1 Introduction

Psychotherapeutic interventions are effective treatments for depression and anxiety, but the mechanisms of action responsible for these effects remain poorly understood (Kazdin, 2007; Carey et al., 2020). In addition, there is considerable variation between individuals regarding treatment response (Goldfried, 2013). Better targeting psychotherapeutic interventions according to individual needs or characteristics might improve therapy effectiveness. This requires understanding how existing psychological treatments work and for whom they work.

Previous research studying the mechanisms underlying psychological treatments has mostly focused on changes after the complete treatment courses (Klug et al., 2012). However, psychotherapeutic treatments are complex interventions involving different components (Luborsky et al., 2002), likely affecting different behavioural processes and acting via different mechanisms. As such, changes observed after the full course of treatment reflect the many many aspects of the intervention. In contrast, little research exists on how different components engage specific mechanisms.

In this study, we build on recent suggestions (Reiter et al., 2021; Wolpert et al., 2021; Holmes et al., 2018) and a promising new research direction (Brown et al., 2021; Huys et al., 2022; Dercon et al., 2023; Norbury et al., 2023), using cognitive computational techniques to study isolated interventions. This approach aims to better characterize and understand the change mechanisms of specific, key psychotherapeutic interventions. Specifically, we examine the effect of distancing—an emotion regulation technique—on the dynamics of emotions.

Emotion regulation strategies are an essential element of many psychotherapeutic treatments (Gross, 1998). Some emotion regulation strategies can alleviate symptoms of mood disorders and generally improve well-being (Berking et al., 2013; Boemo et al., 2022; Powers and LaBar, 2019; Somerville et al., 2022). Here, we define emotion regulation as using explicit strategies to intentionally up- or down-regulate positive or negative emotions. Effective strategies include problem-solving, reappraisal, acceptance, and distancing techniques (McRae and Gross, 2020; Webb et al., 2012). Distancing involves simulating a new perspective to increase the psychological distance from an event or situation and, with that, the emotional impact of a stimulus (Powers and LaBar, 2019; Webb et al., 2012). Distancing has been shown to reduce selfreported emotional experience reliably (Koenigsberg et al., 2009; Vrticka et al., 2012; Winecoff et al., 2011, 2013) and is associated with decreased amygdala activity even beyond the period of active regulation (Eippert et al., 2007; Walter et al., 2009; Domes et al., 2010). Distancing techniques are practical because they can be implemented in various situations with relatively low attentional demands and behavioural disruption (Powers and LaBar, 2019). We focus on distancing to gain insights into the mechanism of this specific treatment component in the hope of better understanding some of the complex processes underlying psychotherapeutic treatment effects.

Furthermore, emotion regulation research has mostly focused on the effects on individual emotions. Different emotions, however, are often related and influence each other. For instance, sadness can increase the likelihood of experiencing anger while emotions of different valence or arousal tend to inhibit each other: inducing happiness reduces experienced sadness, yet mixed states with both sadness and happiness can also occur. These interactions induce temporal dependencies between emotions, meaning that emotional states as a whole form a dynamical system fluctuating over time (Malamud and Huys, 2024; Durstewitz et al., 2020; Kuppens and Verduyn, 2017; Lange et al., 2022). As such, emotion regulation may be best conceptualized as the regulation of a dynamical system of emotions rather than as involving the regulation of individual emotions in isolation.

In recent years, network models have been developed to account for the dynamical systems properties of emotions (Borsboom and Cramer, 2013; Bos et al., 2017; Bringmann et al., 2013; Epskamp et al., 2018). This work has identified individual differences in affect dynamics which are linked to mood disorders (Bringmann et al., 2016; Kuppens et al., 2012; Pe et al., 2015, 2016; Sperry et al., 2020; Trull et al., 2015; Leemput et al., 2014). For example, increased inertia (temporal autocorrelation or how well an emotion can maintain itself) of negative affect has been identified in people with depression (Brose et al., 2015; Houben et al., 2015; Kuppens et al., 2010; Koval et al., 2012, 2013). Most interestingly, it has been suggested that there are discrete stable states (e.g. a depressed vs a happy state), so-called attractor states, between which people can transition (Durstewitz et al., 2020; Leemput et al., 2014; Wichers et al., 2016; Kuppens et al., 2012; Hosenfeld et al., 2015). Within an attractor state, the system is usually resistant to change, and under small disturbances (e.g. a stressful week), a person converges back to the current attractor state. A transition to another attractor state may occur if a perturbation is large enough or accumulated over time (Nelson et al., 2017). The transitions between states in a dynamical system are influenced by two important factors: the system’s intrinsic characteristics and its sensitivity to external driving forces.

Past work mostly focused on dynamical properties inferred from the emotion self-reports alone and has often neglected the role of external factors (Boemo et al., 2022; Malamud and Huys, 2024). This is a critical omission as the dynamical properties of a system are not fully identifiable unless the inputs are known — inputs can nearly arbitrarily alter the apparent dynamical system. For instance, persistent sad mood could be due to a constant external stimulus producing sadness rather than due to an internal persistence of sad mood. Ignoring the immediate context within which emotions fluctuate may hence lead to wrong conclusions about the underlying affective system. Indeed, it is well known that external stimuli profoundly impact the dynamics of emotional states, particularly in laboratory settings (Asutay et al., 2022; Rutledge et al., 2014; Villano et al., 2020; Vanhasbroeck et al., 2022).

Since both the natural changes in emotions over time and the impact of external factors on emotions are important, there is a compelling rationale to explore the potential effects of emotion regulation on these two key aspects of emotion processes. By doing so, we can gain valuable insights into the mechanisms underlying emotional regulation and better understand how emotions are controlled. Understanding which emotions can be most effectively changed through a certain techniques can provide clearer insights into the targeted effects of such interventions. Additionally, identifying reliable indicators of whether the emotional system is resistant or adaptable to changes could open up possibilities for creating personalized interventions.

Therefore, our aim was to examine the dynamic network effect of emotion regulation, specifically by considering an individual’s immediate context. We positioned emotion regulation within the framework of dynamical system theory and utilized tools from control theory to characterize the overall control properties of the emotional system. To briefly explain, a dynamical system is a series of linked differential equations (Brunton and Kutz, 2019; Durstewitz et al., 2020), each describing how one variable (here an emotion) changes over time. It permits emotions to influence each other and exhibits rich dynamical properties. The equations can incorporate the concept of control by allowing an input to drive one or more variables. Controllability, in this context, is a characteristic that depends on both how sensitive the system is to inputs and its inherent dynamics. It reflects how easy or hard it is to drive the system towards certain states. For instance, if all emotions are positively linked to sad mood, then a happy state would be challenging to achieve, reducing the system’s controllability of single emotions.

In this study, we investigated how external emotionally-charged inputs influenced self-reported emotions over time (across multiple dimensions), and whether these inputs were essential to explaining the evolution of a rich, multidimensional emotional state. This enabled us to formally examine the impact of a distancing intervention on emotion dynamics whilst disentangling effects on intrinsic dynamics from alterations of external inputs. We also examined whether intervention-induced changes were moderated by measures of depressive or anxiety symptoms or difficulties in regulating emotions.

2 Methods

2.1 Participants

109 participants 18 years or older with current UK residence were recruited online on Prolific Academic (www.prolific.co). Prolific is widely used and reliable platform for online research due to its diverse participant pool and robust quality control measures (Peer et al., 2017; Palan and Schitter, 2018).

An a priori power analysis based on data from a pilot study estimated a minimum sample size of N = 109 (cf. Supplementary Materials D Power Analysis).

2.2 Procedure and Task

After indicating interest in the online recruitment platform, participants were forwarded to an electronic form of the participant information sheet. They could then provide electronic consent through an online form before being redirected to the experiment. The study duration was approximately 45 minutes, and participants were reimbursed £7.50/h through Prolific Academic after completion of study procedures.

In the experiment (Fig. 1), participants saw a sequence of short emotional video clips, each lasting 2–10 seconds and chosen for their efficacy in eliciting certain emotions. Video clips were from a previously-published database, with validated emotion ratings across multiple categories (cf. 2.2.2 Emotion-Inducing Stimuli; Cowen and Keltner 2017). After each video clip, participants reported their current emotional state in terms of two positive (amused and calm) and three negative emotions (disgusted, anxious, and sad). Emotions of disgust, anxiousness, and amusement were chosen as they were thought to be highly sensitive to video clip inputs. Conversely, sad and calm appear to be more persistent emotions which we expected to be informative about stability. Participants were instructed to use a slider to indicate how strongly they felt each of the emotions at that moment in time, with options ranging from “not at all” to “very”. Participants had 30 seconds to report their emotional state. If they did not manage to rate all emotions within 30 seconds, the experiment moved on to the next video without their completed rating.

After watching the first block of 54 video clips, participants were randomized to undergo either a distancing (emotion regulation) or a relaxation (control) intervention (cf. 2.2.1 Intervention). Following the intervention, participants watched a second block of 54 video clips and again rated their emotions after each video. A different set of video clips was shown, but the sequence of emotions targeted was matched to the first block.

Figure 1

2.2.1 Intervention

The emotion regulation intervention was based on a distancing appraisal strategy, i.e. “Leaves on a Stream” (adapted from Hayes et al. 2006). This technique involves viewing emotions and thoughts as events passing through one’s mind rather than getting “sucked in” by them. The script employed a visualization strategy, instructing participants to imagine they were standing by a stream with leaves floating gently past them. They were then told: “When an emotion or thought comes up, imagine you place the thought on one of those leaves and that you are watching the leaf - carrying your emotion or thought - float away, disappearing behind a corner or in the distance.” In the control intervention, participants were asked to engage in a relaxation exercise. They were told the same storyline as in the distancing intervention but without connecting the stream and leaves to their emotions and thoughts (the full text of both interventions is reproduced in the Supplementary Materials A Intervention Text).

Furthermore, in the group allocated to the distancing intervention, the phrasing of the question about their feelings in the second video block reminded participants about the intervention, stating: “You observed your emotions and let them pass like the leaves floating by on the stream.” This was not the case for the control group.

To reduce demand effects, the instructions were framed to suggest that the experiment was attempting to understand whether the distancing was helpful or not, i.e. participants were explicitly encouraged to report that the intervention was not helpful if they did not perceive it as effective.

2.2.2 Emotion-Inducing Stimuli

The emotion eliciting video clips stem from a validated database (Cowen and Keltner, 2017) (https://s3-us-west-1.amazonaws.com/emogifs/uncensored.html). This study analyzed emotional responses to 2,185 short videos, identifying 27 distinct emotional experiences categorized through a survey completed by 853 English-speaking US participants. The videos were collected from online sources depicting diverse emotionally significant situations, including cute animals, natural landscapes, distressing scenes such as feces and vomit, accidents and dangerous stunts, and many others.

For our experiment, we selected video clips that fit into five target emotion categories: Amusement/Joy, Disgust/Horror, Sadness/Sympathy, Calmness/Aesthetic Adoration, and Anxiety/Fear. We chose clips that showed a high mean and a low entropy in the ratings from Cowen and Keltner (2017) for these emotion categories, to ensure they would specifically evoke the intended emotion. We identified 20 videos from each of the five categories, resulting in a total of 100 videos. The ratings from Cowen and Keltner (2017) for each chosen video and the mean ratings over videos from an emotion category are shown in Supplementary Materials B Video Clips Fig. B.2, respectively Fig. B.1.

2.2.3 Study Sequence

In total, each participant viewed 54 video clips before and 54 video clips after the intervention. The video order was pseudorandomized for the first half. In addition, two randomly chosen videos were repeated three times within the first block to investigate the reliability of the ratings. The second block of videos contained different video clips, but the sequence of target emotions was the same as in the first block (including the repeated videos). All participants saw the identical video clip sequences, but before and after intervention sequences were counterbalanced across participants. Participants provided 110 ratings in total (55 before and 55 after the intervention) including a baseline rating before the first video of each block. The length of the experiment was based on simulation and recovery work (cf. Supplementary Materials C Experimental Design).

2.2.4 Self-Report Measures

At the end, participants were asked to complete three self-report questionnaires. To assess depressive and anxiety symptoms, we used the Patient Health Questionnaire (PHQ-9; Kroenke et al. 2001) and the Generalized Anxiety Disorder Assessment (GAD-7; Spitzer et al. 2006), respectively. In addition, we used a short version of the Difficulties in Emotion Regulation Scale (DERS-18; Victor and Klonsky 2016) to assess participants’ ability to identify, accept, and manage their emotional experiences. The questionnaires were conducted after the experiment to prevent them from affecting participants’ behaviour during the study.

2.2.5 Attention Checks

To maintain and monitor attention, participants were asked to detect a black cross, which could be shown briefly before the video clip started. 10 such attention checks were included, 4 in the first block and 6 in the second. Participants with an accuracy of less than 70% on the attention checks were excluded.

2.3 Computational Modelling

During the experiment, we asked participants to report their emotions after watching each video, resulting in a sequence of emotional state reports. To capture the temporal structure of this data, we used a linear Gaussian state space model, specifically the time-invariant Kalman Filter (Durbin and Koopman, 2012; Roweis and Ghahramani, 1999). This model is simple and tractable, accounting for possible errors in participants’ self-reports and allows for external inputs that might influence their emotions. Essentially, this model helps us track the true emotional process as it evolves based on the participants’ reports.

The Kalman Filter suggests an underlying latent process, referred to as the true emotional process, evolving in response to a sequence of emotional state reports x_tt = 1^T conditional on video inputs u_tt = 1^T (cf. to Fig. 2A).

The latent (unobserved) emotional state vector z_t comprises the activation of each emotion category at time t. These latent emotions are assumed to evolve according to a discrete, linear first-order Markov process. The matrix A defines the dynamics matrix, which captures the degree to which an emotion carries over from one time point to the next and the degree to which it predicts future emotions. The matrix C captures the impact of videos, with the entry C_ij capturing the impact of a video of category j on emotion category i. The video category shown at each time point was identified through one-hot labelling in the binary input vector u_t, i.e. each video was identified in the vector u by the main emotion it was targeting. The subjects’ ratings x_i on each category i were mapped directly onto the latent emotion states z_i. Critically, however, Gaussian noise was added to both the latent temporal evolution and the observation processes with separate diagonal covariances Σ and Γ, respectively. This is one of the key differences to standard emotional time-series analyses (Borsboom et al., 2021), in that this explicitly allows for noise or errors in the emotion ratings, and this noise can be ‘smoothed over’ through the filtering process.

2.3.1 Model Comparison

To understand the dynamics of the emotion reports elicited by the video sequences, we asked whether the different components of the Kalman Filter were indeed necessary to provide a parsimonious account of the observed data. To do this, we built increasingly complex models. The simplest model included only Gaussian noise, i.e. it assumed emotion ratings varied randomly over time. The next model additionally contained either a dynamics matrix (A), an input weight matrix (C) or both. The most complex model included a dynamics matrix (A), an input weight matrix (C) and a bias (h). Additionally, we examined variations of these models where we constrained the input matrix C to be diagonal. Finally, models were fitted separately to each individual’s emotion time-series using the python package Pykalman (https://pykalman.github.io/).

We calculated the Bayesian Information Criterion (BIC; Schwarz 1978) for each individual for each model based on an individual’s model loglikelihood by penalizing for the number of parameters in the model. Models were then compared using the BIC at the group level. Cumulative model weights for the most parsimonious model are computed as a proportion of the total amount of predictive power provided by the full set of models contained in the model being assessed: where ΔBIC_i = BIC_i — min(BIC), j indicates the most parsimonious model and N the number of models.

2.3.2 Stability

After extracting the parameters of the most parsimonious model, we investigated the eigenstruc-ture of the dynamical system. Briefly, a linear dynamical system where variables interact, like the Kalman Filter model, can be decomposed into separate systems of non-interacting variables. This is achieved through an eigendecomposition of the dynamics matrix. By projecting the vector of state variables z on each of the eigenvectors, new combined state variables (eigenmodes) can be defined, which evolve independently, i.e. no longer interact. Hence, these new combined state variables identify the effective emotional combinations which determine the evolution of an individual’s affective state. The eigenvector corresponding to the largest eigenvalue of the dynamics matrix A identifies the most stable combination of emotions. In contrast, the eigenvector corresponding to the smallest eigenvalue identifies the combination of emotions that is most transitory and least persistent (for an example cf. Fig. 2B-D).

2.3.3 Controllability

Next, we investigated the controllability of the dynamical system. A system is more controllable if smaller inputs u are required to move its state z to any required value. We computed the controllability Gramian (C) for each participant as follows:

The controllability Gramian (C) combines the dynamics matrix (A) and the weights of the external input (C) to the dynamical system. If the rank of this controllability matrix is equal to the system’s dimension, the system is controllable. A controllable system means that any state z can be achieved through the appropriate choice of external inputs u. How controllable the system is captured by the strength of input |u| required. We investigated the characteristics of the controllability Gramian using singular value decomposition. Unitary vectors of the controllability Gramian define an energy ellipsoid (Fig. 2E). Unitary vectors corresponding to higher singular values identify the more controllable directions in the state space and vice versa. The more controllable a direction is, the less input energy is required to steer the system in that specific direction. In other words, an input of a given strength |u| can move the system further in a direction which aligns with a more controllable direction than a less controllable one.

Figure 2

2.4 Statistical Analysis

We used one-sided two-sample t-tests to test whether the emotion ratings averaged over video clips from the same video category for the emotion which was aimed to be elicited were higher than for the other emotions. In addition, two-sided one-sample t-tests were performed to test whether the mean emotion ratings, autocorrelation coefficients, and cross-correlation coefficients of emotion time-series significantly differed from zero. Those tests were all conducted on data before the intervention.

To investigate intervention effects, the principal analyses was a two-sample Hotelling T² tests to compare multivariate variables (e.g. eigendirections) between groups after the intervention. The randomized group allocation allowed us to focus on potential effects after the intervention. We also performed multivariate ANOVAs (MANOVAs) to test for an interaction effect between time (before and after intervention) and group. To zoom into single emotions, we used non-parametric tests because most dynamical and controllability features were not normally distributed. Mann-Whitney U tests were conducted to compare emotion variables, such as mean emotion ratings and eigenvector directions, between the intervention groups and one-sample Wilcoxon signed-rank test to compare variables before and after the intervention within an intervention group.

Multiple linear regressions were performed to investigate associations between emotion dynamics (dependent variable; DV) and symptoms (independent variable; IV) controlling for the intervention group (G): DV = β₀ + β₁IV + β₂G. Finally, to investigate whether psychological well-being moderated the effect of the intervention on emotion ratings, we examined the interaction effect between symptom score and intervention group: DV = β₀ + β₁IV + β₂G. All variables were z-scored for the regressions. For all above-mentioned analysis types, we used Bonferroni-correction to correct for the number of conducted tests.

3 Results

3.1 Participants

109 participants completed the experiment, but one participant was excluded due to attention check failure. Analyses hence focused on, 108 participants (57 randomized to the distancing intervention).

3.2 Eliciting Complex Emotional States With Videos

In the first video block before the intervention, each video induced the dominant (targeted) emotion as intended (Fig. 3A). Changes in the dominant emotion ratings for each video were significantly higher than changes in other emotions (t ∈ [5.9, 26.2], all p < 0.001; Fig. 3B and Supplementary Material Table I.2). This shows that the sequence of emotional videos reliably induced the targeted emotions. The correlation between our participants’ emotion ratings and those reported by Cowen and Keltner (2017) was moderate to strong across all emotion categories, with correlations of r = 0.74 for Disgust/Horror, r = 0.65 for Amusement/Joy, r = 0.5 for Calmness/Aesthetic Adoration, r = 0.71 for Anxiety/Fear, and r = 0.6 for Sadness/Sympathy (all p < 0.001). Thus, we replicated the ratings from Cowen and Keltner (2017) reasonably well.

Furthermore, changes in emotions other than the dominant one within a video category were significantly different from zero (|t| ∈ [5.1, 19.3], all p < 0.001; Fig. 3B and Supplementary Material Table I.2). This indicates that the videos induced complex and multi-faceted emotional states. We also observed that emotional responses had a dynamic component. This was evident in the autocorrelation of each emotion rating, where an effect of the previous time-point is apparent during the rating of the next video (AR(1) ∈ [0.07 - 0.25], all p ≤ 0.001; cf. Fig. 3C and Supplementary Material Table I.3).

Figure 3

Dynamic effects can also be observed in the cross-correlation between emotion time-series showing that emotions interact with each other (|r| ∈ [0.28 - 0.52], all p < 0.001; cf. Fig. 3D and Supplementary Material Table I.4).

Finally, the test-retest reliability of emotions elicited by repeated video clips varied accordingly to emotion type. Specifically, it was observed to be good for Amusement/Joy (video sequence 1: ICC(2, 1) = 0.79, CI = [0.69,0.86], p < 0.001, video sequence 2: ICC(2, 1) = 0.8, CI = [0.69, 0.87], p < 0.001) and moderate for Disgust/Horror (video sequence 1: ICC(2, 1) = 0.59, CI = [0.43, 0.72], p < 0.001, video sequence 2: ICC(2, 1) = 0.59, CI = [0.43, 0.73], p < 0.001).

In summary, the experimental setup resulted in reliable elicitation of complex, high-dimensional emotional states, allowing for the joint characterization of emotional input sensitivity and emotion dynamics.

3.3 Establishing a Dynamical Model

We next examined the dynamical properties of the emotion ratings, and the interaction with the emotion inputs using a Kalman Filter. First, we compared different models based on the group-level BIC to evaluate which dynamical components are required to capture the data over the whole experiment, i.e. the concatenated time-series before and after the intervention (Fig. 4A). We found that the most parsimonious model, carrying 99% of the cumulative model weight, included a dynamics matrix A, a full input weight matrix C and diagonal noise covariances Σ and Γ. Importantly, data generated from this model accurately captured the observed data sequences as shown in the blue-shaded part in figure 4C. Hence both external inputs and intrinsic dynamics are required to explain the self-reported emotion ratings. The recoverability of the matrices A and C in the most parsimonious model is shown in Supplementary Materials F Parameter Recovery.

Figure 4

3.4 Effects of Distancing on Emotional Responses

We first examined the effect of the intervention on the multivariate reported emotions averaged over trials (Fig. 5A). The mean ratings averaged over the video block after the intervention were significantly different between the distancing and the control group (T² = 24.48, F = 4.71, p < 0.001). In contrast, before the intervention the mean ratings did not show a significant difference between groups (T² = 6.53, F = 1.26, p = 0.29). The within-subject change in average ratings (after minus before intervention) differed significantly between groups(T² = 52.66, F = 10.14, p < 0.001). Additionally, we observed a significant interaction between time and intervention group (F (5, 208) = 2.6, p = 0.026).

At the group-level, all emotion ratings were significantly reduced after the distancing intervention (U ∈ [688,910] for all comparisons, all p ≤ 0.001), except for ratings of calmness which were increased (U = 1824, p = 0.02; though this does not survive Bonferroni correction p ≤ ≤ 0.01). Furthermore, while this pattern was observable in the distancing group (W ∈ [68, 308] for all comparisons, all p < 0.001, before vs after), no changes were detectable in the control group (W ∈ [401,561] for all comparisons, all p ≥ 0.01, except for amused W = 273.0, p < 0.001).

Distancing also affected the temporal variability in emotion ratings (group comparison after intervention: T² = 36.53, F = 7.03, p < 0.001). The variances of all emotions were reduced (U ∈ [576, 983] for all comparisons, all p ≤ 0.004) in the distancing group compared to the control group and they significantly differed before and after the intervention within the distancing group (W ∈ [133, 246] for all comparisons, all p < 0.001). However, the interaction effect in a MANOVA was not significant (F (5, 208) = 1.72, p = 0.13).

Overall, the distancing intervention strongly affected the mean emotions subjects reported and the variability of emotions (cf. full table in Supplementary Materials Table I.5).

To examine whether the observed group differences are attributable to a demand effect, we analyzed the time taken by participants to rate their emotions on the sliders. We reasoned that if a demand effect were present, participants would respond more quickly as they would already have decided in advance of the question how to respond. Using a mixed ANOVA with time (before vs after the intervention) and intervention groups as factors, we found evidence of a significant interaction effect between time and group (F (1, 106) = 6.46, p = 0.01). However, interestingly, the control group demonstrated a decrease in reaction time (before: M = 12029, SD = 2813 (ms); after: M = 10964, SD = 2713 (ms); t = 5.87, p < 0.001), while the distancing group did not show a significant difference in reaction time before and after the intervention (before: M = 11876, SD = 2796 (ms); after: M = 11518, SD = 2896 (ms), t = 1.73, p = 0.09).

3.5 Effects of Distancing on Dynamics of Emotions

Next, we examined whether the intrinsic dynamics or the input weights or both were altered by the distancing intervention (Fig. 4C). In principle, the observed effect of distancing on the mean and variance of emotion ratings can be explained either by changing the internal dynamics or by changing the input weights alone (cf. Supplementary Material Figure G.5). We hence applied model comparison to examine whether either a change in the dynamics, or in the input weights, or in both was required to capture the data. In the control group, the most parsimonious model (99% of model weight) was the one where the dynamics before and after the intervention stayed the same. That is, there was no evidence for a change in either input weights or dynamics. By contrast, in the distancing group, a model where noise, dynamics, and input weights changed with the intervention provided the most parsimonious account of the data (99% of model weight). Again, data generated from this model was able to capture the observed data sequences accurately (cf. Fig. 4D). Overall, this suggests that the distancing intervention changed both the dynamics and the influence of the videos.

We then examined the specific dynamical features that changed in response to the distancing intervention. Four participants had to be excluded as they were outliers in dynamical characteristics (cf. Supplementary Materials E Exclusion). The following analyses were hence based on 104 participants (54 randomized to the distancing intervention).

Distancing altered the input weights (C matrix) shown in a group comparison of the matrix norm (after intervention: distancing group M = 256, SD = 218; control group M = 400, SD = 222; U = 1897, p < 0.001) and in Figure 5B&C.

Furthermore, a linear dynamical system can be decomposed into eigenmodes - parallel, independent dynamical systems - using an eigendecomposition of the dynamics matrix A (cf. 2.3.2 Stability). Distancing altered the composition of the emotional eigenmodes (T² = 14.81, F = 2.85, p = 0.019; Fig. 5D). This component was also more stable (decayed more slowly) in the distancing group (distancing group M =0.69, SD = 0.21; control group M = 0.52, SD = 0.22; U = 762, p < 0.001; Fig. 5D) after the intervention. Hence, when controlling for the emotional input, the distancing intervention had specific effects on how different emotional states persisted and interacted.

3.6 Effects of Distancing on Controllability of Emotions

The dynamics matrix A and the input weight matrix C jointly determine the extent to which the emotional state can be controlled by external inputs. This can be formally assessed through a measure called controllability, which we turn to next (cf. 2.3.3 Controllability). Controllability formalizes how strong the inputs to the system have to be to move the dynamical system around, i.e. how ‘reactive’ the dynamical system is to inputs.

The intervention altered controllability overall (group comparison of matrix norm after intervention: distancing group M = 335, SD = 284; control group M = 509, SD = 292; U = 1851, p = 0.001).

Controllability can, however, vary, with the system being more controllable in certain directions than others. This can be examined by studying the eigenspace of the controllability Gramian C, which is based on a combination of dynamics and input matrices, A and C. The eigenspace corresponding to the dominant eigenvalue of the controllability matrix, describing the most controllable direction, differed between the intervention groups after (T² = 24.67, F = 4.74, p < 0.001), but not before (T² = 3.69, F = 0.71, p = 0.618), the intervention. A posthoc MANOVA revealed a significant interaction between time and intervention group on the most controllable direction (F (5, 200) = 2.5, p = 0.03). Distancing altered which combination of emotions was most controllable (Fig. 5F), with combinations involving more calm (U = 874, p = 0.002) and less sad emotions (U = 1926, p < 0.001) being most controllable. This direction was, overall, less controllable (lower singular value; U = 1844, p = 0.001; Fig. 5E) in the distancing group.

Figure 5

3.7 Psychopathological correlates

The control of emotional states is thought to be altered in mental illness. Hence we examined controllability in relation to the three assessed psychological questionnaires, focusing on the self-reported emotion regulation difficulties. All questionnaires showed a good internal consistency (C_a ∈ [0.89,0.91]). The total scores of the three questionnaires were highly correlated (r ∈ [0.69,0.75], p < 0.001) and distributions of scores were skewed towards lower values (cf. Supplementary Material Figure H.6).

Psychological well-being was significantly related to emotion ratings at baseline (t₀), emotion ratings averaged over the first video block (t₁) and the second video block (t₂). Ratings of disgust, sadness and anxiousness were positively associated with PHQ-9, GAD-7, and DERS-18 total scores (β ∈ [0.18,0.56] for all comparisons, all p ≤ 0.03; except for GAD-7 and disgust at t₀ and t₂ β < 0.12, p > 0.2). Ratings of calmness decreased with increasing symptoms (β ∈ [-0.18, -0.4] for all comparisons, all p ≤ 0.05). There was no relationship between amusement and symptoms. However, critically none of the symptom scores interacted with group allocation in predicting change in emotion ratings (all p > 0.05; cf. Supplementary Material Table I.7).

Psychopathological symptoms were related to aspects of the dynamics of emotions. Difficulties in distancing as measured by the DERS-18 were related to the most controllable direction in the emotion space. In those participants with high DERS-18 scores, the most controllable direction pointed towards disgust (β = 0.26, p = 0.006), and away from amusement (β = -0.26, p = 0.005) and calmness (β = -0.24, p = 0.011; though this did not survive Bonferroni correction). In other words, self-reported emotion regulation difficulties were related to needing less effort to drive disgust and more effort to steer the emotional experience towards calm and amused. The effect of DERS-18 total score on disgust was even more prominent after the intervention (β = 0.35, p < 0.001).

There was no evidence that the symptoms moderated the effect of distancing (all p > 0.05; cf. Supplementary Material Table I.8).

4 Discussion

Psychotherapeutic approaches effectively treat a variety of psychiatric conditions. However, the mechanisms underlying these psychotherapeutic effects remain unclear (Kazdin, 2009). By isolating a specific intervention component, such as emotion regulation, we aim to gain a deeper understanding of the processes involved in this specific treatment effect. Emotion regulation techniques are core components of psychotherapy (McRae and Gross, 2020; Powers and LaBar, 2019; Gross, 2015). To study emotion regulation strategies, it is essential to investigate emotions and consider that they fluctuate in intensity and frequency over time, potentially giving rise to a complex dynamical system. We believe that by examining the emotion dynamics of a particular individual, we can better understand how emotions change and how they respond to different interventions.

Here, we studied the impact of an emotion regulation technique called distancing on the dynamics of emotions over time. We used rich and powerful video stimuli to evoke and alter a complex emotional state in participants. This approach allowed us to achieve three main objectives: first, we established how different emotions influence each other over time in a dynamic system; second, we assessed the relative impact of the video clips on these emotions; and finally, we disentangled the effect of distancing on the stability and controllability of these emotional states.

Importance of external inputs in a dynamical system

Our findings revealed that video clips evoked complex patterns in self-reported emotional experiences, including interrelated emotional trajectories. This highlights the significance of considering multidimensional emotional experiences, their interactions, and temporal dependencies, rather than focusing on a single emotion in isolation (Kendler, 2016; Hitchcock et al., 2022; Durstewitz et al., 2020; Kuppens and Verduyn, 2017; Lange et al., 2022). Computational modeling results suggest that external inputs (video clips) were important in explaining a higher dimensional emotional state. In other words, models that included these inputs provided a better explanation of the self-reported emotion responses. This is in line with recent experimental research demonstrating how unexpected and personally-relevant events are associated with measurable changes in the time course of individuals’ emotional responses (Villano et al., 2020; Rutledge et al., 2014; Eldar et al., 2016; Asutay et al., 2022; Lapate and Heller, 2020). Omitting inputs when studying the properties of a dynamical system can lead to inaccurate conclusions as the inputs can mask or alter the apparent dynamics of the system. For instance, Vanhasbroeck et al. (2022) has observed that nonlinearity observed in affective time series in some individuals was the result of external inputs rather than underlying nonlinearity in affect. Hence, to ensure an accurate understanding of the affective system, it is crucial to consider the relationship between affect dynamics and the immediate environment.

Distancing effect on emotional controllability

First, the distancing intervention reliably reduced ratings and variability of both positive and negative emotions but increased ratings of a specific variable, namely feeling calm.

Second, the modeling approach enabled a formal, quantitative assessment of the impact of the distancing intervention on these components. Model comparison showed that the combination of dynamic and controllability signatures changed due to the distancing intervention. Specifically, a brief distancing intervention stabilized intrinsic emotional dynamics and reduced the impact of external stimuli. This finding is significant because static mean differences could be attributed to changes in either dynamics or input sensitivity alone. Interestingly, the intervention affected emotions differently: the controllability of calmness decreased, while sadness increased relative to other emotions. This suggests that some emotions may be more responsive to regulation through distancing.

Emotional controllability and psychopathology

Psychopathology has been associated with deficits in cognitive control (Grahek et al., 2018; Snyder, 2013). The belief that emotions can be controlled to some extent was linked to a decrease in symptoms of anxiety and depression. This connection can be attributed, at least in part, to the fact that individuals with such beliefs tend to employ adaptive strategies for regulating their emotions more frequently (Somerville et al., 2022).

Distancing involves several cognitive control processes, such as taking a step back from a situation, observing it objectively, and cognitively re-framing the experience to focus on positive aspects rather than negative feelings (McRae and Gross, 2020; Ochsner et al., 2004; Dorfel et al., 2014; Staudinger et al., 2009). These processes may include inhibiting pre-potent evaluations, shifting attention away from external stimuli towards the self, and maintaining an intention to detach (McRae and Gross, 2020; Ochsner et al., 2004; Dorfel et al., 2014; Staudinger et al., 2009). Our study demonstrated that the distancing intervention effectively reduced emotional variability and increased feelings of calmness, indicating enhanced emotional control. Furthermore, our modeling showed that the distancing intervention stabilized intrinsic emotional dynamics and reduced the impact of external stimuli. This suggests that distancing can improve emotional stability by enhancing cognitive control. This is consistent with evidence that individuals with high self-control are more successful in regulating emotions (Paschke et al., 2016) and that emotional stability is linked to self-control (Daly et al., 2014; Tangney et al., 2004; Oaten and Cheng, 2006).

An interesting consideration is that cognitive biases may influence emotion regulation ability, thereby contributing to sustained negative affect and reduced levels of positive affect (Joormann and Tanovic, 2015; McRae et al., 2012). For instance, individuals with depression often have difficulty inhibiting negative thoughts or shifting their attention away from negative stimuli. This can lead to a cycle of negative thinking that worsen symptoms (Beck and Haigh, 2014). Our study found that difficulties in emotion regulation were specifically linked to the controllability of emotions such as disgust, amusement, and calmness, indicating that these emotions may be more intrinsically tied to individuals’ perceived ability to regulate their emotions (Gross, 2015; Mitchell, 2021). Notably, emotions like amusement and disgust are strongly influenced by external events, suggesting that the emotional impact of external stimuli plays a critical role in the complexity of emotion regulation difficulties in psychopathology. However, contrary to our expectation, we did not find a correlation between symptoms of psychopathology and the efficacy of the distancing intervention.

Future directions

Our investigation confirms that emotional dynamics and their controllability are complex and context-dependent. Future research needs to be examined whether the findings discovered in this study can be applied beyond the realm of video-induced emotions. The key challenge here will be the appropriate, but necessary, characterisation of inputs. Unless inputs are well-known, the true internal dynamics are not identifiable. However, in more naturalistic environments this appears very difficult (Malamud and Huys, 2024).

4.1 Limitations

This study comes with several limitations. First, it is challenging to identify the degree of influence of possible demand effects. We attempted to avoid this influence by providing participants with the sense that distancing does not work for everyone, and we were interested in how it works for them; however, this might not have been enough. On the other hand, the specifics of the effects of the intervention are probably not predicted from simple demand effects.

Second, employing a standard Kalman Filter approach to analyze the time-series of emotion ratings and video inputs, was based on several considerations. i) There are ample tools for the analysis and characterization of Kalman Filters readily available. ii) The Kalman Filter allows for observations to be noisy. This contrasts with typical analyses of EMA and similar timeseries emotion ratings data, which do not allow for noise in the observations. This is important because the noise in ratings influences estimates of parameters as the rating error ‘persists’ in the modelled future. Nevertheless, one drawback of the Kalman Filter approach we employed was that Gaussian observation noise was assumed, and this is likely to impact the details of the results. However, reconstructed time-series were qualitatively close to the real time-series, and hence we do not believe that the fundamental conclusions here are likely to be affected by this.

Finally, it is possible that eye gaze redirection away from emotionally charged regions in the videos could have acted as an intervening factor in emotion downregulation. Future research could tackle that problem by tracking eye movement.

4.2 Conclusion

In conclusion, we used a novel methodological approach to characterize a key aspect of emotional states, namely how they can be controlled. We found that a brief distancing intervention can effectively regulate emotional experiences, reduce emotional variability and enhance the feeling of calmness. Moreover, distancing leads to qualitatively different changes in the dynamical structure of emotional states. First, it increases the intrinsic emotional stability, and second it reduces the impact of external inputs. Together, these alter the extent to which emotional states are externally controlled. Further computationally detailed characterization of emotional state dynamics and psychotherapeutic interventions may be useful on the path towards understanding differential and specific effects of different psychotherapeutic interventions.

Supplementary Material

A Intervention Text

A.1 Distancing intervention text

For the second part of the study, we would like you to try out an emotion regulation technique called distancing. This technique involves viewing your emotions and thoughts as events passing in your mind rather than getting sucked in by them. We are interested in hearing whether and how well this works for you. It works for some people, but not for all.

What do I have to do? Usually, when an event evokes an emotion, we get sucked in. One way of regulating emotions is to avoid getting sucked in, and instead attempt to stand back and observe the emotion that happens to you as if it was a passing event. To illustrate this, we will walk you through a short mindfulness exercise called “Leaves on a Stream”.

Imagine you are resting by the side of a gently flowing stream watching the water flow. Focus on the stream, the sound of the water and other ambiance, the physical sensations, and anything else that comes to mind. Imagine that there are leaves from trees, of all different shapes, sizes, and colors, floating past on the stream and you are just watching the leaves float on the stream. The stream does not stop, it goes on continuously, and the water can easily carry the leaves down/away. Now try to be aware of your emotions and thoughts. When an emotion or thought comes up, imagine you place the thought on one of those leaves and that you are watching the leave - carrying your emotion or thought - float away, disappearing behind a corner or in the distance. Some of the clips you are about to see are likely to elicit emotions. When the emotions start to come, try to notice them without judgment. Emotions will intensify with each video clip. Try to feel them, allow them to come, and then also allow them to go again, like the leaves floating past. Try to treat all your emotions the same, whether comfortable or uncomfortable. The goal is to become aware of your emotions — not to change or improve them. Allow them to come, and then to go again.

A.2 Control intervention text

Before you continue to the second part of the study, we would like to ask you to engage in a relaxation exercise.

What do I have to do? We are going to walk you through a relaxing exercise. Just read the next pages and try to relax.

Imagine you are resting by the side of a gently flowing stream watching the water flow. Focus on the stream, the sound of the water and other ambiance, the physical sensations, and anything else that comes to mind. Imagine that there are leaves from trees, of all different shapes, sizes, and colors, floating past on the stream and you are just watching the leaves float on the stream. The stream does not stop, it goes on continuously, and the water can easily carry the leaves down/away. Now keep thinking of the river and try to relax. Imagine you are standing next to the river, and you are watching the leaves floating by, passing in front of you and then disappearing in the distance. For the next part of video clips, we would like to ask you to keep doing what you have been doing in the first part: watching video clips and reporting your emotions.

B Video Clips

The video clip database referenced in Cowen and Keltner (2017) has been validated and contains 2185 videos (https://s3-us-west-1.amazonaws.com/emogifs/uncensored.html) that have been labelled by 853 subjects across 34 emotion categories. Out of this database, we selected video clips with a high rating and low entropy in the five emotion categories of interest (Amusement/Joy, Disgust/Horror, Sadness/Sympathy, Calmness/Aesthetic Adoration, Anxiety/Fear). 20 videos per emotion category were chosen resulting in 50 videos per sequence. It was not feasible to find videos that elicited only the emotion of interest. However, since 10 videos from each category were presented in each sequence, differences were likely to be smoothed out.

Figure B.1

Figure B.2

C Experimental Design

In a simulation study, we utilized a linear KF to generate time-series and determine the appropriate number of trials needed for accurate parameter recovery. We simulated 100 datasets, each containing five-dimensional emotion trajectories and five-dimensional inputs (according to our experimenal setup) for varying numbers of trials (T = [10, 30, 50, 70, 90]). Next, we estimated the parameters for each simulated dataset and computed similarity measures such as correlation and dot-product between the known parameters used for simulation and the estimated parameters from the simulated data.

Our findings showed that with 50 measurement points (Fig. C.3), the parameters of interest (i.e. dynamic matrix and input weights) could be recovered almost perfectly. Based on this, we opted to use 50 trials before and after the intervention, which allowed us to fit the model independently to the ratings obtained before and after the intervention while still ensuring accurate recovery of the parameters.

Figure C.3

D Power Analysis

To estimate the sample size, we collected pilot data online (N=40). In the pilot study, 3 participants failed the attention checks leaving 37 participants for the analyses. Two main hypotheses were tested: that 1) the first eigenvector of the dynamics matrix and 2) the first unit vector of the controllability matrix differ between intervention groups after the intervention. The lower effect size across both tests in the pilot study (Hotelling T² effect size = 0.81) was used for our power analysis, which suggests that a sample of N = 102 is sufficient to reach 90% power for both hypotheses (G*Power (Faul et al., 2007, 2009); Hotelling T² : Two group mean vectors). We added 7 extra participants because we observed an exclusion rate of 7% due to failed attention checks.

E Exclusion

Two participants were excluded from the analysis due to their dominant eigenvalue of the dynamics matrix being greater than 1, indicating an unstable process. Additionally, two other participants were excluded because of outliers in the singular values of the controllability matrix, which resulted from large values in the input weights. Outliers were identified using IQR outlier detection. IQR outlier detection is based on the interquartile range (IQR), which is the difference between the first and third quartiles of a dataset. Outliers are defined as data points that fall outside of the range of the first quartile minus 1.5 times the IQR to the third quartile plus 1.5 times the IQR. For the singular values of the controllability matrix the IQR ranged from -519.81 to 1263.54. Two subjects had values outside that range (-595.63, 1363.61) and hence were excluded.

F Parameter Recovery

We investigated the recoverability of the parameters in our datasets. Initially, we estimated the parameters for every individual. Subsequently, we utilized the derived parameter estimates to generate surrogate mood trajectories for each individual. Afterward, we re-estimated the parameters based on the surrogate time-series. We calculated the Spearman correlation coefficient between the known and re-estimated dynamics matrices (A), resp. input weight matrices (C), for each individual.

Figure F.4

G Replication of Distancing Effect in Simulated Data

In order to demonstrate the replicability of the distancing effect in mean emotion ratings, we conducted simulations for each participant using two distinct models. The first model involved allowing changes solely in the dynamics matrix (A) before and after the intervention, while keeping the input weight matrix (C) constant (Fig. G.5 A). The second model, on the other hand, allowed changes exclusively in the input weight matrix (C) before and after the intervention, while keeping the dynamics matrix (A) unchanged (Fig. G.5 B). The mean and variance of simulated ratings obtained from both models showed significant differences between the distancing and control groups after the intervention (Table G.1).

Table G.1

Figure G.5

H Psychopathological Questionnaires

Here, we show the distributions of and the relations between the total sum scores of the three acquired psychological questionnaires measuring symptoms of depression (PHQ-9), generalized anxiety (GAD-7) and self-reported emotion regulation difficulties (DERS-18).

Figure H.6

I Additional Tables

Table I.2

Table I.3

Table I.4

Table I.5

Table I.6

Table I.7

Table I.8

Table I.9

Data and Code Sharing Statement

Fully anonymised data and code for data analysis of this study is available from a Github repository (https://github.com/huyslab/emotioncon_public).

Acknowledgements

The authors would like to thank Tim Loossens for his early feedback on the experimental design and Agnes Norbury, Anahit Mkrtchian, Tore Erdmann, Jiazhou Chen, Jenny Fielder, Anna Hall, Jakub Onysk, Jade Serfaty, and Lana Tymchyk for their feedback on the manuscript.

Additional information

Funding

JM was supported by an International Max Planck Research School on Computational Methods in Psychiatry and Ageing Research (IMPRS COMP2PSYCH) and a Wellcome Trust grant awarded to QJMH (221826/Z/20/Z). In addition, we acknowledge support by the UCLH NIHR BRC.

Ethical Approvals

The UCL research ethics committee approved the study procedures (REC No 21029/001). The participants in the study provided electronic consent to participate in the research and to allow for the publication of the study.

Author Contributions

QJMH and JM collaborated on the study design. JM developed the methodology with guidance from QJMH, and was responsible for conducting the study and analyzing the data under the supervision of QJMH. JM initially drafted the manuscript, which was subsequently revised by QJMH.