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Assessing Human Emotional Response to Aversive Stimuli in the Context of Contagion Dynamics

By Lina Sorg

Emotional contagion is the communication of emotion in a way that triggers a similar reaction in other people. This transmission occurs via behavioral cues, like facial expressions or body movement. If an individual looks curiously out a window, for example, other people in the room will likely follow suit. The same phenomenon often occurs in mass crowds, especially during negative or high-stress situations that evoke fear. Once someone triggers a response, the consequential spread of that response resembles an escape wave. While suppressing ongoing waves of emotional contagion is nearly impossible, slowing them down with external stimuli might be an achievable goal. During a minisymposium presentation at the 2019 SIAM Conference on Applications of Dynamical Systems, which took place this week in Snowbird, Utah, Sachit Butail of Northern Illinois University modeled the temporal dynamics of human subjects exposed to aversive images to assess the effectiveness of extrinsic emotion regulation.

Butail opened his presentation with a real-world video of emotional contagion in action. On May 4, 2010, a man in a crowded Amsterdam street screamed, immediately inducing fear in the gathered people and triggering a rapid escape wave that resulted in a stampede. Dozens of people were injured in the panic. “It’s really important for us to understand what’s going on and how we can mitigate these kinds of disasters,” Butail said. Various mathematical models attempt to replicate this type of situation by focusing on networks. Yet Butail is specifically interested in the dynamics of a single node, and whether individuals can regulate escape waves by working on their own emotions. This type of study requires empirical evidence supporting the viability of external stimuli. And given the necessary data, can the resulting model successfully simulate a representative network?

Figure 1. Psychologist James Gross' model for emotion generation and regulation functions as a feedback loop.

Because emotion generation is such a large subset of psychology, Butail began with a psychological analysis of the aforementioned problem. He presented a model for emotion generation and regulation—created by psychologist James Gross—that functions as a feedback mechanism (see Figure 1). Psychologists typically view emotional response as an intrinsic process, meaning that individuals deploy and control their own emotions. Butail offered a sample scenario as an example. Looking at a negative image—with blood, gore, etc.—raises the same type of emotion that one would experience in a fearful situation. This is called negative-watch. Negative-distract occurs when subjects are then instructed to think of something happy to distract themselves from the disturbing image in front of them. Unsurprisingly, a corresponding graph of this situation reveals that negative-distract has less intensity than negative-watch, and that subjects’ responses appear to settle to a steady-state value (see Figure 2). 

Unfortunately, intrinsic emotion regulation is difficult to engineer; this prompted Butail to wonder if one can achieve emotion regulation extrinsically. He specifically wanted to know whether application of an extrinsic distraction would prompt a change in event-related potential (ERP). ERP is measured brain response to discrete sensory, cognitive, or motor events. It is quantified via electroencephalography (EEG), a reliable electrophysiological monitoring method that records activity in different parts of the brain via noninvasive electrodes on the scalp. Averaging the EEG time series removes background noise and provides a measurement of emotion.

Figure 2. When examining emotion regulation from an intrinsic point of view, negative-distract has less intensity than negative-watch.

Because he could not find any extrinsic experiments of this type in the existing literature, Butail devised his own. He showed each of his human subjects a negative image for five seconds, then asked them to rate the image on a valence scale representing the intrinsic attractiveness or adverseness of the material, with “9” being happy and “1” being sad. Butail used a similar system to rate the images’ level of emotional arousal. He then showed the same subjects a neutral image (like a photo of a cell phone on a table) and asked them to rate that material on the same scales. Finally, the subjects looked at a negative image for one second, after which a positive image appeared in the corner of the negative image at various levels of closeness or distance and after a random time delay. 

Butail placed the electrodes on sites on the scalp that yield robust ERP. He began with 22 subjects but had to discard two of them because too much movement was present in their data. “As expected, people rated neutral images much higher than negative images,” Butail said; negative and neutral images thus generated different ERPs. Depending on the position and closeness of the distracting images, those too had an impact on ERP. “These subjects were not instructed to do anything, they simply looked at what they were shown,” Butail continued. “There was a significant difference in ERP, which basically confirmed our hypothesis.”

Next, Butail created a model of ERP to simulate complex, high-stress scenarios. Previous researchers have modeled ERP with competent analysis, neural field models, and the like. Yet upon seeing the data, Butail decided that ERP is reminiscent of a linear dynamic system subject to step input. He also wanted to create a network with linear node dynamics, and noted that one can use an array of tools in control systems to analyze such a network. Therefore, Butail chose to model ERP as a linear dynamic system with the images as input. “Ultimately we sought to model ERP as an input/output system,” he said. He used a least-square fits method to determine the right number of coefficients on the numerator and denominator, since too many coefficients can limit the quality of the model’s explanation.

When his model displayed instability, Butail wondered whether that instability was a function of the way he was modeling. Upon investigating further, he found that instability is consistent across different models. He also determined that neither valence nor arousal are predictors of instability. With this in mind, Butail’s team is now examining eye and head movements from video analysis to determine whether those movements produce unstable responses.

To successfully represent ERP as a stable linear dynamic system, a model must meet the three following qualifications:

  • It should be stable
  • The maximum of the response should lie between 500 and 1,000 ms
  • The signal should peak with a positive value less than 20 \(\bf{\mu} \textrm{V}\).

To determine whether his model met these specifications, Butail simulated 104 runs with coefficients sampled uniformly within the range for stable system fits. All of his runs were stable, but the maximum of the response fell between 500 and 1,000 ms only 28.5 percent of the time and the signal peaked with a positive value of 14.5 \(\pm\) 8.4 \(\bf{\mu} \textrm{V}\). Butail then wondered whether the coefficients were in an embedded space. He again simulated 104 runs of his model, but this time with coefficients sampled uniformly along the lines connecting the different coefficient combinations for seven stable subjects (see Figure 3). All of his runs were stable, the maximum of the response fell between 500 and 1,000 ms 78.5 percent of the time, and the signal peaked with a positive value of 8.8 \(\pm\) 2.9 \(\bf{\mu} \textrm{V}\). Butail’s model thus yielded the best results when the coefficients were sampled uniformly along the lines.

Figure 3. 104 runs of Butail's model, first with coefficients sampled uniformly within the range for stable system fits (left) and then with coefficients sampled uniformly along the lines connecting the different coefficient combinations for seven stable subjects (right).

The results of Butail’s study confirm the effect of positive distracting cues placed at various locations within the field of view of his subjects. In short, external emotion regulation allows one to manipulate the reaction of an individual’s response—and a crowd’s response by extension—to a perceived threat. “Modeling ERP as a linear dynamic system looks like a viable approach for taking it to a larger setting,” Butail said.

Lina Sorg is the associate editor of SIAM News
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