Neuroscience 277 (2014) 872–884

NEUROSCIENCE FOREFRONT REVIEW PERCEPTUAL DECISION NEUROSCIENCES – A MODEL-BASED REVIEW M. J. MULDER, a,b  L. VAN MAANEN a  AND B. U. FORSTMANN a*

Contents Introduction Evidence accumulation models of perceptual decision making DDM LBA model Decision-making mechanisms Regions associated with the accumulation of evidence Discussion Regions associated with the decision threshold Discussion Regions associated with response or choice bias Discussion Regions associated with non-decision processes Discussion Summary and conclusion Conclusion Acknowledgments References

a

Department of Psychology, University of Amsterdam, The Netherlands b Institute for Psychological Research & Leiden Institute for Brain and Cognition, Leiden University, The Netherlands

Abstract—In this review we summarize findings published over the past 10 years focusing on the neural correlates of perceptual decision-making. Importantly, this review highlights only studies that employ a model-based approach, i.e., they use quantitative cognitive models in combination with neuroscientific data. The model-based approach allows capturing latent decision-making processes such as strategic adjustments of response thresholds and relate these to interindividual differences or single-trial blood-oxygenated level dependent (BOLD) functional Magnetic Resonance Imaging (fMRI) responses. The review shows that different cortico-subcortical networks are responsive to different latent decision-making processes. More concretely, we show that evidence accumulation is associated with a frontoparietal network which is partly overlapping with choice bias in perceptual decision making. The setting of decision thresholds is associated with fronto-basal ganglia networks which are also found for choice bias. In sum, we argue that the model-based approach holds great promises to understand the neural correlates of latent cognitive processes. Ó 2014 IBRO. Published by Elsevier Ltd. All rights reserved.

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INTRODUCTION Deciding on the category of a noisy perceptual stream of information is arguably the most important skill of the brain, being constantly confronted with perceptual input that requires classification. For this reason, decision making has been studied from many different angles, including biological, psychological, and mathematical perspectives. All of these have produced crucial insights into the mechanisms underlying judgment and decision making. The development of mathematical models of decision making has furnished the field with a mechanistic account of the decision process that describes and predicts choice behavior remarkably well. These models build upon the old idea that observed behavior such as response times (RTs) and accuracy can be decomposed in latent processes (Stone, 1960; Edwards, 1965; Laming, 1968; Ratcliff, 1978; Luce, 1986; Smith and Vickers, 1988). Many models are available today (e.g., the Ratcliff Diffusion Model, Ratcliff, 1978; Proportional-rate Diffusion model, Palmer et al., 2005; EZ, Wagenmakers et al., 2007; Linear Ballistic Accumulator (LBA) model, Brown and Heathcote, 2005; Single-trial LBA (STLBA), van Maanen et al., 2011; Leaky Competitive Accumulator model, Usher and McClelland, 2001; Decision Field Theory, Busemeyer and Townsend, 1993; Linear

Key words: evidence accumulation model, Drift Diffusion Model, Linear Ballistic Accumulator, fMRI.

*Corresponding author. Address: Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands. Tel: +31-20-525-6281. E-mail address: [email protected] (B. U. Forstmann).   Shared first authorship. Abbreviations: ACC, anterior cingulate cortex; aI, anterior Insula; BOLD, blood-oxygenated level dependent; DDM, Drift Diffusion Model; DLPFC, dorso-lateral prefrontal cortex; FEF, frontal eye field; fMRI, functional Magnetic Resonance Imaging; IFG, inferior frontal gyrus; IPS, intraparietal sulcus; ITG, intra temporal gyrus; LATER, Linear Approach to Threshold with Ergodic Rate; LBA, Linear Ballistic Accumulator; LIP, lateral intraparietal area; LOC, lateral occipital cortex; MNI, Montreal Neurological Institute; OFC, orbitofrontal cortex; pre-SMA, pre-supplementary motor area; SAT, speed-accuracy tradeoff; SDT, Signal Detection Theory; STLBA, single-trial LBA; STN, subthalamic nucleus; VMPFC, ventromedial prefrontal cortex. http://dx.doi.org/10.1016/j.neuroscience.2014.07.031 0306-4522/Ó 2014 IBRO. Published by Elsevier Ltd. All rights reserved. 872

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experimental manipulations

accuracy

model parameters

Explanatory levels

neuronal processes

Fig. 1. The formal model as a middle ground between observed data and neuronal processes (see also, Forstmann et al., 2011).

Accumulation to Ergodic Rate model, Carpenter and Williams, 1995) that can describe and explain the observed behavioral data from a broad range of choice experiments, using several fitting methods (e.g., Hierarchical drift diffusion model (HDDM), Wiecki et al., 2013; fastDM, Voss and Voss, 2007, 2008; DMAT, Vandekerckhove and Tuerlinckx, 2007, 2008). In its most simple form, these models all share the same assumption that a decision between two alternatives can be described by an accumulation of evidence that initiate a response as soon as the decision threshold for one of the alternatives is reached. The theoretical appeal of these accumulator models has been strengthened by findings from neurophysiological studies, showing similar patterns of accumulation processes in individual neurons (e.g., Cook and Maunsell, 2002; Roitman and Shadlen, 2002, see also Gold and Shadlen, 2007). Furthermore, formal models of decision making have been adopted by the neuroscientific community, where it has been used as an intermediate level between the observed behavioral data and its underlying neuronal substrate (Fig. 1). Such an approach has multiple advantages. Firstly, the model provides a formal account of how changes in reaction time and error distributions can be explained by a single mechanism. Secondly, the parameters can be related to a latent cognitive level of explanation. Thirdly, the model often has an intuitive relationship with the underlying neuronal substrate. For instance, firing rates of neurons in the monkey LIP (lateral intraparietal area) reflect the accumulation process prior to the actual choice, which is initiated when the neurons reach a critical firing rate (for review, see Gold and Shadlen, 2007). In this article we review the current state of the modelbased approach toward perceptual decision making. In particular, we review functional Magnetic Resonance Imaging (fMRI) studies that explicitly link bloodoxygenated level dependent (BOLD) activation to properties of formal models of decision making. Obviously, other neuroimaging methods have provided important insights into perceptual decision making as well. For example, single-cell recordings in non-human primates have provided the crucial link between ramping neuronal firing rates and evidence accumulation in lateral intraparietal area (LIP, Shadlen and Newsome, 1996, 2001; Roitman and Shadlen, 2002). However, in humans we rely on non-invasive measures to understand the biological perspective on cognition. In this review, we are especially interested in studies that show which

regions are functionally involved when making a perceptual judgment. Therefore, we focus on fMRI only, as it provides the best spatial resolution in human imaging studies. This way, we hope to identify the brain areas that dominate the mechanistic levels of perceptual decision making. Put differently, these brain regions might be

decision threshold drift rate starting point non-decision time

RTs Alternative A

Alternative B

B. Linear Ballistic Accumulator (LBA) model RTs Alternative A

Alternative B

Fig. 2. Two examples of formal decision making models. (A) Drift Diffusion Model. (B) Linear Ballistic Accumulator model. Visualizations of the crucial mechanisms are presented at the beginning of each section below.

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at the basis of the neural processes that drive the mechanisms that are implemented in formal perceptual decision making models. Evidence accumulation models of perceptual decision making In the class of formal decision making models mentioned above (see also Ratcliff and Smith, 2004, for a taxonomy of models), it is assumed that a choice depends on the accumulation of evidence for the various response alternatives. To illustrate this, we will discuss two specific implementations of this idea in more detail. The first is the Drift Diffusion Model (DDM, Ratcliff, 1978) which, although not the first evidence accumulation model, is one of the most applied models in model-based neuroscience and cognitive modeling in general. Part of its success is the breadth of data that it accounts for. The second is the LBA model (Brown and Heathcote, 2008). The LBA model is considered the simplest complete model of choice response time as it does not assume a stochastic but rather a ballistic evidence accumulation process, yet can still account for many benchmark phenomena. DDM Fig. 2A illustrates the DDM. Essentially, the model assumes that the difference in evidence for two response alternatives is represented by a biased random walk process. This process is captured by the drift rate parameter. Decisions are made as soon as the random walk hits one of two absorbing boundaries, with each boundary representing one response alternative. Because the drift is a noisy process, each boundary can in principle be reached. However, a positive drift rate means that it is more likely that the random walk will be toward the upper boundary, making the associated responses more likely. The time required to reach a boundary represents the decision time, which is a function of both the drift rate as well as the boundary separation. That is, higher drift rates as well as boundaries that are more close together lead to lower decision times. The observed response time is then the sum of the decision time and the time required for additional, non-decision-related processes. The DDM can be seen as a dynamic extension of the Signal Detection Theory (SDT, Green and Swets, 1966) framework. Within the DDM, each step of the accumulation process resembles a sample from one of the two alternative distributions as described by SDT (e.g., Ratcliff and McKoon, 2008; Starns et al., 2012). Despite the resemblance between DDM and SDT, here we opt not to include studies using the SDT framework, as the model can only account for the effects observed in accuracy but not RT data (Ratcliff et al., 1999). This limitation is unfortunate, as both accuracy and RT are informative to identify different types of processes underlying perceptual decisions (e.g., Criss, 2010; White et al., 2010). As a consequence, conclusions drawn from SDT analyses might be incomplete or even incorrect. Therefore, we do not include papers that use SDT in this review.

LBA model The LBA model is considered the simplest complete model of choice response time because it accounts for many standard behavioral phenomena with a minimal set of assumptions. It differs in some respects from the DDM, although the general principle is the same. Two properties of the LBA model deserve extra attention. The first property is that the model assumes that evidence accumulation occurs in separate, independent accumulators (Brown and Heathcote, 2008, see also Fig. 2B). This entails that the probability of making one response over the other is determined by the difference in drift rates. The drift rates in combination with the separate boundaries again specify the decision time. The assumption of separate accumulators allows the model to naturally consider more than two response alternatives (e.g., Ho et al., 2009, see also Van Maanen et al., 2012a). The standard implementation of the DDM does not have this property (although extensions are possible, Ratcliff and Starns, 2013). The second property of the LBA model is that the model assumes that the evidence accumulation process can be satisfactorily approximated by a ballistic process (Brown and Heathcote, 2005). That is, contrary to many evidence accumulation models including DDM, the LBA does not require a stochastic process to account for RT and choice variability. Rather, the model relies on between-trial differences in average evidence accumulation (drift rate) and response caution. The LBA can be seen as an extension of the LATER (Linear Approach to Threshold with Ergodic Rate) model (Carpenter and Williams, 1995; Reddi and Carpenter, 2000). The LATER model also assumes a random walk, but does not account for the within-trial variability in the process of evidence accumulation. Furthermore, contrary to the LBA, the LATER model cannot account for incorrect response time distributions (Brown and Heathcote, 2008, but see Nakahara et al., 2006). Decision-making mechanisms In addition to the DDM and the LBA model, there are many other models that assume some form of evidence accumulation (for an overview see, e.g., Ratcliff and Smith, 2004). Although all models differ in their implementation and their focus on specific mechanisms, they all share the following four basic mechanisms: First, all of these models share the property that evidence is accumulated over time until a certain response criterion is reached. The rate of evidence accumulation is often referred to as drift rate. Second, all models assume that evidence accumulation stops at a certain criterion value or decision threshold. Usually, this criterion is thought to be under control of the decision maker and may reflect response caution (Bogacz et al., 2010). Third, most models allow for the possibility that certain response alternatives are a priori more likely (when this is not assumed it is for reasons of simplification, Wagenmakers et al., 2007). The behavioral effects of such an asymmetry are captured by a parameter that reflects response or choice bias. Finally, all models share that a certain proportion of the response

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time is not accounted for by the decision process, referred to as non-decision time. This includes for example the time required to encode the stimulus or the time required to execute a motor response. At this point it is important to emphasize the goal of the model-based approach. It is a common misconception that the model-based approach is aimed at identifying which brain areas reflect the parameters of a cognitive model (O’Reilly and Mars, 2011). The aim is not to equate specific parameters with specific mechanisms. Rather, the aim is to distinguish between the different processes that drive the differences in choice behavior, and to decompose behavioral data in components that drive the observed behavioral changes. For example, an experimental manipulation that limits the time in which people are required to make a choice typically leads to fast and inaccurate responses. This effect is thought to be captured by the decision threshold. Therefore, variability in this parameter may reflect variability in how cautious people are (e.g., Forstmann et al., 2008). In turn, correlational analyses between the decision threshold and the underlying brain activity will help to identify brain areas that are involved in the adjustment of cautiousness due to the experimental manipulation. As such, by using the model-based approach, one is able to identify brain activity that relates to changes in latent cognitive processes, which cannot be observed by investigating neural correlates of RT and accuracy distributions. In short, a cognitive model does not necessarily represent the underlying neuronal processes itself. Rather, the model adds an intermediate explanatory layer between the neuronal and behavioral level, providing associations and relationships that are meaningful in understanding how neuronal processes drive behavioral observations (Fig. 1). Below we will review the neuroimaging studies that used the model-based approach to investigate the underlying neuronal substrate that gives rise to changes in the speed and accuracy of perceptual decisions. For each parameter we will report the most prominent findings showing brain activity related to the mechanisms associated with changes in the model parameter.

REGIONS ASSOCIATED WITH THE ACCUMULATION OF EVIDENCE Within an evidence accumulation model, the process of evidence accumulation is central. Accumulating evidence entails the extraction of information from the stimulus, in order to make a decision based on this evidence. Because this is an inherently noisy process, multiple evidence samples are required before enough evidence is obtained to make a decision (Green and Swets, 1966). This is why decisions take time. A particularly important concept is the rate with which evidence favoring one of typically two choice alternatives is accumulated (i.e., drift rate, Fig. 3). At first glance, a straightforward method to identify ‘accumulation’ regions in the brain is to investigate which brain areas are associated with changes in the drift rate within and between individuals (Forstmann

Evidence accumulation

drift rate

Fig. 3. Accumulation of evidence toward a decision threshold. When the quality of evidence per time unit is low, the rate of accumulation is slower (solid line), leading to longer response times and more errors.

et al., 2011). However, before one can interpret the relation between the BOLD response and the drift rate parameters, it is important to consider the predictions of such a relation. In other words, if the drift rate for one condition compared to the other is larger, what would one expect of the difference in BOLD response between the two conditions? One proposal is that neuronal activity and BOLD responses increase with the difference in sensory information between stimuli: the larger the discriminability between stimuli (i.e., higher drift rate), the larger the BOLD response. Rolls et al. (2010) provide an underlying mechanism for such a neural signature, found in the dorso-lateral prefrontal cortex (DLPFC). Using an attractor network (Wang, 2002), the authors show that DLPFC activation correlates with the difference in firing rate in pools of neurons representing the choice alternatives, thus giving credence to the idea that DLPFC computes a decision variable (Gold and Shadlen, 2002). Indeed, one of the first studies that interpreted their findings in the light of an accumulation model reported a higher BOLD response for easier decisions in the DLPFC (Heekeren et al., 2004), suggesting that the rate of evidence accumulation, which is closely related to choice difficulty, is processed by the DLPFC. Similar patterns are found in other regions as well. For example, the anterior Insula (aI) is often reported to relate to task difficulty in perceptual decision-making (Binder et al., 2004; Grinband et al., 2006; Philiastides and Sajda, 2007; Thielscher and Pessoa, 2007; Domenech and Dreher, 2010; Liu and Pleskac, 2011). However, although choice difficulty is behaviorally closely related to and often reflected by the drift rate parameter, other studies have suggested that they are processed separately by different brain regions. For example, Philiastides and Sajda (2007) showed effects of difficulty in (a.o.) DLPFC and aI, while the lateral occipital cortex (LOC) was identified as the most likely region for the integration of sensory evidence. As opposed to a positive correlation between drift rate and the associated BOLD response, other studies have provided an alternative hypothesis, where the expected BOLD response is negatively correlated with drift rate. According to these studies, the BOLD response should reflect the integrated activity of pools of neurons (e.g., Boynton et al., 1996; Logothetis and Wandell, 2004; Logothetis, 2008). Therefore, one would expect a smaller BOLD response for higher drift rates (Ho et al., 2009; Kayser et al., 2010b; Noppeney et al., 2010). Within this view, Ho et al. (2009) argued that, based on fits of the

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LBA model, easy trials – involving a high drift rate – lead to smaller BOLD responses with an earlier peak than hard trials – involving a low drift rate. The difference between these activation patterns was found in right Insular cortex, suggesting that this region might serve an important role in processing the accumulation of sensory evidence. However, other regions are associated with a negative correlation between drift rate and brain activity as well. A subset of studies reports such a relation in sensorimotor areas (frontal eye field – FEF – and intraparietal sulcus – IPS, Ho et al., 2009; Basten et al., 2010; Kayser et al., 2010b; Liu and Pleskac, 2011). Liu and Pleskac (2011) report higher fMRI responses on difficult trials than on easy trials in FEF and IPS. These findings are in line with previous primate single-cell recording studies. In particular, IPS is thought to be the human homolog of macaque LIP (Sereno et al., 2001; Grefkes and Fink, 2005), an area that has previously been implicated in evidence accumulation processes (e.g., Britten et al., 1992; Roitman and Shadlen, 2002). Presumably because of the wide variety of experimental paradigms, other brain areas than the areas discussed above have also been associated with drift-related processes. For example, inferior frontal gyrus (IFG) activation was found to covary with drift rate parameters in a stop-signal paradigm (White et al., 2014). A similar pattern of activation was reported by Rowe et al. (2010). Using an experimental paradigm where participants were given a free choice rather than a forced choice, these authors found activation in the IFG, anterior cingulate cortex (ACC), and premotor and (pre-) supplementary areas to correlate with the accumulated evidence on a trial-by-trial basis. Taken together, fMRI studies incorporating drift-related changes point toward a frontoparietal network that is involved in evidence accumulation in the brain. Discussion For the process of evidence accumulation, studies reported primarily regions from the fronto-parietal network to be associated with changes in drift rate, with a predominant role for the lateral prefrontal cortex (LPFC) (dorsal and ventral) and the Insula. Note, however, that there are several methodological issues that seem to be problematic to find a consensus across different studies and paradigms. Firstly, the predictions about drift rate related activity differ across studies. That is, some studies assume a positive correlation between drift rate and a BOLD response, while others expect a negative relationship. Secondly, the process of evidence accumulation is often collinear with cognitive processes that are closely related to, but maybe not the same as the rate of accumulation itself. For example, when the quality of sensory information is low, more time is needed to collect the required amount of evidence to hit the decision threshold. Such a slower process will be reflected by a lower drift rate. However, as the quality of information is low, the decision will be more difficult, and might induce the need for attentional resources. As such, a lower drift rate is often directly related to difficulty, which in turn will evoke a change in motivational and

attentional resources of the decision maker. As a result, the process of evidence accumulation might be related, or even be equal to processes of attention and motivation. The challenge for cognitive neuroscience is to develop clever experimental designs to separate the multicolinearity between these different processes. Several studies already set the stage for this purpose (Philiastides and Sadja, 2007; Ploran et al., 2007; Ho et al., 2009; Kayser et al., 2010a). However, no clear consensus in accumulation-related regions was found across these studies. This calls into question the specificity and external validity of the results of experiments that use drift rate as a covariate to identify ‘accumulation regions’. A third problem that might arise when investigating accumulation processes in the brain, is the question how specific brain regions are expected to be, in terms of the type of information that is accumulated. For example, would one expect a region that is associated with the accumulation of visual information to be involved in the accumulation of auditory information as well? Noppeney and colleagues (2010) investigated the accumulation of integrated auditory and visual sensory evidence. The authors found that the IFG showed the expected pattern of an audio-visual accumulator, suggesting that this region combines different sources of information for the accumulation process, which it receives from auditory and visual sensory areas. The ventro-lateral prefrontal cortex has been associated with the accumulation process by other studies as well (Philiastides and Sajda, 2007; Rowe et al., 2010; White et al., 2014), suggesting that this region might be involved in an accumulation process independent of sensory modality. Alternatively to processing stimulus information, one might expect an accumulator region to process response related information. For example, when an alternative requires a left vs. a right button press, the drift rate might just be a reflection of a gradual preparation of a motor response associated with the sensory information. Indeed, single-cell recordings in non-human primates show an accumulation process in sensori-motor regions that are assumed to be involved in motor planning (Gold and Shadlen, 2007). Along these lines, one might expect less variability in findings across studies, since many studies involve a similar type of response such as button presses or eye-movements. However, some studies show accumulator-related activity independent of the type of response-modality (e.g., saccades vs. button presses; Heekeren et al., 2006; Ho et al., 2009; Liu and Pleskac, 2011), suggesting that the accumulation process might arise earlier in the stream of action selection before the actual response is executed by the response-specific brain areas. Combined, most studies show that the fronto-parietal network is involved in the accumulation processes driving a perceptual decision. However, to gain a better understanding of what is accumulated and where, several challenges still have to be met. One such challenge is to identify the linking properties (Teller, 1984), by which the cognitive model translates into the neuronal model. It already has been shown that such a

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translation might not be a one-on-one projection of modelproperties onto the neuronal substrate (e.g., Churchland et al., 2011). As such, one needs to understand how the neuronal substrate gives rise to the observed changes in model parameters, at different spatial and temporal scales. For example, computational studies of perceptual decisions have begun to investigate how biologically plausible neuronal networks might drive the observed changes in the behavioral data, and the underlying model parameters (e.g., Purcell et al., 2010; Ratcliff and Frank, 2012; Zandbelt et al., 2014). At the same time, it is important to understand how these neuronal networks and their firing patterns are represented by the fMRI BOLD responses, aiding the interpretation of the associated BOLD responses.

REGIONS ASSOCIATED WITH THE DECISION THRESHOLD In many situations, decisions have to be made very quickly running the risk of committing errors. Finding the right balance of response speed while trading with response errors is called the speed-accuracy tradeoff (Fig. 4, SAT, Fitts, 1966; Schouten and Bekker, 1967; Wickelgren, 1977; Bogacz et al., 2010). Crucially, in experimental psychology as well as the cognitive neurosciences, the SAT is thought to affect specifically a decision threshold. The SAT has been studied extensively, both in non-human primates (e.g., Heitz and Schall, 2012) and humans, and on the behavioral level (e.g., Fitts, 1966; Ratcliff, 1985; Ratcliff and Rouder, 1998; Mulder et al., 2010, 2013; Schneider and Anderson, 2012) as well as in combination with functional and structural brain measures (e.g., Boehm et al., 2014; Forstmann et al., 2008, 2010b; Van Maanen et al., 2011). Initial studies using perceptual-discrimination tasks and fMRI pointed to a prominent role of a corticosubcortical network implementing SAT. Ivanoff et al. (2008), van Veen et al. (2008), Forstmann et al. (2008), and Winkel et al. (2012) found that the pre-supplementary motor area (pre-SMA) together with the striatum, a subcortical nucleus and part of the basal ganglia, revealed increased activation under speed compared to accuracy emphasis. Importantly, Forstmann and colleagues (2008) showed that the individual differences in the adjustment of the LBA decision threshold correlated with brain activity in the fronto-striatal network. More specifically, increased activity in the pre-SMA and striatum was positively correlated with a decrease in the LBA

decision threshold

Fig. 4. Adjustments of the decision threshold explain the speedaccuracy tradeoff. A lower threshold (solid line) leads to shorter response times and more errors.

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decision threshold, reflecting speeded, but less cautious responses. This led to the conclusion that SAT is modulated in pre-motor and association areas rather than in sensory or primary motor areas and that activity in these areas is modulated by inter-individual differences in response caution (see also Bogacz et al., 2010). Recently, van Maanen and colleagues (2011) elaborated these findings by using the single trial LBA (STLBA) model, which allows one to measure changes in the decision threshold from trial to trial. Such a method is able to capture a within-subject variance in brain activity, related to subtle changes in the decision threshold. The authors found that the fronto-striatal network updates the required response caution, with respect to the current task demands. In particular, when participants were required to respond quickly, trial-to-trial measures of brain activity in the pre-SMA and dorsal ACC correlated positively with trial-to-trial fluctuations in the height of the decision threshold. In contrast, on trials that required a change from a speeded response mode to a more accurate response mode (or vice versa), a positive correlation between response caution and activity in the ACC proper was found. These results confirm the idea that the frontostriatal network is involved in controlling the speed and accuracy of perceptual decisions. In addition to a fronto-striatal network, SAT effects are also observed in sensory areas. Ho et al. (2012) employed the STLBA model to investigate effects of speed-accuracy tradeoff in early sensory visual areas such as V1. They found a correlation between V1 activation and STLBA drift rate parameter, suggesting that decreased task performance during decision making was related to a failure to optimally process sensory signals. This result suggests that SAT effects are not only modulated in pre-motor areas but are associated with changes in primary visual areas as well. A different manipulation to selectively affect decision thresholds and gain a deeper understanding of response caution is the amount of prior information of the upcoming trial. Mansfield and colleagues (2011) used a cued-trial task-switching paradigm. The main goal was to probe regions from fronto-striatal and fronto-subthalamic networks. EZ diffusion model parameters showed that fully and partially informative switch cues produced more conservative threshold settings compared to repeat cues. Repeat cues were associated with higher activation in the pre-SMA and striatum than switch cues. For all cue types, individual variability in decision threshold was associated with variability in the BOLD response in preSMA, with higher activation linked to lower threshold settings. In the striatum, this relationship was found for repeat cues only. These findings support the notion that pre-SMA biases the striatum to lower response thresholds under more liberal response regimes. In contrast, a high threshold for switch cues was associated with greater activation in right subthalamic nucleus (STN), consistent with increasing response caution under conservative response regimes. In summary, neural models of decision threshold adjustments can help explain executive control processes in task switching.

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Discussion Neuroimaging studies focusing on how the brain controls the speed and accuracy of perceptual decisions often report the use of a task manipulation that requires the participant to respond either very accurately or very fast. Typically, a speed-accuracy tradeoff is observed which is related to the amount of evidence that is required in formal models of perceptual decision making. Studies repeatedly report the involvement of regions of the fronto-basal ganglia network. More specifically, these studies show that the pre-SMA, ACC, and striatal regions are associated with the level of the decision threshold. These findings are in line with suggested models of how the brain might control the speed and accuracy of required actions. Within these models, cortical regions monitor and control nuclei of the basal ganglia, which in turn release or withhold the brain from responding (Bogacz et al., 2010 for a review of possible mechanisms). Along these lines, one could argue that frontal regions, like the ACC, serve as a control unit to adjust the response threshold via the striatum. Possibly, the (STN is involved in this process as well: where higher activation in the striatum seems to promote speeded choices, increased activation in the STN prevents the brain from responding too fast and thus increases caution. The interplay in adjusting and controlling the speed and accuracy of perceptual decisions between these different nuclei of the basal ganglia is the topic of future research.

REGIONS ASSOCIATED WITH RESPONSE OR CHOICE BIAS Within the framework of evidence accumulation models, prior knowledge can bias the decision process via two mechanisms (Fig. 5). The first mechanism, here referred to as starting point bias, involves a change in the distance between the starting and ending point of the accumulation process. When prior knowledge is in favor of one of the alternatives, less evidence is needed to reach the decision threshold, resulting in faster and

Starting point bias

drift rate starting point

Drift rate bias

Fig. 5. Biasing the evidence accumulation process. Either a bias occurs in the amount of prior evidence (starting point bias) or a bias influences the rate of evidence accumulation (drift rate bias).

more choices for that alternative. The second mechanism involves a bias in the sensory information itself (a shift in the drift rate criterion, i.e., a drift rate bias). As a result, the rate of evidence accumulation increases in favor of the preferred alternative giving rise to faster and more choices for that alternative. Although both mechanisms result in faster choices and improved levels of accuracy for the preferred alternative, the underlying mechanisms are very different. A starting point bias is often driven by a discrepancy in (prior) contextual information about each alternative. For example, an individual might have information about one alternative being more likely to be correct, or having a larger payoff. Such a conditional asymmetry biases the decision process toward the expected or preferred outcome, resulting in faster and more choices for that alternative. In contrast, a drift rate bias is not driven by prior information about the conditional differences between the alternatives. Rather, it is driven by a change in the interpretation of the observed sensory signal, leading to a difference in the criterion that determines whether a sample of sensory information is evidence for one alternative or the other. For example, when participants have to make a choice whether a line is ‘short’ or ‘long’ depends on the point of reference (e.g., what is defined as ‘a short line’ or ‘a long line’; White et al., 2012). When the point of reference changes due to prior knowledge, the classification of sensory evidence will change as well. As such, samples of evidence that were previously assigned to one alternative are now assigned to the other alternative, resulting in a change in the rate of evidence accumulation toward the decision threshold. Since a starting point bias is often associated with differences in reward or expectancy, one might expect a relationship between changes in the starting point and regions that are involved in processing value and expectancy. Indeed, one of the first imaging studies using the model-based approach on choice bias showed that individual differences in LBA choice bias were related to activity in the orbitofrontal cortex (OFC), a region often associated with value-based decision making (Forstmann et al., 2010a). In this study, the decision process was manipulated by providing prior knowledge about the likelihood of occurrence for a particular stimulus in the upcoming trial. Participants consistently choose faster and more often for the alternative that was most likely, which was captured by a smaller distance between the start and ending point of the biased accumulator in the LBA model. In addition to the OFC, individual differences in the BOLD response in the putamen were also associated with individual differences in the LBA bias parameter, suggesting a role for the cortico-striatal network in biasing choices. In line with this finding, Summerfield and Koechlin (2010) also found a bias-related signal in the OFC. In their study, a starting point bias was induced using a parametric manipulation of the amount of costs and benefits associated with the choice outcome. This was quantified using an Ornstein–Uhlenbeck model (Busemeyer and Townsend, 1993) to measure the onset

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of the accumulation process (equivalent to the starting point in the DDM, or the threshold adaptation in LATER and LBA). Interestingly, bias signals have been found in regions associated with the accumulation of evidence as well, such as IPS (Summerfield and Koechlin, 2010) and DLPFC (Nagano-Saito et al., 2012). Nagano-Saito et al. (2012) found that a reward-based bias signal (LATER) was processed by the ventral striatum and cortical regions including premotor cortex and the DLPFC, again suggesting a role for the cortico-striatal network in biased perceptual choices. A study by Domenech and Dreher (2010) showed that the ACC was associated with starting point bias, as measured by the LATER model. However, the DLPFC only showed activity related to the accumulation of evidence. Mulder et al. (2012) studied the biasing effects of both value-based and likelihood driven bias in perceptual choices. They found that frontal-parietal regions, including regions of the DLPFC, ACC, ventromedial prefrontal cortex (VMPFC), and parietal regions (IPS) were associated with a shift in the starting point of the accumulation process, independent of the type of prior information. In turn, frontal regions, like the DLPFC, might feedforward this prior bias signal toward regions that are sensitive to the upcoming accumulation process resulting in a modulation of the amount of evidence that is needed to reach a response threshold. Not many studies have investigated the biasing effects of a shift in the drift rate criterion (drift rate bias). However, using a clever experimental design, White and colleagues (2012) investigated where changes in perceptual criteria are processed by the brain. In this study, participants were required to classify a line as being short or long. Before each block of trials, the participants were shown a line that served as the point of reference. Different lines were used for several blocks of trials, resulting in a change in the speed and accuracy for one alternative over the other. The DDM was used to quantify this perceptual bias, which was captured by a change in the drift rate criterion. Individual differences in the criterion were associated with differences of activity in the intra temporal gyrus (ITG), a region also associated with the accumulation of sensory evidence (Ploran et al., 2007). In short, although the experimental manipulations to induce bias are very specific, the brain networks that correlate with bias parameters are remarkably similar to the brain networks identified with evidence accumulation and decision threshold. A possible explanation lies in the model parameters that capture behavioral effects related to bias: A change in starting point is closely related to a change in decision threshold, since both affect the amount of evidence that is required for a decision; A change in drift rate criterion results in a similar change in drift rate as a change in task difficulty.

processes result in a smaller distance between the starting and ending point of the accumulation process, resulting in faster choices. For biased choices, the involvement of the fronto-basal ganglia network might be related to the increase in speed similar to a change in the decision threshold. However, changing the decision threshold(s) results also in a higher probability of an incorrect choice, whereas a shift in the starting point results in the opposite effect, where more (correct) choices are made for the biased alternative. The mechanism that drives the higher proportion of correct choices for the biased alternative might be related to the fronto-parietal network, which is involved in processing of sensory evidence. Along these lines, one might reason that the fronto-parietal network is involved in processing prior (sensory) information as well, which serves as already collected evidence for the alternative that is more likely or has a larger payoff. To the best of our knowledge, only one fMRI study reports evidence for drift rate bias in relationship with fMRI BOLD responses and the change in the drift rate criterion. White and colleagues (2012) showed such a relationship in the ITG. Interestingly, this area has been associated with the comparison of perceptual expectations and the real sensory observations (Summerfield and Koechlin, 2008), suggesting a role in stimulus identification for this region.

REGIONS ASSOCIATED WITH NON-DECISION PROCESSES The mechanisms discussed so far account for most of the variance of the actual decision process. Most models, however, assume that in addition to decision-related processes, part of the response time is explained by non-decision-related processes (Fig. 6). Typically, these processes are thought to involve perceptual encoding and response execution (Ratcliff and McKoon, 2008). Some accumulator models simply assume that non-decision time is a constant (e.g., Palmer et al., 2005; Brown and Heathcote, 2008), while other models assume that non-decision time is a random uniformly distributed variable (e.g., Ratcliff, 1978; Ratcliff and Tuerlinckx, 2002). Additionally, there are models that consider the decision process only as a small segment of the complete time course, and hence extensively model the remaining RT (e.g., Van Maanen et al., 2012b; Zylberberg et al., 2012). These models are not considered here.

Sensory & motor processes

non-decision time

Discussion Both the fronto-parietal and fronto-basal ganglia network seems to be involved in biasing perceptual decisions. Note that a change in the starting point of the accumulation process is conceptually closely related to a change in the decision threshold. That is: both

Fig. 6. Other processes not directly involved in the central decision processes are referred to as non-decision processes.

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Contrary to the mechanisms discussed so far, there has been surprisingly little research on non-decision time. An obvious explanation for this is that the term itself is underspecified. That is, every process in a task can be referred to as non-decision time as long as it is not referred to as decision time. Consequently, many aspects of behavior are linked to the non-decision time parameter, including aging (Ratcliff et al., 2004), increased attention (e.g., Jepma et al., 2012; Heathcote and Love, 2012; Heitz and Schall, 2012; Ho et al., 2012; Rae et al., in press), and dual-task interference (Sigman and Dehaene, 2005; Mulder and Van Maanen, 2013). Additionally, the properties of the distribution of non-decision times are not well understood (cf. Ratcliff, 2013). The traditional interpretation of non-decision time as a compound of perceptual encoding and response execution processes is supported by only a few behavioral studies. Donkin et al. (2009) have shown that word frequency effects in lexical decision are best explained by non-decision time. They argue that this reflects that word frequency affects early word-form processing that precedes the lexical decision. Ho et al. (2009) show in a four-alternative choice task that non-decision times for saccadic responses are smaller than non-decision times for manual responses. This study illustrates the response execution component of nondecision time, and shows that saccadic motor programs are faster than manual motor programs. Additionally, some studies find circumstantial evidence for the role of non-decision time in motor processing (e.g., decreased non-decision time for clear stimulus response mappings (Mulder et al., 2012), or increased non-decision time for high alcohol intake (van Ravenzwaaij et al., 2012). To date, there is only one study that has quantitatively studied which brain areas show a BOLD response that relates to non-decision time (White et al., 2014). White et al. (2014) aimed to understand behavior in a stopsignal paradigm. Because the stop-signal paradigm does not entail a traditional two-choice decision task, they developed an extension of the diffusion model that allowed for an additional accumulation process, representing the evidence for the stop signal. In their study, non-decision times correlated negatively with activation in the right parietal cortex on successful stop trials (contrasted with go activation). Thus, participants that were characterized by slower motor execution on go trials displayed less activation in right parietal areas (on successful stop trials as compared to go trials). Surprisingly, the authors report no correlation between non-decision time and activation on go-trials. Based on the work of Filimon et al. (2013) and Liu and Pleskac (2011), a clear prediction of the White et al. (2014) study would have been that BOLD in motor areas such as pre-SMA and SMA correlated negatively with non-decision time. However, the authors did not report such a finding. Filimon et al. (2013) and Liu and Pleskac (2011) reported (pre-)SMA activation during motor preparation in tasks in which the decision and motor stages were explicitly separated. Filimon et al. (2013) additionally reported that motor areas such as the pre-SMA show greater activation for hand movement preparation in high sensory versus low

sensory trials. It should be stressed, however, that since these authors did not fit an accumulator model, a specific link between the model mechanisms and brain data remains hypothetical. Discussion In sum, it should be noted that for non-decision time, the pattern of regions identified with fMRI using the nondecision time parameter, is not clear. Presumably, this is due to the fact that non-decision time processes are too diverse. However, should such a network exist, we hypothesize that it involves areas that are known to be related to response execution, such as primary and supplementary motor cortices.

SUMMARY AND CONCLUSION From the above reviewed articles, a diverse picture emerges. To obtain better insight into where in the brain a relation with decision-making model parameters has been observed, we summarized the articles in the following way. From each article that explicitly reported an fMRI analysis that was informed by model parameters, we took the reported peak coordinates and transformed them to Montreal Neurological Institute (MNI) space if necessary.à For each MNI peakcoordinate, a small sphere with a 1-mm radius was created. Next, each of these spheres was labeled using automated anatomical labeling (AAL, Tzourio-Mazoyer et al., 2002). The labels were chosen from the Atlas of Human Brain Connections (Catani and De Schotten, 2012; Forstmann et al., in press). For each model parameter, peak-coordinates were grouped according to their label. Then, a group-coordinate was calculated by averaging the x, y, and z coordinates across all peaks with the same label, for each hemisphere separately. Fig. 7 displays these group coordinates. The diameter of the sphere is proportional to the number of studies included in the group. Despite the large variation in regions that are involved in perceptual decision-making (Fig. 7), and in particular in the processes that are associated with parametric changes of the accumulator models, some global patterns emerge. First, the accumulation of evidence is mainly associated with regions from a fronto-parietal network (Fig. 7). Second, adaptation and individual differences in the decision threshold are related to a fronto-basal ganglia network, and third, choice bias is associated with a fronto-parietal network as well as with a fronto-basal ganglia network. For the non-decision time parameter, the pattern is less clear. Conclusion In the past decade, a new field called ‘model-based cognitive neurosciences’ has emerged. Examining the literature, it is clear that the model-based approach has been fruitful by showing a relationship between changes à We excluded studies that report a regions-of-interest analysis based on masks (Philiastides and Sajda, 2007; Mansfield et al., 2011; Ho et al., 2012) as well as one study that used a functional localizer task (Liu and Pleskac, 2011).

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Evidence accumulation frontal lobe parietal lobe temporal lobe occipital lobe limbic lobe insula Decision threshold

basal ganglia

1

4 7 nr. studies

Starting point bias gp

Drift rate bias

Non decision time Non-decision

Fig. 7. 3D renderings of the peak-coordinates reported by studies that include model parameters in fMRI analysis. Seven studies are included for evidence accumulation, two studies are included for decision threshold, five studies are included for starting point bias, one study is included for drift rate bias, and one study is included for non-decision time. The size of each sphere is proportional to the number of studies that report a specific region of interest. See text for details.

in the speed and accuracy of perceptual choices, and the underlying processes driving these behavioral changes. Such an approach seems especially successful for processes involving the decision threshold (e.g., SAT) and the starting point (e.g., choice bias). The other

processes that make up a perceptual decision are more difficult to study, resulting in predictions about the BOLD response that are less clear and reliable (e.g., changes in drift rate and non-decision time). Nevertheless, we believe that the model-based approach helps to

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understand cognitive processes, which can be decomposed in separate components by using an accumulator model. Note, however, that these components are not to be considered as neurological processes themselves, but are merely an extra explanatory level to understand the relationship between the observed speed and accuracy of a perceptual choice, and the underlying neuronal substrate that drives it. Acknowledgments—This research line is financially supported by the European Research Council (BUF), and a VIDI grant (BUF) from the Netherlands Organization for Scientific Research (NWO). We would like to thank Roger Ratcliff for helpful comments.

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(Accepted 21 July 2014) (Available online 29 July 2014)