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Twenty-six undergraduate or graduate students (11 males, mean age 22 years, SD 2.81) participated in this study. Three participants were excluded from the analyses because of excessive head motion. All participants were in good health with no previous history of psychiatric or neurological disease, and they gave written informed consent. The study was approved by both the Institutional Review Board of the Institute of Psychology, the Chinese Academy of Sciences, and the Institutional Review Board of the Beijing MRI Center for Brain Research.
We constructed 60 pairs of two-outcome monetary bets: one featuring a high probability of winning/losing a modest amount of money (the P bet), and the other featuring a low probability of winning/losing a relatively large amount of money (the $ bet) (Figure 1A). Outcome probabilities of the P bet ranged from 81% to 97% in 2% or 3% increments, and the outcome probabilities of the $ bet ranged from 19% to 39% in 2% or 3% increments. The expected values for the P bets and the $ bets ranged from Chinese Yuan (CNY) ±16 to ±44.
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0014756.g001 Task trial structure.A. Trial types. B. Trial timing. Two bets were presented and the participants' task was to indicate their decision by pressing one of two buttons on a response pad.
In the preferential choice task, participants were asked to select their preferred bet from each pair. To make the participants perform a compensatory process, we developed a judgment-based choice task using the certainty equivalent method [42], [43]. This method has traditionally been based on expected utility theory [41]. This technique uses a lottery to assess a decision maker's preferences over a single attribute (which was either probability or payoff) range and trade-offs [40]. In the judgment-based choice task, participants were asked 1) to use the certainty equivalent method to assess the certain gain/loss equivalent of each bet (in other words, the cash equivalent that the participants felt would make them indifferent to the given bet), and 2) the participants were asked to select the bet with the higher-certainty gain/loss equivalent from each pair. Participants did not explicitly indicate the certainty equivalent for each bet before indicating their choice. In this manner, a compensatory process of trading off probability against payoff was performed. The order of the tasks was counterbalanced between the participants. In each of the preferential and judgment-based choice tasks, half of the participants were assigned to view the gain trials before the loss trials, and the other half viewed the trials in the opposite order. The order of the trials within each domain was randomized, and the order of domain was counterbalanced between the two tasks and within the participant group. Each participant performed both the preferential and judgment-based choice tasks with an interval of at least 7 days between the two tasks. Prior to entering the scanner, the participants played a practice version of either the preferential choice task or the judgment-based choice task to minimize learning effects during the actual scanning and to enable them to fully understand the paradigm. During the scanning, the participants were asked to perform the tasks with no time constraints. They made their decisions by pressing one of two buttons corresponding to the location of the bets on the screen. After the participants' response, there was a delay of 8 s before a 2 s fixation procedure started and indicated the next bets (Figure 1B). There was a 10-min interval between the gain trials and loss trials for each participant. During this period, high-resolution structural images were acquired, but these data were not used in this study. After the scan, participants were asked whether they integrated the probability and the payoff to estimate the certainty equivalent for each bet by using a method similar to the mathematical expectation in the judgment-based choice task. Twenty-one of twenty-three participants reported that they integrated the probability and the payoff to estimate the certainty equivalent for each bet using a method similar to mathematical expectation. The two negative answers came from participants who claimed that they did not know about mathematical expectation. Participants were also checked to ensure that they had been fully engaged in each task and clearly understood the tasks. All participants reported a belief that they would win or lose money at the end of the tasks. They were told that at the end of each task, two of their decisions would be randomly selected to be played for real (one in the gain domain and the other in the loss domain), and another random device would determine the outcomes of the selected bets. Both of the random choices were performed by a MATLAB program. If the result turned out to be a gain, the participants would receive money from the experimenter. If the result turned out to be a loss, the participants would give money to the experimenter or sign an IOU if they could not afford to make a cash payment. The average real gain over the two selected bets was ¥29.57 per participant, whereas the average real loss over the two selected bets was -¥31.52 per participant. At the completion of the study, the participants were paid ¥100 in cash for participating, and the debts/winnings determined by the above method were deducted from/added to the final payment.
MR images sensitized to changes in BOLD signal levels were obtained by an echo planar imaging sequence on a 3.0-Tesla Siemens MR scanner (repetition time = 2,000 msec; echo time = 30 msec; flip angle = 90°, matrix = 64×64; field of view = 220×220 mm2; slice thickness = 3 mm; slice gap = 1 mm and, thus, acquisition voxel size = 3.4×3.4×4 mm3). Each brain volume was composed of 32 axial sections. Stimuli were presented with E-prime software (Psychology Software Tools, Pittsburgh, PA) on a personal computer, back-projected onto a screen using a liquid crystal display projector and viewed by participants through a mirror mounted on the MRI head coil. We also acquired a brief (6-min) resting-state scan, which was composed of 180 volumes (the data were not used in this study).
Image preprocessing and analyses were performed using statistical parametric mapping (SPM5, Wellcome Department, London, UK) that was run on a MATLAB 7 platform (MathWorks, Natick, MA). The first three volumes in each scan series, which were collected before equilibrium magnetization was reached, were discarded. The remaining images were corrected for within-scan acquisition time differences between the slices and then realigned to the first volume to correct for inter-scan head motions. Based on a visual inspection of the motion correction estimates, three participants who had more than 2-mm maximum displacement in any of the x, y or z directions or more than 2° of angular rotation about any axis for multiple volumes were excluded from this study. An additional two participants showed sudden head motion only in the first trial, which allowed the use of the imaging data obtained from these two participants after the first trial was removed. The realigned images were spatially normalized to the standard EPI template, resampled to 3×3×3 mm3 and smoothed using an 8-mm full-width-at-half-maximum Gaussian kernel to decrease spatial noise. Motion parameters were stored and used as nuisance variables in the following generalized linear model (GLM) analysis. Individual participant data were analyzed using the general linear model (GLM) with separate models for each task. Events were modeled with a variable-duration boxcar function convolved with a canonical hemodynamic response function (HRF). To quantitatively describe the relationship between brain activation and decision parameters, parametric analyses were performed. Trials were modeled with parametric regressor modeling (in the following order): (1) the intradimensional difference in the probability dimension or in the payoff dimension, and (2) the unidimensional difference between overall values/utilities of two bets on the unidimension alone. To avoid a choice in which one bet dominated the other, all of the bets used in our study were designed to be choices between high payoffs with low probabilities and low payoffs with high probabilities. As a consequence, we observed a significant correlation (r = 0.483, p = 0.007) between the differences on the payoff dimension and the differences on the probability dimension. Thus, an increase in the difference in the payoff dimension would result in an increase in the difference in the probability dimension. To avoid the problems induced by severe co-linearity, we chose one intradimensional difference to enter into the regressor model at a time. Therefore, there were two parametric analyses for each task. For example, Model I was analyzed for the intra-dimensional difference in the probability dimension and the unidimensional difference, and Model II was analyzed for the intradimensional difference in the payoff dimension and the unidimensional difference. To estimate the intradimensional difference in the payoff dimension and the intradimensional difference in the probability dimension, we calculated the utilities for the objective payoff and the decision weights for the objective probability separately. The utility function and the probability weighting function were borrowed from cumulative prospect theory [4], which is a compensatory theory that is considered to be empirically successful [3]. The selected utility function was the power function , and the selected probability weighting function was an S-shaped weighting function, i.e., for gains and for losses. We used the following values for each of the parameters: α = β = 0.88, λ = 2.25, γ = 0.61 and δ = 0.69, as suggested by Tversky and Kahneman [4]. To estimate the unidimensional difference between the overall values/utilities of two bets in the unidimension alone, we calculated the cumulative prospect utilities of the two bets by applying the function of cumulative prospect theory [4]. According to cumulative prospect theory, the utility function is , and the probability weighting functions are for gains and for losses. The function of overall utility is , where . All effects were modeled as linear functions of parameter values. Regressors were serially orthogonalized with the regressors that were entered later, accounting only for the variance unaccounted for by regressors that were entered earlier. Participant-specific movement parameters and linear drift were modeled as covariates of no interest. A high-pass filter with a cutoff period of 128 s was used to remove low-frequency noise. Global scaling was not applied. First-level (single participant) contrasts were performed separately over the mean trial activity (relative to baseline) and for each of the parametric regressors described above. Second-level (group) random effect analyses were completed by performing one-sample t-tests over each of these contrasts. Corrections for multiple comparisons were carried out at the cluster level using Gaussian random field theory implemented in SPM5 (min T(22)>2.5; cluster significance: p<0.05, corrected). By using the intradimensional difference in the probability/payoff dimension and the unidimensional difference between the cumulative prospect utilities of two bets as parameters, parametric analyses were conducted to identify brain regions that were sensitive to intradimensional difference and unidimensional difference. Paired t-tests were used to further verify the differences in the sensitivity to the specific decision parameters (p<0.005, uncorrected). To control for the difference in task difficulty between the two tasks, the average RT of each participant within each task was taken as an index of task difficulty and entered into the paired t-test analysis as a covariate. Finally, a mask composed of the conflict-related regions that were sensitive to the unidimensional difference and the intradimensional difference in the payoff or probability dimension was generated. According to our hypothesis, the conflict-related regions should be those regions in which the unidimensional difference between the two offered bets shows a negative modulation effect or regions in which the intradimensional difference on the probability/payoff dimension shows a positive modulation effect (min T(22)>2.5; cluster significance: p<0.05, corrected). Thus, a mask was formed in which each voxel value was set to one if the voxel satisfied one of the above criteria. The mask was set to zero if the criteria were not satisfied. To compare activities (relative to baseline) in the conflict-related regions between the two tasks, another random-effect paired t-test analysis controlling for the effect of task difficulty was used to determine where the second-level group contrasts differed between the preferential choice task and the judgment-based choice task. This analysis was limited to the mask (p<0.005, uncorrected).
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