Time-Resolved fMRI-fMRS measures simultaneous Neurotransmitters and BOLD-fMRI...
Honors Thesis
1. Washington University in Saint Louis
Undergraduate Honors Thesis
Analysis of Effective Connectivity under
Different Anesthetic Conditions Using
Resting-State fMRI Data
Author:
Wenshuai Ye
Supervisor:
Nan Lin
A thesis submitted in fulfilment of the requirements
for the degree of Bachelor of Arts
in the
Department of Mathematics
December 2013
2. WASHINGTON UNIVERSITY IN SAINT LOUIS
Abstract
Department of Mathematics
Bachelor of Arts
Analysis of Effective Connectivity under Different Anesthetic Conditions
Using Resting-State fMRI Data
by Wenshuai Ye
Functional Magnetic Resonance Imaging (fMRI) is a procedure that measures brain ac-
tivity by detecting associated changes in blood flow. Anesthesiologists are interested in
learning the change in brain functional activity within networks linking different cortical
areas under different sevoflurane concentrations by studying resting-state fMRI data. In
this thesis, we perform a mixed effects vector autoregressive model analysis [1] for such
data to analyze the connectivity between different regions of interest (ROIs). This model
captures the condition-specific connectivity (fixed effect), subject-specific connectivity
(random effect), and run-specific connectivity nested within conditions (random effec-
t). In our analysis, we use a simplified version of the original model in SAS based on
efficiency and feasibility. Our results show that the number of significant effective con-
nectivity effects decreases as the anesthetic concentration gets higher. And at the highest
concentration level in the experiment, no cross-ROI connectivity remains significant.
3. Acknowledgements
I would like to thank Professor Nan Lin for his invaluable assistance and insights leading
to the writing of this paper. My sincere thanks also go to the Professor Ronald Freiwald,
Professor Edward Spitznagel, Professor Jimin Ding, Professor Mladen Wickerhauser,
Doctor Blake Thornton for helpful comments.
ii
5. Chapter 1
Introduction
Functional Magnetic Resonance Imaging (fMRI) is a procedure that measures brain
activity by detecting associated changes in blood flow. Usually volunteers are recruited
to perform a set of tasks or in rest while their brains are being scanned by a functional
Magnetic Resonance Imaging machine. It is a technique developed in the last decade and
is mainly used in the area of psychology and neuroscience, including anesthesiology [2].
In recent years there has been explosive growth in the number of neuroimaging studies
performed using fMRI [3]. The primary form of fMRI uses the blood-oxygen-level-
dependent (BOLD) contrast. As a type of specialized brain scan, it maps neural activity
in the brain or spinal cord of humans or animals by imaging the change in blood flow
related to energy use by brain cells. fMRI analysis is an interdisciplinary field involving
collaboration among people specializing in different skills. From a statistical perspective,
this thesis applies the mixed effects vector autoregressive model to an anesthetic study
based on fMRI data.
1.1 Resting-State fMRI Study
Typical fMRI research focuses on the change in blood-oxygen-level-dependent (BOLD)
signal caused by the neural response to external stimulus. Recently the attention has
been shifted to investigating the features of the baseline state of the brain, which repre-
sents the state of the human brain in the absence of goal-directed neuronal action and
external input [4]. This type of fMRI is called resting-state fMRI. As a relatively new
and powerful discipline, resting-state fMRI evaluates regional interactions that occur
when a subject is not performing explicit tasks. Because brain activity is present even
in the absence of an external prompted task, any brain region will have spontaneous
1
6. Chapter 1. Introduction 2
fluctuations in BOLD signal. By studying the BOLD signal, scientists are usually in-
terested in two types of connectivity: functional connectivity and effective connectivity.
Functional connectivity is defined as statistical dependencies among remote neurophys-
iological events, whereas effective connectivity refers explicitly to the influence that one
neural system exerts over another [5]. A more distinguishable difference is that func-
tional connectivity is defined at the voxel level while effective connectivity is defined for
regions of interest, which is discussed later. Driven by the rapid growth of the interest,
many programs have been created for processing resting state fMRI data accompanied
with these goals. Some common programs include Statistical Parametric Mapping (SP-
M) and Analysis of Functional NeuroImages (AFNI). To process and acquire the resting
state fMRI data with these programs, scientists have come up with many methods, yet
there are two methods that have become the most popular methods for the analysis
of functional and effective connectivity in the brain. One is independent component
analysis (ICA). The other is the method used in this thesis, which is based on regions of
interest (ROIs). Frequently a ROI is drawn on a homogenous area of an MRI image, and
the corresponding voxels are extracted from a coregistered fMRI image. ROI analysis
of the fMRI data requires scientists to pre-specify ROIs, followed by the extraction of
signal from specified ROIs. The selection of ROIs is based on structural or function
features, depending on the motivation to perform the ROI analysis [6]. However, even if
the ROIs have been determined, it is usually difficult to measure the signal within every
ROI. Many imaging experts believe that in order to obtain the information with the
best quality, fMRI and electroencephalography (EEG), a test that measures and records
the electrical activity of the brain, should be used simultaneously. In this thesis, EEG
was adopted in gathering the data.
With the preprocessed data in hand, Statisticians have come up with various com-
plex models to analyze the connectivity between pre-specified regions based on the ROI
analysis and relevant information acquired. One popular model is the mixed effects
vector autoregressive model (ME-VAR).
1.2 Data Collection and Description
Anesthesiologists are interested in learning the change in brain activity under d-
ifferent levels of anesthetic-induced unconsciousness. In this thesis, we analyze fMRI
data from a real study using a mixed model to test whether and how different doses of
anesthesia affect brain functional connectivity. Washington University medical school
acquired and preprocessed the fMRI data by conducting the following experiment.
7. Chapter 1. Introduction 3
Twenty five human volunteers were initially selected for the study. For each volun-
teer, a facemask connected to a semi-closed anesthetic gas machine circuit was placed
over the nose and mouth. Sevoflurane with various concentrations used for induction
and maintenance of general anesthesia was delivered through this machine. Different
sevoflurane inspired concentrations were implemented for corresponding targeted con-
centrations. During these periods, BOLD-MRI signals were recorded. Meanwhile, EEG
signals were recorded continuously to obtain information with higher quality. The re-
sponse was designed as followed.
Every 30 seconds, volunteers were instructed to respond to block-randomized record-
ed auditory commands “Left” or “Right” by squeezing a pressure transducer in the cor-
responding hand. The motor response was recorded and synchronized to vital signs,
EEG waveforms, and MRI images. Responsiveness was defined as the appropriate re-
sponse to command within the allotted 10 seconds of an auditory command, with the
clinical endpoints of interest being loss of responsiveness (LOR) and return of respon-
siveness (ROR). The focus of the study is on the neural signals recorded at anesthetic
concentrations flanking LOR.
The fMRI data have been preprocessed and twenty two subjects for analysis were
selected from the results of a step that regressed out the global average MR signal
during functional connectivity processing. This step was used to ”clean up” the data by
removing putative physiologic sources of common noise in the signals.
We set two specific goals for this study. The first goal is to estimate and test the
significance of effective pairwise connectivity under different levels of anesthetic-induced
unconsciousness. The second goal is to examine the changes in brain connectivity as the
sevoflurane concentration increases.
8. Chapter 2
The Mixed Effects Vector
Autoregressive Model
This section presents an introduction and discussion of the mixed effects vector au-
toregressive model (ME-VAR). The model captures (i.) the expected condition-specific
connectivity matrix (fixed effect) over different runs, (ii.) a subject-specific component
(random effect) to model between-subject variation in connectivity, and (iii.) a run-
specific component (random effect) to model the random effects of different runs nested
within conditions. However, along with the comprehensive and complicated structure
of the model come its shortcomings such as the large number of parameters needed
to be estimated. When fitting the model in SAS, several issues are likely to appear.
Some common problems include “insufficient memory” or “convergence criteria does
not meet”. We performed a simplified version of the original model in SAS to overcome
these problems based on feasibility and efficiency.
2.1 Setup
Consider a brain network with R ROIs. This model is proposed to describe the
BOLD response E(s)(t) (dimension R × 1) under different anaesthetic conditions of the
resting state, that is, conditions with different sevoflurane concentrations. Our focus lies
on the neural signals recorded at anesthetic concentrations flanking loss of responsive-
ness (LOR), a concentration denoted as the clinical endpoint of interest. Five conditions
were initially selected (labeled as condition 1 - condition 5). However, condition 4 and
condition 5 have the same sevoflurane concentrations as condition 2 and condition 1 re-
spectively. As such, we only focus on the first three conditions with different sevoflurane
4
9. Chapter 2. The Mixed Effects Vector Autoregressive Model 5
concentrations. For a specific subject s, the model is written as
E(s)
(t) =
P
k=1
[β
(s)
1j,kW
(s)
1 + β
(s)
2j,kW
(s)
2 + β
(s)
3j,kW
(s)
3 ]E(s)
(t − k) + (s)
(t), (2.1)
where t = P +1, ..., T are the time points up to time T and s = 1, ..., S denotes the subject
with S subjects in total. The vector (s)(t) (dimension R × 1) is a white noise process
with E( (s)(t)) = 0 and Cov( (s)) = Γ (dimension R×R). We assume that Cov( (s)) = Γ
does not change over time and is constant across all participants. k = 1, ..., P denotes
the time lag with maximum order P, and j represents the experimental run, which is
nested within conditions. Other basic elements are more complicated and important.
To understand the model in a more comprehensive way, we enumerate other detailed
elements in the following.
The subject-specific indicator parameter for condition i, denoted as W
(s)
i
This parameter is used as a tool to examine brain connectivity across different
conditions. Suppose that at time t0 a stimulus, a change of sevoflurane concentrations
for condition i was presented; followed by a different sevoflurane concentrations, denoted
as condition i at the time t1. We specify the function W
(s)
i as a time window on which
the brain connectivity present is attributed to condition i in subject s. In this case, this
time window takes a value of 1 in the interval [t0, t1] and takes the value 0 elsewhere.
For example, if the anesthetic concentration in the interval [t0, t1] remains unchanged,
then the corresponding W
(s)
i takes a value of 1.
Optimum for the maximum lag order P
The optimal order can be objectively selected using information theoretic criteria:
Bayesian Information Criterion (BIC), Akaike Information Criterion (AIC), and AIC
with a correction for infinite small sample sizes (AICC). BIC penalizes model complexity
more severely compared with the other two approaches. We take BIC as the desirable
criterion to simplify the model in SAS for the complexity of the model in our analysis.
We first use P = 3. If every parameter from every region turns out estimable with this
maximum order, we choose both higher and lower maximum orders and compare their
BIC. On the other hand, if some of the parameters cannot be estimated with P = 3,
only lower maximum orders should be used. To sum up, the first priority for choosing
the model is to guarantee that every single parameter we are interested can be estimated
in SAS. Then, from these models, we select the one with the lowest BIC.
The subject-specific direct connectivity matrix at lag k, denoted as β
(s)
ij,k
The subject-specific connectivity matrix at lag k, denoted β
(s)
ij,k, includes a subject-
specific random effect to describe the variability in the connectivity pattern across dif-
ferent subjects. This R × R matrix quantifies exactly how E(s)(t − k) directly predicts
10. Chapter 2. The Mixed Effects Vector Autoregressive Model 6
E(s)(t) under experimental condition i. It also includes an indicator j denoting repli-
cates (runs) of the experiment nested in conditions. As a result, β
(s)
ij,k contains both
random components and fixed components. To correctly specify the model in SAS,
it is important to separate them, that is, to decompose β
(s)
ij,k into random and fixed
components.
Before decomposition, we demonstrate the parameters of the model in vector and
matrix forms. Below is an example to illustrate the matrices and the vectors in the
model under condition 1.
E(s)(t)(1)
E(s)(t)(2)
...
E(s)(t)(R)
=
P
k=1
β
(s)
1j,k(1, 1) β
(s)
1j,k(1, 2) · · · β
(s)
1j,k(1, R)
β
(s)
1j,k(2, 1) β
(s)
1j,k(2, 2) · · · β
(s)
1j,k(2, R)
...
...
...
...
β
(s)
1j,k(R, 1) β
(s)
1j,k(R, 2) · · · β
(s)
1j,k(R, R)
×
E(s)(t − 1)(1)
E(s)(t − 1)(2)
...
E(s)(t − 1)(R)
+ (s)
(t) (2.2)
2.2 Decomposition
Modeling variation across replicates
One important element in the connectivity matrix β
(s)
ij,k is the subscript j indicating
that brain connectivity is allowed to vary over runs. Here, we decompose the connectivity
matrix into two components.
β
(s)
ij,k = β
(s)
i,k + φ
(s)
i(j),k, (2.3)
where β
(s)
i,k is the condition-subject-specific connectivity matrix and φ
(s)
i(j),k is the run-
specific effect nested within conditions or subjects. It models the deviation of each run
from the common condition-subject-specific connectivity matrix associated to lag k. The
elements of the matrix φ
(s)
i(j),k are assumed to be mutually independent normal random
variables.
φ
(s)
i(j),k(r, r ) ∼ N(0, σ2
k(r, r ) + σ 2
k (r, r )) (2.4)
where σ2
k(r, r ) comes from the subject effect and σ 2
k (r, r ) comes from the run effect.
Modeling variation across subjects
Another important element in the connectivity matrix β
(s)
ij,k is the superscript (s)
indicating that brain connectivity is allowed to vary over subjects. This random com-
ponent can be separated from the connectivity. It allows us to further decompose β
(s)
i,k
into a fixed component and a random component.
β
(s)
ij,k = βi,k + b
(s)
k + φ
(s)
i(j),k, (2.5)
11. Chapter 2. The Mixed Effects Vector Autoregressive Model 7
where βi,k is the expected condition-specific connectivity matrix and b
(s)
k is the subject-
specific effect which models an individual subject’s deviation from the common population-
specific connectivity matrix associated to lag k. We model the elements of the matrix
b
(s)
k as identically distributed independent variables following normal distribution.
b
(s)
k (r, r ) ∼ N(0, σ2
k(r, r )). (2.6)
Decomposition of the ME-VAR model
To illustrate the features of the model, we assume lag order to be P = 1 for simplicity
so that conditional mean of the observed BOLD signal at time t depends only on the
observations at the previous time point t − 1. The model for subject s is specified as
E(s)
(t) = [β
(s)
1j,1W
(s)
1 + β
(s)
2j,1W
(s)
2 + β
(s)
3j,1W
(s)
3 ]E(s)
(t − 1) + e(s)
(t). (2.7)
From the decomposition derived, we can decompose the connectivity matrix into a ran-
dom and two fixed components. The model for subject s becomes
E(s)
(t) =[(β1,1 + b
(s)
1 + φ
(s)
1(j),1)W
(s)
1 + (β2,1 + b
(s)
1 + φ
(s)
2(j),1)W
(s)
2
+ (β3,1 + b
(s)
1 + φ
(s)
3(j),1)W
(s)
3 ]E(s)
(t − 1) + (s)
(t).
(2.8)
However, in real study, even though common variance have been assumed across
subjects and runs, the combined effects of all the factors may still paralyze the software.
In this case, we may have to simplify the model by ignoring the run-specific connectivity
matrix (random effect) and analyze the data for each replicate separately. For each run,
the model then becomes
E(s)
(t) =
P
k=1
[β
(s)
1,kW
(s)
1 + β
(s)
2,kW
(s)
2 + β
(s)
3,kW
(s)
3 ]E(s)
(t − k) + (s)
(t). (2.9)
Without the run-specific connectivity component, β
(s)
1,k can only be decomposed into a
random component and a fixed component;
β
(s)
i,k = βi,k + b
(s)
k . (2.10)
2.3 Hypothesis testing and Effect Estimates
As mentioned, there are two goals for our analysis. The first one is to estimate and
test the significance of effective pairwise connectivity. This process contains 50 × 50 × 3
12. Chapter 2. The Mixed Effects Vector Autoregressive Model 8
hypothesis testings. The other goal is to examine the changes in brain connectivity
across conditions. The process also contains 50 × 50 × 3 hypothesis testings.
Testing for significance of connectivity
Our interest is to determine whether the past activity at ROI r during condition
i can significantly explain the current activity at ROI r. Given For the model with
maximum order P, the null and the alternative hypothesis can be written as
H0 : βi,1(r, r ) = βi,2(r, r ) = ... = βi,P (r, r ) = 0,
and H1 : At least one of the coefficients parameters are not 0.
(2.11)
βi,k(r, r ) denotes the expected value of β
(s)
ij,k(r, r ), which is the expectation of the random
effect run indicated by the subscript j and the random effect subject indicated by the
superscript (s). In this case, we can say that activity at ROI r “Granger causes” the
activity at ROI r if the null hypothesis is rejected. That is, the activity at ROI r
provides statistically significant information about future activity at ROI r.
Testing for changes of connectivity across conditions
Our second interest is to investigate the differences of brain connectivity across
different conditions. As the sevoflurane concentration changes, we need to determine
if the connectivity within networks linking the thalamus, frontal and parietal cortical
areas change too. The null and the alternative hypothesis can be written as
H0 : βi,k(r, r ) = βi ,k(r, r ),
and H1 : βi,k(r, r ) = βi ,k(r, r ).
(2.12)
This hypothesis testing measures the difference between the expected causality effect of
the brain activity at ROI r and lag order k on ROI r under condition i and that under
condition i . If the null hypothesis is rejected, we can say that the brain connectivity
between ROI r and ROI r under condition i is different from that under condition i .
Both hypothesis testings contain multiple correlated testings. Therefore, it is nec-
essary to control the expected proportion of incorrectly rejected null hypotheses. False
Discovery Rate (FDR) is used to correct for multiple comparisons. Compared with Fam-
ilywise Error Rate (FWER), FDR increases the power at the cost of increasing the rate
of type 1 errors. It is particularly useful in the analysis using datasets with relative-
ly small sample sizes and large numbers of variables being measured per sample. The
threshold q-value for the FDR is 0.1.
13. Chapter 3
Connectivity Analysis of fMRI
Data
This chapter presents the result of our study. We use statistical packages R and
SAS 9.2 to perform the analysis. R is mainly used for structuring the dataset and graph-
ing relevant plots, whereas SAS is the primary tool to analyze the dataset under proc
MIXED. Under models that incorporate the run-specific connectivity matrix, SAS shows
insufficient memory of the computer. Therefore, to guarantee that every parameter is
estimable in SAS, we simplify the model by using the data from the first run. That is,
we only fitted the model to the first replicate of the data. Moreover, models with 2 lags
and 3 lags do not guarantee that every parameter is estimable. In this situation, we pick
the model with 1 lag eventually when specifying it in SAS, regardless of the BIC.
3.1 The Granger Causality Test
We test the significance of each element in the connectivity matrices βi,k to investi-
gate the lag cross-dependence structure in each condition. k equals 1 here since we fitted
the model with only 1 lag. To identify the effective connectivity in pairs of brain regions,
we perform a Granger causality test, as discussed in Chapter 2. For each condition, a
heatmap (Figure 3.1) containing information on the effect of all regions of interest(ROIs)
is presented. Column ROIs are response ROIs. Row ROIs represent regions that help
us predict the influence on the response ROIs. In other words, Column regions are the
response in our model, whereas row regions are regions with a time lag (lag 1).
Each heatmap in Figure 3.1 represents the connectivity between different ROIs under
each condition. Black here denotes that the Granger causality is significant after FDR
9
14. Chapter 3. Connectivity Analysis of fMRI Data 10
Figure 3.1: Granger Causality Heatmaps
correction. As for those insignificant effects, we use grey and white colors. The color
gets deeper as the connectivity gets stronger. We notice that the lag dependence of a
ROI on its own region is always significant under any condition. Besides, there are 19
significant cross-dependence effects under condition 1, as shown in the heatmap. Under
condition 2 with the increase of sevoflurane concentration, the number of significant
cross-dependence effects reduces to 9, all of which are not the same ROIs as those shown
in condition 1. As the sevoflurane concentration increases further, none of the cross-
dependence effects becomes significant. The only significant lag dependence of a ROI
is its own region. The details of the significant cross-dependence effects are listed in
Appendix A. The overall pattern implies that as the concentration of sevoflurane goes
15. Chapter 3. Connectivity Analysis of fMRI Data 11
up, the overall connectivity between two ROIs decreases. To improve the accuracy of
our findings, we implement a test of changes in connectivity across different conditions.
3.2 Connectivity Changes Across Conditions
To investigate whether there is a change in connectivity across conditions, we test
if the two connectivity matrix βi,k and βi ,kare equal as the sevoflurane concentration
changes. This procedure is implemented in SAS 9.2. We then used the “qvalue” package
in R to calculate the corrected threshold for the p-values by converting them to q-values.
It turns out that none of the q-values are significant in this case. As a result, none of
the connectivity changes is actually significant. However, it is still valuable to dig out
more information based on SAS outputs and heatmaps. Our focus lies primarily on the
significant connectivity based on the Granger causality test discussed in the previous
section. If the connectivity does not exist, it does not make much sense to discuss the
changes in connectivity further.
These heatmaps in Figure 3.2 represent the connectivity changes under different
conditions. Darker colors indicate that the changes are larger. However, since none of the
changes are significant, black does not mean the changes are significant. It only implies
the changes are strong. The heatmaps help us to identify patterns. As shown, there is
no explicit pattern in the first two heatmaps. However, with a more significant increase
in the sevoflurane concentration, the connectivity changes become noticeable as shown
in the third heatmap. The diagonal color gets deeper in general compared with the first
two heatmaps. From the pattern, we guess that the changes in connectivity are in one
direction - either the connectivity gets stronger when the sevoflurane concentration goes
up, or it gets weaker. Figure 3.1 shows that the connectivity weakens with the increase
in sevoflurane concentration. However, since our focus is on the significant connectivity,
it is necessary to investigate those values to see the direction of connectivity changes.
To find out the direction, we referred to the significant estimated values of the Granger
causality effect under all conditions. From Figure 3.1, we can see no cross-dependence
under condition 3. As a result, for each ROI, we only focused on the causality effects
from itself with a time lag (lag 1).
Appendix B shows the estimated effect of each region under each condition. From
condition 1 to condition 2 as the sevoflurane concentration increases, the estimated ef-
fects of the connectivity go up except for ROI36, ROI42, and ROI46. However, from
condition 2 to condition 3, as the sevoflurane concentration increases further, the con-
nectivity trend in general becomes vaguer, though the connectivity still weakens in total
as shown in Figure 3.3. Each line represents a sevoflurane concentration across ROIs.
16. Chapter 3. Connectivity Analysis of fMRI Data 12
Figure 3.2: Connectivity Changes Heatmaps
The horizontal axis denotes ROIs, whereas the vertical axis denotes estimated effects for
each corresponding ROIs.
18. Chapter 4
Conclusion
In this thesis, we explored the effect of anesthesia on brain effective connectivity. We
used a mixed effects vector autoregressive model (ME-VAR) to analyze a resting-state
fMRI dataset. This model captures the expected condition-specific component (fixed
effect), the subject specific component (random effect), and the run-specific component
(random effect). Theoretically, this is a comprehensive model for the analysis of the
resting-state FMRI data. However, when applying to large datasets with many ROIs,
it exceeds the limit of SAS and hence simplification of the model is necessary. Based
on feasibility, we removed the run-specific component from the model and only demon-
strated the result from the first replicate of the dataset. Since evaluation or testing of a
single item does not allow for item-to-item variation and may not represent the batch or
process, the model without a run-specific matrix is likely to contain bias. Moreover, even
with the simplified model and data information, the maximum lag order is restricted to
1 in SAS, which is another limit of the model in this analysis.
Based on the heatmap, the result shows that 69 Granger causality effects are signif-
icant under condition 1. 50 of them are effects within ROIs over time. Under condition
2, 59 Granger causality effects are significant. Among them, 50 effects within ROIs over
time are still significant. As the sevoflurane concentration goes up further (condition
3), there are only 50 significant Granger causality effects, all of which are effects within
ROIs over time.
We then tested for the significance of the connectivity changes. It turns out that
none of the changes is significant. Despite the insignificance presented, we can still find a
trend that from condition 1 to condition 2 with the increase in sevoflurane concentration,
the connectivity generally becomes weaker, with few exceptions. From condition 2 to
condition 3, the direction of the changes become vaguer. However, the connectivity still
gets weaker on aggregate. In the future study, the difference of sevoflurane concentration
14
19. Chapter 4. Conclusion 15
among conditions can be more substantial in order for us to visualize the connectivity
changes better.
22. Bibliography
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[2] Nicole A. Lazar, William F. Eddy, Christopher R. Genovese, and Joel Welling. Sta-
tistical issues in fmri for brain imaging. International Statistical Review, 69:105127,
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[3] Martin A. Lindquist. The statistical analysis of fmri data. Statistical Science, 23:
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[4] J. S. Damoiseaux, S. A. R. B. Rombouts, F. Barkhof, P. Scheltens, C. J. Stam,
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2:6770, 2007. doi: 10.1093/scan/nsm006.
18
![WASHINGTON UNIVERSITY IN SAINT LOUIS
Abstract
Department of Mathematics
Bachelor of Arts
Analysis of Effective Connectivity under Different Anesthetic Conditions
Using Resting-State fMRI Data
by Wenshuai Ye
Functional Magnetic Resonance Imaging (fMRI) is a procedure that measures brain ac-
tivity by detecting associated changes in blood flow. Anesthesiologists are interested in
learning the change in brain functional activity within networks linking different cortical
areas under different sevoflurane concentrations by studying resting-state fMRI data. In
this thesis, we perform a mixed effects vector autoregressive model analysis [1] for such
data to analyze the connectivity between different regions of interest (ROIs). This model
captures the condition-specific connectivity (fixed effect), subject-specific connectivity
(random effect), and run-specific connectivity nested within conditions (random effec-
t). In our analysis, we use a simplified version of the original model in SAS based on
efficiency and feasibility. Our results show that the number of significant effective con-
nectivity effects decreases as the anesthetic concentration gets higher. And at the highest
concentration level in the experiment, no cross-ROI connectivity remains significant.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)