Mathematical Characterization of Changes in Fear During Exposure Therapy

Published:January 25, 2021DOI:



      During exposure therapy, patients report increases in fear that generally decrease within and across exposure sessions. Our main aim was to characterize these changes in fear ratings mathematically; a secondary aim was to test whether the resulting model would help to predict treatment outcome.


      We applied tools of computational psychiatry to a previously published dataset in which 30 women with spider phobia were randomly assigned to virtual-reality exposures in a single context or in multiple contexts (n = 15 each). Patients provided fear ratings every minute during exposures. We characterized fear decrease within exposures and return of fear between exposures using a set of mathematical models; we selected the best model using Bayesian techniques. In the multiple-contexts group, we tested the predictions of the best model in a separate, test exposure, and we investigated the ability of model parameters to predict treatment outcome.


      The best model characterized fear decrease within exposures in both groups as an exponential decay with constant decay rate across exposures. The best model for each group had only two parameters but captured with remarkable accuracy the patterns of fear change, both at the group level and for individual subjects. The best model also made remarkably accurate predictions for the test exposure. One of the model’s parameters helped predict treatment outcome.


      Individual patterns of fear change during exposure therapy can be characterized mathematically. This mathematical characterization helps predict treatment outcome.


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