Appendix
Independent Component Analysis and fMRI Imaging
Christopher G. Green, Victor Haughton, and Dietmar Cordes
Introduction
Independent component analysis (ICA)1–9 is a statistical method for estimating a collection of unobservable signals from observations of their mixtures. This scenario falls into the more general class of blind source separation (BSS) problems, in which we wish to recover the original source signals and the method of mixing solely from mea- surements of their mixtures and certain assumptions about the sources.
Independent component analysis, which assumes that the sources are statistically independent, has emerged as a powerful tool for solving (BSS) problems. It has also shown great promise in the fields of exploratory data analysis3and feature extraction.10
The classical example of a blind source separation problem is the cocktail party problem, in which there are N distinct conversations being held at a party and M microphones placed throughout the room recording the conversations. The recorded sounds are linear mixtures of the actual conversations, and the task is to recover the individual conversations from the mixtures. Separating and selectively tuning to the individual conversations has proven to be quite difficult computa- tionally. Independent component analysis is one of many methods that attempt to perform this separation, and, in the special case of instan- taneous mixing (no time delays and no echoes), arguably one of the more successful.
Independent component analysis is also an example of unsupervised learning. In unsupervised learning, a representation of the data is con- structed from the data alone, that is, without outside assistance from a
“teacher.” (Contrast this with supervised learning, where feedback from an external omniscient observer is used to modify the representation iteratively.) Learning a representation of the data is equivalent to esti- mating the hidden factors responsible for the data. It can be proven that linear ICA provides a linear representation of the data that is as struc- tured as possible from an information-theoretic standpoint.7
Independent component analysis was pioneered in the early 1980s by Herault, Jutten, and Ans,1and later advanced by Common,3Bell and
503
Sejnowski,4 and Hyvärinen and Oja,5 among others. The field is growing in popularity and applicability, as is evidenced by the recent appearance of texts devoted to the subject.7–9
Review of Relevant Mathematical Concepts
Introduction
In the present work, it will be assumed that the reader is familiar with elementary mathematical concepts such as random variables, expecta- tion, and variance. A thorough review of these concepts can be found in any standard textbook on probability.
For brevity, the following notational conventions will be adopted.
Random variables will usually be denoted by X, while X will usually stand for a random vector of dimension M. Probability density func- tions (pdfs) will be denoted by p(X) or p(X), as appropriate. The expec- tation operator will be denoted by E·Ò. We will use m to denote the population mean E·XÒ of the distribution and to denote the population variance E·(X-m)2Ò.
Kurtosis
Kurtosis is a mathematical quantity that roughly describes the peakedness of a distribution. Kurtosis usually is normalized so that a Gaussian distribution has a kurtosis of zero. Random variables hav- ing a positive kurtosis are called supergaussian, whereas those with a negative kurtosis are called subgaussian. Supergaussian random vari- ables are characterized by pdfs that are relatively large near their mean m and have heavier tails than a Gaussian. A typical example is a random variable with a Laplace distribution (Figure A.1). Subgaussian random variables, on the other hand, typically have flat or bimodal distribu- tions. The uniform distribution (shown in Figure A.1 for the interval [-6,6]) is an example of a subgaussian distribution.
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Figure A.1. Examples of supergaussian, Gaussian, and subgaussian distributions.
Entropy and Mutual Information
In information theory, entropy measures the average amount of infor- mation that an observation of X yields. The entropy of X is given by the equation
(A.1) Entropy is small for distributions whose mass is concentrated on certain values (for example, the Laplace distribution shown in Figure A.1): because the values of a random variable coming from such a distribution are known a priori to be localized to small regions with high probability, observation of these variables does not convey much information.
On the other hand, it can be demonstrated that of all distributions with zero mean and a fixed covariance matrix S the zero-mean multi- variate Gaussian distribution with covariance matrix S has the largest entropy.12Hence, from an information-theoretic viewpoint, the Gauss- ian distribution is the most random of all distribution.17
A closely related concept is that of mutual information, which mea- sures the amount of information about one random variable that is con- tained in another. Equivalently, mutual information is the amount of uncertainty in one random variable that is cleared up by observation of another random variable. It can be shown that the mutual informa- tion I[X; Y] between two random vectors X and Y is always nonnega- tive, and equals zero precisely when X and Y are independent. This agrees with our intuition about independent random variables—
observation of either of a pair of independent random variables conveys no information about the other, so their mutual information should be zero.
Principal Component Analysis
Principal component analysis (PCA) computes a linear transformation of the observed data such that the resulting observations are uncorrelated.
The covariance matrix S of the data has a factorization of the form S = PLPT, where L is a diagonal matrix and P is matrix such that P-1= PT 13. The transformation Y= PT(X- X¯) then yields a coordinate system in which the components of Y have mean zero and are uncorrelated.
Independent Component Analysis
Recall that the aim of ICA is to estimate a collection of unobservable source signals S = [s1. . . sN]Tsolely from measurements of their (possi- bly noisy) mixtures X = [x1. . . xM]Tand certain assumptions about the sources. In the simplest formulation of ICA, linear mixing can be assumed, that is, that there exists an M ¥ N mixing matrix A such that X= AS. For the linear ICA problem, M ≥ N is usually assumed, so that Ahas rank N. (The need for this condition arises from standard results in matrix algebra on the solvability of linear equations.13) When M < N
H[ ]X ∫ -Elogp( )X .
(the so-called underdetermined case), modifications must be made to standard linear ICA methods.14To simplify this presentation, attention will be restricted to the case of a square (N ¥ N) mixing matrix for the remainder of this article.
Obviously, given only X, it is impossible to determine the pair (A, S) uniquely; certain structural assumptions must be made about A and S to be able to solve this problem. In ICA, it is assumed that the source signals S are mutually statistically independent, that is, that the joint probability density function p(S) of S equals the product of the mar- ginal probability density functions pi(si) of the individual sources.
Roughly speaking, this assumption means that information about any one signal siconveys no information about any other signal sj, i π j.
Some caveats regarding ICA are to be noted:
(1) We can only recover the sources up to a scale change, for we may multiply any source by any non-zero number so long as we divide the corresponding column of A by the same number. Moreover, the order of the sources is ambiguous, since permuting the rows or columns of Adoes not affect our ability to solve X= AS.
(2) Independent component analysis cannot separate a mixture of Gaussian signals. This follows from the observations that (a) a sum of Gaussian random variables is another Gaussian random variable; and (b) the Gaussian distribution is rotationally symmetric (see Figure A.2).
Therefore, the directions of the original signals cannot be inferred from rotations of the mixture alone. The upshot of this is that ICA can extract one Gaussian source from a data set; multiple Gaussian sources, if present, will be agglomerated in this one source.
(3) Independent component analysis assumes that statistical prop- erties of the source signals are unchanging over time. In practice, this is not always true, and it is currently unknown exactly how the break- down of this assumption affects ICA.
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Figure A.2. Scatterplot of a mixture of Gaussian signals. The cloud is rota- tionally symmetric, so no amount of rotation will yield any new information.
It is sufficient to estimate only the mixing matrix A, for then the esti- mate of the sources is simply S= A-1X. It turns out that it is easier (from a numerical standpoint) to estimate W∫ A-1, so that the source esti- mate is given by S= WX.
The general idea underlying ICA algorithms is to find the unmixing matrix W that makes the estimate sources WX as independent as pos- sible. This is achieved by constructing a contrast function (a function to be optimized) involving the unmixing matrix W that quantifies the independence of the estimated sources. This function, when optimized with respect to W, gives not only the best estimate of W, but also the most statistically independent sources.
There are several different flavors of ICA. Their differences arise from their measure of independence and/or their contrast functions. The one that will be discussed here is called the Information Maximization method.
Information Maximization
The Information Maximization (or Infomax, for short) principle is based upon a study by Nadal and Parga15demonstrating that a non- linear network transmits the most information when its weights and transfer function are chosen to produce outputs that are as statistically independent as possible. Intuitively, this statement makes sense: the closer the outputs are to independent, the less redundancy between them and the more information they can carry. The (Bell and Sejnowski) Infomax algorithm4,8is a learning rule for a neural network that per- forms this maximization.
To use the Infomax algorithm, the unmixing process is viewed as a neural network whose inputs are the observations X and whose outputs are the sources S. The observations are multiplied by W, a matrix containing the weights of the neural network, and fed-forward to a nonlinear function g = (g1, . . . , gN) (see Figure A.3). The nonlinear function g, through its Taylor series expansion, allows the network to utilize information contained in the higher-order statistics of U= WX.8 In view of Nadal and Parga’s result, we seek to maximize the joint entropy of the output sources over all possible weight matrices W.
Upon carrying out the requisite manipulations, we arrive at the Infomax learning rule of Bell and Sejnokswi4,8,16
(A.2) where a is an adjustable scalar (the learning rate) and the score func- tion j(u) is defined as
(A.3)
j ∂
u ∂
u u ( )= - u
( ) 1 ( ) p
p .
W W W
W I u u W
new old
T old
, ,
= +
= [ - ( ) D]
D a j
Figure A.3. Neural network depiction of ICA.
The score function is implicitly a function of the source densities, and therefore plays a crucial role in determining what kinds of sources ICA will detect. In the original study by Bell and Sejnowski,4 the nonlinearity was fixed to be a logistic function. This choice is generally good for detecting supergaussian distributions, but cannot be used to detect subgaussian or skewed distributions. Shortly thereafter, Girolami and Fyfe17 and Lee and colleagues18 derived an extended Infomax algorithm that overcame this limitation. The extended Infomax algorithm is more robust than the original Infomax algorithm in the sense that it is capable of separating mixtures of supergaussian and subgaussian sources.
Finally, it is noted that the Infomax learning rule can be derived by many other approaches, such as Maximum Likelihood Estimation.8
ICA and fMRI
Introduction
In this section, a description of how ICA may be used to analyze func- tional magnetic resonance imaging (fMRI) data will be provided. Func- tional MRI data consist of a series of three-dimensional (3D) matrices collected over time. At each time point, the MR-induced signals from the brain are sampled over a discrete grid of volume elements (voxels).
In the most common setup, the entries in the data matrix for a given time point are the magnitudes of the measured signals at the corre- sponding voxels. The signals obtained from the scanner are assumed to be a linear mixture of signals arising from various biological processes, some of which are presumed to be a associated with the administered functional task. We desire to recover spatial activation maps and time courses of activity related to the functional task in ques- tion. Independent component analysis provides one manner of accomplishing this goal.20
Because the fMRI data set contains both spatial and temporal infor- mation, it is theoretically possible to look for signals independent over space (spatial ICA) or over time (temporal ICA). In practice, however, it is very difficult to obtain accurate and meaningful results from a tem- poral ICA of fMRI data due to severe dimensionality issues (more will be said about this later). Therefore, spatial ICA is the method of choice for fMRI.
A spatial ICA, performed on the full fMRI dataset, will yield statis- tically independent spatial maps (areas of brain activation) and their corresponding time courses. The consequences of this decomposition are twofold: (1) the voxels of a given map effectively function as a mathematical unit; and (2) the activity produced by each such unit is independent of the activity produced by any other unit.
The interpretation of these abstract units requires researcher inter- vention. Spatial ICA assumes only that the source signals underlying the observed signals have independent distributions over space (an assumption justified from fMRI, positron emission tomography (PET), and electroencephalogram (EEG) studies demonstrating that brain 508 C.G. Green et al.
activity is sparse and highly localized8); it does not make any assump- tions about underlying functional organization of the brain. It is up to the researcher to identify physiologically relevant components.
Typically, some knowledge of the task design is needed to make this identification (see below).
As stated in earlier, ICA is ideal for exploratory data analysis.
Independent component analysis, in contrast to traditional confir- matory (hypothesis-based) methods, can be used to examine data in the absence of a priori knowledge of the hemodynamic response or of the paradigm. Furthermore, whereas simple correlation with a refer- ence function can only detect consistently task-related (CTR) activity, ICA is capable of detecting CTR, transiently task-related (TTR), slowly varying, quasiperiodic, and movement-related activity.20
Another important difference between ICA and confirmatory methods is the lack of an associated level of significance.20This is not a significant drawback, however, as one can determine the statistical significance of a spatial map using advanced statistical techniques such as the jackknife or the bootstrap.20One can also use receiver operating characteristic (ROC) methods to evaluate the accuracy of independent components.21
Independent component analysis should be considered complemen- tary to available hypothesis-based methods. It can be used to gain valu- able insight into the data and can provide a researcher with many new ideas for further exploration.
Implementation
The data from a scan are placed into a matrix X indexed by time and voxel: the columns of X correspond to time courses of individual voxels while its rows correspond to the voxel intensities in a given volume (see Figure A.4). Due to its simplicity and the size of the data, the linear ICA model is usually employed for fMRI: we seek an unmixing matrix W such that the source estimates S are maximally statistically independent.
To simplify the calculations, the mean of each input signal is removed. To improve the convergence of ICA methods further, the input data are then whitened: the input signals are decorrelated and nor- malized to unit variance.
Figure A.4. Graphical depiction of ICA setup.
In this model, the number of sources estimated is equal to the number of volumes: if 200 volumes are collected, then a naïve spatial ICA will extract 200 sources. Some of these sources will be task-related;
others will correspond to noise sources. When the functional task has structure, such as periodicity, identification of task-related components is easy: the correlation between the reference function for the paradigm and the associated time course of the spatial independent component is simply computed. Only these few components need then be investi- gated further. When more complicated paradigms are used, however, it can be difficult to identify task-related components automatically, and we must fall back to the tedious approach of examining each spatial map by hand.
As has been mentioned earlier, ICA is typically not performed in the time domain for fMRI data. If the linear model described above were used for temporal ICA, we would extract as many temporal sources as there are voxels in our grid. For example, with a 64 ¥ 64 acquisition matrix and 10 slices, there are 40960 voxels in the data set. After stan- dard thresholding (at 10% of maximum intensity), approximately 10000 voxels remain. Thus, temporal ICA would attempt to extract 10000 sources. There are two problems with this approach: first, the whiten- ing step requires the computation of the correlation matrix, which, in this example, would contain 10000 ¥ 10000 entries. Hence, this approach is not computationally feasible on the average computer.
Second, it is highly unlikely that there are that many temporally inde- pendent signals in the brain; most of the sources extracted by tempo- ral ICA will be artifactual. Some form of dimensionality reduction must be employed. Principal component analysis, the most common reduc- tion method, again requires computations involving a large matrix. In addition, there are other drawbacks to using PCA for dimension reduc- tion (discussed below). Thus, temporal ICA has not yet seen significant usage in fMRI.
Current Applications of the ICA Method in fMRI
Independent component analysis may be a useful adjunct to conven- tional methods for the processing of fMRI data sets in which the time course of signal intensity within each voxel is compared to a ref- erence function. In special circumstances, the application of ICA to the data sets may produce more complete or better maps than the con- ventional data analysis methods. When the hemodynamic response for a specific task is not known or cannot be predicted accurately, ICA may be useful. For example, 20 seconds of finger tapping produces a tran- sient activation in the putamen that contrasts with the sustained acti- vation in the sensorimotor cortex and supplementary motor area.22 When the conventional boxcar reference function was applied to the analysis of finger-tapping tasks, the putamen activation was not as consistently demonstrated, as was that in the sensorimotor cortex.
Independent component analysis demonstrated the activation in the putamen and the time course of that activation. Because the hemody- namic response may vary from one brain region to another, ICA may 510 C.G. Green et al.
identify regions of activation that are not found with the boxcar reference function.
In clinical studies, the hemodynamic response may be difficult to predict because the patient does not comply with the instructions or the patient moves during the performance of the task. Either error or neurologic deficit may alter a hemodynamic response or the timing of the task performance. For example, Figure A.5 illustrates the fMRI maps obtained with conventional reference function and with ICA in a subject who misunderstood the cues to initiate and to terminate finger tapping. The maps prepared with ICA showed more activation in the sensorimotor cortex and showed the time course of the activation iden- tified with the program. The time course illustrates that after the initial finger-tapping epoch, the subject started finger tapping when asked to stop and stopped when asked to start.
When the subject of an fMRI study moves his/her head, the effects of motion confound the data. Conventional reference functions may fail to identity activation effectively in these cases. In many of these cases, ICA identified components due to the motion and components due to the activation. The fMRI maps prepared with ICA are superior in these cases to the ones created with conventional reference functions (Figure A.6).
Current Limitations of the ICA Method in fMRI
The most pressing obstacle to the use of ICA in fMRI is the dimen- sionality problem. The linear ICA model assumes the number of sources is equal to the number of volumes (time points), but there is strong experimental evidence that actual dimension of fMRI data is often quite less.23,25The consequence of overestimating the dimension of fMRI data is severe: it has been observed by numerous researchers that ICA will split true components to meet dimensionality require- ments; for instance, a source signal having a relatively large spatial extent may be split amongst several independent components, each having similar time courses and smaller regions of activation.20This is due to the use of a nonlinearity biased towards supergaussian sources:
a spatial map that is highly localized will have a supergaussian pdf. A spatial map with a large spatial extent will have a Gaussian or sub- gaussian distribution and will not occur intact as an independent component using the supergaussian nonlinearity.
The most common solution for this problem is to use PCA for dimen- sionality reduction. Principal component analysis is performed on the input data, and those principal components with comparatively small variance are factored out of the input data set. Depending on the threshold employed, this can provide significant dimension reduction (for instance, from 200 components to 40 components). This particular method, however, is not entirely reliable for fMRI data; most fMRI data is characterized by a low contrast-to-noise ratio (CNR), and the signal change due to the functional task is a small fraction of the total signal.
The upshot of this is that most of the variance in the observed data is due to uninteresting signals, not the task activation. Thus, the task
(A)
(B)
Figure A.5. Comparison of maps prepared with ICA (A) and with the conventional reference function (B) in a patient who performed the finger-tapping task incorrectly. In the ICA map, activation is evident in the sensorimotor cortex and SMA, whereas in the map prepared with the reference function, less activation is evident in either area. The error in the performance is demonstrated by the time course of the independent component (C) in which the second epoch of finger tapping was not terminated on time and each subsequent performance of the task was displaced in time.
(A)
(B) Figure A.6. Comparison of activation maps prepared with ICA (A) and with the conventional refer- ence function (B) in a patient who moved during the performance of the finger-tapping task. The ICA map shows robust activation in the sensorimotor cortices bilaterally and in the supplementary motor area (SMA). With the reference function, activation in the sensorimotor cortex is less apparent, and is unapparent in the SMA. Motion analysis was carried out in AFNI (Robert Cox, NIH). The amount of movement during the acquisition is shown in (C) in which yaw (top line), pitch, roll, A-P, R-L, and I-S motion (bottom row) are graphed. The effect of motion on the time course of activation is shown in (D).
activations tend to have relatively smaller variances, and the use of an arbitrary threshold will actually mask the important signals.23
The dimensionality problem remains the most significant obstacle to the use of ICA for fMRI. It is currently under investigation by many researchers.22,23,25
Another current limitation of ICA is the lack of an ICA method for group analysis. Unlike hypothesis-based methods, there is no obvious extension of ICA to the analysis of group studies. Some initial work in this area has been done by Calhoun and colleagues.22Their results are promising.
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(C)
Figure A.6. Continued.
Conclusions
We have presented an introduction to independent component analy- sis, a new statistical method, and discussed its application to functional magnetic resonance imaging. The empirically demonstrated corre- spondence between task-related spatial independent components and known functional cognitive networks is striking. Although there are some problems that remain to be solved, the method is a promising new technique for exploratory data analysis.
References
1. Herault J, Jutten C, Ans B. Détection de grandeurs primitives dans un message composite par une architecture de calcul neuromimétique en apprentissage non supervisé. In: Actes du Xème colloque GRETSI, Nice, France; 1985:1017–1022.
2. Jutten C, Herault J. Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture. Signal Processing. 1991;24:
1–10.
3. Comon P. Independent component analysis, a new concept? Signal Processing. 1994;6:287–314.
4. Bell AJ, Sejnowski TJ. An information maximization approach to blind separation and blind deconvolution. Neural Comput. 1995;7(6):1129–1159.
5. Hyvärinen A, Oja E. A fast fixed-point algorithm for independent compo- nent analysis. Neural Comput. 1997;9(7):1483–1492.
6. Hyvärinen A, Oja E. Independent components analysis: algorithms and applications. Neural Netw. 2000;13(4–5):411–430.
7. Hyvärinen A, Karhunen J, Oja E. Independent Component Analysis. New York: John Wiley & Sons, Inc.; 2001.
8. Lee T-W. Independent Component Analysis: Theory and Applications. Boston, MA: Kluwer Academic Publishers; 1998.
9. Roberts S, Everson R. Independent Component Analysis: Principles and Practice. Cambridge, UK: Cambridge University Press; 2001.
10. Olshausen BA, Field DJ. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature.
1996;381:607–609.
11. Papoulis A. Probability, Random Variables, and Stochastic Processes. 3rd. New York: McGraw-Hill; 1991.
12. Cover TM, Thomas, JA. Elements of Information Theory. New York: John Wiley & Sons, Inc.; 1991.
13. Horn RA, Johnson CR. Matrix Analysis. Cambridge, UK: Cambridge University Press; 1985.
14. Porrill J, Stone JV. Undercomplete independent component analysis for signal separation and dimension reduction [online]. Technical Report, Department of Psychology, Sheffield University, England; 1998 [cited 3 April 2002]. Available at: ftp://ftp.shef.ac.uk/pub/misc/personal/pc1jvs/
papers/ica_dim_red_nips98_WWW.ps.gz.
15. Nadal J-P, Parga N. Non-linear neurons in the low noise limit: a factorial code maximizes information transfer. Network. 1994;5:565–581.
16. Amari S, Cichocki A, Yang H. A new learning algorithm for blind separation. In: Advances in Neural Information Professing Systems 8. 1996:
757–763.
17. Girolami M, Fyfe C. Extraction of independent signal sources using a defla- tionary exploratory projection pursuit network with lateral inhibition. IEE Proc Vision Image Signal Processing J. 1997;144(5):299–306.
18. Lee T-W, Girolami M, Sejnowski TJ. Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and super- gaussian sources. Neural Comput. 1999;11:417–441.
19. Huber PJ. Projection pursuit. Ann Stat. 1985;13(2):435–475.
20. McKeown MJ, Makeig S, Brown GG, Jung T-P, Kindermann SS, Bell AJ, Sejnowski TJ. Analysis of fMRI data by blind separation into independent spatial components. Hum Brain Mapp. 1998;6:160–188.
21. Esposito F, Formisano E, Seifritz E, Goebel R, Morrone R, Tedeschi G, Di Salle F. Spatial independent component analysis of functional MRI time- series: To what extend do results depend on the aligorithm used? Hum Brain Mapp. 2002;16:146–157.
22. Calhoun VD, Adali T, Pearlson GD, Pekar JJ. A method for group infer- ences from functional MRI data independent component analysis. Hum Brain Mapp. 2001;14:140–151.
23. Green CG, Nandy RR, Cordes D. PCA Preprocessing of fMRI Data Adversely Affects the Results of ICA. Paper presented at: ISMRM 10th Scientific Meeting and Exhibition; May 18–24, 2002; Honolulu, Hawaii.
24. Brockwell PJ, Davis RJ. Time Series: Theory and Methods. New York:
Springer-Verlag; 1993.
25. Beckmann CF, Noble JA, Smith SM. Investigating the intrinsic dimen- sionality of FMRI data for ICA. Paper presented at: Seventh International.
Conference on Functional Mapping of the Human Brain; 2001.
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Acetylcholine, 446
AD. See Alzheimer’s disease Adenosine, 446
ADHD. See Attention deficit hyperactive disorder AEDs. See Antiepileptic drugs
Aging
BOLD fMRI changes and, 483 brain activity changes and, 225, 226 brain atrophy and, 232
cognitive strategy and, 237 episodic encoding hindered by, 225 fMRI for, 236–237
HFR and, 236–237, 483 language LI and, 259 memory and
episodic, 222–223, 237 fMRI of, 221–238 remote, 227 semantic, 232–234 working, 234–236, 238
neurovascular system changes and, 482–483 tasks and, 237
Allodynia
capsaicin-induced, 433 fMRI of, 432–433
Alzheimer’s disease (AD), 110–111. See also Dementia
brain activity and, 229–230 early detection of, 233–234
fMRI, 232
language tasks and, 233–234 neuroimaging technique, 230, 231 fMRI, 232, 497
FTD differentiated from, 236 memory and
episodic, 228–232 semantic, 233 Amblyopia, 349–351
causes, 349 early onset, 351
fMRI, 350–351 late-onset, 351 neuroimaging for, 349 Amnesia, retrograde, 227 Amobarbital, 407 Amygdala
affective behavior and, 209–210, 212 emotional processing and, 212 Analysis of variance (ANOVA), 172 Anesthesia, 282
Anterior temporal lobectomy (ATL), 265 Antiepileptic drugs (AEDs), 305, 316 Aphasia, 111, 246–247
Arterial spin labeling (ASL), 7, 91–93 BOLD v., 458–459
CBF, 91–92 continuous, 91 fMRI application of, 92 pulsed, 91
ASD. See Autism spectrum disorders ASE. See Asymmetric spin-echo ASL. See Arterial spin labeling Asperger’s disorder, 185, 418
Astonishing Hypothesis of Francis Crick, 176 Asymmetric spin-echo (ASE), 34, 52–53, 90
BOLD sensitivity of pulse sequence for, 34 pulse sequence of, 53
susceptibility artifacts and, 105 Attention
neuroanatomy, functional of, 169–171 selective, 170
Attention deficit hyperactive disorder (ADHD) anatomical markers of, 415
fMRI applications in, 395, 415
medication treatment studies for, 454–455 pediatric, 415–417
fMRI for, 395
tasks, go-no go for, 454–455 T2and, 415–416
tasks for, 415, 416, 454–455
Index
517
518 Index
Auditory activation detecting, 370
hearing loss and, 386–387 scanner noise and, 375–376 sound-evoked, 378, 379 tinnitus, lateralization, 383 Auditory cortex
composition, 365–366 contralateral, 387 fMRI of, 364–389
acoustic noise and, 374–377 challenges, technical for, 371–377 clinical application for, 364–365, 380–387 future applications for, 388–389 implant device and, 372–374 paradigms for, 377–379 scanner noise and, 377–378 sound preservation and, 371–372 organization, 366–369
pediatric evaluation of, 405–406 region, primary of, 368 subdivisions of, 368 Auditory system
anatomical organization of, 365–371 subcortical, 365–366
belt regions in, 369 field arrangement of, 368 fMRI, 500
functional reorganization of, 380 imaging anatomy of, 369–371 information distribution in, 366 nonprimary regions in, 369, 370 parabelt regions in, 369 tonotopic areas in, 370–371
Autism spectrum disorders (ASD), 185 facial processing and, 186
fMRI for, 186, 395
markers for understanding and treatment of, 188 neuroimaging for, 185–186
pediatric, 395 treatment, 188
BBS. See Blind source separation Bipolar disorder
facial expressions and, 206 fMRI, 206, 207
fMRI differential diagnosis between schizophrenia and, 204–206
frontal function, altered in, 205–206 Blind source separation (BBS), 505 Blood
magnetic properties of, 76
neural activity and flow of, 140–141
Blood oxygenation level-dependent (BOLD), 3–4, 183.
See also BOLD fMRI altered response of, 358
anatomical source for signal of, 10 ASE pulse sequence sensitivity to, 34 ASL v., 458–459
brain activation, regional with, 184
contrast, 76
dHb-induced contrast of, 10–11 discovery, 144
draining vein problem and, 83 drug action and, 450
onset time of, 452–453 drug-induced effect on, 450, 451 DSC-MRI v., 191
epilepsy, 305
epileptic seizures and abnormalities of, 325–326, 420–421
EV component of, 12–16 go-no go task, 172–174 gradient-echo, 15
sensitivity of, 16 spin-echo v., 15–16 gradients, diffusion and, 84 hemodynamic response, 178 initial dip and, 84, 85, 106 IV component of, 10–12 MRI, 3–4
neuronal activation measured by, 93 pediatric, 400, 407
sedation/sleep examination and, 400 sensitivity, 45
signal, 144
age/gender and intensity changes of, 184 alcohol and, 448–449
brain structure tasks for, 455–457 CBF, regional increases and, 446 CBV, regional increases and, 446 comparing, 483–484
delayed-response task, 478, 479
drug administration altering, 446–448, 467 increase of, 474, 476
initial dip and, 84, 85 measuring, 450
medications and changes of, 184 neurophysiological basis of, 479–480 origin of, 144, 145
vascular differences affecting, 483 spatial resolution and, 475–476 spin-echo, 15, 80
gradient-echo v., 15–16 TE for, 78
temporal resolution of, 86–88
BOLD. See Blood oxygenation level-dependent BOLD fMRI, 1–135, 25
acquisition parameters and, 9–10
adult brain images, normal-functioning, 127–135 age-related changes in, 483
auditory tone represented on high, 130
low, 130
brain activity monitored by, 445–446 cerebellum: coordinating motor task on
axial/coronal/sagittal, 134 cocaine, 189, 452, 453 data, 58
data preprocessing for, 67–69
distortion correction and, 67 motion correction and, 68 slice acquisition correction and, 67 spatial normalization and, 68–69 spatial smoothing and, 69 dementia study with, 227–228 detection power of, 325–326
drug administration combined with, 446–447 drug effect on brain activity measured by, 452 experiments for
designs, 62–64, 65–66
event-related designs and, 65–66
neural-onset asynchrony designs for, 66–67 rapid randomly ordered designs for, 66 sparse designs for, 66
temporal structures of, 65–67 face representation, brain, 129 foot representation, brain, 128 frontal lobe represented on, 132–133 hand representation, brain, 129 HFR and, 474
hippocampal activation, temporal lobe represented on, 135
HRF and, 58, 62
inferior frontal gyrus, frontal lobe represented on, 132
inferior parietal lobule, parietal lobe represented on, 133
knee representation, brain, 128 limbic lobe (anterior cingulate), 131 limbic lobe (posterior cingulate), 131 low-frequency noise presence and, 62
medial frontal gyrus, frontal lobe represented on, 132
middle frontal gyrus, frontal lobe represented on, 132
motor cortex somatotopic mapping and, 135 neuroanatomical atlas, 127–135
noise and, 64, 482 HRF shape and, 64
temporal autocorrelation of, 58 OCD, 209, 211
parietal lobe represented on, 133
parietal occipital lobe: object naming task on, 134 pharmacological applications of, 446–460
future directions for, 458–460
imaging modalities combined with, 459 power spectrum of, 64
s. Broca’s motor area on, 134 schizophrenia, 197, 202 signal origin for, 445 statistical analysis for, 69–73
covariates in, 69–72 FDR threshold for, 73 regions of interest and, 72–73 sulcal localization of, 117
superior frontal gyrus, frontal lobe represented on, 133
temporal lobe represented on, 133, 135 tongue representation, brain, 130
trunk representation, brain, 128 visual cortex, 131
alcohol and, 448–449
Wernicke’s area, temporal lobe represented on, 133 wrist representation, brain, 129
Brain activity. See also Auditory activation; Language activation
AD, 229–230
age-related changes in, 225, 226 BOLD fMRI, 445–446
depression, 455–456 drug effects on
BOLD fMRI for, 452 depression, 455–456 Brain activity, memory
pictorial, 225–227 semantic, 233, 487–488 working, 235, 470
task for, 485–486 Brain areas
amnesia, retrograde associated, 227 attention, 166–167
behavior and, 140, 144 cocaine, 189
cognitive process disrupted by inactivation of, 469–470
cortical, specialized
identification/preservation of, 146–161 tasks for, 148–150, 154
eloquent region localization in, 496
functional specialization hypothesis, 144–146 language, 156, 165–166, 250
memory, working, 234–235 pain experience related to, 432 visual system, 145–146 Brain-behavior relationships, 468 Brain function
cognitive process associated with systems of, 469 damage to
reorganization after, 352–353 vision, residual after, 351–352 injury to
brain plasticity and, 418 maturational changes in, 396 myelination of, 396
neuronal activity related to, 444–445 pediatric, 396
fMRI for, 394–395 research, 496 Brain mapping
activation-based, 113
brain function preservation and, 147 clinical
analysis methods and, 99–100 group, 99–100
history of, 100 individual, 99–100 disruption-based, 113 fMRI, 99
functional specialization hypothesis for, 144–146
520 Index
Brain mapping (cont.) language, 156, 247–249, 254
case example, 153–154
early bilingual, case example, 157–159 intraoperative, 153, 156
late bilingual, case example, 157, 158 mathematical function series for, 101 motor region, 147, 153–155, 159–161 neural correlate, 168–174
neuroscience, cognitive, 139–178 neurosurgery, 139–178
registration, 162–163 sensory region, 147, 155 Brain plasticity
brain injury and, 418 pain, phantom and, 438 pediatric, 418–420 Broca’s area, 134, 140, 245
Carbamazepine, 316 CBF. See Cerebral blood flow CBV. See Cerebral blood volume Central nervous system (CNS), 449–450 Cerebral blood flow (CBF), 3
ASL for, 91–92 CBV changes and, 5, 6
initial dip, 84
DSC-MRI detected changes in, 458 FAIR measurement of, 8
fMRI based on, 8 measured, 93 regional, 445
alcohol and, 449 BOLD signal and, 446 response specificity of, 17–18 tack period changes of, 8 Cerebral blood volume (CBV), 4
CBF changes and, 4, 5 initial dip, 84 cocaine use and, 191
DSC-MRI study of, 459 DSC-MRI detected changes in, 459 lorazepam and, 459
regional
BOLD fMRI signal and, 445 BOLD signal and, 446
Cerebral metabolic rate of glucose (CMRglu), 3, 4–5 Cerebral metabolic rate of oxygen (CMRO2), 3, 85 Chiasmal anomalies, 351
Children
ADHD in, 415–417 studies of, 454–455
auditory cortex evaluation in, 405–406 BOLD response in, 400, 407
brain function, 407 fMRI for, 394–395
maturational changes in, 396 brain function in
injury to, 395
brain plasticity in, 418–420
cognition in, 417–418 development of, 421
disorders, neurological/psychiatric in, 395 epilepsy in, 420–421, 421
fMRI of, 394–421, 472, 499
applications, current/future for, 403–408 challenges in, 396–400
disorders and, 421
image processing for, 400–401 immobilization aids for, 397–398 lesions and, 419
mock scanner for, 397, 398 patient movement and, 396–398 pre-surgical planning and, 406–408 sedation and, 396, 398, 399–400, 403–408,
412–414
sleep examination, 398 statistical analysis for, 401–403 study design for, 397
task difficulty and, 397 thresholding for, 402–403 visual cortex, 404–405 hemodynamic response in, 402 language assessment in
development of, 406 lateralization of, 406–407 language mapping in
fMRI, 408–411 tasks for, 409–411 memory in, 416–421 motor cortex mapping in
fMRI, 411–415 sedation and, 412–414
motor/sensory function assessment in, 406 neurological development in, 395
PET studies of, 472 sensory activation in, 415
visual activation patterns in, 399–400 Chloral hydrate, 399
CMRglu. See Cerebral metabolic rate of glucose CMRO2. See Cerebral metabolic rate of oxygen CNR. See Contrast-to-noise ratio
Cocaine
BOLD fMRI, 189, 452, 453 brain areas associated with, 189 CBV change and, 191
DSC-MRI study of, 459 DSC-MRI study of, 191, 459 fMRI, 189–190, 499
motor/visual cortex functional connectivity and, 457
Cochlear implantation, 386–387 fMRI and, 386
preoperative test for, 386 fMRI and, 388 Cognition
development of pediatric, 421 epilepsy patient, 304–305 neural basis of, 471–472
neurodevelopmental abnormalities in, 304 pediatric, 417–418
Cognitive conjunction, 163–164 Cognitive function mapping
auditory, 415 pediatric, 415
Cognitive interference, 169–171
Cognitive process. See also Cognitive conjunction;
Cognitive subtraction aging and, 237
attention direction and, 166–167 brain damage and, 145
brain region inactivation disruption of, 469–470 brain structure and, 140, 141
brain systems associated with, 469 cognitive subtraction and, 61–62 conventional definitions of, 140 high level, 176–178
lateralization/localization of, 280 lesions disrupting, 469–470 manipulation of, 61–62 neural basis for, 162
neuroimaging study of, 468–469 interference in, 469–477 language-related, 141–142 physiological bases of, 139 surgery and, 280
tasks, 163–164
cortical areas specialized for, 161–164 functionally specialized area integration with,
164–167 Cognitive subtraction
assumptions for, 478 tasks, 163
Cognitive theory
neural correlate mapping and, 168–174 tests, 168–169, 170
Conjunction analysis, 114–116, 164 Consciousness
language process and, 249 masking paradigms, 178
neuroimaging technique study of, 176, 178 neuronal work space, global and, 176–177 resting-state, 178
task to vary, 177–178
Consistently task-related (CTR) activity, 509 Continuous Performance Task (CPT), 202 Contrast-to-noise ratio (CNR)
field strength and, 102–103 fMRI, 17
noise sources and, 17 Cortical development, 324 Cortical mapping, 411 Cortical stimulation mapping
basis of, 264
fMRI compared to, 263–264 language, 263–264
decline and, 264 Covariates
BOLD fMRI statistical analysis, 69–72
of interest, 70 generating, 70, 72 of no interest, 70
confounds, 71
neural activity changes and, 71 nuisance coverts, 71
CPT. See Continuous Performance Task CTR. See Consistently task-related activity
D-amphetamine, 395
Dementia. See also Alzheimer’s disease;
Frontotemporal dementia BOLD fMRI study of, 227–228 early detection of, 238
neuroimaging technique for, 230, 231 fMRI, 236–237
memory in fMRI of, 221–238 semantic, 232–234 working, 234–236
treatment monitoring for, 238 Demyelination, 347
Dephasing effect MRI with, 13–14 spin
gradient field, extra and, 40 isochromat, 39
vessel and
orientation of, 12, 13 size of, 12–13 voxel, 14 Depression
drug effect neural responses of, 455–456 fMRI, 206, 207
Diffusion, 36. See also Einstein’s diffusion equation Dopamine, 446
Drugs action of
BOLD and onset time for, 452–453 BOLD for studying, 450
onset time for, 452–453 activation, 453
administration of
BOLD fMRI combined with, 446–447 BOLD signal altered by, 446–448, 467 tasks, 453–454
BOLD effect induced by, 450, 451 brain activity affected by
BOLD fMRI for, 452
MR spectroscopy for, 459–460 challenges
activation paradigms and, 452–457 acute, 449–452
block design with parametric variation of level of difficulty for, 455
event related designs for, 454 tasks, reaction time for, 455 neuronal vascular coupling and, 448 response maximized in, 460 selecting, 460
522 Index
Drugs (cont.) tasks, 453, 455
validating procedure for, 448–449
DSC-MRI. See Dynamic susceptibility contrast MRI Dynamic susceptibility contrast MRI (DSC-MRI), 185
BOLD v., 191
CBF/CBV changes detected with, 458–459 cocaine and, 459
cocaine, 191, 459 Dysgenesis, 412–414
Echo planar imaging (EPI), 33 acquisition window of, 49–50 field mapping obtained using, 89 fMRI, 103
gradient echo-recalled, 51–52 k-space transversed by, 48, 49, 51 methods, 47–53
pulse sequences, 48–51
echo-formation mechanisms of, 48 gradient coils and, 50
intrinsic decay of, 49, 50 k-space transversed and, 51 schematics of generic, 48, 49 sensitivity, 80
spin-echo recalled, 52–53 spiral, 53–56
Archimedean, 53, 54 k-space transversed and, 53 trajectory shapes of, 54 spiral sequences of, 53–54
susceptibility artifacts and, 104–105 Echo time (TE), 76, 78
Echo train length (ETL), 35
ECT. See Electroconvulsive shock therapy EEG. See Electroencephalography Einstein’s diffusion equation, 36
Electroconvulsive shock therapy (ECT), 279 Electrocortical stimulation map (ESM), 115, 116,
319–320
Electroencephalography (EEG) artifact removal in, 327–329 epilepsy, 330–333
fMRI and, 326–329, 421 epilepsy, 330–333 MRI scanning, 473
object obscuring and, 327, 328 Electrophysiology, 153
EPI. See Echo planar imaging
Epilepsy. See also Antiepileptic drugs; Epileptic focus;
Epileptic seizures; Mesial temporal lobe epilepsy; Temporal lobe epilepsy absence, juvenile, 331
asymmetric MTL activation in, 298 BOLD response in, 305
cognition and, 304–305
cortical areas, eloquent in, 316–324 fMRI of, 304–305, 315–333, 500
EEG correlated, 330–333 pediatric, 319, 420–421
preoperative, 315 intractable, surgery for, 315 language assessment in, 318
fMRI, 284–287, 290, 292–293
language lateralization in, 289–290, 316–320 language localization in, 316–320
language processing and, 317 LI, 259–260
localization-related, 291 pediatric, 319, 420–421, 421
refractory, cortical development and, 324 special issues in patients with, 315–316 Epileptic focus, 324–333
Epileptic seizures
BOLD abnormalities and, 325–326, 420–421 focus localization of, 421
pediatric, 407
ESM. See Electrocortical stimulation map Estrogen, 235–236
ETL. See Echo train length EV. See Extravascular component Event-related potential studies, 489 Executive processes
mapping, 174–176
neuroanatomy, functional of, 171–172 Extravascular (EV) component, 10, 12–16
FAIR. See Flow-sensitive alternating inversion recovery
False-discovery rate (FDR), 73 Fast Fourier transformation (FFT), 55
Fast imaging with steady precession (FISP), 43, 44, 90 Fast, Low, Angle SHot (FLASH), 40–41
FDR. See False-discovery rate Fentanyl, 439
FFT. See Fast Fourier transformation Fibromyalgia
fMRI of, 433, 434 LBP, chronic and, 437 FID. See Free Induction Decay Field strength
CNR, 102–103 fMRI and, 102–103 increased
advantages of, 102–103 problems with, 103 spatial resolution and, 103 SNR, 78, 102–103
FISP. See Fast imaging with steady precession FLASH. See Fast, Low, Angle SHot
Flow artifacts, 38
Flow-sensitive alternating inversion recovery (FAIR), 7, 8
fMR-A. See Functional MR-adaption fMRI. See Functional MRI
Fragile X syndrome fMRI, 417–418 pediatric, 417–418
Free Induction Decay (FID), 39–40 Frontotemporal dementia (FTD), 236
