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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.
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Summary and Discussion
V
ariability seems to be an integral part of cognitive functioning, as evidenced in both behavioral and neuroimaging studies (Chapter 1). Increased variability is of-ten found in clinical groups. For example, people diagnosed with ADHD or autism show increased variability in behavioral and neurological responses. These effects are also evidenced in studies of aging or intelligence, where older people or peo-ple with lower intelligence are characterized by increased variability in responding. Quantifying this variability is therefore important as it may reflect the cognitive pro-cess better than methods based on the average alone. Evidence for this phenomenon was found in the reaction time study of Chapter 2. By analyzing the entire distribu-tion of reacdistribu-tion time data by means of a drift diffusion model (DDM), psychological processes like quality of information processing, response caution, and non-decision time could be distinguished. Results have shown that a drift diffusion model of the en-tire reaction time distribution can better account for differences between high and low intelligent people, than the mean reaction time. These results suggests that ex-plicitly modeling intraindividual variability of psychological processes better reflects actual cognitive functioning. Quantifying this variability in neuroimaging methods like EEG and fMRI is therefore an important avenue of research.NEW METHODS FOR THE ANALYSIS OF TRIAL-TO-TRIAL VARIABILITY IN NEUROIMAGING STUDIES
7.1 Variability in neuroimaging data
There are two sources of variability in neuroimaging data. First, variability may be due to measurement error (i.e., noise unrelated to the signal). Second, variability may originate in actual variability of the signal, the actual process we are interested in. The main problem with analyzing neuroimaging data on a trial-to-trial basis, is that the signal-to-noise ratio (SNR) of single-trial data is very low: it is therefore difficult to extract information from a single trial. As outlined in Chapter 1 we have approached this issue by modeling multiple trials by a sparse model that consists of both deterministic and stochastic components, where the stochastic components are incorporated to model trial variability. The next section will shortly summarize these methods, discuss the main assumptions and highlight avenues for future research.
7.1.1 Simultaneous Estimation of Waveform Amplitude and Latency
The SWALE method (Chapter 3) provides a way to analyze both the waveform of a signal and single-trial estimates of its amplitude and latency. The method works by assuming that the shape of the waveform is equal across trials but can differ between trials in amplitude and latency. It is embedded in a model selection framework to explicitly test if multiple signals are present in the data. Simulations have shown that under conditions of varying latency and noise, the method can successfully recover the actual waveform, and correctly estimate single-trial amplitude and latency. Also, the method can identify if multiple waveforms are required to model the data. Appli-cation to real data has shown that the SWALE method produces informative results and outperforms traditional peak picking methods for amplitude and latency estima-tion. Furthermore, the method was able to discern two different underlying signals in the real dataset consistent with a two component structure often found in choice reaction time studies.
The SWALE method has a number of advantages. The main assumption of the SWALE method is that the underlying signal can be modeled by a constant wave-form, modified by trial specific amplitude and latency parameters. This greatly re-duces the number of parameters that has to be estimated. Another assumption in 164
the analysis of EEG data, is that one is mainly interested in detecting relatively large deflections in the EEG (i.e., low frequency peaks with high amplitude). Inherently it is therefore assumed that the actual signal contains mostly low frequencies. Capital-izing on this assumption the SWALE method models the signal by use of polynomial basis functions that are relatively smooth. This further reduces the number of param-eters that has to be estimated. Also, the parameter estimation procedure is split into two steps, further reducing the complexity of the optimization problem.
A drawback of the SWALE method lies in the use of a derivative to model latency. While very flexible, there is a limit to the actual latency that can be modeled. Fur-thermore, the use of polynomial basis functions restricts the analysis to modeling relatively low frequency peaks in the data. Finally, the SWALE method currently works on single-electrodes, that is, no information shared by electrodes is used in the analysis.
Future work can address some of these issues. First, another set of basis functions to model the signal could be used. For example, one could use wavelets to model the signal, broadening the frequencies that can be detected. Finally, the SWALE frame-work might benefit when extended to include multiple electrodes. Using information from multiple electrodes might increase the signal-to-noise ratio and improve estima-tion.
7.1.2 Activated Region Fitting
In fMRI data an informative (and often discarded) part of the signal is its spatial distribution. The ARF method incorporates spatial information by assuming a spa-tial model consisting of multiple Gaussian shapes to model each active brain region (Chapter 4). This spatial model can be directly used to estimate trial-by-trial ampli-tude of the active brain regions (Chapter 5). Simulations have shown that the ARF method has increased power to detect activation in comparison with standard meth-ods, under several levels of noise, even when the signal is misspecified in shape. Furthermore, using the spatial model to estimate the covariation (i.e., connectivity) between regions, leads to better estimates of connectivity than standard procedures. Applications to real data have shown that the ARF method produces sensible
re-NEW METHODS FOR THE ANALYSIS OF TRIAL-TO-TRIAL VARIABILITY IN NEUROIMAGING STUDIES
sults with higher power than standard analysis methods. Implementation in a user-friendly package (Chapter 6) allows researchers to directly use this method within their fMRI analysis pipeline.
At the heart of the ARF method is its central assumption, that each area of activa-tion can be modeled by a Gaussian shaped funcactiva-tion. While this is the great advan-tage of the method, it can also be a drawback. The ARF framework was developed with increased power in mind, by trading off spatial specificity for increased power. Even while the Gaussian model is flexible in shape, the model is spatially smooth. This limits the analysis to detecting relatively smooth regions of activation, but it has increased power to detect this activation. In addition, ARF does not make any anatomical assumptions1: Regions can cross gray/white matter, cover sulci and gyri,
etc. Taken together, this makes the current implementation of ARF less suitable for analyses where highly irregular shaped regions of activity are expected.
There are several modifications possible that can accommodate these issues. First, the trade-off between spatial specificity and increased power can be adapted by us-ing multiple Gaussians to model one region of activation. This will better describe the shape of the region (thus increase spatial specificity), but the increase of parame-ters will also make it harder to detect activation (lower power). Second, future work may also consider to incorporate anatomical information in the framework. For ex-ample by not allowing activated regions to cross tissue types. Finally, the spatial model could be further expanded, allowing to better model the shape of activated regions function. This would require using other spatial functions. With respect to estimating connectivity, the current implementation does not explicitly model the noise (co)variance structure. Future work may take into account measurement noise of single-trial amplitudes, reducing attenuation of the connectivity estimates due to noise
The ARF framework is implemented in R, a free multi-platform framework for sta-tistical analysis. R is especially suited for developing and extending neuroimaging analysis methods and pipelines. While R, as any statistical software, has a reasonably steep learning curve, the use of it within standard fMRI analysis methods is rather
1Note that standard GLM analysis with FWHM smoothing does not make any anatomical assumption
either.
straightforward. This allows researchers to directly use the ARF method within their analysis pipeline. Still, there are a number of issues that future releases of the pack-age may include. First, the model selection procedure might be more automated. Currently, there are some routines for automatic selection but these do not provide (statistically) optimal solutions. Second, routines might be optimized to further re-duce computation time. Also, new releases could make more efficient use of new multiple core (64bit) processors, parallelizing computations when possible, reducing computation time even further. Finally, although this is more an aesthetic point, im-provements might be made in terms of the user interface. Currently, most operations are command line, but these could be made much more intuitive when embedded in a graphical interface.
7.2 Why the analysis of trial-to-trial variability is
important.
The main theme of this thesis is that trial-to-trial variability is an important, if not an essential, part of neuroimaging data, and that analysis methods should take into account this variability. However, discerning the underlying signal from noise on a single-trial level is very challenging as it is complicated by the inherent noisiness of neuroimaging data. In this endeavour, using as much available information about the signal as possible, can be advantageous. That is, by assuming a sparse model with de-terministic and stochastic parameters, estimation of single trial characteristics can be improved over methods in which all parameters are stochastic (i.e., non-parametric models).
The SWALE method (Chapter 3) has shown improved estimation over standard tech-niques. This improved estimation is mainly due to two factors. First, SWALE esti-mates a waveform based on a set of basis functions instead of at each time-point separately (as is customary in a non-parametric model), this makes the SWALE es-timates less receptive to noise. Second, by using the derivative of the waveform to estimate latency in stead of estimating the latency by peak-picking on smoothed data, bias introduced in the single-trials, by for example the smoothing kernel, is reduced
NEW METHODS FOR THE ANALYSIS OF TRIAL-TO-TRIAL VARIABILITY IN NEUROIMAGING STUDIES
in the SWALE method. Within the SWALE framework, by assuming a smooth wave-form that is constant over trials, but varying in amplitude and latency, the estimation is tuned towards only the relevant characteristics of the signal, leading to improved estimation over standard (non-parametric) techniques.
In standard fMRI analysis an ignored part of the data is the spatial information (no use is made of spatial information as each voxel is analyzed separately, each voxel thus constitutes a parameter in these analyses). The ARF framework (Chapter 4 &
5) makes explicit use of the spatial information available in fMRI data by assuming a spatial model underlying each active brain region. Incorporating the spatial structure of the data leads to increased power to detect activation and better estimates of trial-by-trial amplitude than standard methods, as the number of parameters that has to be estimated in ARF is greatly reduced.
To summarize, by using a sparse model that is informed by characteristics of the signal of interest, trial-to-trial variability can be estimated better than using standard approaches. This allows (cognitive) psychologists to further unravel the dynamics of human cognitive functioning. In this endeavour, the SWALE and ARF frameworks provide new methods in the (cognitive) psychologists’ arsenal especially made . . . to be variable.
