New methods for the analysis of trial-to-trial variability in neuroimaging studies - 1: Introduction

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

New methods for the analysis of trial-to-trial variability in neuroimaging studies

Weeda, W.D.

Publication date

2012

Link to publication

Citation for published version (APA):

Weeda, W. D. (2012). New methods for the analysis of trial-to-trial variability in neuroimaging

studies.

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.

Introduction

T

he working of the human brain has intrigued scientists for centuries: how are hu-mans able to perform complex cognitive tasks like facial recognition, problem solv-ing, or even simple tasks like pressing a button (which of course can also be seen as very complex act). Cognitive psychologists are usually interested in disentan-gling these tasks into more fundamental psychological processes. From the early days of F.C. Donders, who pioneered the systematic exploration of human cognition (Donders, 1969), reaction times have been (and still are) the most widely used out-come measure in cognitive psychology. In recent years more direct measures have become available in the form of electro/magneto-encephalography (EEG/MEG) and func-tional magnetic resonance imaging (fMRI), allowing researchers to study the underlying mechanisms of cognition more directly.

A general observation with almost all studies of cognitive functioning, independent of the outcome measure, is that within-subject (or intraindividual) performance in these studies is variable (Fiske and Rice, 1955; Arieli et al., 1996; Aguirre et al., 1998). In other words, the reaction of a single subject varies from trial to trial. Traditionally this variability is seen as measurement error and therefore ignored or discarded from analyses (Jensen, 1992; Jung et al., 2001; Duann et al., 2002). There is, however, a large (and growing) amount of evidence suggesting that this variability conveys important

information (MacDonald et al., 2009).

For example, reaction time (RT) studies have shown that increased variability in RT corresponds to lower intelligence (Baumeister, 1998; Jensen, 1992; Hultsch et al., 2002), lower cognitive performance (Bielak et al., 2010), older age (Deary, 2005; L ¨ov-d´en et al., 2007), and clinical conditions like Attention Deficit Hyperactivity Disorder (ADHD) and autism (Geurts et al., 2008). These differences are also evidenced when analyzing neuroimaging studies using for example Event Related Potentials (ERPs), stimulus-locked deflections in EEG signals. For example, high intelligence partici-pants show less trial-to-trial variability in both amplitude (Fjell and Walhovd, 2007) and latency (Saville et al., 2011) of ERPs. Increased variation is observed in clinical groups diagnosed with Alzheimer’s disease (Hogan et al., 2006) or ADHD (Lazzaro et al., 1997), and in older subjects (Fein and Turetsky, 1989; Fjell et al., 2009). In ad-dition, and somewhat surprisingly, higher variation in amplitude of fMRI BOLD re-sponses, the brain’s metabolic response to a stimulus, is correlated with younger age (Garrett et al., 2011).

These studies suggest that variability in responding conveys important information on how the brain performs cognitive tasks (MacDonald et al., 2006; Moy et al., 2011), more so than the average response alone. Analysis methods should therefore take into account this variability, which can be a daunting task since noise should be sepa-rated from true variability in the signal of interest. This thesis therefore concerns new methods for the analysis of trial-to-trial variability, specifically for the analysis of re-action time (RT), electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data.

1.1 A general model of trial-to-trial variability

Variability in reaction time and neuroimaging data can have two underlying sources. First, variability may come from measurement error. Second, variability may reflect trial-to-trial variability of the actual signal. The latter being the variability of interest. The major hurdle in analysis of variability is thus discerning noise variance and vari-ance in the signal of interest at each single trial. To quantify this distinction between

signal and noise we pose a general model. In this model the measured data on each trial are seen as a function of an underlying neurological or psychological process and measurement error. More formally this can be stated as:

yi = f (d, si) + εi (1.1)

In Eq. 1.1 yi is the measured response to a stimulus on trial i = 1, . . . , N . The

un-derlying process is described by a non-linear function f (d, si)with deterministic

pa-rameters d and stochastic papa-rameters si1. The deterministic parameters define

char-acteristics of the response that are equal across trials. The stochastic parameters can have different values at each trial and therefore define characteristics that are variable across trials. Finally, εidefines measurement error. In the case of reaction time data yi

is a single value, namely the reaction time at trial i. The function f can be defined as the process underlying this reaction time, that is, the process of evaluating the stimu-lus, making the decision and executing the response. In the case of EEG/MEG data yi

is a time-series of the brain’s response on trial i (usually a short time-window around stimulus presentation and response), with f characterizing the shape of this response over time. For fMRI data yiis a (2 or 3 dimensional) image of the brain’s response on

trial i, with f modeling the spatial pattern of this image.

The key in characterizing trial-to-trial variability is the estimation of the signal f (d, si)

at each trial. This requires estimation of deterministic parameters d and trial specific parameters si. Since parameters d are equal over trials, estimation of these

param-eters benefits from multiple trials. Paramparam-eters si are variable over trials and cannot

benefit from multiple trials as they have to be estimated at each trial separately. Given the high levels of noise in single-trial data (Faisal et al., 2008; Parrish et al., 2000; Kuriki et al., 1994), this makes estimating the stochastic parameters very difficult. The next paragraphs will give a detailed description of how single-trial parameters are estimated in RT, EEG, and fMRI data.

1_{The terms deterministic and stochastic are used to indicate parameters that are fixed over trials and}

parameters that vary over trials respectively. The terms are not used in their statistical interpretation to indicate fixed and random variables.

1.1.1 Reaction time (RT)

Reaction time is one of the most widely used outcome measures in cognitive psy-chology. It is used, for example, in Simon tasks (Simon, 1969), Erikson-flanker tasks (Eriksen and Schultz, 1979), Go/No-go tasks (Mesulam, 1985), and Choice Reaction Time (CRT) tasks (Hick, 1952; Hyman, 1953). Usually, variability in reaction times is attributed to measurement error (Jensen, 1992). Therefore, in most studies, reaction time is summarized (i.e., by calculating the median or mean) to get a better measure of the ‘real’ reaction time, thereby ignoring trial-to-trial variability.

The easiest way to characterize variability in reaction times is by simply computing the standard deviation of the entire response time distribution (instead of calculating the mean over this distribution). This, albeit a successful measure in reaction time studies (van Ravenzwaaij et al., 2011), ignores the assumption that reaction times might be a reflection of the timing of underlying (cognitive) processes (Sternberg, 1969). That is, variability of reaction times does not necessarily say anything about variability of underlying processes. Delineating the processes underlying reaction times, and characterizing their variability may therefore be beneficial.

In order to extract the underlying processes a model of this process has to be assumed. There are multiple models available, but one that has proven to be very versatile is the ”drift diffusion model” (DDM, Ratcliff, 1978). This model for Two-Choice decision tasks translates the reaction time distributions for correct and error responses into psychological processes like quality of information accumulation, response caution, and non-decision related processes. In addition, the DDM can account for important phenomena often found in reaction time studies (Ratcliff et al., 2008; Wagenmakers et al., 2005; Wagenmakers and Brown, 2007; Schmiedek et al., 2009; van Ravenzwaaij et al., 2011).

The DDM assumes that evidence for one of two choices accumulates over time at each trial via a noisy random walk process (gray lines in Fig. 1.1) until one of two response boundaries is reached (horizontal lines 0 and a in Fig. 1.1). The rate of this accumulation (drift-rate) at each trial is defined as coming from a normal distribution with mean ν (bold arrow in Fig. 1.1) and standard deviation η. The width of the

Figure 1.1: Schematic representation of the drift diffusion model. The gray lines indicate noisy

informa-tion accumulainforma-tion from starting point z to boundary a or 0; the solid arrow indicates the mean rate of information accumulation v. On the top and bottom are the hypothesized response time distributions. Total RT equals Terplus the decision time.

boundaries (boundary separation) is defined by parameter a. The non-decision related processes at each trial (non-decision time), the reaction time that cannot be explained by the diffusion process, is defined as coming from a uniform distribution with mean Terand width St.

The DDM estimates parameters from the reaction time distributions of correct and incorrect responses. This makes direct estimation of the characteristics of the under-lying process at each trial impossible. However, variability of the underunder-lying process is captured by the η and Stparameters. To relate the diffusion model to our general

model, let yibe the reaction time of trial i. The underlying process f can be

charac-terized as the diffusion process with stochastic parameters s coming from a normal distribution of drift rate (with ν and η) and a uniform distribution of non-decision time (with Terand St). The deterministic parameter d is defined as boundary

separa-tion a.

The added value of using an explicit model to analyze reaction times, is that different cognitive processes can be discerned from reaction time data, instead of only descrip-tive measures like the mean or standard deviation. Furthermore, variability of these cognitive processes can be estimated, allowing researchers to test specific hypotheses

about them (for example, that aging subjects have a higher variability in quality of information accumulation). There is evidence that these cognitive processes, have a neurological basis. Specifically, quality of information accumulation, is shown to be related to trial-to-trial variability in EEG (Ratcliff et al., 2009). Neuroimaging meth-ods like EEG thus allow researchers to further unravel these underlying cognitive processes.

1.1.2 Electroencephalography (EEG)

Electroencephalography (EEG) captures electromagnetic changes in the brain by mea-suring this signal via electrodes on the scalp. The signal is sampled very fast, allowing it to record changes within millisecond precision. EEG data consist of a time-series measured at each electrode on the scalp. The amount of noise in EEG data is often much larger than the signal (Jung et al., 2000), making it difficult to estimate charac-teristics of this signal at each trial.

EEG analysis is usually performed on data locked to the presentation of a stimulus or an overt response to this stimulus. Given the high amount of noise in single-trial EEG data, the analysis requires multiple measurements of the same condition to clearly identify these evoked or event-related potentials (ERPs) (Glaser and Ruchkin, 1976). The single trials are then averaged to filter out random noise. Thereafter, the resulting ERP is examined for profound positive or negative deflections (amplitude), occurring at specific latencies across different electrodes (McCarthy and Wood, 1985). These deflections (often referred to as complexes) are subsequently linked to different cognitive processes.

In estimating single-trial EEG data there are to steps two be taken. The first is to estimate the shape of the ERP, obtained by averaging stimulus- or response-locked EEG data. The second is estimating the single-trial characteristics of the ERP (or a specific complex of interest), more specifically, calculating its amplitude and latency at each trial. This second step, estimating single-trial estimates of amplitude and latency, requires a correct estimation of the shape of the ERP. Subsequently, estimates of amplitude and latency at each single-trial can be obtained.

In terms of our general model the single-trial EEG data of a single electrode yi are

modeled by a neural process f determined by deterministic parameters d, that model the shape of the ERP, and stochastic parameters sithat determine the amplitude and

the latency of this ERP.

The major advantage of using single-trial parameters in EEG analysis is that these give a more detailed description of the underlying neurological process. An addi-tional advantage is that it can improve estimation of the shape of the ERP (Woody, 1967; Handy, 2004; Saville et al., 2011). Furthermore, the variability of single-trial pa-rameters can be used to highlight individual differences in brain responses between people.

1.1.3 Functional Magnetic Resonance Imaging (fMRI)

Functional Magnetic Resonance Imaging (fMRI) visualizes brain activity by contrast-ing the ratio of oxygenated versus deoxygenated blood, termed the blood oxygena-tion level dependent (BOLD) contrast (Ogawa et al., 1990; Logothetis et al., 2001). An fMRI scanner measures this activity by dividing the brain into small cubes (voxels), approximately 3 × 3 × 3 mm, and measuring changes in BOLD contrast within these voxels at multiple points in time (Boynton et al., 1996; Glover, 1999).

The main goal in (task-related) fMRI analysis is localizing regions in the brain that are active during a specific cognitive process (Friston, 2011). In recent years studies have not only focused on localizing active brain regions, but also on describing the inter-actions between these regions. These so-called connectivity analyses focus on the co-variation of activity of regions over time (functional connectivity) or on establishing directionality (i.e., causal relations) between active regions (effective connectivity).

The key in localizing regions of brain activity is to estimate the spatial extent (i.e., shape) of these regions. Since fMRI analysis is performed on each voxel separately estimating the extent of a region is usually done by counting active voxels and depict-ing regions of these voxels graphically. Improvements in these analyses can be made by posing a spatial function to model the spatial extent of activated brain regions (see for example, Hartvig, 2002; Weeda et al., 2009).

In terms of our general model the spatial map reflecting the brain’s response to a stim-ulus yiis modeled by a spatial function f determined by deterministic parameters d,

that model the spatial extent of each active brain region, and stochastic parameters si

that determine the height of activity2_{of these regions at each single trial.}

An additional problem in localizing active brain regions is that, in standard analysis, all voxels are tested using a massive univariate method (Friston et al., 1995). That is, each voxel is tested separately for activity, and with often over 30000 voxels included in the analysis, the chances of finding false positive results (marking a voxel as ac-tive while it is actually not) increase dramatically (Forman et al., 1995). To control the number of false positives (i.e., the familywise error rate), this type of analysis re-quires a correction for multiple comparisons. A major problem with these correction methods, however, is that they are often conservative (Nichols and Hayasaka, 2003), leading to decreased power to detect active brain regions.

Conservativeness of localization can be problematic since connectivity analyses (i.e., analysis of trial-to-trial variation) and especially effective connectivity analyses re-quire that all regions in a network associated with a particular task are known. Fail-ing to include regions can bias connectivity analyses (Eichler, 2005). In addition to this, connectivity analyses require an estimate of single-trial amplitude for each re-gion in the network. This can be problematic due to the low signal-to-noise ratio of single-trial data.

The major advantages of using a spatial function to model the spatial extent of ac-tive brain regions are increased power to detect activation and improved estimates of trial-to-trial variability (Weeda et al., 2011). The main use of trial-to-trial variabil-ity in fMRI analysis is to define functional or effective networks of localized brain regions. These can give more insight into the underlying mechanisms involved in a particular task as it highlights the interaction between regions as opposed to just localizing them (Biswal et al., 1995). Effective connectivity goes even a step further as it can highlight directionality within these networks, showing which regions exert in-fluence over others (Friston et al., 2003; Waldorp et al., 2011). Furthermore, estimates

2_{Due to the nature of fMRI data, the latency of the BOLD response may differ between trials. In contrast}

to EEG this latency is not of interest in most neuroimaging studies. Therefore the latency of the BOLD response is usually taken into account within the analysis, or corrected for a-priori

of trial-to-trial variability can also be used to highlight differences between groups.

1.2 Why trial-to-trial variability is important

There are mainly two reasons why it is important to take into account trial-to-trial variability. First of all, trial-to-trial variability may better reflect the working of the human brain. Evidence from multiple behavioral and neuroimaging studies has shown that intraindividual variability conveys important information on cognitive functioning. Reaction time studies have shown that taking into account this variabil-ity leads to better estimates of, for example, intelligence. Variabilvariabil-ity in this case thus seem to capture the underlying mechanism of cognitive processing better than the average alone.

This observation is further strengthened by EEG studies, where differences in vari-ability are also observed between (clinical) groups. In this sense varivari-ability is an in-trinsic part of cognitive functioning and may be a reflection of how the brain actually processes information. This may become apparent in connectivity studies, where not only the locations of regions involved in a cognitive process are of interest, but also the interactions between these regions. Cognitive processes are then defined not only based on their location but also on there role within a functional network. Correct localization of active brain regions and estimation of their trial-to-trial amplitudes is therefore essential.

This highlights the second point of why trial-to-trial variability is important: From a methodological standpoint, taking into account variability is essential for correct analyses. This has mainly two reasons: First, not taking into account trial-to-trial variability, thus only using the average, ignores the accuracy information of that av-erage (contained in the trial-to-trial variability). For example, two runs of a similar condition can have the same average, but completely different trial-to-trial variability. Second, ignoring trial-to-trial variability can lead to biased estimates. For example, latency variation can have an impact on the estimated shape of ERPs and taking into account these differences can correct for this phenomenon.

To summarize, the correct estimation of trial-to-trial variability may not only better reflect the mechanisms underlying cognitive functioning, it is also essential for a cor-rect analysis of reaction time and neuroimaging data. For these reasons, this thesis focuses on the development of new methods to estimate single-trial characteristics of neuroimaging data.

1.3 Outline

The outline of this thesis is as follows. Chapter 2 discusses a reaction time experi-ment where evidence of a commonly found effect in reaction time studies, namely that the slowest reaction times are a better predictor of cognitive functioning than the fastest reaction times, is not found when looking solely at reaction times, but is found when analyzing the underlying decision process. This chapter highlights the impor-tance of taking into account trial-to-trial variability when analyzing reaction times and serves as proof-of-concept for the further chapters. As learned from the reaction time study in Chapter 2, the importance of assessing the properties of a neurological signal at a single-trial level is clear: trial-to-trial variability may convey more infor-mation than the average alone. Chapter 3 therefore introduces a new method for the analysis of single-trial EEG data. This method not only determines the waveform of an event-related potential (ERP) but also determines its amplitude and latency at each single-trial. To further discern cognitive functioning, fMRI allows analysis of location of, and interactions between, areas in the brain associated with a cognitive function. Chapter 4 therefore introduces a new method for the localization of active brain regions using fMRI that uses a spatial model for these regions. This method has increased power to detect activation and has clear advantages for further analy-ses used to estimate trial-to-trial variability. Chapter 5 extends the initial method of

Chapter 4to be used with functional connectivity analysis, showing increased power

and better estimates of trial-to-trial amplitude than standard approaches. Chapter 6 describes the accompanying software package of this method as implemented in R, and gives an overview of the method, its functions and its extensions. The thesis ends with a summary and a concise discussion of the advantages and disadvantages of the methods.

1.4 Articles resulting from this thesis

Chapter 3

Weeda, W.D., Grasman, R.P.P.P., Waldorp, L.J., van de Laar, M.C., van der

Molen, M.W., and Huizenga, H.M. (in revision). Simultaneous Estimation of Waveform Amplitude and Latency of Single-Trial EEG/MEG data. PLoS One.

Chapter 4

Weeda, W.D., Waldorp, L.J., Christoffels, I., and Huizenga, H.M. (2009).

Activated Region Fitting: A Robust High-Power Method for the Analysis of fMRI Data. Human Brain Mapping, 30(2), 2595-2605.

Chapter 5

Weeda, W.D., Waldorp, L.J., Grasman, R.P.P.P., van Gaal, S., and Huizenga,

H.M. (2011). Functional Connectivity Analysis of fMRI Data using Parameterized Regions-of-Interest. NeuroImage, 54(1), 410-416.

Chapter 6

Weeda, W.D., de Vos, F., Waldorp, L.J., Grasman, R.P.P.P., and Huizenga, H.M.

(2011). arf3DS4: An Integrated Framework for Localization and Connectivity Analysis of fMRI Data. Journal of Statistical Software, 44(14), 1-33.

Other articles resulting from this Ph.D. project:

Van Duijvenvoorde, A.C.K., Figner, B., Jansen, B.R.J., Weeda, W.D., & Huizenga, H.M. (in preparation). Heuristic or Rational? The Neural Mechanisms Underlying Decision Strategies.

Harsay, H.A. , Cohen, M., Spaan, M., Weeda, W.D., Nieuwenhuis, S. & Ridderinkhof, K. R. (submitted). Pupil Dilation Predicts Shifts Between Default-Mode and Task-Focused Brain Networks During Error Awareness. Zeguers, M.H.T., Snellings, P., Tijms, J., Weeda, W.D., Tamboer, P., Bexkens A., &

Huizenga, H.M. (2011). Specifying Theories of Developmental Dyslexia: A Diffusion Model Analysis of Word Recognition. Developmental Science, 14(6), 1340-1354.