Memory models

​​Here is the discussion for memory models, how they have been applied to study PTSD and Alzheimer's Disease, and how they could be used to study other disorders. 150 words.

When Fear Shrinks the Brain: A Computational Model of

the Effects of Posttraumatic Stress on Hippocampal

Volume

Briana M. Smith,a,b Madison Thomasson,b Yuxue Cher Yang,b

Catherine Sibert,b Andrea Stoccob

aDepartment of Bioengineering, University of Washington

bDepartment of Psychology, University of Washington

Received 11 January 2020; received in revised form 24 April 2021; accepted 26 April 2021

Abstract

Post-traumatic stress disorder (PTSD) is a psychiatric disorder often characterized by the unwanted

re-experiencing of a traumatic event through nightmares, flashbacks, and/or intrusive memories. This

paper presents a neurocomputational model using the ACT-R cognitive architecture that simulates

intrusive memory retrieval following a potentially traumatic event (PTE) and predicts hippocampal

volume changes observed in PTSD. Memory intrusions were captured in the ACT-R rational analysis

framework by weighting the posterior probability of re-encoding traumatic events into memory with

an emotional intensity term I to capture the degree to which an event was perceived as dangerous

or traumatic. It is hypothesized that (1) increasing the intensity I of a PTE will increase the odds of

memory intrusions, and (2) increased frequency of intrusions will result in a concurrent decrease in

hippocampal size. A series of simulations were run and it was found that I had a significant effect on

the probability of experiencing traumatic memory intrusions following a PTE. The model also found

that I was a significant predictor of hippocampal volume reduction, where the mean and range of

simulated volume loss match results of existing meta-analyses. The authors believe that this is the first

Co-author Madison Thomasson is now at Department of Psychology, University of Nevada Reno

Correspondence should be sent to Briana M. Smith, Department of Bioengineering, University of Washington,

Campus Box 355061, Seattle, WA, 98915, USA. E-mail: [email protected]

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model to both describe traumatic memory retrieval and provide a mechanistic account of changes in

hippocampal volume, capturing one plausible link between PTSD and hippocampal volume.

Keywords: Post-traumatic Stress Disorder; Hippocampus; Amygdala; Declarative Memory; Long-

Term Memory; ACT-R; Cognitive Architecture

1. Introduction

Post-traumatic stress disorder (PTSD) is a psychiatric disorder that is caused by

experiencing or witnessing a traumatic event, such as rape, domestic violence, assault, a

serious accident, or military combat. At the behavioral level, PTSD is characterized by persistent

avoidance and alterations in mood, as well as cognitive distortions surrounding the

trauma. One of the most characteristic and disruptive behavioral effects of PTSD, however,

is the unwanted re-experiencing of the trauma through nightmares, flashbacks, and/or

intrusive memories. Traumatic experiences evoke an emotional response that is accompanied

by increased activation of subcortical areas such as the amygdala (Liberzon & Sripada,

2008; Shin, Rauch, & Pitman, 2006). Intrusive memories are thought to occur because of the

simultaneous activation of the amygdala and hippocampus during memory encoding (Marks,

Franklin, & Zoellner, 2018). At the subcortical level, PTSD is also characterized by a marked

reduction in the volume of the hippocampus—a medial temporal lobe structure necessary

for memory functioning. It is important to note that this change is primarily structural, and

although often remarkably apparent, decreased hippocampal volume is not accompanied by a

functional impairment in long-term memory (LTM) performance (Karl et al., 2006).

The goal of this paper is to derive predictions about the changes in hippocampal volume

observed in PTSD by using a neurocomputational model to simulate intrusive memories

over time within an integrated cognitive architecture. The central idea of the model is that

intrusive memories operate within the context of a general theory of declarative memory,

specifically episodic memory. Within this framework, the maladaptive memory intrusions

observed in PTSD can be seen as the runaway process of an otherwise adaptive memory

system.

As memory is retrieved more frequently, its priority increases and its rate of decay

decreases. A traumatic memory, however, tends to out-compete more contextually appropriate

memories due to the fact it was encoded in a highly emotional state.With each retrieval

of the traumatic memory, disproportionately more resources are allocated to it, leading to the

further preservation and growth of these unwanted memory intrusions. In this framework, it is

proposed that the corresponding changes in hippocampal volume associated with PTSD can

be explained as the natural result of a biological process to efficiently allocate resources to

changing memory demands.

The model presented herein is framed within the Adaptive Control of Thought - Rational

(ACT-R) theory of declarative memory (Anderson, 2007). This choice was motivated by

three advantages offered by ACT-R over other cognitive architectures. First, ACT-R is the

most commonly adopted cognitive architecture in psychology and cognitive neurosciences

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 501

(Kotseruba & Tsotsos, 2018). Second, ACT-R has a long and established history of application

to brain sciences, making the process of drawing new inferences at the neural level easier

and less tentative (Anderson, Fincham, Qin, & Stocco, 2008). Finally, ACT-R is based on

a rational analysis framework, which provides an elegant foundation of declarative memory

retrieval processes and can be easily extended to incorporate the proposed theory of memory

retrieval according to their emotional intensity.

2. The model

Before introducing the model from a neural and an algorithmic point of view, it is important

to frame it within Anderson’s "rational analysis" of human episodic memory (Anderson,

1990). Throughout this paper, this analysis will be referred to as a guiding principle to modify

ACT-R and make inferences about its neural substrates.

In rational analysis, maintaining and retrieving memories is considered a costly process. For

instance, storing and retrieving a memory consumes neural resources to properly represent it

(this consideration will play an important role later on) and metabolic costs in re-activating

during retrieval.Whatever its nature, the existence of memory costs and finite neural resources

implies that different memories should be given different amounts of resources on a rational

basis so that the most useful memories are better allocated and faster to retrieve when needed.

One important metric to decide how to allocate resources is the likelihood that a given

memory will be encoded again given the statistics of the environment (Rao & Ballard, 1999;

Sims, 2018). In his landmark analysis, Anderson’s (1990) assumed thatmemories are discrete,

countable elements of a finite set LTM. The availability of a memory m in a given context Q,

made of discrete symbolic elements q1, q2, …, qN, is a function of both the past history of

m and the degree to which each contextual cue q is associated to m. In Anderson’s (1990)

formulation, the availability of a memory m is indicated by its activation function A(m) and,

in a context Q, is proportional to the posterior odds of being used in the presence of Q.

Following the odds form of Bayes rule, the posterior odds can be separated into two different

quantities, the prior odds and the likelihood odds:

A (m) = log [P (m|Q) /P (°˛m|Q)]

= log [P (m) /P (°˛m)] + log [P (Q|m) /P (Q|°˛m)]

Assuming that the distributions of environmental cues q are independent of each other, the

likelihood odds can be further simplified

A (m) = log[P (m) /P(°˛m)] + log

 

q

 

P (q|m) /P (q|°˛m)

 

Finally, assuming that LTM is large, then P(q | ¬m)   P(q):

A (m) = log[P (m) /P(°˛m)] +

 

i<N

log

 

P (qi|m) /P (qi )

 

(1)

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In ACT-R, it is customary to give different names to the two quantities that make up the

right-hand side of Eq. 1, referring to the prior odds log [P(m) / P(¬m)] as the base-level

activation or B(m), and to the likelihood odds  i<N log [P(qi | m) / P(qi)] as the spreading

(or contextual) activation S(m). Both terms have an algorithmic implementation, which is

described below.

A memory’s base-level activation B(m) increases with the frequency of its usage and

decreases over time, reflecting the effects of frequency and recency. Each successive encoding,

re-encoding, or retrieval of a memory m results leaves a new trace of the memory. The

odds of retrieving any trace decay exponentially over time with a decay rate d, which represents

an individual-specific rate of forgetting (Sense, Behrens, Meijer, & van Rijn, 2016; Zhou

et al., 2021). Thus, the odds of retrieving m correspond to the sum of the odds of retrieving

any of its individual decaying traces, and the base-level activation B(m) can be expressed as

the log of this sum:

B(m) = log

 

 

i

ti

−d

 

(2)

where ti represents the time elapsed since the encoding of the ith trace.

Spreading activation S(m) instead can be interpreted as activation propagating through a

semantic network, in which memories are connected by associative links and activation flows

through the links to associated nodes in the network. In this case, the activated nodes represent

the elements q in the context Q, and the links represent the degree of association or similarity

between q and each memory’s features. By means of spreading activation, the proper context

enhances the availability of memories whose base-level activation would otherwise be

too weak. Algorithmically, the amount of spreading activation is proportional to the product

between the strength of the link connecting q to m (indicated as sq➝m) and an attentional

weight. Algorithmically, the amount of spreading activation is proportional to the product

between the strength of the link connecting q to m (indicated as sq➝m) and an attentional

weight. The weight is usually simplified as a single scalar quantity, W, divided over the number

of active elements in the context, N:

S (m) =

 

q∈Q

(W/N)sq→m (3)

Different values of W in Eq. 3 alter the degree to which memory retrieval depends on

spreading (i.e., contextual cues Q) and base-level activation (i.e., statistical priors). Because

W can be seen as a way to focus resources to activate a subset of memories in LTM, W can

be interpreted as a proxy for attentional control in working memory (Daily, Lovett, & Reder,

2001; Kane, Bleckley, Conway, & Engle, 2001).

2.1. ACT-R in the context of memory consolidation

Although ACT-R has been described in many ways, it is useful, given the goal of this

paper, to compare it to a prominent neural theory of memory consolidation, the multiple trace

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 503

Fig. 1. A neuroanatomical interpretation of the model is presented herein. The red lines represent the encoding

process, with a particular context made of cues q1, q2, …, qN being encoded as a new memory m with attributes

a1, a2, …, aN. The blue lines represent the retrieval process, with the retrieval of m giving rise to a re-enactment

of the original memory and the creation of a new trace for m.

theory (MTT: Moscovitch et al., 2005). The MTT assumes that episodic memories originate

from distributed representations that span multiple cortical areas (Fig. 1). During the encoding

phase (red lines in Fig. 1), the different cues of an event (q1, q2, …, qN) are encoded

in different cortical areas and bound together into a single memory m in the hippocampus

(as attributes a1, a2, …, aN) through the multiple descending pathways that converge from

the cortex through the dentate gyrus. MTT posits that the hippocampus is the permanent

store of episodic memories and that each encoding episode leaves a permanent trace. During

retrieval, the hippocampus reaches a stable pattern that represents a memory trace and,

through ascending pathways from the temporal lobe to the cortex, causes the reactivation of

the original neurons (blue lines in Fig. 1). This reactivation, in turn, might be re-encoded as a

second trace.

Base-level activation and spreading activation reflect, therefore, two distinct neural processes.

Specifically, base-level activation reflects processes that are internal to the hippocampal

network, such as decay or interference due to accumulation of memory traces (Alvarez

& Squire, 1994), while spreading activation reflects the mechanism by which cortical inputs

might trigger contextual memory retrieval (Rolls & Treves, 1998).

2.2. Extending ACT-R to include trauma

It has been noted several times, even by Anderson himself (Anderson, 2007, Chapter 3),

that one limitation of this approach is that it assumes all memories as equally important. However,

not all memories are. Memories of emotional events are thought to persist longer and

be more readily available for retrieval than nonemotional memories because of the activation

of the amygdala during memory encoding (Marks et al., 2018). Specifically, memories of

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threatening or fearful events are of greater importance evolutionarily because they are often

critical for survival (Ledoux, 1998). Although some authors have advanced strong arguments

that all emotions could be modeled in this way, this paper will limit itself to the responses of

the amygdala, which are directly connected to PTSD and well understood in neurophysiological

terms (Bryant et al., 2008).

The role of emotion, however, can be accommodated within the rational analysis framework.

In the original formulation (Anderson, 1990), a memory’s availability simply reflected

its probability of being re-encoded. If memories differ in terms of importance, a natural metric

to allocate resources to memories is the product of a memory’s probability and its survival

importance, which would be captured by the emotional effect at the time of encoding.

This product is analogous to the concept of expected utility in decision-making (Schoemaker,

1982), which is defined as the product of an outcome’s probability by its utility. In this case, a

memory represents an outcome, its probability is the memory’s posterior probability of being

re-encoded, and its “utility” is its survival importance. The importance can be captured by an

emotional intensity term, 0 < I(m) < ∞, which represents the degree to which an event was

potentially dangerous or traumatic.

Because rational analysis is framed in odds instead of probabilities, the term I(m) will

be transformed into an equivalent odds-like formulation and scaled by the mean intensity

of all the other M memories; that is, I(¬m) =  i  = m I(i) / M. Thus, just like a memory’s

availability depends on the ratio between a memory’s probability and the probabilities of all

other memories, its importance depends on the ratio between its intensity and the intensity of

all other memories. With these assumptions in place, our activation function now becomes:

A (m) = log[P (m|Q) /P(°˛m|Q) °ø I (m) /I (°˛m)]

= log [P (m|Q) /P (°˛m|Q)] + log [I (m) /I (°˛m)]

= B (m) + S (m) + log I (m) − log I (°˛m)

= B (m) + S (m) + log I (m) − k (4)

The last passage is motivated by the consideration that, over a lifetime, I(¬m) would

approach the mean traumatic value of all memories and thus could be considered a background

constant k.

In summary, the proposed analysis suggests that traumatic events add a constant bias that

makes a memory more likely to be retrieved, even in the absence of contextual cues and in

proportion to the perceived intensity of the traumatic event. In biological terms, this perceived

intensity bias can be interpreted as the contribution of the amygdala to hippocampal activation

(Fig. 1). The amygdala is bidirectionally connected to the hippocampus and is known to play

a key role in processing event salience (Anderson & Phelps, 2001), fear (LeDoux, 1998),

and in boosting memory for stressful events (references). Importantly, and consistently with

our interpretation, the amygdala is hyperresponsive in individuals suffering from PTSD (Shin

et al., 2006).

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 505

2.3. Deriving ACT-R predictions for hippocampal volume

The final step to test this theory consists of deriving predictions about the hippocampal volume

from the augmented ACT-R framework. To calculate hippocampal volume, the following

analysis was adhered to. In general, it is known that the volume of the hippocampus changes

with experience. For instance, in a landmark study (Maguire, Woolett, & Spiers, 2006), cab

drivers of London were shown to have larger hippocampal volume than the general population.

Additionally, another study showed the volume of the hippocampus co-varies with the

years of education (Noble et al., 2012). An accepted explanation for this effect is that the

volume of the hippocampus reflects the biological investment in storing memories that need

to be re-used often (Wollet & Maguire, 2011).

An efficient memory storing system would encode cells so memories that need to be

accessed more frequently use less resources (in neural terms, less cells or synapses) than

memories that need to be accessed less often (Huffman, 1952). In the rational analysis framework

described above, memories that are accessed more often have the highest priors and, in

ACT-R terms, the higher base-level activations. Knowing the priors of memory utilization,

the volume of the hippocampus could then be approximated by a measure of the homogeneity

of the distribution of the priors. Here, the LTM’s information entropy, H, was utilized; that is,

the quantity (Shannon, 1948):

H = −

 

m

P (m) log [P (m)] (5)

This quantity captures how much information is represented in declarative memory, once

the different probabilities of each memory are taken into account. Consider, for example,

the case of two London cab drivers who have memorized the same number of addresses but

use them with different probabilities. For one driver, all addresses are equally likely to be

retrieved, reflecting the fact that his clients are equally likely to request a ride to all of these

locations. For the second driver, on the other hand, one single address is requested all the time,

while all the others are seldom, if ever, requested by clients. Information entropy is high for

the first driver because it is impossible to predict which address will be requested by the next

client. For the second driver, on the other hand, entropy is low, since one memory is highly

predictable and all the others can be ignored. Biologically, the first driver needs to allocate

more resources (hippocampal cells) to maintain all of these memories than the second for

whom a small number of cells could be used to encode the single memory that predicts most

of the clients’ rides in their daily routine.

In the proposed neurobiological interpretation of ACT-R (Fig. 1), the allocation of

neural resources to store memory is divided between the hippocampus and the corticalhippocampal

projections. The allocation of neural resources in the hippocampus reflects

a memory’s base-level activation B(m) and its intensity I(m). Note the base-level activation

B(m) reflects the memory’s prior log odds rather than true probabilities. To translate

them into probabilities, base-level activations were exponentiated and normalized across all

506 B. M. Smith et al. / Topics in Cognitive Science 13 (2021)

memories into LTM:

P (m) = eB(m)+I (m)

 

i∈LTM eB(i)+I (i) (6)

2.4. Hypotheses and predictions

Given the theory outlined above, it is hypothesized that (1) Increasing the emotional intensity

I of a potentially traumatic event (PTE) will increase the odds of the event memory

being retrieved out of context, predicting intrusive memory occurrence observed clinically

in patients with PTSD; and (2) increased intrusion occurrence will result in a concurrent

decrease in hippocampal size, driven by the altered landscape of memory recall priors, and

thereby capturing the relationship between trauma and hippocampal volume.

3. Methods

To test the hypothesis driving this experiment, a series of computational simulations were

executed. The following sections describe the details of the simulations.

3.1. Memory representations

The simulations described herein differ significantly from most ACT-R models because

they focus on modeling episodic memories over extended durations (∼6 months) rather than

on specific tasks for very short times. Thus, they adopt a uniform memory representation

for all memories instead of different, task-dependent structures. Specifically, all memories

are vectors of N = 8 cues. Each cue is given a randomly selected value, called an attribute.

The attributes for all “normal” events are always selected from the same pool of possible

values, which captures the common cues found in one’s daily environment. Attributes of

PTEs are selected from a different pool of attributes, representing the unique extraordinary

cues associated with traumatic circumstances.

3.2. Model behavior

The model performs routine behaviors following a perceive–retrieve–respond loop. The

loop initiates when a new event occurs in the external world. The features of the event are

then perceived by the model; perception results in the features becoming the sensory cues

that, together, form the current context Q (Fig. 1). The model responds to the current context

by retrieving the memory with the highest total amount of activation, A(m). The retrieval

process is influenced by three factors: (1) the base-level activation of the model’s memories of

previous events, B(m); (2) the spreading activation from the current context S(m), modulated

by the model’s working memory parameter W; and (3) the emotional intensity I(m) of the

memory m. This loop captures a simple decision-by-sampling strategy (Stewart, Chater, &

Brown, 2006): Facing a new situation, the model responds by retrieving the most contextually

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 507

appropriate memory of a similar situation faced in the past, balancing recency, frequency, and

contextual cues through spreading activation. The retrieval creates a new trace of the retrieved

memory, increasing its base-level activation. Finally, a new memory is formed that encodes

the current event using the contextual cues q1, q2 …, qN as its attributes (Fig. 1).

3.3. Daily event distribution and simulation time window

To model the accumulation of memories in a plausible manner, new events are presented to

the model at a frequency that follows a gamma distribution and a realistic daily schedule. On

average, themodel is presented with approximately∼20 events per day. Events occur between

8:00 a.m. and midnight, with a peak probability at around noon. This event distribution was

chosen to reflect the normal waking hours of a person, with a greater concentration of events

during working hours (8:00 a.m.– 4:00 p.m.). Each event’s emotional intensity I was randomly

selected from a uniform distribution between 0 and 2 so that their mean was equal to 1 (and

thus the bias term k in Eq. 4 was equal to 0).

Each simulated run of the model lasted 160 consecutive days, starting 100 days before the

occurrence of a traumatic event and extended 60 days after that. On the midnight of day 0,

a PTE was generated and presented to the model. The intensity of the PTE was explicitly

manipulated throughout the simulations, given the values of IPTE = 1 (control condition), 20,

40, 60. The model’s time window extended to another 60 days after the PTE.

3.4. Dependent variables

Two dependent variables are the focus of this study. The first is the probability of experiencing

an intrusive memory during the day. This is defined as the probability that the model

retrieves a memory of the PTE in response to a situation throughout the day. Note that because

the PTE’s attributes are different from those of the daily events, its retrieval is always contextually

inappropriate, and thus its recall qualifies as intrusive.

The other variable is the hippocampal volume reduction, which is measured as a percent

change from a control condition. To get a suitable baseline, the average value of H (as a proxy

for hippocampal volume) over the last 10 days of the simulation (corresponding to days 50–

60 after the PTE) was compared to the average value of H for the same period of a model run

with an identical combination of parameters except I = 1.

3.5. Simulations

In addition to the intensity I of the traumatic event, a number of other parameters were

manipulated parametrically. These parameters were derived from a recent review of the PTSD

literature (Marks et al., 2018) and reflect idiographic factors that moderate the behavioral

outcomes of traumatic stress. They include the vividness of memory re-experience γ; the

vividness of sensory encoding, modeled as the size of attributes pool A; individual differences

in working memory capacity W (see Eq. 3); the tendency to ruminate over the traumatic event

R; and the potential overlap C between cues of the traumatic event and attributes of daily

508 B. M. Smith et al. / Topics in Cognitive Science 13 (2021)

Table 1

Model parameters manipulated in the simulations

Parameter Meaning Values

I Intensity of potentially traumatic event (PTE) 1, 20, 40, 60

A Size of attributes pool 6, 8

γ Vividness of memory re-experience 0.80, 0.90, 0.95

W Working memory 4, 8, 12

C Similarity between PTE and daily events 0, 0.25, 0.5, 0.75

R Number of rumination events in a day 0, 20

situations. Although these parameters will not be discussed in this paper, they are summarized

in Table 1 and were left in the analysis as they contribute to representative variability in the

simulated results. To obtain stable estimates, the model was run 50 times for each of the 576

combinations of parameter values. In total, the simulations spanned 4,608,000 simulated days

and 103,330,000 simulated events.

4. Results

Given the large number of simulations that were run, it is impossible to fully report the

complete set of results. For the purpose of this paper, there are two aspects to concentrate on.

First, as expected, the model does indeed show worse clinical outcomes in response to more

traumatic events. Fig. 2 shows the daily incidence of traumatic memories. A 3 °ø 60 ANOVA,

using emotional intensity I and the days after PTE as factors, revealed that I had a significant

effect on the relative frequency of experiencing traumatic memories in the days following a

traumatic event [F(2, 1295345) = 37,115.6, p < .0001], with higher values of I corresponding

to the higher relative frequency of memory intrusions. Furthermore, I interacted significantly

with the day [F(118, 1295345) = 10.3, p < .0001], resulting in different recovery trajectories

(Fig. 2).

Having established that the model succeeds in capturing these signatures of PTSD, the

results were further examined to estimate the effects of traumatic stress on hippocampal volume.

It was observed, across all parameters, that there was a general reduction of simulated

hippocampal volume, ranging from 0% to 33.89% with a mean decrease of 7.35% [t(21599)

= 140.83, p < .0001]. Both the mean decrease and the range of variation match the results of

existing meta-analyses. For example, in Smith’s (2005) review of structural Magnetic Resonance

Imaging studies, the decrease in hippocampal volume ranged between 0% and 44%

with a mean of 6.9%. A second question was whether the severity of the reduction was

predicted by the severity of trauma. To this end, the model simulation results suggest that

the emotional intensity I was a significant predictor of hippocampal volume reduction [F(2,

21594) = 774.7, p < .0001], with the decrease in hippocampal volume growing with greater

values of I (all pairwise comparisons significant at p < .0001, Bonferroni corrected). This is

shown in Fig. 3, which shows the distributions of predicted decreases of hippocampal volumes

in the simulations, visualized (as violin plots) separately for different values of intensity I.

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 509

Fig. 2. The predicted increase in memory intrusion following a potentially traumatic event (PTE) on day 0 (black

dashed line) as a function of emotional intensity I. Error bars represent standard errors of the mean; the shaded red

area marks the time interval in which the hippocampal volume was calculated.

4.1. Correlation between hippocampal model reduction and symptom severity

The final analysis investigated was whether or not the degree of hippocampal volume was

correlated to the degree of symptom severity. This is important because, although symptom

severity is clearly driven by the severity of the traumatic event, it also depends on other factors

that were explicitly manipulated in the simulations (see Section 3 and Table 1). To do so, the

mean daily relative frequency of memory intrusions in the last 10 days of the simulations (red

shaded area in Fig. 2) and the corresponding percentage decrease in hippocampal volume

were calculated for each run of the model. Three separate linear regressions, one for each

level of I = 20, 40, and 60, were then computed. In all cases, a significant linear regression

was found [I = 20: β = -20.55, t(7198) = –157.9, p < .0001; I = 40: β = –25.18, t(7198) =

–225.6, p < .0001; I = 60: β = -27.35, t(7198) = 205.1, p < .0001] as shown in Fig. 4.

4.2. Hippocampal volume as a precursor to PTSD severity

Because studies relating PTSD and hippocampal volume are correlational in nature, it is not

possible to exclude the possibility that a smaller hippocampal volume might represent a risk

510 B. M. Smith et al. / Topics in Cognitive Science 13 (2021)

Fig. 3. Effect of trauma intensity I on hippocampal volume. The violin plots represent the distribution densities

of model runs resulting in the corresponding decreases of hippocampal volumes. Solid circles and lines represent

mean °æ standard deviation. In the control condition, the hippocampal decrease is zero.

factor for PTSD. This is, in fact, one of the most debated topics in the field, and some evidence

in this sense can be found in the literature. In one of the most remarkable studies, Gilbertson

et al. (2002) examined pairs of twins in which one of the siblings suffered PTSD after being

exposed to combat and found that the volume of the hippocampus in the nonexposed twin

predicted the severity of the PTSD symptoms in the exposed one.

Although our model predicts that a decrease in hippocampal volume is a consequence of

PTSD symptoms, it does allow for a potential way in which an initially smaller hippocampus

could lead to worse clinical outcomes, thus explaining these results. In essence, our model

predicts that the same set of conditions that would allow a traumatic event to dominate over

all other memories could also lead to other uneven distribution of memory activations before

any traumatic event. In other words, a smaller hippocampal volume could not be a risk factor

per se but evidence of the presence of other conditions (in this case, specific values of model

parameters) that represent significant risk factors.

To examine this hypothesis, we conducted a new analysis of our simulations. In this analysis,

as in the previous analysis, the hippocampal volume was measured as a percentage of

the volume difference from a baseline condition in which no traumatic event occurs (I =

1). Unlike the previous analysis, however, the hippocampal volume was estimated from the

average entropy in the 10 days preceding the traumatic event (days 11 to 1 in Fig. 2). The

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 511

Fig. 4. Correlation between the relative frequency of traumatic memory intrusions to hippocampal volume for

varying levels of trauma intensity. Each point represents a single run of the model; solid lines represent the mean

regression line. For the sake of clarity, all of the points corresponding to the control condition (I = 1) are omitted

since they are overlapping in the original of coordinates (0, 0).

percentage in volume difference from the baseline was then correlated with the mean severity

of symptoms experienced by the model after the traumatic event, which was measured, like

in the previous analysis, on days 50–60.

To avoid any spurious effect in our analysis, two precautions were taken. First, the simulations

in which the model was spontaneously ruminating over previous memories (R = 20,

Table 1) before any traumatic event were excluded since this condition would artificially warp

the distribution of memory entropy and thus the predicted hippocampal volume. As a second

precaution, the results of this simulation were analyzed separately for the different values of

the working memory parameter W (i.e., W = 4, 8, 12; Table 1). This was done to prevent

Simpson’s amalgamation paradox (Wagner, 1982) in examining our data since higher values

of working memory are likely to increase entropy (and thus predicted hippocampal volume)

before a PTE, but to decrease entropy and PTSD symptoms after it.

The results of our analysis are presented in Fig. 5. For each of the three working memory

conditions, a significant negative linear effect was found (W = 4: β = −0.11, t(3598) =

−23.0, p < .0001; W = 8: β = −0.03, t(3598) = −16.9, p < .0001; W = 12: β = −0.02,

t(3598)=−11.7, p < .0001). Thus, our results confirm that, as hypothesized, conditions that

make the model vulnerable to significant PTSD symptoms following a traumatic event do

512 B. M. Smith et al. / Topics in Cognitive Science 13 (2021)

Fig. 5. Hippocampal volume as a potential risk factor for posttraumatic stress disorder (PTSD). Changes in hippocampal

volumes (measured as percentage differences from baseline) were negatively associated with the severity

of PTSD symptoms following the PTE. As shown in Fig. 4, points corresponding to the initial baseline condition

I = 1 are concentrated on the axes origin (0, 0) and omitted for clarity.

have a significant tendency to manifest themselves in the form of predicted smaller hippocampal

volume. Furthermore, the values of the linear regression coefficients were significantly

different across working memory conditions (p < .0001), suggesting that, as hypothesized,

working memory plays a significant role in modulating the effect.

5. Discussion

This paper has presented a computational model that draws a link between the prevalence

of intrusive memories and the changes in hippocampal volume observed in patients with

PTSD. To the best of our knowledge, this is the first model to do so and provide a connection

between rational analysis theories of memories and the underlying neurobiology. The results

of our model simulations are also consistent with estimates from the clinical and medical literature.

As such, the model may shed light on a number of cognitive factors, such as traumatic

memory activation, that contribute to neurophysiological changes associated with PTSD.

In the presentation of this computational model, there are a few obvious limitations.

Although an effort was made to account for numerous idiographic factors (see Table 1), it was

impossible to account for all various factors that have been deemed clinically important such

B. M. Smith et al. / Topics in Cognitive Science 13 (2021) 513

as age, gender, duration of trauma, recurrence of trauma, comorbidity of other psychiatric disorders,

presence and occurrence of other PTSD symptoms, and genetic predisposition. With

that in mind, it is feasible that this model can be altered to account for some of these varying

factors as well as other individual differences not mentioned before. Something imperative

to take into consideration for future improvements of this model would be, for example, the

specific role of the stress hormone cortisol on hippocampal functioning.

These limitations notwithstanding, the model’s success in capturing some behavioral and

biological factors is encouraging. Theoretically, this model, along with the other research

concerning PTSD and its perceived effects on the hippocampus and amygdala, could be used

in the future to enhance clinical practice. Targeted, individualized treatments could be developed

in which an individual’s biological and behavioral measures are used to parametrize a

computational model which is, in turn, used to predict long-term recovery trajectories under

different medical options.

Open Research Badges

This article has earned Open Data and Open Materials badges. Data and materials are

available at https://osf.io/qpfr4/.

Acknowledgments

This work was supported by a scholarship from the University of Washington Institute for

Neuroengineering (UWIN) to BMS and partially supported by an award from the Defence

Advanced Research Project Agency (DARPA, Grant No. FA8650-18-C-7826) to AS. All of

the model code, simulation data, and analysis scripts can be found in the Cognition & Cortical

Dynamics Laboratory’s Github repository at http://github.com/UWCCDL/PTSD and on the

Open Science Framework’s platform at https://osf.io/qpfr4/

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