Simulating the computational mechanisms of cognitive and behavioral psychotherapeutic interventions: insights from active inference

Abstract

Cognitive-behavioral therapy (CBT) leverages interactions between thoughts, feelings, and behaviors. To deepen understanding of these interactions, we present a computational (active inference) model of CBT that allows formal simulations of interactions between cognitive interventions (i.e., cognitive restructuring) and behavioral interventions (i.e., exposure) in producing adaptive behavior change (i.e., reducing maladaptive avoidance behavior). Using spider phobia as a concrete example of maladaptive avoidance more generally, we show simulations indicating that when conscious beliefs about safety/danger have strong interactions with affective/behavioral outcomes, behavioral change during exposure therapy is mediated by changes in these beliefs, preventing generalization. In contrast, when these interactions are weakened, and cognitive restructuring only induces belief uncertainty (as opposed to strong safety beliefs), behavior change leads to generalized learning (i.e., "over-writing" the implicit beliefs about action-outcome mappings that directly produce avoidance). The individual is therefore equipped to face any new context, safe or dangerous, remaining in a content state without the need for avoidance behavior-increasing resilience from a CBT perspective. These results show how the same changes in behavior during CBT can be due to distinct underlying mechanisms; they predict lower rates of relapse when cognitive interventions focus on inducing uncertainty and on reducing the effects of automatic negative thoughts on behavior.

Figure 1

Illustration of how the structure of the computational model described in this paper captures the cognition-affect-behavior triangle, using the example of spider phobia. (A) Cognition-affect-behavior triangle, as used in CBT. Each component has reciprocal links to the other two components. For example, a thought can promote congruent emotions and behaviors, and an emotion can also promote congruent thoughts and behaviors. In this case, the thought “the spider is dangerous” may promote “negative affect’ and “running away” (circles on the right-hand side of each apex). (B) Simplified depiction of the computational model structure, designed to capture the outcomes an individual expects if they choose approach or avoidance behavior after seeing a feared stimulus (a spider in this example), depending on their thoughts (here, beliefs that a spider is dangerous or safe). Cognition and behavior within the CBT triangle form the model states. Affect and arousal are outcomes, which depend on cognitions and chosen behaviors, as well as their interactions. This figure includes icons created by the Noun Project (https://thenounproject.com/).

Figure 2

Outline of the generative model. (A) Graphical depiction of the generative model, displaying the patient’s beliefs about how different combinations of hidden states generate different combinations of outcomes, as well as how behavior states can transition over time. Red arrows indicate transitions and outcomes generated under “danger” beliefs, while green arrows indicate those under “safe” beliefs (as well as associated avoidance vs. approach transitions, respectively). All other arrows are not dependent on safety/danger beliefs. (B) Formal depiction of the model in terms of specification of A, B, and C matrices, and D vectors (see text for details and Supplementary Materials: Appendix 1 for associated equations). In these grayscale depictions, lighter values approach 1 and darker values approach 0. CAB-I = cognition-affect-behavior interactions; Safety + Cost = reaching safety along with opportunity costs that promote negative affect. Note that the identity matrix (within the A matrices) mapping behavioral states to observed behavioral outcomes is omitted for clarity in both panels.

Figure 3

Illustration of single-trial simulations. Within the left column of each panel, darker values indicate stronger beliefs favoring the associated states, whereas darker values in the right column of each panel indicate stronger preferences for the associated outcomes. Cyan dots indicate the true states and outcomes. See main text for interpretation. (A) Simulation under precise danger beliefs (danger = 1). (B) Simulation under precise safety beliefs (danger = 0). (C) Simulation under precise safety beliefs with ineffective CAB interactions. (D) The percentage of simulated trials (out of 100) in which the simulated patient chose to approach the spider, given different explicit beliefs about the probability that the spider was safe. Each colored line illustrates the behavioral curve under CAB interactions of different efficacies (higher = more efficient). CAB-i = parameter encoding the efficacy of cognition-affect-behavior interactions; Safety + Cost = reaching safety along with opportunity costs that promote negative affect.

Figure 4

Exposure therapy under strong explicit danger beliefs (i.e., as in the absence of cognitive restructuring; $P(safe)=.1$) and different CAB interaction strengths. Approach behavior increased with length of exposure (panel A), but the underlying mechanisms differed depending on CAB interaction strengths. When CAB interactions were moderate (CAB-i = .5, orange outline) or strong (CAB-i = .9, grey outline), behavior change was the result of updates in explicit beliefs (panel B)—leaving implicit beliefs (panel C) unchanged and creating a vulnerability to the re-emergence of negative affect and avoidance responses in other contexts. Under weak CAB interactions (CAB-i = .1, blue outline), explicit danger beliefs remained unchanged (e.g., the simulated patient continued to have the automatic thought “this spider is dangerous”; panel B), but implicit beliefs (panel C) slowly adjusted such that avoidant affective responses attenuated over time—and were independent of changes in explicit beliefs. Learning was slower under moderate CAB interactions (.5, orange outline; panel A). As discussed in the main text, this is because the formal matrix structure in this case can also be interpreted as the patient being unsure that a safe context is possible (i.e., the hidden state for the possibility of another context started out making completely uninformative predictions)—thus, the patient needed to first infer the presence of a meaningfully distinct context. CAB-i = parameter encoding the efficacy of cognition-affect-behavior interactions; Safety + Cost = reaching safety along with opportunity costs that promote negative affect.

Figure 5

Exposure therapy under strong explicit safety beliefs (i.e., such as after cognitive restructuring; $P(safe)=.9$) and different CAB interaction strengths. When CAB interactions were strong (grey outline), approach behavior was present immediately (panel A). Under moderate or weak CAB interactions (orange or blue outline), behavior change occured rapidly. Implicit beliefs (panel C) associated with explicit beliefs in danger (panel B) remained unchanged, creating a vulnerability to the re-emergence of negative affective responses and avoidance behavior in other contexts (i.e., upon the return of thoughts of danger). CAB-i = parameter encoding the efficacy of cognition-affect-behavior interactions; Safety + Cost = reaching safety along with opportunity costs that promote negative affect.

Figure 6

Exposure therapy under uncertain explicit beliefs (i.e., as could also be facilitated by cognitive restructuring; $P(safe)=.5$) and different CAB interaction strengths. Approach behavior increased with length of exposure at a faster rate than under strong danger beliefs, but the underlying mechanisms differed depending on CAB interaction strengths (panel A). When CAB interactions were moderate or strong (orange or grey outline), behavior change was the result of updates in explicit beliefs (panel B)—again leaving implicit beliefs unchanged (panel C) and creating a vulnerability to the re-emergence of avoidance if thoughts of danger were to return. Under weak CAB interactions (blue outline), explicit danger beliefs remained uncertain (e.g., the simulated patient continued to have the thought “this spider may or may not be dangerous”; panel B), but implicit beliefs (panel C) slowly adjusted such that avoidant affective responses attenuated over time—and were independent of changes in explicit beliefs (panel B). Learning was slower under moderate CAB interactions (panel A). As mentioned in the legend for Fig. 4, this was because the formal matrix structure can in this case also be interpreted as the patient being unsure that a safe context is possible (i.e., the hidden state for the possibility of another context started out making completely uninformative predictions)—and must therefore first infer the presence of a meaningfully distinct context. CAB-i = parameter encoding the efficacy of cognition-affect-behavior interactions; Safety + Cost = reaching safety along with opportunity costs that promote negative affect.