Advancing the understanding and treatment of post-traumatic stress disorder with computational modelling

ABSTRACT

The existing theories of post-traumatic stress disorder (PTSD) have inspired large volumes of research and have contributed substantially to our current knowledge base. However, most of the theories are of a qualitative and verbal nature, and may be difficult to evaluate and compare with each other. In this paper, we propose that one way forward is to use computational modelling to formulate more precise theories of PTSD that can be evaluated by (1) assessing whether the model can explain fundamental phenomena related to PTSD, and (2) comparing simulated outcomes with real data. Computational modelling can force us to describe processes more precisely and achieve stronger theories that are viable for testing. Establishing the theoretical groundwork before undertaking empirical studies can help us to avoid doing research with low probability of valid results, and counteract the replicability crisis in psychology. In conclusion, computational modelling is a promising avenue for advancing the understanding and treatment of PTSD.

HIGHLIGHTS

• Computational modelling can help us to specify the psychological processes involved in PTSD, which may increase our understanding of how best to help people to recover after traumatic events.

• With computational models of PTSD, we can simulate the consequences of the theoretical principles and make sure to design research studies that are theoretically well grounded.

• To validate the computational models, high-quality empirical data are still needed.

Las teorías existentes sobre el trastorno de estrés postraumático (TEPT) han inspirado grandes volúmenes de investigación y han contribuido sustancialmente a nuestra base de conocimiento actual. Sin embargo, la mayoría de estas teorías son de naturaleza cualitativa y verbal, lo que puede dificultar su evaluación y comparación entre ellas. En este artículo, proponemos que una forma de avanzar es utilizar el modelado computacional para formular teorías más precisas sobre el TEPT, que puedan ser evaluadas mediante: (1) evaluar si el modelo puede explicar fenómenos fundamentales relacionados con el TEPT, como ráfagas de hiperalerta tras recordatorios del trauma, y (2) comparar los resultados simulados con datos reales. El modelado computacional puede forzarnos a describir los procesos con mayor precisión y lograr teorías más sólidas, que sean viables para someter a pruebas. Un mayor trabajo de base teórica, antes de emprender estudios empíricos, puede ayudar a evitar investigaciones costosas e inútiles y contrarrestar la crisis de replicabilidad en la psicología. En conclusión, el modelado computacional es una dirección prometedora para avanzar en la comprensión y tratamiento del trastorno de estrés postraumático.

KEYWORDS:

• PTSD
• theory
• system dynamics
• agent-based
• computational modelling
• mathematical modelling

PALABRAS CLAVE:

• TEPT
• teoría
• dinámica de sistemas
• basado en agentes
• modelado computacional
• modelado matemático

1. Introduction

Traumatic events may lead to a set of different but interconnected psychological reactions. Involuntary intrusions of memories about the traumatic event (re-experiencing) are followed by physiological and psychological reactions (hyperarousal), which a person often attempts to cope with by avoiding reminders of the trauma. Other symptoms, such as maladaptive trauma-related appraisals and problems with sleeping, may exist alongside these reactions. These reactions often subside over time, but for some people they persist and then become post-traumatic stress disorder (PTSD). Although risk factors that increase the probability of developing PTSD have been identified (e.g. Shalev et al., 2019; Tortella-Feliu et al., 2019), we lack a precise understanding of exactly how these reactions subside or persist and how best to strengthen the factors that help to reduce post-traumatic reactions. Developing more precise and quantitative theories of PTSD may advance this understanding, and ultimately contribute towards the improved treatment of PTSD.

2. Theories of PTSD

Several theoretical frameworks for understanding PTSD have been proposed. For example, Ehlers and Clark (2000) proposed an influential cognitive model of PTSD, suggesting that negative appraisals and poor elaboration of trauma memories lead to a sense of serious current threat, which in turn leads to persistent PTSD. According to this theory, changing the appraisals through, for example, cognitive reprocessing should help to reduce PTSD. Another prominent theory is the emotional processing theory (Foa et al., 2006), which proposes that experiencing traumatic events leads to fear structures in which previously neutral stimuli are linked to a fear response. These fear structures are naturally weakened when the individual repeatedly activates them in the absence of feared consequences. However, when an individual avoids the trauma reminders, PTSD may develop. Thus, according to this theory, exposure to trauma reminders without negative consequences should contribute towards recovery from PTSD.

Other compelling frameworks focus on other aspects of PTSD and may prescribe different interventions (Brewin & Holmes, 2003; Kube et al., 2020; Rubin et al., 2008). These theories have sparked a substantial body of highly valuable research. However, they use different terminology and are based on different underlying assumptions, and it is therefore difficult to evaluate them against each other, or to decide whether and how they can be combined into the same overarching theoretical framework. Whereas all of the theories address central factors of PTSD, they are quite general in nature and do not explicitly consider the change in symptoms and conditions over time. These features make the theories less helpful in understanding precisely how traumatic reactions unfold from week to week, or how one can prevent common early symptoms from establishing themselves and leading to full-blown PTSD.

A potential path towards deeper understanding is to formulate more precise and quantitative theories on how PTSD evolves; for instance, how aspects of the traumatic event (e.g. threatening sensory stimuli) lead to memory features (e.g. vividness) that give rise to physical arousal (e.g. sweating) and negative feelings (e.g. fear). After identifying and describing such relationships using verbal statements, the natural next step to increase the level of precision is to formalize the theories as mathematical and computational models (Borsboom et al., 2021; Fried, 2020; Haslbeck et al., 2022). The essence of this modelling step is to write rules, in the form of mathematical relationships or algorithmic rules, for how elements of the model relate to each other. Models of this kind are indispensable tools in most fields of natural science, including life sciences such as physiology (Keener & Sneyd, 2009) and epidemiology (Cooper et al., 2020). They have also been used in social sciences such as sociology (Bianchi & Squazzoni, 2015) and cognitive science (Gregorová et al., 2024), but they are not yet widely used to describe the psychological aspects of mental disorders such as PTSD. Two classes of commonly used models are the system dynamics models and agent-based models, both of which can be useful in trauma research.

3. System dynamics models and agent-based models

System dynamics models are formulated in terms of mathematical equations that specify how parts of a system interact to govern its overall dynamics. The most common formulation of such models is in terms of ordinary differential equations, which provide a mathematical description of how core quantities change over time. Specifically, the model defines a set of state variables, and describes how the rate of change of these variables depends on their values and on time. In the context of PTSD, the state variables may represent given symptoms or conditions, and one can, for instance, formulate that symptom X declines with a given percentage per time unit (e.g. per day), or that there is an exponential relationship between symptom X and symptom Y. With such models, we can simulate fundamental phenomena related to PTSD; for example, how a trauma reminder may instigate a new burst of symptoms even when the general level of symptoms is low. We can also use the framework to formulate precise mathematical descriptions of proposed mechanisms (e.g. a feedback loop between re-experiencing events and physiological stress reactions) and provide output (e.g. how levels of PTSD stabilize or change over time) that can be compared with real data from real people who have experienced trauma. Thus, system dynamics modelling is a tool for specifying exactly how elements of the model influence each other, and on which time scale this happens. Such precise formulations are useful for developing theoretical models for PTSD, and in particular for comparing the theoretical models with observed data. One particular strength of these models is the ability to define and analyse feedback loops between elements of the model. For example, vivid memories may lead to physical arousal that may lead to avoidance and attempted thought suppression, which may again lead to more frequent and vivid memories. A theoretical model should, in this context, not be confused with a statistical model. A statistical model specifies mathematical associations between observed (measured) variables but it does not attempt to provide information on the mechanisms that generated the data. A theoretical model, however, is not constricted to include only the variables that can be supported with observed data; it can model continuous change over time, and one may make assumptions in a more flexible way than in statistical models. While statistical models are data driven, theoretical models as discussed here are hypothesis-driven models, which, in their essence, are nothing but precise mathematical formulations of accepted knowledge or proposed hypotheses.

Existing computational models in the field of post-traumatic stress include several biologically oriented models within computational psychiatry (Formolo et al., 2017; Linson & Friston, 2019; Radell et al., 2017), which may be useful for understanding the neural dynamics of mental illnesses, but are less useful in understanding individual differences in mental illnesses and their phenomenology. In particular, the phenomenology of mental illnesses is heavily influenced by beliefs and other contextual information, and information about context and time should be included in our computational models of mental illnesses such as PTSD (Hitchcock et al., 2022). Excellent system dynamics models that have included information on context and time have been specified for panic disorder (Robinaugh et al., 2019) and treatment of panic disorder (Ryan et al., 2023), as well as suicide (Wang et al., 2023).

Agent-based modelling is a computational approach in which the main entities are simulated individuals. By specifying the behaviours and interactions of these individuals, we can run simulations and observe how aggregated population-level patterns emerge (Tracy et al., 2023). This approach can be useful in understanding interactions between individuals and processes of contagion through networks (of diseases, but also of ideas and emotions), as well as effects from multiple predictors at different levels and at different time-points. Agent-based models can be used as a virtual laboratory to explore outcomes under different conditions (Auchincloss & Diez Roux, 2008). In the trauma field, such models have been used, for instance, to compare the effects of different interventions and policy changes on community violence (Goldstick & Jay, 2022; Keyes et al., 2019; Mooney et al., 2022) and on strategies for health services for PTSD (Cerdá et al., 2015). A review of applications of agent-based modelling in the trauma field is presented by Tracy et al. (2023).

Both agent-based and system dynamic models can be useful for theory building. However, they highlight different aspects of the system being modelled. Agent-based models are well suited for linking processes at micro- and macro-levels together (e.g. individuals who behave in ways that create a pattern in the population), and for modelling heterogeneity in individual attributes and the network of interactions between entities in the system. System dynamics models are more directed towards the processes themselves and are commonly presented in terms of figures showing causal relations, which may facilitate thinking and communicating about causal feedback loops. Thus, to build theories about how elements of post-traumatic stress reactions reinforce each other and create feedback loops, and to understand how these turn into PTSD, system dynamics models may be the best approach. To understand how ideas about what it means to be traumatized (expectations about consequences) spread between individuals, or to estimate the number of trauma-exposed people in a given context (e.g. after an earthquake) who may develop PTSD and need health services, agent-based models may be the better choice.

4. Advantages

Computational modelling can advance the understanding and treatment of PTSD in at least two ways. First, this approach forces us to describe our theories more precisely (Guest & Martin, 2021). A theory can be defined as ‘a scientific proposition described by a collection of natural-language sentences, mathematics, logic, and figures – that introduces causal relations with the aim of describing, explaining, and/or predicting a set of phenomena’ (Lakatos, 1976; see Guest & Martin, 2021). With computational modelling, we need to think explicitly about how elements of post-traumatic stress reactions relate to each other and, for example, to specify whether we would expect a linear or an exponential relationship between them, whether there is reason to expect thresholds where some process is instigated, whether there are feedback loops in which symptoms and processes reinforce each other, or whether the processes are conditioned on contextual factors. Such detailed assumptions are often challenging to extrapolate from the traditional verbal theories of PTSD. According to Fried (2020), weak theories are verbal or imprecise hypotheses (such as stating that two variables are significantly correlated). In contrast, strong theories are precise sets of assumptions and axioms that explain or predict phenomena explicitly and can be compared with observations. Mathematics and computational models provide suitable tools for formulating these assumptions, and thereby turn weak theories into strong ones with precise and quantitative predictions. The precise language of these tools can remove the vagueness and difficulties in communicating about theories.

Secondly, using computational models may help to reduce the ongoing replicability crisis. It has been argued that there is too much hypothesis testing on weak ground within the field of psychology, and that this has contributed towards the replicability crisis (Scheel et al., 2021). Weak theories may give rise to general hypotheses that are not easy to operationalize, and as a result we may end up carrying out expensive and possibly underpowered data collection that may not contribute towards the development of new knowledge. In contrast, by improving theories iteratively (van Rooij & Baggio, 2021) and ensuring that we have strong theories with plausible hypotheses before testing them, we may be better prepared for doing empirical investigations that are more likely to yield valid conclusions. Theoretical principles can be formalized as mathematical models, and then evaluated on whether they can indeed explain the relevant phenomena in a realistic and meaningful way and provide outcomes that are comparable to already existing data. By testing the consequences of the theoretical principles with simulations, it will be easier to spot errors and make amendments before designing an expensive and time-consuming empirical study on, for example, improving treatment of PTSD. Thus, computational models provide a better basis for testing theories and may propel the development of new knowledge that is relevant to mechanisms of the development, maintenance, and treatment of PTSD.

5. Challenges

There are several challenges that may hinder the use of computational modelling of PTSD. One challenge is that theories within psychology may not be sufficiently precise to specify mathematical relationships between the components. For example, it is necessary to choose a stable and defined phenomenon that one wants to explain, since poorly defined constructs are not a suitable starting point for developing theories. With very vague and broad theories, it may be difficult to define the relevant elements and causal links between them. Certain branches of psychology, for instance, cognitive psychology, where more precise theories and computational models have started to emerge (Lockwood & Klein-Flügge, 2020), may be more ready for this than others. Within clinical psychology, theories are typically more general, and principles may be difficult to spell out with mathematical equations. For PTSD, there is general agreement on a set of symptom clusters (re-experiencing, hyperarousal, and avoidance), but the roles of biological processes, cognition, and context are less clear. Formulating our assumptions in mathematical relationships and computational algorithms should, at least, help us to improve our current theories within psychology and to move in a more precise direction.

Another challenge is that the models need to be validated with real data. Some data may be relatively easy to obtain, but in other cases it can be difficult to collect sufficient data of the right kind. Certain parts of a model may be particularly difficult to validate with data, since some constructs are difficult to measure and the data are not easily available. For example, the immediate reactions to exposure to trauma reminders would require experience sampling data, which may be burdensome for participants to provide. Furthermore, to validate agent-based models, one may need large data sets including many participants with mixed characteristics. To validate processes proposed in system dynamic models, one may need data with a very high resolution in terms of time. However, it may not be feasible to collect data over very short timescales (e.g. over seconds or minutes), even though some of the processes are assumed to be very rapid. Still, formalizing theories as computational models can help us to understand what kind of data are needed to acquire a better theoretical understanding of the development, maintenance, and reduction of PTSD.

A third challenge may be that most researchers within psychology are not educated in developing theories. Several scholars have provided ideas on how one can develop theories (Borsboom et al., 2021; Crielaard et al., 2024; Haslbeck et al., 2022; Smaldino, 2020, 2023). As the modelling requires knowledge of and experience with applied mathematics, and developing plausible theories requires expertise and experience within trauma research, it is unrealistic to expect that people from either profession could develop the models on their own. Therefore, trauma researchers and computer scientists need to collaborate, and (1) collect input to be used in formalizing the models (e.g. existing theories and empirical studies, expert knowledge on PTSD from people with lived experience of having PTSD, their clinicians, and trauma researchers), (2) formalize the models as computational models and simulate the outcomes of these models, (3) assess whether these simulated outcomes seem valid, through both qualitative and quantitative assessment, and (4) iteratively improve the model.

6. Conclusion

Computational modelling may enable us to integrate perspectives from overlapping fields of psychology, as well as from people with lived experience of trauma, clinicians, and basic researchers. As a result, computational modelling may help to advance the understanding and treatment of PTSD.