Impaired complex choice after FPl disruption
Previous neuroimaging findings showed that FPl is specifically involved in decision making in the presence of complex information9. Particularly, FPl decomposes and integrates complex choice information and passes that digested information to posterior cingulate cortex (PCC) for guiding decision making (Fig. 1A). In this study, we further examined the causal role of FPl in digesting complex choice information and its precise computational mechanisms. To this end, in Experiment 1 we tested whether and how disruption of FPl would impair complex choice behaviour. Participants were required to perform a two-stage decision making task, in which choices in Stage 1 involved complex information and choices in Stage 2 involved simple information. Specifically, Stage 1 involved choosing between two collections of gambles (Fig. 1B). Each collection involved complex information of twenty gambles – individual probabilities of the twenty gambles (represented by the heights of twenty bars) and the average reward magnitude of these gambles (represented by a number). After choosing a collection, from which two gambles were randomly drawn and offered subsequently in Stage 2. Each of these simple gambles in Stage 2, similar to many typical studiese.g. 15–18, was associated with certain levels of reward probability (represented by a bar) and magnitude (represented by a number). Complex choice in Stage 1 therefore required digesting and integrating multifaceted information. To examine the causal role of the FPl in complex choice, participants received TMS, using a continuous theta-burst stimulation (cTBS) protocol, to disrupt their FPls before performing the task (Fig. 1C). On another day, they underwent an active control condition where they received TMS over the vertex. On both days, participants also performed the task with no prior TMS as additional control conditions. The sequence of the conditions (TMS vs no TMS; FPl vs vertex) was counterbalanced across participants.
We hypothesized that the FPl is critical to complex choice, but not simple choice. To test whether this was the case, we first performed a repeated measures two-way ANOVA [Region (FPl or vertex) and Stimulation (TMS applied or not applied)] on participants’ percentage optimal choice data, in which optimal choice was defined according to the normative expected value (EV). Two additional controlling factors were included to account for variance due to individual differences, which were the distance between the intended and actual FPl-TMS position and the peak resting-state functional connectivity (rsFC) between FPl and PCC. When the ANOVA was applied to the complex choice behaviour, a significant Region × Stimulation interaction was found (F(1, 24) = 7.4142, p = 0.0119; Fig. 2A, Extended Data Table 1). A post hoc analysis showed that participants made less optimal choice on TMS trials than no TMS trials in the FPl session (p = 0.0313; Extended Data Table 1). In contrast, in the vertex session participants’ proportions of optimal choice were comparable on TMS and no TMS trials (p = 0.1969; Extended Data Table 1).
On the other hand, we applied the same ANOVA to the simple choice data and found no significant effect of FPl-TMS on optimal choice. Specifically, there was no Region × Stimulation interaction (F(1, 24) = 0.0157, p = 0.9014; Fig. 2B, Extended Data Table 1) nor main effects (F(1, 24) < 1.2731, ps > 0.2703; Extended Data Table 1). Crucially, this specific FPl-TMS effect on impairing complex choice, but not simple choice, could not be explained away by any difference in difficulty level between complex choice and simple choice, because the overall percentages of optimal choice were comparable in the two stages (F(1, 24) = 0.0173, p = 0.8966).
Previously, correlational neuroimaging data showed that PCC has a role in utilizing the complex information that is decomposed in the FPl to guide decision making9. In addition, greater efficacy of TMS is related to stronger intrinsic functional connectivity19. Hence, we estimated the degree in which FPl and PCC were functionally connected using each participant’s rsFC data (cluster-based thresholding Z > 3.1, p < 0.0001; Fig. 3A) and tested whether that was also related to the extent of TMS effect. We found that participants with greater FPl-PCC connectivity exhibited fewer optimal choices after FPl-TMS (r = -0.5537, p = 0.0027; Fig. 3B), while such relationship was absent in all three control conditions (|r|s < -0.3075, ps > 0.1186; Fig. 3C). In contrast, in simple choice a correlation between FPl-PCC connectivity and optimal choice was absent in all four conditions (Extended Data Fig. 1). These results support the notion that complex choice involves not only the FPl per se, but also its connection with the PCC.
Developing computational models for understanding the FPl-TMS effect mechanistically
Thus far we showed that disruption of FPl resulted in impaired complex choice by demonstrating less optimal choices. However, the precise computational mechanism of FPl in complex choice remains unclear. To tackle this problem, we need computational models for describing the mechanistic processes of making complex choice. To this end, we conducted Experiment 2, an experiment using the same behavioural task without any TMS or fMRI, and went through a series of model development. We considered that the space of model development should involve two dimensions. First, we considered possible ways by which choice attributes (i.e. reward magnitude and reward probability) were represented. Hence, the first dimension considers four possible attribute functions: (1) linear; (2) cumulative prospect theory (CPT) that involves a non-linear transformation of the attributes20; (3) mean-variance-skewness model (MVS) that involves parallel decompositions of high dimensional attribute components into low dimensional distribution parameters21–24 and; (4) a combination of MVS and CPT (MVS + CPT). Second, we considered possible ways by which choice attributes could be integrated25,26. Hence, the second dimension considers three possible integration functions: (1) a multiplicative function; (2) an additive function and; (3) a composite function that arbitrates between multiplicative and additive approaches. Altogether, the four attribute functions and three integration functions produce twelve models (Fig. 4; see Experiment 2 – Computational modelling in Methods for details). Note that the normative EV model for defining optimal choice in Fig. 2 is the same as the model that consists of a linear attribution function and a multiplicative integration function.
We fitted participants’ complex choice data of Experiment 2 with all the twelve models and compared their goodness-of-fit using Bayesian model selection. The results revealed the Composite MVS+CPT model significantly outperforms all other models (estimated frequency Ef = 0.9563; exceedance probability Xp = 1.0000; Fig. 4B), suggesting that the high dimensional choice attributes were non-linearly transformed and decomposed into low dimensional summary statistics (e.g. the mean, variance, skewness). Intriguingly, the results also revealed participants arbitrated between two integration strategies in parallel, which are the multiplicative approach and additive approach. Finally, the findings were replicable in the Experiment 1 data – the Composite MVS+CPT model best describes complex choice behaviour in all TMS conditions (estimated frequency Efs > 0.9694; exceedance probability Xps = 1.0000; Fig. 4C). Together, we showed that the Composite MVS+CPT model provides the best account of participants’ complex choice behaviour – a model that involves considering choice attributes non-linearly, decomposing complex information into multiple digested parameters (i.e. mean, variance and skewness), and arbitrating between additive and multiplicative integration strategies. This is consistent in the data of Experiments 1 and 2.
The winning Composite MVS+CPT model involves a push-pull mechanism of arbitrating between a multiplicative approach and an additive approach for information integration. The balance between the two strategies is controlled by an integration coefficient. However, in light of the presumed role of FPl in processing complex choice information, we hypothesized that to better account for FPl’s function, the push-pull system should instead arbitrate between a computationally complex process and a simple heuristic. To this end, we further developed two variants of the Composite MVS+CPT model. One variant, the ComplexMul – SimpleAdd model, involves keeping the complex MVS + CPT function in the multiplicative arm and simplifying the additive arm by dropping out the MVS component (Fig. 5A, middle panel). As such, the additive arm no longer involves parallel decomposition processes of digesting the complex information, instead it simply employs the mean of the complex information for guiding decisions. Another variant, the ComplexAdd – SimpleMul model, involves keeping the additive arm complex and simplifying the multiplicative arm by dropping out the MVS component (Fig. 5A, right panel). Importantly, in both models, the balance between the complex and simple processes is controlled by a complexity coefficient Ψ.
We fitted the two variant models to the Experiment 2 data and compared their goodness-of-fit with the previously winning Composite MVS+CPT model. The ComplexMul – SimpleAdd model was found outperforming the other models in describing the complex choice behaviour (estimated frequency Ef = 0.8657; exceedance probability Xp = 1.0000; Fig. 5B). Figure 5C shows each participants’ fitted parameters of the ComplexMul – SimpleAdd model, including the complexity coefficient Ψ, softmax temperature T, and magnitude/probability weighting ω. The winning of the ComplexMul – SimpleAdd model suggests that participants’ complex choice behaviour was better described by the arbitration between a computationally complex integration process and a simple heuristic process.
FPl-TMS inhibits the complex integration process
So far, we have demonstrated that complex choice was disrupted by FPl-TMS (Fig. 2) and complex choice is best described by a push-pull mechanism that arbitrates between complex and simple processes (Fig. 5). Next, we investigated more closely the precise mechanistic processes that were disrupted by FPl-TMS. We hypothesized two possible ways in which complex choice was impaired by FPl disruption. First, FPl disruption resulted in a completely different strategy of information integration, i.e. behaviour after FPl-TMS was best described by a different model. Alternatively, the same strategy remained after FPl-TMS, but the computational parameters of that strategy were altered.
To test which hypothesis was the case, we repeated the same model comparison procedures as in Fig. 5B, but now using data from the four conditions of Experiment 1 (Fig. 6A). In all three control conditions, as in Experiment 2, we found that the ComplexMul – SimpleAdd model best describes complex choice behaviour (estimated frequency Efs > 0.9085; exceedance probability Xps = 1.0000). Interestingly, after FPl-TMS the ComplexMul – SimpleAdd model remained as the best fit model (estimated frequency Ef = 0.7239; exceedance probability Xp = 0.9967). Our findings precluded the first hypothesis that FPl disruption resulted in a switch in strategy (i.e. a change in the best fit model), but instead participants continued to use the same strategy after FPl-TMS. We therefore examined more closely the computational parameters of the best fit ComplexMul – SimpleAdd model across the four TMS conditions to test the second hypothesis – whether FPl disruption altered computational parameters.
Figures 6B-D show participants’ computational parameters of the ComplexMul – SimpleAdd model in the four TMS conditions in Experiment 1. These parameters include the complexity coefficient (the extent to which they used a complex process for digesting choice information), softmax temperature (degree of choice randomness), and magnitude/probability weighting. Each parameter was analysed using a repeated measures two-way ANOVA [Region (FPl or vertex) and Stimulation (TMS applied or not applied)], controlled for model prediction accuracy and TMS stimulation distance to account for individual differences. We found that there was a significant Region × Stimulation interaction on the complexity coefficient (F(1, 21) = 10.6494, p = 0.0037; Fig. 6B). A post hoc analysis showed that the complexity coefficient was significantly smaller (i.e. participants became more likely to use a simple heuristic) after TMS was applied to FPl than the control vertex (p = 0.0009; Extended Data Table 1), whereas there was no significant difference in complexity coefficient in the no TMS condition during the FPl and vertex sessions (p = 0.1921; Extended Data Table 1). Finally, we found no significant Region × Stimulation interaction effect on the softmax temperature parameter (although approaching significance; F(1, 21) = 3.7840, p = 0.0653; Fig. 6C) and magnitude/probability weighting parameter (F(1, 21) = 3.9350, p = 0.0605; Fig. 6D). Extended Data Table 2 shows all the fitted parameters of the ComplexMul – SimpleAdd model. These results support our second hypothesis that FPl-TMS disrupted specific computational parameters, i.e. the complexity coefficient, instead of qualitatively switching participants’ choice strategy.
Subsequent between-participant analyses provide further support that the impaired optimal choice due to FPl-TMS (Fig. 2A) was related to the disruption of a computationally complex integration process. Here, we calculated the deviation in percentage of optimal choice, as well as the deviation in computational parameters, after FPl-TMS from that of the three control conditions. Crucially, we found that participants with greater reductions in complexity coefficient also exhibited greater impairments in percentage optimal choice (r = 0.5433, p = 0.0041; Fig. 6E). In addition, greater impairments in percentage optimal choice were correlated with larger increases in softmax temperature (r = -0.6114, p = 0.0009; Fig. 6F), suggesting those became more stochastic after FPl TMS also showed more impaired optimal choices. Finally, the impairment in percentage optimal choice was unrelated to the deviation in magnitude/probability weighting (r = 0.0787, p = 0.7025; Fig. 6G).
Next, we performed further analysis to demonstrate that the FPl-TMS effect was captured particularly well by the ComplexMul – SimpleAdd model. A key feature of this model was that it arbitrates between complex and simple processes – where the complex process involves decomposing complex attribute components and combining them via a multiplicative approach. In contrast, the ComplexAdd – SimpleMul model (an alternative model in Fig. 5) involves a “complex” arm that decomposes attributes in a complex way, but integrates reward magnitudes and probabilities in a simpler additive way. Not only that this model was a poorer fit to participants’ behaviour overall (Fig. 5B, 6A), but its computational parameters also failed to capture the FPl-TMS effects. Particularly, a repeated measures two-way ANOVA [Region (FPl or vertex) and Stimulation (TMS applied or not applied)] revealed no significant Region × Stimulation interaction on the complexity coefficients (F(1, 21) = 3.2785, p = 0.0845; Extended Data Fig. 2A, softmax temperature (F(1, 21) = 0.6931, p = 0.4145; Extended Data Fig. 2A), nor the magnitude/probability weighting (F(1, 21) = 0.0059, p = 0.9396; Extended Data Fig. 2A). In addition, the changes in these fitted computational parameters was unrelated to the impaired optimal choice due to FPl-TMS (|r|s < 0.2579, ps > 0.2033; Extended Data Fig. 2B).
Similarly, we repeated the same analyses using the Composite MVS+CPT model, which is half-way between the best-fit ComplexMul – SimpleAdd model and the poorer ComplexAdd – SimpleMul model – it involves an identical decomposition process of complex attribute components in both the multiplicative and additive arms. We found that the Composite MVS+CPT model yielded similar findings to the ComplexMul – SimpleAdd model – FPl-TMS gave rise to reduced integration coefficient (Extended Data Fig. 3A), and the impaired optimal choice behaviour was related to the reduced integration coefficient and heightened softmax temperature (Extended Data Fig. 3B). These additional results showed that the best fitting ComplexMul – SimpleAdd model captures both the overall behaviour (Fig. 5B, 6A) and FPl-TMS effects (Fig. 6B-G) particularly well because it involves all the complex processes in one arm and all the simple processes in another arm. To summarize, aided by the ComplexMul – SimpleAdd model, we showed that the way FPl-TMS impaired complex choice could be explained mechanistically by a disruption of the complex integration process such that participants had to rely on simple heuristics.
FMRI data showed that FPl signal was related to a complex integration process
Our findings thus far revealed that FPl disruption led to an impairment of a complex information integration process. As such, we should expect that, in the absence of any extrinsic disruption, individuals who exhibit stronger decision signals in FPl should also be more inclined to use more complex strategies. Thus, in Experiment 3, we further investigated the relationship between decision signals in FPl and the complexity coefficient. Experiment 3 involved measuring neural activity using fMRI while participants were performing a decision task similar to that of Experiments 1 and 2 (Extended Data Fig. 4A). Previously, data of Experiment 3 reliably showed a signal in FPl that was specifically related to complex choice9 (Fig. 7A). To make it possible to apply the same set of computational models to the behavioural data of Experiment 3, we focused on a subset of the trials in Experiment 3 that was most similar to those in Experiments 1 and 2 (Extended Data Fig. 4A). We first ensured that a decision signal in FPl can be identified even with this smaller set of trials, as in what was shown using the full set of trials9. We performed a timecourse analysis and showed that FPl’s activity significantly correlated with the complex choice value and peaked at approximately 4s after stimulus onset (β = 0.0772, t23 = 2.4163, p = 0.0240; Fig. 7B, Extended Data Fig. 4B). This suggests that the selected subset of trials could reliably capture a signal in FPl related to complex choice.
Next, we applied the same set of computational models to the behavioural data of Experiment 3 and showed, consistently, that the ComplexMul – SimpleAdd model best describes participants’ complex choice behaviour. Specifically, we followed identical model fitting procedures as in Experiments 1 and 2. Participants’ complex choice behaviour was first fitted using the twelve models that are derived from four different attribute functions × three integration functions (as in Fig. 4B, C). A Bayesian model selection showed that the Composite MVS+CPT model outperforms all other models (estimated frequency Ef = 0.9633; exceedance probability Xp = 1.0000; Fig. 7C, left panel). Next, we further fitted the ComplexMul – SimpleAdd and ComplexAdd – SimpleMul models and compared their performance with the Composite MVS+CPT model. We replicated the results of Experiments 1 and 2 that the ComplexMul – SimpleAdd model best describes participants’ complex choice behaviour (estimated frequency Ef = 0.8008; exceedance probability Xp = 0.9995; Fig. 7C, right panel). The fitted parameters of the ComplexMul – SimpleAdd model are shown in Fig. 7D.
We performed the key analysis to scrutinize whether participants’ complexity coefficient was related to their FPl signal during complex choice. Considering that the decision value of the ComplexMul – SimpleAdd model was a combination of a complex integration process and a simple heuristic, we broke down the FPl signals into these two components (see Experiment 2 – ComplexAdd – SimpleMul model in Methods). Then, to estimate the contribution of the complex component to the FPl signal (i.e. FPl signal complexity), we divided the complex component of the FPl signal by the sum of the complex and simple components. Interestingly, we found that the complexity coefficient was positively correlated with the FPl signal complexity (r = 0.4758, p = 0.0218; Fig. 7E, left panel). This is in line with the findings of Experiment 1 that greater FPl-TMS induced choice impairment was associated with larger decreases in complexity coefficient (Extended Data Fig. 4C). This suggests that the FPl signal reflected the employment of a complex integration process during decision making. In addition, we found that the softmax temperature was negatively correlated with the FPl signal complexity (r = -0.5234, p = 0.0104; Fig. 7E, middle panel), suggesting that participants showing greater FPl signal complexity were less stochastic. We found, surprisingly, a positive correlation between the magnitude/probability weighting and the FPl signal complexity (r = -0.4710, p = 0.0233). This correlation was possibly confounded by the softmax temperature as we identified a marginally significant correlation between them (r = 0.3530, p = 0.0907). The magnitude/probability weighting was no longer related to the FPl signal complexity when the softmax temperature was included as a covariate (r = -0.3405, p = 0.1210; Fig. 7E, right panel). Taken the results of our computational modelling, neurostimulation and neuroimaging studies, we provided evidence from three experiments showing that the FPl is causally involved in a complex integration process for decomposing choice information.