal s'
deoxyHb q'
Buxton et al. 1998, MRM 39855-864 Obata et al.
2004, NeuroImage 21144-153 Friston et al. 2000,
NeuroImage 12466-477
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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
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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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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 44 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

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Artificial activations

• The artificial BOLD responses were generated
  using the Balloon model
• Response amplitude was scaled 5 above the fMRI
  time series baseline

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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

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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

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Artificial activations

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

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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

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Simulated data sets

• The neuronal delays were assumed to be ?2
  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

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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 ?
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Results
Independent data set
Dependent data set
?i1 0.5968 ?i2 0.1220 ?i3 0.0850
?d1 0.6055 ?d2 0.1390 ?d3 0.0711
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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
• (??i23 0.0370 vs. ??d23 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