The main idead behind the model is that intrusive memories in PTSD are memories who additional emotional boost leads to "hijacking" the (otherwise rational) declarative memory system. When the emotional boost increases the activation of a memory beyond a certain threshold, the memory becomes "intrusive" because its strength overrides declarative decay and cue-based filtering during memory retrieval. This, in turns, leads to a positive feedback loop, leading the memory's activation to self-perpetuation.
We can calculate the probability of retrieval of an average memory (sliding window) since the moment is introduced, against the probability of the traumatic memory.
Odds = P(c)/P(-c) * P(Q|c)/P(Q|-c)
P(c)/P(-c) * P(Q|c)/P(Q)
A rational approach to memory is that we should retrieve chunks according to ther probability of being used. This approach assumes that all information is, potentially, equally important, and the only important issue to allocate the availability of information so that the more likely relevant information can be retrieved more easily.
However, in more general terms, one can calculate the expected utility of information, E[c]. The expected utility conveys both the probability of needing the piece of information, and the additional value of using it. This is akin to the concept of expected utility in economic theory, which is calculated as the product of the probability of the event by its future rewards. In simple terms, we can write:
E[c] = P(c|Q) * V(c)
V(c) represents the value of a chunk, or the opposite of the costs incurring in using the information. For simplicity, we can assume that the value of a chunk c is independent of its context Q. We know how to calculate P(c|Q); a detailed analysis was proposed by Anderson 1991. In essence, Anderson calculated that P(c|Q) could be expressed in odds:
P(c)/P(-c) * P(Q|c)/P(Q)
Thus, the expected utility becomes
P(c)/P(-c) * P(Q|c)/P(Q) * V(c)
Anderson, 1991 proposed that these terms could be decomposed into the log sum:
log(P(c)/P(-c)) + log P(Q|c)/P(Q) + log V(c)
The first two terms have been extensively discussed in the context of ACT-R. In particular, the first can be captured by the equation log Sum t (t0 –t)^-d. The second, represents contextual activation, and is the result of an empirical co-occurrence between the contents of c and the contents of Q.
The third term is the topic of this model. Specifically, for events that have an very high emotional costs, such as traumatic events, the additional term can result in catastrophic runoff. This is due to the peculiar interaction between memory and environment: When items are retrieved, they become more likely to be retrieved in the future. This positive feedback loop is typically kept at bay by the contextual factor, which favor elements based on co-occurrence. When the third factor V overtakes both, it generates two contextual effects: First, it leads to dominate the base-level probabilities. Second, it tends to generate even stronger associations with other cues, thus contaminating them and eventually taking over the contextual factor as well. Both of these mechanisms are known, under different names, in the field. Furthermore, this model provides an explanation of why certain treatments work, and why other fail.
The model is a simple perceive-retrieve-respond loop based on
ACT-R. The model perceives a situation (represented as a chunk in
ACT-R's imaginal buffer), retrieves a relevant memory, and uses the
retrieved memory as a response. Thus, response to a new situation is a
simple is a simple cue-based retrieval process.
Specifically, when a new situation is encountered, the model sets a goal to process the new situation. The goal leads to initiating a retrieval process; when a relevant memory is retrieved, the goal is accompolished and marked as such.
At fixed intervals of time, new situations are encountered.
All new situations eventually become episodic memories, and end up in the long term memory store.
Chunks becomes intrusive memories because they “take over” the retrieval process.
How do we assign an emotional value to chunks? We can imagine V values being normally distributed with a small variation---most things are neither good nor bad. Traumatic events are incredibly bad, so they have high emotional value. The sign, in many ways, does not matter.
The environment simulates the life of an agent. This is a simple function in pseudocode:
def life ()
while actr.mp_time() < end:
if time = PTET:
present_new_situation(traumatic = True)
else:
present_new_situation(traumatic = False)The model responds to any new situatiobn by retrieving the past situation that best matches the current one.
In this implementation, the emotional valence V of each chunk is stored in a separate table, the V table. Every time a chunk c is created, the pair <c, V(c)> is stored in the table. Its value V(c) is calculated as follows. For "normal" chunks, V = 1.0 +/- noise. For a potentially traumatic event (PTE), it is set to a predefined value PTEV >> 1.0.
An alternative implementation (not pursued here, but worth considering) is that the emotional valence of each chunk is calculated as a function of its cues. Each cue has a value of V(q) ~ N(0).
One cue, Q*, is defined as having an incredibly high value emotional valence V, which is fixed. In this implementation, the V table contains only values for cues, not for chunks. This makes the management of V tables easier. We can calculate exactly the emotional value of each chunk as the sum of the emotional valences of its cues, V(chunk) = Sum[q] V(q).
In ACT-R, associations are stored in Sij values, and are supposed to be learned through experience. In the current implementation, association is purely defined by similarity: The more similar two chunks are, the more they are associated. To keep the implementation consistent with the ACT-R principle of Sji representing the shared contents of two chunks, the similarity between two chunks is calculated as the proportion of slots in which the two chunks share the same value.
In the future, it would be helpful to learn associations. To do so, we could just keep two tables: One is the table of co-occurrence of memories, that is, the probability that c is needed when q is present in the context. This is simple enough to calculate.
The other is the emotional association Vs. Sij has an additive term, which is the emotional nature of the chunk being retrieved. W(Sij+V).
The recommended way to use the code is to use the new, object-oriented
version of the simulations. In this new version, every simulation is
encapsulated as a Simulation object. This make it possible to handle
several simulation parameters without affecting the internal variables
of the ptsd module.
To start a simulation, one must first load the ptsd
module:
import ptsdThis will automatically load the actr.py module and establish a
connection, if it hasn't been done before.
The next step is to then create an instance of a Simulation object:
mysim = ptsd.Simulation()At this point, the simulation parameters can be controlled by setting appropriate variables of the simulation object. For example, to create a simulation over V values of 2.0 and 5.0, with N = 100 runs per value, and a maximum duration of 100,000 seconds, one would type this:
mysim.Vs = [2.0, 5.0]
mysim.n = 100
mysim.max_time = 100000The entire simulation can be executed through the run method:
mysim.run()Once the simulation is done, the data is saved in the TRACE variable
of the mysim object. The trace can be saved to a file:
mysim.save_trace("mysim.txt")The following parameters can be set for each simulation:
-
PTEV The "emotional" value of a traumatic memory. It can be set to either a number or to a list of numbers; in the latter case, the simulations will loop over the given values.
-
PTES The degree of similarity between the traumatic event and all the other events in memory. It can be set to either a number 0 <= n <=1, or to a list of numbers 0<= n <= 1; in the latter case, the simulations will loop over the given values. Similarity is controlled by selecting the slot values for the PTE from a different set. If similarity is 1.0, then all the slots of the PTE will come from the same set of slot values as the other events. If PTES = 0.0, on the other hand, the slots will come from a different set.
-
num_slots The number of slots in each chunk. These slots will be named
slot1,slot2...slotN. -
n: The number of runs for each combination of parameters. Must be a non-negative integer.
-
PTET: The (ACT-R) time (in seconds, starting 0.0) at which the PTE is scheduled to occur.
-
event_step: The distance between two consecutive situations being presented to the model.
-
model: The ACT-R model to be loaded and used for the simulation.
-
model_params: A dictionary of model parameters to be set in the model. These are supposed to be meaningful ACT-R parameters; no check is performed on their consistency.
The simulations.py file provide an example of script that can be
used to run simulations. In essence, simulations can be easily managed
by looping through the desired parameters:
for ia in [0, 2, 4, 6, 8, 10]:
for blc in [0.3, 0.4, 0.5, 0.6, 0.7]:
s = ptsd.Simulations()
s.PTEV = [1, 5, 10, 15, 20]
s.PTES = [0, 0.25, 0.5, 0.75, 1]
s.model_params = {":imaginal-activation" : ia,
":blc" : blc}
s.n = 100
s.max_time = 100000
s.run()
s.save_trace("trace_ia=%d_blc=%.2f.txt" % (ia, blc))Note that the code assumes that ACT-R is running in the background; a fully-functional script would start an ACT-R process in the background and run the simulatins afterwards.