Neurology and Clinical Neurophysiology 2004:24 (November 30, 2004)
Detection of Power Changes between Conditions using Split-Half Resampling of Synthetic Aperture Magnetometry Data Chau, W, Herdman, AT, Picton, TW The Rotman Research Institute of Baycrest Centre, University of Toronto, Toronto, Canada Corresponding Author: Wilkin Chau, The Rotman Research Institute of Baycrest Centre, 3560 Bathurst Street Toronto, Ontario, M6A 2E1, CANADA. Phone: +1-416-785-2500 Email:
[email protected] ABSTRACT Synthetic Aperture Magnetometry (SAM) measures changes in task-related power using pseudo-t values which are affected by changes in both signal and noise. Detecting significant signal power changes between two separate experimental conditions should not be done directly due to possible fluctuation in the noise as well as the response. This study proposes a method to estimate the noise within a single condition, which is then used to test the null hypothesis of no difference between the conditions. The noise estimation is based on a split-half resampling technique. For each resampling, the data of a given condition is divided into two halves. The difference of the pseudo-t volumes between the pair of the datasets is calculated. After multiple resamplings, the confidence limits of the differences within this single condition are computed for a given p-value so that one can test the null hypotheses that the second condition is within the same distribution as the first. The limits are calculated using a bootstrap technique to correct for any bias in the estimated threshold. Power changes between the two conditions are considered significantly different if the difference of the pseudo-t value is larger than expected within conditions. To demonstrate the effectiveness of the technique, the proposed method was applied to MEG responses to two distinct visual stimuli recorded from a single subject. Major differences of brain activity between the two conditions were found in the occipital region. These results were validated using four pairs of split-half datasets, generated from either the odd or even trials in each condition. The method of split-half resampling should therefore be useful for localizing significant differences in brain activity between conditions within individual subjects. KEY WORDS Synthetic aperture magnetometry, Split-half resampling, Bootstrap, Nonparametric statistic. INTRODUCTION Synthetic Aperture Magnetometry (SAM), developed based on the concept of beamformer technique, is a useful tool to analyze MEG data, especially for complex tasks that involve activity in multiple different brain regions. For a given location in the brain, SAM first derives a spatial filter to suppress the interference of unwanted signals from other locations [Robinson, 1998]. The source power at that location is then estimated from the filtered signals. The task-related power change is represented by a pseudo-t value, which is a measurement of the power difference between the active and control conditions normalized by the power of the noise. Due to temporal fluctuation of both response and noise, the obtained pseudo-t value for a given condition can vary. To make the pseudo-t values as stable as possible, the active and control conditions should be close together in time. When the two experimental tasks are separated by more than 1 second, the pseudo-t value may not accurately reflect the signal power change between the tasks when one task serves as an active condition and the other as a control condition. Any difference could just as easily reflect changes in the background noise levels. To compare the brain activity between the two conditions, the pseudo-t SAM volume of each condition, calculated relative to an adjacent baseline period, should be computed separately, and statistical analysis performed based on the
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Neurology and Clinical Neurophysiology 2004:24 (November 30, 2004)
difference of the pseudo-t values between the conditions. In this study, we propose a statistical procedure to detect the difference of the brain activity between two experimental conditions. By assuming that the pseudo-t values within a volume are independent, the variation of the pseudo-t value within a single condition is estimated. Confidence limits can then be used to identify the brain regions with significant difference in activity between two conditions. METHODS The proposed analysis method is based on the idea that if the difference of pseudo-t values between the two conditions is significant larger than the variation of the pseudo-t values within each condition then it is highly probable that the difference is due to the difference of brain responses for the two conditions. Each pseudo-t value can be broken down into two components, one for the stable response (S) and the other for the variant component (E) that due to either signal fluctuations or noise. For the proposed method to work, the variant component has to be extracted from the pseudo-t value. By just knowing the pseudo-t value, it is not possible to separate the components. However, one can obtain the difference of E from the multiple measurements. Let T1 and T2 be the pseudo-t values of the same condition obtained from the two measurements. Their absolute difference is ∆T12 = | T1 – T2 | = | (S1 + E1) – (S2 + E2) |. Since S1 is equal to S2 by definition, ∆T12 = | E1 – E2 |. With multiple measurements, one can estimate the distribution of the ∆T within the condition. Now consider the absolute difference of the pseudo-t values between the two conditions, A and B: ∆TAB = | TA – TB | = | (SA + EA) – (SB + EB) | = | (SA-SB) – (EA-EB) |. We can then test a null hypothesis that the brain responses are identical in both conditions, by considering the two data sets as separated measurements of the same condition. In this case, ∆ TAB should have the same distribution as the ∆T within the condition. On the other hand, if the value of ∆TAB is significant different from the ∆T values, the brain responds differently for the two conditions. Since we have no model of the distribution of ∆T within a condition, we used a nonparametric method to estimate the confidence limits. To avoid the high experimental cost of repeated measurements, a splithalf resampling technique was used to estimate the distribution of ∆T values. For each experimental condition, the dataset is divided into two halves, each containing half of the trials. The pseudo-t values for each brain location from the split-half datasets are obtained. Their differences are used to estimate the expected range of the ∆T values for a given p value. The process can be visualized using the scatter plot of the pseudo-t values of the two half datasets. Due to the signal fluctuation, the pseudo-t values form a cloud of values along the diagonal. The deviation between a point and the line represents the difference between two pseudo-t values from the same brain location. Geometrically, this is the projection of the point to the line orthogonal to the 45o line (Fig. 1). Based on the distribution of the absolute values of the projected points, a critical value of the ∆T can be determined for any given p value. For example, the point at the upper 5th percentile of the distribution defines the critical point for p = 0.05. Any values below this confidence limit are within the expected range of the ∆T values for the condition. The above procedure determines the expected range of ∆T values from a pair of the split-half datasets; however, the critical value may change when the dataset is divided differently. Ideally, the ∆T distribution should be estimated based on all the splithalf datasets. With total of N trials, there are NCN/2 different ways to split the dataset. It is usually not
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Figure 1. Distribution of pseudo-t values of two conditions
Neurology and Clinical Neurophysiology 2004:24 (November 30, 2004)
feasible to use each pair of the possible split-half datasets to estimate the distribution. Instead a subset of split-half datasets is used to determine the critical value. The mean of the critical values from the splithalf resamplings is then used for the significant test. With only small number of samples, the estimated critical value may be biased. A bootstrap technique [Efron, 1993] can adjust for this bias. Once the critical value for the confidence limit is defined, one can test whether a brain location response differs significantly in a second experimental condition. RESULTS To demonstrate the effectiveness of the technique, the proposed method was applied to MEG responses to two distinct visual stimuli recorded from a single subject. The data was obtained from two experimental conditions in a visual attention task. The two conditions, referred to as Complex and Easy, have different stimulus sets. A total of 64 different stimuli, different in shape, color and slantingorientation, occurred in the Complex condition, and 4 stimuli, different shapes with white color and no shading, in the Easy condition (Fig. 2). The subject identified specific target stimuli within each condition. There were total of 20 targets for each condition. For each target block, a target cue was shown for 3 seconds followed by twenty-four trials with test stimuli. The inter-stimulus interval was varied between 2 to 2.5 seconds. MEG recordings were taken between 400 ms before and 700 ms after the onset of each test stimulus. For each trial, the subject responded by pressing a button on his right side if the test stimuli matched the target and on his left side if not. Only the mismatch trials with correct response are analyzed in this study. The total number of trials for each condition is 328. Five pseudo-t volumes of each condition are generated using the band-pass filters of 4-8Hz, 8-16Hz, 16-30Hz, 30-60Hz, and 60-100Hz, the time interval 50-350ms after stimulus onset for the active window, and 0-300ms before stimulus onset for the control window. To estimate the normal range of the pseudo-t value difference within a single condition using the proposed method, 100 pairs of the split-half datasets are randomly sampled from the original dataset to obtain the critical value for each pair for the p value of 0.01. The bias of the mean critical value is then estimated by performing 1000 bootstraps on the values. The bias corrected critical value is compared against with the pseudo-t value differences between the Easy and Complex conditions.
Figure 2. Visual Stimuli. (a) for the Complex condition; the shape, color and orientation were mixed to generate all 64 stimuli (b) for the Easy condition.
Figure 3. Regions with different power changes between the Complex and Easy Conditions
The responses (Fig. 3) show their main activity in the occipital areas. Among the five frequency bands, relatively large response differences are found in occipital region at the frequency bands of 4-8Hz and 1630Hz. Compared to the Easy condition, Complex condition has larger pseudo-t values at 4-8Hz band (red areas), but a smaller values at 16-30Hz band (blue areas). Inspecting the pseudo-t values of each condition in the region, both conditions show event related synchronization at 4-8Hz and desynchronization at 1630Hz. The responses may be due to the visual stimuli alone or the target matching process.
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DISCUSSIONS This novel statistical analysis method can detect the power change between the two experimental conditions based on the pseudo-t values for each condition. The method estimates the confidence limits for the difference in the pseudo-t value using the split-half resampling technique, with bootstrap bias correction. Brain regions with difference of pseudo-t value significantly larger than the expected range are classified as having different response for the two conditions. The proposed method can localize the significant brain activity within individual subjects. It is particularly useful for the studies for which only a few subjects are available. However, several issues have to be addressed to improve the performance of the method. Traditionally the split-half resampling technique is used for reliability testing [Cronbach, 1951] to detect the consistency of measurement. Strother et al. [Strother, 2002] used it to derive the prediction and reproducibility metrics for crossvalidation. In our method, split-half resampling is used to estimate the expected range of the pseudo-t value deviation. The major drawback for all applications of the split-half technique derives from reducing the sample size by half. Since only half of the trials are used to estimate the expected range, there would be more noise in the variant component of the pseudo-t value. Consequently, the critical value for the significant test is higher (more conservative) than it should be. In addition, there are some situations in which the region with different response for the two conditions is not detected. The pseudo-t value difference between the conditions, ∆TAB, can be small even for the region that responds differently for the two conditions. This happens when the difference of the stable component, (SA -SB), and the variant component, (EA-EB), are similar. Results were validated using four pairs of split-half datasets, generated from either the odd or even trials in each condition. Some extra spurious regions were found in each of the four results; however, the regions identified with the original dataset are the common detected regions to all the split-half results. The spurious regions of the split-half results are caused by the reduction of the data. Further study is needed to determine the number of trials required to obtain reliable results. The proposed method is the first statistical analysis technique designed to handle the problem of instability of the pseudo-t values for comparing power changes between conditions. Since this technique also provides a way to analyze differences between conditions in single subjects, it will be useful for studies with only a few subjects. REFERENCES Cronbach, LJ. Coefficient alpha and the internal structure of tests. Psychometrika 1951;16:297-334. Efron B, Tibshiran R. An introduction to the bootstrap. London: Chapman and Hall; 1993. Robinson SE, Vrba J. Functional neuroimaging by synthetic aperture magnetometry (SAM). In: Yoshimoto T, Kotani M, Kuriki S, Karibe H, Nakasato N, editors. Recent advances in biomagnetism. Sendai: Tohuku University Press; 1998. p. 302–5. Strother SC, Anderson J, et al. The quantitative evaluation of functional neuroimaging experiments: The NPAIRS data analysis framework. NeuroImage 2002;4:747-71.
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