The Role of Dorsal Premotor Cortex in Resolving Abstract Motor Rules: Converging Evidence From Transcranial Magnetic Stimulation and Cognitive Modeling

Abstract

In this study, repetitive transcranial magnetic stimulation (rTMS) was applied over left dorsal premotor cortex (PMd) while participants performed a novel task paradigm that required planning of responses in accordance with both instructed rules and present stimuli. rTMS is a noninvasive form of neurostimulation that can interfere with ongoing processing of a targeted cortical region, resulting in a transient “virtual lesion” that can reveal the contribution of the region to ongoing behavior. Increased response times (RTs) were observed specifically when rTMS was applied over PMd while participants were preparing to execute a complex response to an uninstructed stimulus. To further delineate the effect of stimulation, condition-specific RT distributions were modeled as three-parameter Weibull distributions through hierarchical Bayesian modeling (HBM). Comparison of the estimated parameters to those of a paired control demonstrated that while PMd-rTMS slightly decreased nondecision time, it also greatly increased the variability in the RT distribution. This increased variability resulted in an overall increase in predicted mean RT and is consistent with a delay in cognitive processes. In conjunction, an ACT-R cognitive model of the task was developed in order to systematically test alternative hypotheses on the potential cognitive functions that may be affected by stimulation of PMd. ACT-R simulations suggested that participant’s behavior was due to an effect of TMS on a “re-planning” process, indicating that PMd may be specifically involved in planning of complex motor responses to specific visual stimuli. In conjunction with the HBM modeling effort, these results suggest that PMd-rTMS is capable of pausing or slowing the execution of a motor response-planning process.

1. Introduction

Rules that guide behavior often consider categories of stimuli and responses; for instance, a particular color may indicate that a specific finger should be used to press a button. Specific identities within these categories are linked through a conditional association to form an exemplar of the rule—following the rule above, a conditional association may be, “If the light is blue, use your ring finger to respond.” This format necessitates representation of rules in an abstract way that allows for consideration of a potentially wide range of stimuli and responses. A growing body of research suggests that abstract rules are represented by frontal cortices (Badre, 2008; Koechlin, Ody, & Kouneiher, 2003). For example, activation of prefrontal cortex (PFC) has been observed while humans either learn task rules or execute behavior in accordance with previously learned rules (Stocco, Lebiere, O’Reilly, & Anderson, 2012).

Despite this, it is obvious that behavior itself is concrete: Specific effectors are utilized in specific manners in response to specific stimuli. For effective control, potential/present concrete stimulus identities must be utilized in conjunction with known rules in order to “resolve” a concrete behavioral response. Compared to the representation of abstract rules, relatively little is known regarding this process of response resolution in the brain. A potential candidate to execute a response resolution process is the dorsal premotor cortex (PMd). Anatomically, PMd receives input from both PFC, responsible for abstract rule representation, and posterior parietal cortex, a site of multisensory integration (Tomassini et al., 2007). Electrophysiology conducted in nonhuman primates has revealed that PMd neurons encode movement kinematics (such as direction or amplitude of to-be-performed movements), but that this activity is dependent on the context the movement is performed within (Cisek & Kalaska, 2005). As a result, it has been proposed that PMd may serve to transform simple contextual cues into motor responses (Wise, Boussaoud, Johnson, & Caminiti, 1997).

To investigate whether PMd activity is necessary to resolve behavioral responses in accordance with known rules and stimuli, we constructed a novel task based on the rapid instructed task learning (RITL) paradigm, which allows for the independent examination of encoding, planning, and execution of rules (Cole, Laurent, & Stocco, 2013). On each trial, the participants were first required to encode a trial-specific conditional association (a stimulus-response association that indicates the correct response to be made, conditional on some feature of the stimulus), and then resolve and execute a response after a stimulus was given. Rules could either be “Concrete” or “Symbolic.” In “Concrete” rules, a specific stimulus category (e.g., a digit being “even” or “odd”) was associated with a specific motor effector (right index or middle finger; e.g., “if the number is odd, press the index finger”). In “Symbolic” rules, the specific stimulus category was associated with a placeholder symbol (“A” or “B”) that, upon stimulus presentation, was assigned to a specific motor effector (e.g., “If the number is odd, press the finger associated with ‘A’”). This secondary association was instantiated as a congruent screen position-to-response effector mapping: The placeholder symbols “A” and “B” were randomly presented in the bottom left and right corners of the screen in parallel with the digit stimulus, and the two positions were consistently mapped to the index (screen left corner) and middle (screen right corner) finger of the right hand. While these placeholder symbols appeared across conditions, they only carried meaning in the “Symbolic” condition. Furthermore, stimuli on a subset of trials were designed to violate the instructed conditional association (e.g., a number being odd when the rule specified an “even” stimulus), requiring participants to replan the correct response.

While participants performed this task, high-frequency repetitive transcranial magnetic stimulation (rTMS) was applied over PMd during one of two time points during a given trial: either while presenting the trial-specific conditional association (i.e., “Early” stimulation) or while presenting the stimulus to respond to (“Late” stimulation). By utilizing rTMS to induce a “virtual lesioning” effect within PMd, the extent of this region’s involvement in the encoding and response resolution phases of this task can be examined. If PMd is involved in the encoding of the rule, rTMS should significantly affect response times (RTs) during the “Early” encoding phase. Alternatively, if PMd underpins response resolution, “Late” rTMS should lead to increased RTs during the execution phase.

Interpretation of the effects of rTMS on behavior requires a careful consideration of the possible processes that might be disrupted. A high-frequency pulse train has limited temporal duration (in our experiment, 0.5 s) and its effects crucially depend on the timing of the underlying process. For example, a delay in the response to a stimulus could be interpreted as resulting from an inhibitory effect on the retrieval of a stimulus-response mapping, on the ability to utilize a retrieved mapping to resolve a response, or on motor execution itself. Without a reasonable process model, it is impossible to fully examine the space of possible explanations.

For this reason, we examined the effects of rTMS on response times through two converging modeling approaches. First, we applied hierarchical Bayesian modeling (HBM) to investigate which parameters in a psychologically plausible model of response distributions are affected by TMS. Second, we used a popular and biologically plausible cognitive architecture (ACT-R; Anderson, 2007) to create an interpretable process model of the experiment, and simulated the effects of TMS across all model components. The two modeling approaches can be seen as complementing each other, examining our hypothesis in breadth (ACT-R) and depth (HBM), and ideally should give consistent and converging interpretations of the results.

1.1. Hierarchical Bayesian modeling of response times

A hierarchical parametric Bayesian framework (hierarchical Bayesian modeling; HBM) was used to model RT distributions from each condition in the task as three-parameter Weibull distributions (Rouder, Lu, Speckman, Sun, & Jiang, 2005; Rouder, Sun, Speckman, Lu, & Zhou, 2003). This parameterization of the Weibull distribution includes shape, scale, and shift parameters, and it was chosen because of two appealing characteristics. First, it has a lower bound and is right-skewed, like RT distributions. Second, its parameters have a psychological interpretation. Specifically, the shape parameter reflects the “structure” of the underlying cognitive processes (i.e., the order of cognitive steps, which can be interpreted as the mental strategy utilized to perform the task); the scale parameter reflects the speed of cognitive processes; and the shift parameter reflects the speed of peripheral processes (i.e., nondecision time; Rouder et al., 2003). These interpretations pair well with the format of the ACT-R cognitive architecture: modifying the manner in which the ACT-R model completes the task would constitute a change in the structure of cognitive processes; the speed of execution is reflected by the time over which the model’s processing steps are active; and the nondecision time is reflected in the model’s perceptual-motor processing steps.

1.2. ACT-R model of rTMS effects

ACT-R models are a combination of declarative and procedural knowledge; declarative knowledge is stored as structured records (“chunks”), whereas procedural knowledge is represented as IF-THEN rules (production rules or “productions”). Behavior unfolds as one production at a time is selected for execution, upon which it retrieves, moves, or modifies chunks as part of its actions. Chunks and productions interact with each other through a series of “buffers,” limited-capacity temporary stores that hold a single chunk for extended periods of time, making it accessible to productions.

The ACT-R model follows the same strategy under the experimental and control conditions. Additionally, the manner in which the model performs “Symbolic” and “Concrete” rule conditions is identical with the exception of a visual search component, which is required by the “Symbolic” condition (i.e., finding the position of “A”), but not the “Concrete” condition. In general, the model translates the given conditional association into a response plan for the specified stimulus. The plan is temporarily stored in working memory, to be used if the presented stimulus carries the instructed feature. If the stimulus matches that which was planned for, the response is immediately executed. However, if there is a violation of the expected stimulus, a “re-planning” occurs in which a new plan considering the evident stimulus is prepared and subsequently executed. The only difference between how the model considers the “Concrete” and “Symbolic” conditions is the information content of the chunk produced by “planning” (in addition to the aforementioned visual search). The model’s “planning” and “re-planning” productions reflect the response resolution processes: The productions use known conditional associations and present stimuli to determine an appropriate motor response. rTMS stimulation is simulated by independently interfering with each buffer and production considered by the model. To our knowledge, the effects of TMS on brain and behavior have never been simulated in ACT-R, and ACT-R has never been used to clarify the possible interpretations of TMS effects.¹

2. Methods

2.1. Participants

Twelve right-handed participants (8 females, M_age = 24.7 ± 3.3) with no history of neurological disorder, head injury, or any other contraindications to rTMS were recruited to participate in the study. Recruitment was restricted to individuals who had previously participated in neuroimaging experiments at the University of Washington, and for whom structural and functional imaging data already existed. Data could not be collected for four of the volunteers, as appropriate resting motor thresholds for these individuals could not be determined. All participants received a briefing regarding potential adverse effects before giving verbal consent and received monetary compensation proportional to the total amount of time devoted to the study. The experimental protocol was approved by the University of Washington’s Institutional Review Board as minimal risk.

2.2. Task paradigm

The progression of the task is depicted in Fig. 1. Participants were instructed to determine the parity of a numeric stimulus (restricted to the digits 2–9; presented in the center of the screen during stimulus presentation) and respond on the basis of a trial-specific rule. Responses occurred by pressing the “left” or “right” arrow keys on a standard keyboard with the participant’s right-hand index and middle fingers, respectively.

Fig. 1.

Time course of “Concrete” (left) and “Symbolic” (right) trials. Red lines represent the moments at which rTMS was applied.

Participants were presented with two types of rules: “Concrete” rules, which indicated the association of a specific effector (either index or middle fingers of the right hand) to a specific parity (“EVEN” or “ODD”); and “Symbolic” rules, which indicated the association of a specific letter on the screen (“A” or “B”) to a specific parity. Specific effectors in the “Concrete” condition were indicated during rule presentation by a stylized hand (black on white background), with the rule-specific effector denoted by a red circle around the tip of the finger. Specific effectors in the “Symbolic” condition were indicated during stimulus presentation by the placement of the letters “A” and “B,” which were randomly assigned to the bottom left and right corners of the screen on a trial-by-trial basis. To make the two conditions visually comparable, these letters appeared during the stimulus presentation phase of both “Concrete” and “Symbolic” trials, although they only carried meaning in the “Symbolic” condition. Participants were informed that the bottom left and right corners of the screen corresponded to the “left” and “right” arrow keys, respectively. Due to this manipulation, participants could not prepare a specific motor effector until stimulus presentation during a “Symbolic” trial.

Crucially, instructions specified only half of a trial’s rule. That is, participants may be given the instructions “EVEN:Index” but then asked to respond to a stimulus (e.g., “7”) that is odd. Under these circumstances, participants have to mentally re-plan a new stimulus-response configuration. This created a third experimental factor in which the trial is either “Instructed” (e.g., the instructions mention an even number, and the stimulus is even) or “Inferred” (i.e., the instructions mention an even number, but the stimulus is odd). “Inferred” trials are of particular interest, as re-processing of the rule likely occurs within the window of delivery of a TMS pulse train during “late” stimulation.

The task consisted of four blocks of 60 trials each, with a 5-min break enforced between each block. At the beginning of each trial, a central fixation cross was illuminated for 1 s. Once the fixation was extinguished, the rule informing the participant of the individual trial’s valid associations was displayed for a maximum of 5 s. Presentation of rule condition was randomized across trials within a block. After participants acknowledged the rule (by pressing the spacebar with their left hand), a variable (0.25–2 s) delay occurred while a fixation “asterisk” was displayed (Fig. 1). Once this delay had passed, the stimulus was displayed and participants were given a 5 s window to respond by pressing the left or right arrow key with the index or middle finger of their right hand. Upon response (or after 5 s had passed), a variable inter-trial interval (5–9 s) was enforced while a blank screen was displayed. Including breaks between blocks, the task took approximately 1.25 h to complete.

Event-related, high-frequency rTMS was delivered across two sites (left PMd, experimental; Vertex, control) in alternating blocks, with the order counterbalanced across participants. Commonly used as a control condition in TMS studies, Vertex stimulation provides the same scalp and acoustic sensation as stimulation of the targeted region, but it does not evoke a functionally significant neural response (Jung, Bungert, Bowtell, & Jackson, 2016). As noted above, TMS stimulation was delivered upon presentation of either the rule instructions (“Early” stimulation) or the stimulus (“Late” stimulation; Fig. 1). In one-third of trials in each block, no stimulation was delivered; in all other trials, only one stimulation train occurred (either “Early” or “Late”). Trials were pseudo-randomized so that consecutive series of three trials each contained one instance of “Early” stimulation, one instance of “Late” stimulation, and one instance of no stimulation. Due to the possibility of rTMS delivery either inducing an unwanted motor response or suppressing a genuine response, participants were locked out of responding to either screen for the first 0.5 s of presentation, and they were made aware of this fact. In agreement with rTMS safety guidelines (Rossi et al., 2009), instances of stimulation did not occur more than once every 8 s.

2.3. Transcranial magnetic stimulation

2.3.1. Parameters

High-frequency, event-related rTMS was applied with a 70 mm figure-of-eight coil (Double 70 mm Alpha coil; Magstim, UK) connected to a biphasic transcranial magnetic stimulator (Super Rapid²; Magstim, UK). Each stimulation consisted of a five-pulse train at 10 Hz and 110% of the individual’s resting motor threshold (RMT; discussed below). The coil was placed over the stimulation sites tangential to the skull, with the handle pointed at 45° to the sagittal plane (PMd) or parallel to the midline (Vertex).

2.3.2. Assessment of resting motor threshold

In order to determine each participant’s RMT, electromyography surface electrodes were placed over the muscle belly and corresponding tendon of the right first and third dorsal interosseous (FDI) muscles in a belly-tendon montage. The software utilized for neuronavigation included an EMG interface that allowed imaging of muscle activity time-locked to a single pulse (Fig. 2, top right), which was delivered over the left primary motor cortex (M1). Occurrences of motor-evoked potentials (MEP) in response to stimulation were recorded and entered into a parameter estimation algorithm (PEST: Taylor & Creelman, 1967) in order to derive the RMT. A valid MEP was defined as having at least 50 mV peak-to-peak amplitude.

Fig. 2.

Neuronavigation-guided targeting of PMd and RMT definition. Top: Screenshot of a portion of the Brainsight software display. Top left: A 3D structural MRI with functional imaging data overlaid; the PMd target is indicated by the orange arrow within the red box. Colors indicate the degree of significance in voxels engaged in motor responses. Top right: Time course of an MEP response elicited by single–pulse stimulation of M1. Bottom: PMd target locations overlaid on a glass brain in MNI space. Each dot and color corresponds to a different participant.

2.3.3. Target localization for TMS

Neuronavigation was utilized in order to achieve submillimeter precision in the targeting of stimulation sites. A frameless stereotactic system was used to track the location of the participant’s head relative to the coil with an IR tracker camera. Tracking markers were co-registered with the individual participant’s structural and functional images using the Brainsight software (Rogue Research, Montreal, QC, Canada). The location of PMd stimulation was determined by targeting the most significant voxel in a cluster identified while the participant was making a finger response, ensuring that the location was in good agreement with published anatomical landmarks (Fig. 2, top left). The location of Vertex stimulation was defined as the scalp location above the intersection of sagittal midline and the postcentral gyri (location Cz in the 10–20 system). Trials in which the stimulated area was more than 3.0 mm away from the designated target were excluded from all analyses.

2.4. Hierarchical Bayesian modeling of RT distributions

Condition-specific RT distributions were modeled in a parametric hierarchical Bayesian fashion. Under HBM, prior beliefs are placed on the parameters of a model, in the form of probability distributions over the range of possible values of each parameter considered by the model. These beliefs are updated with respect to the observed data through Bayes’ rule:

$$P(\mathrm{\theta }|D)=\frac{P(D|\mathrm{\theta })P(\mathrm{\theta })}{P(D)}$$ (1)

in which θ represents a point in the joint parameter space and D represents the observed data. Updating the prior probability distributions P(θ) through Bayes’ rule produces posterior distributions of probability P(θ | D) over the range of potential parameter values, adjusted by both the data P(D) and the likelihood of the data, P(D | θ). As the probability distributions that potential parameter values are drawn from are themselves parameterized distributions, hierarchical priors can be placed on these upper-level parameters, allowing for modeling of differences in accordance with condition, group, and the like.

Condition-specific RTs were modeled as being drawn from a three-parameter Weibull distribution with density:

$$f(y_{i,c}|{\mathrm{\beta }}_{i,c},{\mathrm{\theta }}_{i,c},{\mathrm{\psi }}_{i,c})=\frac{{\mathrm{\beta }}_{i,c}{(y_{i,c}-{\mathrm{\psi }}_{i,c})}^{{\mathrm{\beta }}_{i,c}-1}}{{\mathrm{\theta }}_{i,c}^{{\mathrm{\beta }}_{i,c}}}\exp \left\{\frac{-{(y_{i,c}-{\mathrm{\psi }}_{i,c})}^{{\mathrm{\beta }}_{i,c}}}{{\mathrm{\theta }}_{i,c}^{{\mathrm{\beta }}_{i,c}}}\right\},y_{i,c}>{\mathrm{\psi }}_{i,c}$$ (2)

where β corresponds to the shape parameter, θ the scale parameter, and ψ the shift parameter, with i indexing a given response within condition c. β, θ, and ψ parameters were estimated on a condition-specific basis. On the recommendation of Rouder et al., 2003, the β parameter values were modeled as being drawn from a gamma distribution (parameterized by hyper-parameters shape η₁ and rate η₂), restricted to the range β_c > 0.01, needed so that posterior moments exist for θ_c. The values of θ were drawn from a broad, noncommittal uniform distribution on the range of [0.01, 10000]; however, θ values were constrained so that t = θ_c^βc was sampled from an inverse gamma distribution with density:

$$f(t|{\xi }_1,{\xi }_2)=\frac{{\xi }_2^{{\xi }_1}{e}^{-{\xi }_2/t}}{t^{{\xi }_1+1}\mathrm{\Gamma }({\xi }_1)}$$ (3)

ψ parameter values were drawn from a uniform distribution on the range [0, min(RT_c)] (i.e., the minimum RT for the condition). No hierarchical prior was placed on ψ, as the uniform prior is uninformative, and it is unclear that a hierarchical prior would yield any further benefit (Rouder et al., 2003). All hyper-parameters (η₁, η₂, ξ₁, ξ₂) were drawn from gamma distributions with recommended prior values (Table 1; Rouder et al., 2005):

Table 1.

Prior values for hyper-parameter gamma distributions

Parameter	Shape	Rate
η1	1.00	0.02
η2	2.00	2.85
ξ1	1.00	0.02
ξ2	2.00	0.04

The model was implemented in the BUGS language, and sampling of the posterior values was accomplished through Markov chain Monte Carlo simulation through JAGS, linked to the R environment through the package runjags (Denwood, 2016; Plummer, 2003; Thomas, 1994).

As neither the three-parameter Weibull nor the inverse gamma distributions are currently implemented in BUGS/JAGS, the “ones” and “zeros” tricks were used to implement the likelihood functions for the two distributions, respectively (Kruschke, 2014).² Three separate MCMC chains were generated, with 10,000 adaptation steps, 50,000 burn-in steps, and 1,000,000 total saved steps, thinning every five steps.

Analysis of the samples from the posterior distributions was performed with the coda package alongside custom R scripts (Plummer, Best, Cowles, & Vines, 2006). To verify that the MCMC sampling had converged and that the sampled values were genuinely representative of the joint posterior distribution, the effective sample size (ESS), Gelman-Rubin (GR), and Monte Carlo standard error (MCSE) statistics were computed for the posterior distribution of each parameter (Kruschke, 2014). To compare the Weibull distribution parameter estimates between conditions, the difference of the parameter values was calculated by taking the difference between the estimated values at each step of the chain, producing a distribution of differences. Finally, condition-specific posterior predictive Weibull densities were generated by using the mode value of the estimated shape, scale, and shift parameters for a given condition in conjunction with Eq. 2. The fit of the predicted Weibull density to the observed RTs within a condition was evaluated through calculation of the RMSE and a χ² goodness-of-fit test.

2.5. ACT-R cognitive model

The ACT-R model consists of 18 production rules and 30 chunks. The model’s strategy is illustrated in the flowchart of Fig. 3. In broad strokes, during each trial the model proceeds through five consecutive stages: (a) Instruction encoding, (b) Task plan preparation, (c) Parity judgment, (d) Task re-planning (if necessary), and eventually (e) Motor response.

Fig. 3.

ACT-R model’s processing strategy and stages.

Task instructions are first encoded by storing the parity (“EVEN” or “ODD”) and the action (finger: “Index” or “Middle”; or letter: “A” or “B”) into working memory. The model then uses this information to prepare a mental plan of the action to perform (a finger movement for “Concrete” rules, or a visual search followed by a finger movement for “Symbolic” rules) in the event that the parity of the upcoming stimulus matches that which was instructed. The plan contains a detailed chunk specification of the stimulus feature to verify (i.e., the parity of a number) and the action to perform (the motor action or the visuomotor procedure) and is thus specific to the type of rule (as underscored by the yellow and green boxes in Fig. 3). There is ample evidence in the RITL literature for the existence of such intermediate, deeper representations of the task (Cole et al., 2013; Stocco et al., 2012). After planning is completed, the model uses the left hand to proceed to the execution phase.

During the execution phase, the model first retrieves the parity associated with the stimulus (i.e., the declarative fact that “8 is EVEN”). If the parity of the stimulus matches the parity considered by the previously prepared plan, the model proceeds with the response phase. If the parity of the stimulus does not match the condition for the intended action, as in the case of “Inferred” trials, the model discards and re-prepares the mental plan on the basis of the apparent parity of the stimulus. This re-planning is again specific to the type of rule (green and yellow “Re-plan” boxes in Fig. 3). After re-planning, the model proceeds to the response phase, in which the model simply follows the most recently prepared plan and executes the visuomotor commands as specified.

2.5.1. Modeling the effects of TMS

There are neither established guidelines nor precedents on how to model the effects of high-frequency rTMS in ACT-R. For this reason, two complementary methods in which TMS stimulation could be modeled within the ACT-R architecture were considered:

• Method 1: TMS affects the operation of individual ACT-R buffers. This is consistent with the established ACT-R literature, in which buffers correspond to distinct cortical regions specialized for different functions (Anderson, Fincham, Qin, & Stocco, 2008).

• Method 2: TMS affects the execution of individual ACT-R productions. Although the canonical interpretation is that ACT-R productions are related to the basal ganglia (Anderson et al., 2008), it has been previously argued that productions can alternatively be interpreted as cortico-cortical connections (Stocco, Lebiere, & Anderson, 2010). Since productions combine knowledge from different sources, they might be ideally suited to represent the function of cortical associative areas, such as PMd.

In both cases, the effects of TMS were simulated by injecting a delay into the operation time of the corresponding target structure (buffer or production), with the delay extending until the end of the simulated rTMS pulse train. For Method 1, this was achieved by forcing a buffer’s status to “failure” throughout the duration of the TMS train. For Method 2, this was achieved by modifying a production’s “action time” parameter at the moment of selection. This parameter controls the duration of a production cycle and is normally set to 50 ms. If a production was selected during TMS stimulation, its action time was extended to include the entire stimulation window.

3. Results

3.1. Experimental results

Participants were highly accurate throughout the task (M = 95%), with no significant differences in accuracy due to either experimental manipulation or TMS (F < 1.26, p > .30). For this reason, the analyses reported here will focus on the response times.

In both the encoding and execution phases, there was no difference in response times between trials belonging to either of the two control conditions (Vertex stimulation and no stimulation trials). Thus, the no-stimulation trials were excluded from the remaining analyses, so that comparisons were always made between conditions in which the participants received stimulation (on Vertex and PMd sites, respectively).

The main behavioral results of our experiment are summarized in Fig. 4. In the encoding phase, a two-way anova considering the effect of site of stimulation and type of rule revealed no significant main effects or interactions of these conditions on the encoding response time. However, in the execution phase, a four-way anova examining the effect of site of stimulation, timing of stimulation, type of rule, and instruction/inference of rule on response times revealed a main effect of rule (F(1, 7) = 238.3, p < .0001, η² = 0.12) alongside a main effect of instruction/inference (F(1, 7) = 31.44, p = .0008, η² = 0.061). A significant two-way interaction between site of stimulation and type of rule was observed (F(1, 7) = 16.7, p = .0047, η² = 0.006), whereas a significant three-way interaction between site of stimulation, timing of stimulation, and instruction/inference (F(1, 7) = 13.3, p = .0082, η² = 0.006) was also present. Subsequent two-way anovas considering site of stimulation and type of rule, performed within the conditions defined by the conjunction of timing of stimulation and instruction/inference, demonstrated that the Inferred-Late stimulation condition was the only condition in which the two-way interaction between site of stimulation and type of rule occurred (F(1, 7) = 10.11, p = .015, η² = 0.037). These effects were qualitatively similar across the eight participants considered by the analysis. Within the Inferred-Late stimulation condition, paired t tests revealed there to be no difference in mean response times between PMd and Vertex stimulation on “Concrete” trials (paired t(7) = 0.119, p = .909, Cohen’s d = 0.08). Using a TOST equivalence procedure with α = 0.05, our results exclude the existence of any effect larger than d = 0.038. Instead, a significant difference was observed in mean response times between PMd and Vertex stimulation on “Symbolic” trials (paired t(7) = 3.21, p = .015, Cohen’s d = 2.27).

Fig. 4.

Experimental results and ACT-R model simulations. Bars represent mean values ± SEM. Green denotes “Concrete” trials; yellow denotes “Symbolic” trials; red denotes condition in which rTMS had a significant effect on response times. Circles represent ACT-R model predictions.

In summary, rTMS of PMd yielded a very specific effect, significantly delaying response only in the execution of “Symbolic” rules, and only when the rules need to be re-processed (“Inferred” trials: red column in Fig. 4C).

3.2. Hierarchical Bayesian model results

Convergence diagnostics indicated that sampling for all parameters converged and was representative. Only one parameter, the shift parameter for the Concrete-Inferred condition in Vertex “Early” stimulation trials, had an effective sample size below 10,000 (ESS = 5,489). By the last iteration in the chain, each parameter’s GR statistic fell below 1.01, whereas the average MCSE across parameters was 1.78 × 10⁻⁴ ± 6.99 × 10⁻⁴, indicating that there was low noise in the chains. As a significant effect was only found within the Symbolic-Inferred-Late (SIL) stimulation condition (as discussed above), we will focus on comparisons of posterior parameter values estimated for PMd and Vertex stimulation trials within this condition. Fig. 5A–C show the posterior distribution of differences between PMd and Vertex stimulation within the SIL condition for the shape, scale, and shift parameters, respectively.

Fig. 5.

Posterior probability density of differences between PMd-SIL and Vertex-SIL parameters. Red dashed lines indicate zero difference in parameter estimates between the two conditions. Shaded regions indicate 95% highest density interval of the posterior. Inset: Scatterplot of last 10,000 MCMC samples of the corresponding Weibull parameter for PMd-SIL and Vertex-SIL conditions. Dashed black line indicates line of equality.

There was no observed difference in the estimated shape parameters between these two conditions (95% highest density interval (HDI) was inclusive of zero; lower bound = −0.35; upper bound = 0.39). In contrast, a significant difference was observed in the estimated values for the scale parameters, so that the estimated scale for PMd-SIL trials was greater than that estimated for Vertex-SIL trials (95% HDI lower bound = 0.11; upper bound = 0.51). Additionally, the shift parameter for PMd-SIL trials was estimated to be slightly lower than that of Vertex-SIL trials (95% HDI lower bound = −0.15; upper bound = −0.02). To test the reliability of our results, the predicted Weibull densities were directly compared to the corresponding empirical RT distributions. Fig. 6A,B show RT histograms for the PMd-SIL and Vertex-SIL conditions, respectively, with the posterior predictive Weibull densities in blue. RMSEs and χ² goodness-of-fit tests indicated that the Weibull densities for both the PMd-SIL condition and the Vertex-SIL condition did not differ from the observed RT distributions (PMd-SIL: RMSE = 0.037, χ(10) = 0.158, p = 1; Vertex-SIL: RMSE = 0.023, χ(10) = 0.406, p = 1).

Fig. 6.

Response time histograms overlaid with posterior Weibull densities for the PMd-SIL and Vertex-SIL conditions, in blue. Mode values of the condition-specific parameter estimates were used to estimate the posterior Weibull densities, and they are listed in the top right.

3.3. ACT-R cognitive model results

Before examining the effects of TMS, the model was fit to behavioral data from the control conditions. Although ACT-R contains many dozen parameters that control multiple available modules, the model presented herein only uses three components: working memory, memory retrieval, and motor response processes. These components can be parametrically modulated by three parameters only: (a) the imaginal latency L, which determines the time to create or update the mental plan in working memory; (b) the base-level activation B of the parity facts that are retrieved, which determines the time to decide on the parity of a number; and (c) and the motor preparation time M, which determines the time to prepare a motor response from instructions. Of these three parameters, the parameter L can be estimated directly from the experimental data, as the only difference between the execution of “Inferred” and “Instructed” rules is the time necessary to update the mental plan. In our experimental data, this difference was 133 ms. In the model, this difference corresponds to the time to execute a production that updates the imaginal buffer, and it is the sum of the duration of a production’s firing cycle (50 ms) and L, which can then be estimated as 133 − 50 = 83 ms. The values of B = 1.5 and M = 150 ms were estimated through a grid-search procedure to minimize the discrepancy between the model’s predicted mean reaction times and the mean reaction times of the experimental data.

After fitting, the model reproduced three key patterns of participant behavior (blue dots in Fig. 4A,B). First, both type of rules take the same time to encode (Fig. 4A: RMSE = 64 ms, χ(3) = 1.43, p > .69). Second, there is an increased response time for “Symbolic” trials relative to “Concrete” trials (compare green to yellow bars in Fig. 4B). Third, there is an increased response time for “Inferred” trials relative to “Instructed” trials (compare yellow or green bars in Fig. 4B: RMSE = 55 ms, χ(3) = 3.27, p > .35). This is a good indication that the model implementation is representative of the cognitive dynamics required by the task.

After parameter fitting, the two methods of TMS simulation were applied exhaustively to all buffers (Method 1) and productions (Method 2) of the model. A Parameter Space Partitioning (PSP; Pitt, Kim, Navarro, & Myung, 2006) was applied to the simulations to identify the conditions in which the model produced the qualitative pattern of Fig. 4C, that is, a significant effect of TMS only for the SIL condition trials. Interfering with the operation of a given buffer (i.e., Method 1 of TMS simulation) could never reproduce the results observed in the behavioral experiment, as the simulated interference always caused increased response times across multiple conditions (dependent on the exact buffer that is manipulated).

In comparison, Method 2 was capable of replicating the behavioral result in one specific case—when the production responsible for re-planning a symbolic trial was delayed (i.e., the production corresponding to the yellow “re-plan” box in Fig. 3). In this case, the model displayed increased response times specifically for the SIL condition (red dot/bar in Fig. 4C: RMSE = 62 ms, χ(3) = 1.64, p > .65). Disruption of any other production could not reproduce this effect, providing greater support for our conclusion that the behavioral result is explained by assuming a role of PMd in the preparation of concrete responses in accordance with valid conditional associations.

It is important to note that our extensive simulation of TMS effects excludes that module-specific parameters could explain our results. Part of the reason is that the same modules (i.e., retrieval, imaginal, visual, and motor) are used in all conditions (and exactly the same order in the two Concrete and the two Symbolic conditions), as shown in Fig. 3. Thus, changes in module processing times cannot produce the condition-specific effects of the experimental results. In contrast, production rules are by nature condition-specific, as they encode knowledge on how the specific information distributed across different buffers needs to be combined to perform a specific operation. As discussed below, this aspect of a production rule’s function (i.e., combining information from multiple buffers) is compatible with the function of cortical associative regions like PMd.

4. Discussion

Application of rTMS during a RITL paradigm revealed that PMd was specifically involved when participants had to resolve an inferred conditional rule that was symbolically linked to concrete motor effectors, as demonstrated by increased response times in the SIL stimulation condition. In comparison, when the conditional association had been instructed, or when it directly referred to concrete motor effectors, rTMS over left PMd had no significant effect relative to controls.

rTMS could result in increased RTs for a number of reasons. If rTMS disrupts the cognitive strategy participants apply in the control conditions, it could force the use of a less optimal strategy. If, however, PMd recovers quickly from the influence of rTMS, it could instead “pause” a specific stage in the cognitive strategy, leading to increased response times under the same cognitive strategy. In addition, as PMd is classically considered to be a motor-planning region, rTMS could have the simple effect of increasing the nondecision time of a response—that is, the time it takes to determine a response remains the same, but the act of responding takes more time. In an effort to determine if any of these effects contributed to the observed effect in the PMd-SIL condition, we applied a hierarchical Bayesian model in which the RTs from each condition were modeled as being drawn from a three-parameter Weibull distribution.

The Bayesian model estimated probability densities over a range of values for each parameter in each condition, and estimated parameter values for the PMd-SIL condition were compared to those of the Vertex-stimulated paired control condition. It was found that, while there was no difference in the shape of the two RT distributions, the scale parameter was estimated to be significantly larger for the PMd-SIL condition, whereas the shift parameter for this condition was smaller than that of the paired control. Additionally, shift parameter estimates for both conditions were only slightly smaller than the respective condition’s minimum RT. The most likely parameter estimates were then used to test the fit of the predicted Weibull distribution to the observed RTs. RMSE values and χ² goodness-of-fit tests indicated that for both the PMd-SIL and Vertex-SIL conditions, the posterior predicted Weibull distributions fit well to the condition RT distributions. While PMd-rTMS seems to have actually sped nondecision times relative to controls, it concomitantly increased the rightward variability in the RT distribution, resulting in longer RTs on average within the PMd-SIL condition. These results imply that (a) PMd stimulation slows a specific cognitive operation within the response strategy, rather than altering the entire response strategy (such as by causing an omission of a certain cognitive operation, or causing them to be executed in a different order); and (b) PMd-rTMS serves to disrupt this cognitive operation over the duration of stimulation, but the ability of PMd to perform this operation quickly recovers after the period of stimulation has ended.

While the HBM results were indicative that a specific cognitive process was affected by the rTMS intervention, the method provides no information as to what that process may entail. As a significant effect of rTMS only occurs in the PMd-SIL condition, the “specific cognitive step” that is sensitive to PMd-rTMS is most likely unique to the PMd-SIL condition. To identify the potential cognitive operations that were affected by rTMS (and therefore potential cognitive operations performed by PMd), we developed an ACT-R cognitive model of the task. The model first creates a “response plan” on the basis of the trial-specific instructions, thus preparing to respond when a valid stimulus appears. If there is a mismatch between the expected and actual stimulus, a “re-planning” occurs in which the actual stimulus parity is used to create a new response plan to guide response execution. The effect of TMS was simulated through both a buffer-specific method and a production-specific method.

The model reproduced the two major patterns of participant behavior under this task: an increase in response time for “Symbolic” relative to “Concrete” trials, and an increase in response time for “Inferred” trials relative to “Instructed” trials. When simulated TMS was applied to the model’s buffers (Method 1), the model could not reproduce the main behavioral result (i.e., a specific effect of TMS within the SIL condition). Method 2 of TMS simulation was capable of replicating the behavioral results, specifically when the production dedicated to re-planning of “Symbolic” response plans was targeted.

This finding, together with the behavioral data and HBM results, provides strong evidence of an involvement of PMd in the resolution of concrete responses in accordance with specific stimuli and conditional associations that refer to said stimuli. The behavioral results indicate that PMd activity is pertinent to task completion, specifically when an apparent stimulus feature must be evaluated with a relatively complex conditional association in order to resolve a response; the HBM results clarify the effect that rTMS has on the task response strategy, demonstrating that while the overall strategy is not altered, a particular element of the strategy is slowed; and finally, the ACT-R model suggests that the identity of this particular element is that of a response re-planning process, necessary when a previously prepared response plan is made invalid by environmental dynamics. Therefore, these results support the conclusion that the dorsal premotor cortex is involved in complex response resolution processes. However, it should be noted that these analyses were based on a small sample size (8 participants total); future work increasing the number of participants considered would greatly contribute to the generalizability of these findings.

A benefit of the combined modeling approach adopted in this work is that it allows for converging evidence that carries neurophysiological significance. For example, the ACT-R model is consistent with known functional anatomy: PMd receives input from prefrontal and parietal cortices and outputs to the motor cortex; the corresponding ACT-R production takes inputs (in the form of chunk slots) from a retrieval buffer (associated with PFC) and creates a representation that links visuospatial information (associated with parietal cortex) with possible motor responses (associated with motor cortex). From a computational point of view, the ACT-R model results suggest that the function of brain regions not associated with ACT-R buffers (such as PMd) might be interpreted in terms of productions, whose operations (i.e., combining information from multiple buffers) can be seen as akin to what neuroscientists refer to as cortical associative areas. The possibility of associating productions with cortical regions, rather than exclusively to subcortical structures, has important implications for the application of ACT-R to neuroscientific datasets. In particular, Method 2 has general application and can be potentially used to test the effect of TMS on any of the many cortical areas that are not specifically described within the ACT-R architecture. Simultaneously, when compared to behavioral data in which one of these “undescribed” cortical areas has been targeted by TMS, Method 2 serves to test specific hypotheses about cortical function in the form of the ACT-R production that is manipulated.

The use of a plausible computational model provides a new way to predict the effects of stimulation. Examination of the model’s structure allows for a priori predictions of participant behavior in response to varied regimes of TMS application. For example, since the model encodes the task instructions in working memory before creating a response plan, “early” stimulation (i.e., time-locked to presentation of the encoding phase) of the productions responsible for the initial “planning” does not change the model’s behavior. If, however, stimulation were to instead occur later in the encoding phase, the model predicts that response planning would be disrupted and encoding times during Symbolic-Instructed trials would be increased (opposite to what was observed in the present experiment). A secondary prediction is that a different cortical region, distinct from PMd, is responsible for planning and re-planning “Concrete” responses (green boxes in Fig. 2). A likely candidate for this cortical region is the ventral premotor cortex (PMv), a brain area (shown to be anatomically distinct from PMd) which demonstrates functional selectivity for concrete motor actions (Rizzolatti, Fogassi, & Gallese, 2002; Tomassini et al., 2007).

Taken together, the present results suggest that PMd is involved in response resolution processes and may specifically handle resolution of conditional associations that do not directly refer to concrete response effectors. Furthermore, this work demonstrates that computational models and TMS are complementary tools for cognitive neuroscience research, and that their combination opens up new exciting research opportunities.