Trauma as a narrowing world: A dynamical systems approach

How trauma can be understood as a systemic disorder rather than a collection of symptoms

Perspectives on Trauma

When thinking about definitions of trauma, one would probably start by describing an event coupled with a set of symptoms: experienced violence might lead to later avoidance, anxiety or heightened aggression; loss could be associated with depression or helplessness.

This is a very human move: trying to map an abstract concept to a lived or perceived experience. And more so, this is an effective way in clinical settings to understand a client’s suffering and define treatment conditions. What is the client struggling with primarily, and how does it affect their current life? What happened in their past, and how do they try to process it? To what extent is this processing strategy supporting their current state? There is a reason psychologists adhere to standardized symptom checklists when they start to explore a client’s condition[¹]: it helps build an intuition and communicate it accessibly.

Symptoms alone don’t tell the whole story, though. Trying to understand the structure they emerge from gives rise to a whole new layer of inquiry and focus. Network-informed approaches, for example, deliberately shift their attention away from isolated symptoms and try to describe the underlying structural configurations of the brain that give rise to the observed patterns[²]. This approach emphasizes the notion that trauma is not a transient state of anxiety or depression, but a change in the dynamics of the brain that increases the probability of their appearance.

However, I assume that the formation and persistence of traumatic patterns are explained not only by the structure of a network, but also by the movement of information within that network. In the following lines I aim to leverage some of the elegance and intuition-building power of dynamical systems[³] to explore this structural approach to trauma formation.

A disclaimer: I am not offering a mathematical model in the strict sense. I am using mathematical notation to enrich an intuition, by which I hope to render the ideas sharp enough to facilitate inquiry.

An attempt at formalization

I’ll start by defining some basic variables and relations. Let’s assume a clear distinction between internal, organismic states and perceptual contexts. Based on this assumption we can define two domains, S and C, representing the set of all possible organismic states and contexts:

and

respectively. We can then define a transition function φ:

where Δ(S) denotes the probability distribution over all possible future organism-level states. We denote a realization of an element of domains C and S at a point in time t as c_t and s_t. Based on these annotations we can form an expression that hopefully makes the picture a little clearer:

P_φ then gives the probability of one future realization of the domain S given the currently realized states of the organism and the context.

Because the emergent symptoms associated with a traumatic event can vary greatly across individuals — and even within a single lifespan — I want to avoid classifying and defining certain states within S as traumatic, and instead try to understand them by means of their gravity. Let me explain. Certain states of the organism naturally tend to be more pleasant, desirable, or at least safe in the perception of the individual. In the language of dynamical systems, these high-gravity states sit at the bottom of basins of attraction. These states — though highly individual — include things like relaxation, happiness, or more complex ones such as a feeling of self-efficacy in a certain domain. I want to understand the organismic states less as an amalgam of neural patterns and more as the emergent experiences accessible to the individual.

Among those states, I believe there are also some that, from the point of view of an external observer, might seem dysfunctional, but to the individual still seem desirable because they fulfill a specific function: over-performance at work; drug and alcohol abuse; excessive stimulation. What I want to hint at is that even states that seem obviously dysfunctional and harmful in the long run — and sometimes even in the short run — can be basins of experience that individuals gravitate toward.

In the context of the formalization, we can define such basins as a real subset of the individual’s state space S like so:

where each B is a basin of experience within S. Note that, at this point, a basin does not necessarily have to be associated with a dysfunctional or trauma-related response. We can then define, based on expression (2), a vector q_φ giving the probability of the next system state entering one of the basins in B:

Trauma and the Basins

While it is reasonable to assume that traumatic events create their associated basins of (dysfunctional) behavior, I think the significance of another factor in trauma formation can be easily overlooked: it is not the presence of the basins itself that explains the reactions of the individual, but the way the organism relates to them. In ‘healthy’ individuals one can see a broad spectrum of experiential basins — one could call them resources — which ideally exist in some kind of temporal balance. Drastic experiences can result in a hyper-focus on certain basins, essentially altering the probability distribution of q_φ by escalating the probabilities of entering certain basins at the expense of others. We can formalize this by proposing a successive alteration of the transition function φ toward a ‘trauma-induced’ function φ_T, which modifies the distributional properties of q_φ.

This alteration can be understood as a loss of flexibility: the capacity to modify learned responses as circumstances change. This loss is well documented clinically. A deficit of cognitive flexibility is thought to sit upstream of many trauma symptoms rather than beside them[⁴], and psychological inflexibility more broadly is understood to limit an individual’s behavioral alternatives and opportunities for positive experience, deepening suffering over time[⁵].

The distributional narrowing of the probability vector q_φ has another interesting implication: as q_φT moves the distribution further away from an equal distribution of probabilities over the basins, it reduces the uncertainty attached to possible outcomes. The denser the probability mass over a small subset of the basins, the more certain the realization of s within one of those basins becomes. Psychologically, this is reminiscent of a well-known pattern: individuals in psychologically precarious states tend to avoid many contexts and concentrate their life on a small number of ‘seemingly safe’ options. This isn’t an auxiliary symptom but a core dynamic in the self-maintenance of disordered systems (e.g. in OCD, anxiety disorders, PTSD)[⁶]. From a more systemic perspective, one could argue that in a state of high vulnerability and risk — which persists after traumatic events — individuals intuitively try to reduce the number of possible mental states as much as possible, as a safety mechanism. They try to keep their environment, and hence their inner state dynamics, controlled. This can be intuitively grasped through the concept of informational entropy:

where H is the informational entropy of the probability vector. A decrease in informational entropy corresponds to the observed pattern of reducing the uncertainty of the system’s state[⁷].

Concluding Questions

I am neither a mathematician nor a physicist, so this text is only an attempt to enrich some intuitions I built using a language I am still unfamiliar with. I therefore encourage the interested reader to give me feedback on the general structure of my argumentation, and to share ideas for further directions. There are three questions in particular I want to raise — questions I feel my level of knowledge is not yet sufficient to reliably explore.

(1) The change in the transition function φ. I think a significant aspect of trauma I couldn’t address here is the self-reinforcing, possibly recursive nature of this change. How does the transition function change in such a way that the direction of the change vector stays consistent? And how could therapeutic interventions be modeled as transformations of q?

(2) Since I modeled the evolution of the system state S in discrete time steps, I have to ask whether a model using continuous time would be more accurate and richer in intuition.

(3) Which probability distribution could we use to model q_φ and q_φ_T? For the latter I’m thinking of a parameterized softmax function, though for now this is only a first intuitive scaffolding.

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[¹]: American Psychiatric Association. (2013). Diagnostic and Statistical Manual of Mental Disorders (DSM-5), PTSD Criterion A. See also the National Center for PTSD summary of DSM-5 PTSD criteria.

[²]: Birkeland, M. S., et al. (2020). “The network approach to posttraumatic stress disorder.” European Journal of Psychotraumatology.

[³]: Breakspear, M. (2017). “Dynamic models of large-scale brain activity.” Nature Neuroscience, 20, 340–352. DOI: 10.1038/nn.4497.

[⁴]: Fenster, R. J., Lebois, L. A. M., Ressler, K. J., & Suh, J. (2018). “Brain circuit dysfunction in post-traumatic stress disorder: from mouse to man.” Nature Reviews Neuroscience, 19(9), 535–551. DOI: 10.1038/s41583–018–0039–7. (See also the rodent fear-extinction literature on cognitive flexibility deficits underlying PTSD symptoms.)

[⁵]: Hayes, S. C., Luoma, J. B., Bond, F. W., Masuda, A., & Lillis, J. (2006). “Acceptance and Commitment Therapy: Model, processes and outcomes.” Behaviour Research and Therapy, 44(1), 1–25. DOI: 10.1016/j.brat.2005.06.006.

[⁶]: Ball, T. M., & Gunaydin, L. A. (2022). “Measuring maladaptive avoidance: from animal models to clinical anxiety.” Neuropsychopharmacology, 47(5), 978–986. DOI: 10.1038/s41386–021–01263–4.

[⁷]: Carleton, R. N., Mulvogue, M. K., Thibodeau, M. A., McCabe, R. E., Antony, M. M., & Asmundson, G. J. G. (2012). “Increasingly certain about uncertainty: Intolerance of uncertainty across anxiety and depression.” Journal of Anxiety Disorders, 26(3), 468–479. DOI: 10.1016/j.janxdis.2012.01.011. On uncertainty-motivated behavior as a bid for control, see also Krohne, H. W. (1993).