# Know Yourself: An Adaptive Causal Network Model for Therapeutic Intervention for Regaining Cognitive Control

Nimat Ullah, Jan Treur

► To cite this version:

Nimat Ullah, Jan Treur. Know Yourself: An Adaptive Causal Network Model for Therapeutic Intervention for Regaining Cognitive Control. 16th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2020, Neos Marmaras, Greece. pp.334-346, 10.1007/978-3-030-49186-4_28. hal-04060652

HAL Id: hal-04060652

https://inria.hal.science/hal-04060652

Submitted on 6 Apr 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
Know Yourself:

An Adaptive Causal Network Model for Therapeutic
Intervention for Regaining Cognitive Control

Nimat Ullah [0000-0002-0592-8380] and Jan Treur [0000-0003-2466-9158]

Social AI Group, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
nimatullah09@gmail.com, j.treur@vu.nl

**Abstract.** Long term stress often causes depression and neuronal atrophies that in turn can lead to a variety of health problems. As a result of these cellular changes, also molecular changes occur. These changes, that include increase of glucocorticoids and decrease of the brain-derived neurotrophic factor, have the unfortunate effect that they decrease the cognitive abilities needed for the individual to solve the stressful situation. Such cognitive abilities like reappraisal and their adaptation mechanisms turn out to be substantially impaired while they are needed for regulation of the negative emotions. However, antidepressant treatments and some other therapies have proved to be quite effective for the strengthening of such cognitive abilities. This study introduces an adaptive causal network model for this phenomenon where a subject loses his or her cognitive abilities (negative metaplasticity) due to long-term stress and re-improve these cognitive abilities (positive metaplasticity) through mindfulness-based cognitive therapy (MBCT). Simulation results have been reported for demonstration of the phenomenon.

**Keywords:** adaptive causal modeling, negative metaplasticity, positive metaplasticity, mindfulness, cognition, therapy, reappraisal.

# 1 Introduction

Potentially, there can be various reasons and forms of cognitive alteration such as decline in cognitive abilities with age where the rate of decline varies from person to person (Verhaeghen 2011). The decline can be due to long-term stress (Garcia 2002) or due to reduction of flexibility as the person grows older (Charles 2010). This paper, specifically focuses on the consequences caused by long-term stress. Stress has become one of the most common negative emotion these days. Various studies have found that long-term stress can have very severe consequences (Garcia 2002; Mazure et al. 2002; Tennant 2001). These studies highlight the cognitive decline as one of the main consequences of long-term stressors. Decrease in the brain-derived neurotrophic factor (BDNF) as a result of increase in the glucocorticoids was found to be the main reason of cell loss and hence the alteration in synaptic plasticity at a cellular level (Fuchs and Gould 2000; Sapolsky 1999).

However, there are a number of studies like (Garland et al. 2009; Garland et al. 2011) who put forward that mindfulness-based cognitive therapy (MBCT) combining different
techniques from therapies and training helps in strengthening cognitive abilities, specif-
ically those impaired by long-term stress. It works by focusing on present moment, gain-
ing awareness of one's self and accepting the reality. This study considers MBCT instead
of standard CBT, being one of the most studied therapies, due to the fact that some stud-
ies like (Troy et al. 2013) have compared MBCT and CBT in terms of their performance
and found that MBCT is more effective.

Moreover, this study considers an adaptive causal network modeling approach (Treur 2020) to model the above mentioned phenomena because stressful emotions and their effects form an adaptive and cyclic process which this approach particularly handles quite effectively as demonstrated, for example, in (Ullah and Treur 2020; Ullah and Treur 2019). This modeling approach can be considered as a branch in the causal modeling area which has a long tradition in AI; e.g., see (Kuipers 1984; Kuipers and Kassirer 1983; Pearl 2009). It distinguishes itself by a dynamic perspective on causal relations, according to which causal relations exert causal effects over time, and in addition these causal relations themselves can change over time as well. The basic type of network model used is called a *multilevel adaptive temporal-causal network model*. By adding dynamics an adaptation to causal modeling, applications become possible that otherwise would be out of reach of causal modeling. This provides a useful approach to translate (supported by a dedicated modeling environment) qualitative processes as known from empirical literature into adaptive causal network models that can be used for simulation.

In the rest of the paper, Sect. 2 gives brief account of the literature on the subject, Sect. 3 presents the adaptive cognitive network model which is explained by simulation results in detail in Sect. 4. Finally, the paper is concluded in Sect. 5.

## 2 Background Literature

Research on stress, being one of the common negative emotions, has come up with vital long lasting negative consequences of it (Mazure et al. 2002; Tennant 2001). Studies like (Garcia 2002) have shown its contribution to depression and the adaptive causal way it affects one's cognitive abilities. It's worth noting here that the structural and functional changes brought about by stress are similar to those of depression. At a cellular level, stress and depression cause cell and neuronal losses. By (Sapolsky 1999) such cellular changes in the hippocampus are linked to the increase in plasma levels of glucocorticoid hormones like cortisol.

At a molecular level, the cellular deficiencies were found to take place at the hippo-
campus. This happens most of the time due to the decrease in the expression of the brain-
derived neurotrophic factor (BDNF) associated with elevation of glucocorticoids (Fuchs
and Gould 2000; Sapolsky 1999). Similarly, (Smith et al. 1995) also support the notion
that high levels of glucocorticoids induced by stress and its administration are considered
to be down-regulating the hippocampal expression. (Mocchetti et al. 1996) considers the
reduction of BDNF, which supports neuronal survival and function in the hippocampus,
as the potential mediating action of glucocorticoid on hippocampus. The effect of the
boost of glucocorticoids is referred to as negative metaplasticity as it downregulates
adaptivity of the hippocampal synaptic connectivity. In contrast, the boost in the expres-
sion of BDNF is referred to as positive metaplasticity as it strengthens adaptivity of the
connectivity in the hippocampus. As a result of these changes, the subject loses his con-
trol of cognitive abilities and is unable to efficiently regulate his emotions in an adaptive
manner. On the other hand, the same mechanisms can reversibly be used via treatment
as well (Garcia 2002), i.e., through the increase in the expression of BDNF. Synapses
are responsible for the processing and transmission of neural information with some ef-
ficacy and their alteration is referred to as ‘synaptic plasticity’, which is a form of (first-
order) adaptation. The mechanisms described above indicate how synaptic plasticity it-
self also can change, which is a form of second-order adaptation usually called metaplas-
ticity. When metaplasticity enhances the adaptive cognitive function, by Garcia (2002)
it is called positive metaplasticity and if this change brings some impairment to the adap-
tive cognitive function, then it’s referred to as negative metaplasticity this indeed has
been observed in case of long-term stress (Foster 1999; Kim and Yoon 1998); similar
cognitive impairment has been observed in various other studies in both humans (Lupien
et al. 1997) and animals (Mizoguchi et al. 2000).

Cognitive reappraisal, as a strategy, is considered to be a very adaptive strategy which
contributes to positive psychological health by reducing negative effects and it is associ-
ated to improved memory and interpersonal functioning in contrast to, for example, sup-
pression (Butler et al. 2003; Gross and John 2003; John and Gross 2004).

To deal with the cognitive decline caused by long-term stressors, we consider Mind-
fulness-based cognitive therapy (MBCT) as found quite effective by various researchers
in this domain (Garland et al. 2009; Garland et al. 2011). The purpose of MBCT is to
improve psychological health by increasing mindfulness. This therapy combines Kabat-
Zinn's (kabat-Zinn 1990) mindfulness-based stress reduction program with the tech-
niques used in Cognitive Behavior Therapy (CBT). Kabat-Zinn's Mindfulness-Based
stress reduction program involves daily meditation and self-awareness exercises. The
MBCT training program aims at promoting acceptance of thoughts/feelings without be-
ing judgmental, focusing on the present moment and awareness of one's self (Coffey et
al. 2010). According to (Allen et al. 2006) practicing of acceptance is meant to develop
the ability to distinguish oneself from the contents of negative thoughts and recognize
that emotions are non-permanent events. This is achieved by bringing a person in a de-
centered metacognitive state which may help in increasing cognitive flexibility through
disengagement from the initial negative thoughts/appraisal, as has been considered es-
sential by (Garland et al. 2009). After disengagement comes the ability to successfully
switch from negative appraisal to positive appraisal and previous research credits this
ability to mindfulness training (Jha et al. 2007). Similarly, MBCT encourages individuals
to focus on the present moment as it is expected to give insight into one's own (wide
range of) stimuli related physical sensations, feelings and thoughts. Otherwise, chances
of failure increase in the reappraisal/re-interpretation of the thoughts without knowing
about it.

3 Multilevel Adaptive Cognitive Modeling

This section of the paper gives overview of the multilevel adaptive causal network mod-
eling approach (Treur 2016; Treur 2020) that has been used for development and simu-
lation of the adaptive causal network model. Table 1 summarizes the main conceptual
and numerical representations for this adaptive causal modeling approach. The Network-
oriented modeling approach provides a library of over 36 combination functions. Apart from the available combination functions, self-defined combination functions can also be added to the library which makes the approach quite flexible and supports a wide application range.

<table><caption>**Table 1.** Conceptual and numerical representations for the adaptive causal modeling approach</caption><thead><tr><th>Concept</th><th>Conceptual Representation</th><th>Explanation</th></tr></thead><tbody><tr><td>States and connections</td><td>X, Y, X→Y</td><td>Describes the nodes (representing states) and links (representing causal connections between states) of the network structure</td></tr><tr><td>Connection weight</td><td>ω<sub>X,Y</sub></td><td>The connection weight ω<sub>X,Y</sub> ∈ [-1, 1] represents the strength of the causal impact of state X on state Y through connection X→Y</td></tr><tr><td>Aggregating multiple impacts on a state</td><td>c<sub>Y</sub>(..)</td><td>For each state Y (a reference to) a combination function c<sub>Y</sub>(..) is chosen to combine the causal impacts of other states on state Y</td></tr><tr><td>Timing of the effect of causal impact</td><td>η<sub>Y</sub></td><td>For each state Y a speed factor η<sub>Y</sub> ≥ 0 is used to represent how fast a state is changing upon causal impact</td></tr><tr><th>concept</th><th>numerical representation</th><th>explanation</th></tr><tr><td>State values over time t</td><td>Y(t)</td><td>At each time point t each state Y in the model has a real number value in [0, 1]</td></tr><tr><td>Single causal impact</td><td>impact<sub>X,Y</sub>(t)<br>= ω<sub>X,Y</sub> X(t)</td><td>At t state X with a connection to state Y has an impact on Y, using connection weight ω<sub>X,Y</sub></td></tr><tr><td>Aggregating multiple causal impacts</td><td>aggimpact<sub>Y</sub>(t)<br>= c<sub>Y</sub>(impact<sub>X<sub>1</sub>,Y</sub>(t),..., impact<sub>X<sub>k</sub>,Y</sub>(t))<br>= c<sub>Y</sub>(ω<sub>X<sub>1</sub>,Y</sub>X<sub>1</sub>(t), ..., ω<sub>X<sub>k</sub>,Y</sub>X<sub>k</sub>(t))</td><td>The aggregated causal impact of multiple states X<sub>1</sub> on Y at t, is determined using combination function c<sub>Y</sub>(..)</td></tr><tr><td>Timing of the causal effect</td><td>Y(t+Δt) = Y(t) + η<sub>Y</sub> [aggimpact<sub>Y</sub>(t) - Y(t)] Δt<br>= Y(t) + η<sub>Y</sub> [c<sub>Y</sub>(ω<sub>X<sub>1</sub>,Y</sub>X<sub>1</sub>(t), ..., ω<sub>X<sub>k</sub>,Y</sub>X<sub>k</sub>(t)) - Y(t)] Δt</td><td>The causal impact on Y is exerted over time gradually, using speed factor η<sub>Y</sub>; here the X<sub>1</sub> are all states with outgoing connections to state Y</td></tr></tbody></table>

Table 2 provides explanation of the various states of the adaptive causal network model proposed in this paper. In the table and the figure, the background colors differentiate between the (adaptation) levels of the model and are part of the meaning; they are called reification levels as they explicitly represent by their states some of the network characteristics of the level below. For instance, the base model has 17 states, the first reification level modeling synaptic plasticity (first-order adaptation) has 1 state and the second reification level modeling metaplasticity (second-order adaptation) has 2 states. The modeled synaptic plasticity at the first reification level is addressed by the (adaptive) connection weight ω<sub>fsb,csreapp</sub> by representing it by reification state W<sub>fsb,csreapp</sub>. The metaplasticity concerning adaptation of the dynamics of the adaptation of this connection weight is addressed by the second-level reification states M<sub>W<sub>fsb,csreapp</sub></sub> for the persistence of the learnt effects and H<sub>W<sub>fsb,csreapp</sub></sub> for the speed of the adaptation process.
<table><caption>**Table 2.** Overview of the states of the multi-level network model in Fig. 1</caption><thead><tr><th>State</th><th>Explanation</th><th>Level</th></tr></thead><tbody><tr><td>X<sub>1</sub></td><td>ws<sub>s</sub></td><td rowspan="17">Base level</td></tr><tr><td>X<sub>2</sub></td><td>ss<sub>s</sub></td></tr><tr><td>X<sub>3</sub></td><td>srs<sub>s</sub></td></tr><tr><td>X<sub>4</sub></td><td>gs<sub>b</sub></td></tr><tr><td>X<sub>5</sub></td><td>ps<sub>g</sub></td></tr><tr><td>X<sub>6</sub></td><td>es<sub>g</sub></td></tr><tr><td>X<sub>7</sub></td><td>ss<sub>b</sub></td></tr><tr><td>X<sub>8</sub></td><td>srs<sub>b</sub></td></tr><tr><td>X<sub>9</sub></td><td>fs<sub>b</sub></td></tr><tr><td>X<sub>10</sub></td><td>ps<sub>b</sub></td></tr><tr><td>X<sub>11</sub></td><td>es<sub>b</sub></td></tr><tr><td>X<sub>12</sub></td><td>bs<sub>-</sub></td></tr><tr><td>X<sub>13</sub></td><td>bs<sub>+</sub></td></tr><tr><td>X<sub>14</sub></td><td>accp<sub>b</sub></td></tr><tr><td>X<sub>15</sub></td><td>aw<sub>b</sub></td></tr><tr><td>X<sub>16</sub></td><td>pr<sub>b</sub></td></tr><tr><td>X<sub>17</sub></td><td>cs<sub>reapp</sub></td></tr><tr><td>X<sub>18</sub></td><td>W<sub>fs<sub>b</sub>cs<sub>reapp</sub></sub></td><td>First Reification Level</td></tr><tr><td>X<sub>19</sub></td><td>M<sub>W<sub>fs<sub>b</sub>cs<sub>reapp</sub></sub></sub></td><td>Reified representation state for persistence factor μ for W<sub>fs<sub>b</sub>cs<sub>reapp</sub></sub></td><td>Second Reification Level</td></tr><tr><td>X<sub>20</sub></td><td>H<sub>W<sub>fs<sub>b</sub>cs<sub>reapp</sub></sub></sub></td><td>Reified representation state for speed factor η for W<sub>fs<sub>b</sub>cs<sub>reapp</sub></sub></td><td>Second Reification Level</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Adaptive causal network model for therapeutic intervention for long-term stress</figcaption></figure>

The connectivity picture of the model shown in Fig. 1 demonstrates the phenomenon where long-term stress causes negative metaplasticity of cognitive abilities, i.e. loss in the ability to use and adapt cognitive reappraisal for regulation of negative emotions. In contrast, mindfulness-based cognitive therapy has been used as an intervention to obtain
positive metaplasticity through which upregulation of the cognitive reappraisal ability can take place. In Fig. 1, the bottom level represents the base model which performs the basic function of regulation of emotions through reappraisal. Cognitive reappraisal changes one’s perception/belief about the stimulus: from a negative to a positive interpretation in this model. Generally, reappraisal can also be from positive believe to negative belief depending upon the demand of the situation, but in this model, reappraisal refers to the reinterpretation to positive belief from negative. The first reification level modeling first-order adaptation, represents Hebbian learning for the connection from base state $f_{s_b}$ to base state $c_{s_{reapp}}$. The dynamics of this state $W_{f_{s_b}c_{s_{reapp}}}$ represents the learning taking place for this connection at the base level. Learning doesn’t only refer to increase in the strength of the connection, it can also involve decrease in the strength of the connection over time. In this model, as demonstrated in Figs. 2 and 3, initially, this connection from $f_{s_b}$, to $c_{s_{reapp}}$ gets weaker due to long-term stress. When this connection gets weaker, the negative (body) feeling state $f_{s_b}$ gets higher which activates the goal state $g_{s_b}$ to address the problem, as also demonstrated in (Mohammadi Ziarabi and Treur 2019) for such kind of interventions. This goal state represents the intention of the person to undergo some kind of therapy for getting back on track. In the scenario used for this model, goal activation refers to the intention to undergo MBCT (therapy) but in general it can be any kind of intervention, for example, antidepressant treatment as suggested in (Garcia 2002) etc.

The second-order reification states $M_{W_{f_{s_b}c_{s_{reapp}}}}$ and $H_{W_{f_{s_b}c_{s_{reapp}}}}$ represent the persistence factor $\mu$ and the speed factor $\eta$ for $W_{f_{s_b}c_{s_{reapp}}}$ respectively. The M-state refers to how long or short the W-state retains its learned value. Similarly, the H-state controls the speed factor of the W-state managing how fast or slow the W-state learns of forgets the value. Change in the speed and persistence factor is referred to as metaplasticity. The upregulation is called positive while the downregulation is called negative metaplasticity.

The two boxes below give insight into the different dynamics of the network. The colors and the boxes itself are part of the meaning and standard defined by network oriented modeling approach in (Treur 2020). In the boxes below, Box 1 represent the role matrices **mb** and **mcw**. In role matrix **mb**, each state has a row which shows all the incoming connections to that state. It's worth mentioning here that in matrix **mb** each state has only the incoming connections which are either at the same level or come from a lower level. The downward connections are indicated in the other role matrices instead. For instance, in matrix **mcw** the state number $X_{18}$ (i.e., the W-state) represents the adaptive connection from $X_9$ to $X_{17}$ at the base level, the causal effect of which is modeled by the downward connection from $X_{18}$. Moreover, the values between -1 and 1 in role matrix **mcw** represent the connection weights of the incoming connections to that specific state. The specific values in the role matrices allow to get the simulation pattern shown in Fig. 2 and Fig. 3. The values were chosen such that the simulation results exhibit a pattern similar to the ones found in the literature.

In Box 2, role matrices **mcfw**, **mcfp** and **ms** are given. Matrix **mcfw** indicates the combination function used at a state $X_i$ for the aggregation of incoming causal impact from other states to state $X_i$. For instance, state $X_1$ uses the identify function, state $X_{18}$ uses the Hebbian combination function and state $X_{19}$ uses **allogistic**(..) as combination function, defined by
$$ \textbf{alogistic}_{\sigma, \tau}(V_1, \dots, V_k) = \left[ \frac{1}{1+e^{-\sigma(V_1+\dots+V_k-\tau)}} + \frac{1}{1+e^{\sigma\tau}} \right] (1+e^{-\sigma\tau}) \quad (1) $$

Moreover, the first-order adaptation state $X_{18}$ uses the Hebbian learning combination function **hebb(.)** defined by

$$ \textbf{hebb}_{\mu}(V_1, V_2, W) = V_1 V_2 (1 - W) + \mu W \quad (2) $$

<figure><img src="image_4.png" /><figcaption>**Box 1** Role matrices for connectivity</figcaption></figure>

Role matrix **mcfp** provides the parameter values for each of the combination function used as indicated in **mcfw**. In the row for $X_{18}$, in column 2 (for Hebb) of **mcfp**, $X_{19}$ in the red cell indicates the downward causal connection from the second-order reification state to $X_{18}$. In other words, $X_{19}$ is responsible for the persistence factor of $X_{18}$. Similarly, the $X_{20}$ in the red cell at the row for $X_{18}$ in role matrix **ms** indicates the downward causal connection from the second-order reification level to the first-order reification level. In other words, $X_{20}$ is responsible for the speed factor of $X_{18}$. These downward causal connections are essential to causally effectuate the adaptation processes modeled as dynamics at the higher levels.

## 4 Simulation Results

This section of the paper explains the simulation results given in Fig. 2 and Fig. 3 obtained from the adaptive causal network model with connectivity depicted in Fig. 1. These results were obtained using the values in **Box 1** and **Box 2**. Moreover, initial values
of the states are given below in Table 2. Fig. 2 demonstrates the basic phenomenon as discussed in the literature section, where long-term stressors decrease the adaptive cognitive abilities of the subject. The subject decides to undergo MBCT and regains his cognitive abilities. Fig. 2 shows the patterns for all the states at the base level. In the figure, it can be seen that initially the control state $cs_{reapp}$ for reappraisal gets activated as soon as negative belief $bs_-$ gets higher. The control state $cs_{reapp}$ changes the beliefs representing the interpretation of the person and, therefore, $bs_-$ decreases while $bs_+$ increases. But during this time, gradual decrease in the activation level of $cs_{reapp}$ can be observed and that's the time when $bs_-$ also stays higher and $bs_+$ stays lower.

<table><caption>**Table 3.** Initial values serving as inputs to the states</caption><thead><tr><th>State</th><th>WS<sub>s</sub></th><th>All other base states</th><th>W<sub>fsb</sub>,cs<sub>reapp</sub></th><th>HW<sub>fsb</sub>,cs<sub>reapp</sub></th><th>MW<sub>fsb</sub>,cs<sub>reapp</sub></th></tr></thead><tbody><tr><td>Initial value</td><td>1</td><td>0</td><td>0.3</td><td>0.5</td><td>0.9</td></tr></tbody></table>

<table><caption>**Box 2** Role matrices for aggregation and timing</caption><thead><tr><th colspan="5">mcfw aggregation:</th><th colspan="5">mcfp aggregation</th><th colspan="5">ms timing:</th></tr><tr><th colspan="5">Combination function weights</th><th colspan="5">Combination function parameters</th><th colspan="5">Combination function parameters</th><th colspan="5">Combination function parameters</th><th colspan="5">Combination function parameters</th></tr><tr><th></th><th></th><th>1</th><th>2</th><th>3</th><th></th><th></th><th>1</th><th>2</th><th>3</th><th></th><th></th><th>1</th><th>2</th><th>3</th><th></th><th></th><th>1</th><th>2</th><th>3</th><th></th><th>1</th><th>2</th><th>3</th></tr><tr><th></th><th></th><th>allogistic</th><th>hebb</th><th>id</th><th></th><th></th><th></th><th>Alogistic σ</th><th>Hebb τ</th><th>id</th><th></th><th></th><th></th><th>μ</th><th></th><th></th><th></th><th></th><th>σ</th><th>τ</th><th>id</th><th></th><th>μ</th><th></th></tr></thead><tbody><tr><td>X<sub>1</sub></td><td>ws<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>1</sub></td><td>ws<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>1</sub></td><td>ws<sub>s</sub></td><td></td><td>0</td><td></td><td></td></tr><tr><td>X<sub>2</sub></td><td>ss<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>2</sub></td><td>ss<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>2</sub></td><td>ss<sub>s</sub></td><td></td><td>1</td><td></td><td></td></tr><tr><td>X<sub>3</sub></td><td>srs<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>3</sub></td><td>srs<sub>s</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>3</sub></td><td>srs<sub>s</sub></td><td></td><td>1</td><td></td><td></td></tr><tr><td>X<sub>4</sub></td><td>gs<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>4</sub></td><td>gs<sub>b</sub></td><td>18</td><td>0.62</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>4</sub></td><td>gs<sub>b</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>5</sub></td><td>ps<sub>g</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>5</sub></td><td>ps<sub>g</sub></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>5</sub></td><td>ps<sub>g</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>6</sub></td><td>es<sub>g</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>6</sub></td><td>es<sub>g</sub></td><td>10</td><td>0.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>6</sub></td><td>es<sub>g</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>7</sub></td><td>ss<sub>b</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>7</sub></td><td>ss<sub>b</sub></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>7</sub></td><td>ss<sub>b</sub></td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>8</sub></td><td>srs<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>8</sub></td><td>srs<sub>b</sub></td><td>10</td><td>0.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>8</sub></td><td>srs<sub>b</sub></td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>9</sub></td><td>fs<sub>b</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>9</sub></td><td>fs<sub>b</sub></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>9</sub></td><td>fs<sub>b</sub></td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>10</sub></td><td>ps<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>10</sub></td><td>ps<sub>b</sub></td><td>10</td><td>0.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>10</sub></td><td>ps<sub>b</sub></td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>11</sub></td><td>es<sub>b</sub></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td>X<sub>11</sub></td><td>es<sub>b</sub></td><td></td><td></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>11</sub></td><td>es<sub>b</sub></td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>12</sub></td><td>bs_</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>12</sub></td><td>bs_</td><td>8</td><td>0.2</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>12</sub></td><td>bs_</td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>13</sub></td><td>bs_</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>13</sub></td><td>bs_</td><td>10</td><td>0.15</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>13</sub></td><td>bs_</td><td>0.2</td><td></td><td></td><td></td></tr><tr><td>X<sub>14</sub></td><td>accp<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>14</sub></td><td>accp<sub>b</sub></td><td>10</td><td>0.55</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>14</sub></td><td>accp<sub>b</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>15</sub></td><td>aw<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>15</sub></td><td>aw<sub>b</sub></td><td>10</td><td>0.55</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>15</sub></td><td>aw<sub>b</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>16</sub></td><td>pr<sub>b</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>16</sub></td><td>pr<sub>b</sub></td><td>10</td><td>0.55</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>16</sub></td><td>pr<sub>b</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>17</sub></td><td>cs<sub>reapp</sub></td><td>1</td><td></td><td></td><td></td><td></td><td></td><td>X<sub>17</sub></td><td>cs<sub>reapp</sub></td><td>10</td><td>0.44</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>17</sub></td><td>cs<sub>reapp</sub></td><td>0.28</td><td></td><td></td><td></td></tr><tr><td>X<sub>18</sub></td><td>W<sub>fsb</sub>,cs<sub>reapp</sub></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>X<sub>18</sub></td><td>W<sub>fsb</sub>,cs<sub>reapp</sub></td><td></td><td></td><td></td><td>X<sub>19</sub></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>18</sub></td><td>W<sub>fsb</sub>,cs<sub>reapp</sub></td><td></td><td>X<sub>20</sub></td><td></td><td></td></tr><tr><td>X<sub>19</sub></td><td>M<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>X<sub>19</sub></td><td>M<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td>10</td><td>0.85</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>19</sub></td><td>M<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td>0.01</td><td></td><td></td><td></td></tr><tr><td>X<sub>20</sub></td><td>H<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td></td><td>1</td><td></td><td></td><td></td><td></td><td>X<sub>20</sub></td><td>H<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td>10</td><td>0.8</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>X<sub>20</sub></td><td>H<sub>W</sub>,fsb,cs<sub>reapp</sub></td><td>0.01</td><td></td><td></td><td></td></tr></tbody></table>

In the meanwhile, gradual increase in the goal state $gs_b$ takes place, since as a result of decrease in the activation level of $cs_{reapp}$ the intensity of negative feelings $fs_b$ increases which in turn activates the goal $gs_b$ to undergo some therapy to regain cognitive control.
Goal state $gs_b$ activates the states that lay on the casual pathway describing undergoing MBCT therapy. Finally, when the execution state for goal (therapy) $es_g$ gets enough momentum, as a result $cs_{reapp}$ again gets activated. This means that the person has re-gained his cognitive reappraisal ability during execution of the therapy; however, at this stage the person still depends on the therapy for this. While the person is again becoming able to reappraise his or her emotions with a little help from the therapy, due to the achieved lower levels of $fs_b$, the negative metaplasticity at the second reification level turns into positive metaplasticity by increasing the too low values of the two second-order states $M_{W_{fs_b} \cdot cs_{reapp}}$ and $H_{W_{fs_b} \cdot cs_{reapp}}$ to higher values. Therefore, now a learning process takes place (that was blocked before by the negative metaplasticity due to low values of $M_{W_{fs_b} \cdot cs_{reapp}}$ and $H_{W_{fs_b} \cdot cs_{reapp}}$), strengthening the connection from $fs_b$ to $cs_{reapp}$. Due to the successful reappraisal, $fs_b$ goes down, so it deactivates the goal $gs_b$ to undergo therapy. This deactivates the therapy but the person is still able to reappraise his emotions effectively as before. It means that overall the connection has re-strengthened as a result of MBCT. This figure represents two phases of the subject's life. First phase is before his cognitive abilities are impaired by long-term stress where he regulates his emotions multiple times during that phase. The second phase is after the therapy when he's again able to use his cognitive abilities. The fluctuation in the graphs represent the cyclic nature of the stressful emotions that takes place repeatedly in cycles and are regulated accordingly.

This pattern is exactly as various researchers from cognitive and neuro-sciences have described in their articles as summarized in the background study in Sect. 2, for instance (Garcia 2002).

<figure><img src="image_5.png" /><figcaption>Fig. 2. Loss and gain of adaptive cognitive abilities as a result of long-term stressor (base level)</figcaption></figure>
Fig. 3 gives insight into the first and second-level reification states. The states repre-
sented in the figure are $\mathbf{W}_{fs_b,cs_{reapp}}$, $\mathbf{M}_{W_{fs_b,cs_{reapp}}}$, $\mathbf{H}_{W_{fs_b,cs_{reapp}}}$ which represent the ad-
aptation of the indicated connection weight based on Hebbian learning, and the persis-
tence factor and the speed factor for this adaptation, respectively. First it is shown that
all these three states decrease because of the long-term stressors, but after activation of
the therapy in the base model all three states again get higher values. It’s worth noting
here that all the states stay high even after the therapy gets deactivated in the base model.
This shows that the person’s wellbeing does not depend on the therapy anymore.

As already mentioned, **W** represent the Hebbian learning taking place at the connec-
tion indicated by fs<sub>b</sub>, cs<sub>reapp</sub> in the base model. The speed factor and persistence of the
**W** is handled by the **H** and **M**-states respectively. In the Fig. 3 initially negative meta-
plasticity occurs (lower values of the second-order states) because of long-term stressors,
so the learning gets blocked in a sense. Due to this, the connection fs<sub>b</sub>, cs<sub>reapp</sub> gets
weaker. But as the person undergoes MBCT, due to the positive effects that has on the
second-order states M<sub>W<sub>fs_b,cs<sub>reapp</sub></sub></sub> and H<sub>W<sub>fs_b,cs<sub>reapp</sub></sub></sub>, the connection fs<sub>b</sub>, cs<sub>reapp</sub> again gets
stronger and the person is again able to reappraise his emotions even after there is no
more therapy. These results in Fig. 2 and Fig. 3 are completely in line with the findings
from cognitive and neurosciences.

<figure><img src="image_6.png" /><figcaption>Fig. 3. First and second-order reification states for plasticity and metaplasticity over time</figcaption></figure>

**5 Conclusion**

In this paper, the ideas on negative and positive metaplasticity from the (empirical) lit-
erature have been modeled and given a concrete shape in the form of simulations. On
one hand, the multi-order adaptive causal network model presented in this paper gives a
concrete shape to the abstract ideas, on the other hand it also highlights the consequences
of long-term stressors along with the possible treatment for the psychological problems
they cause. Findings from various neurological and psychological studies were brought
together and presented in the form of a concrete computational model. Various therapies
have already been modeled in work like (Mohammadi Ziarabi and Treur 2019), but this
paper considers therapy as a permanent treatment to cope with negative metaplasticity
for the first time.

The paper also shows how the applicability scope of causal modeling, which has a
long tradition in AI (e.g., see (Kuipers 1984; Kuipers and Kassirer 1983; Pearl 2009)),
can substantially be widened by adding dynamics and (multi-order) adaptation to causal
modeling. Doing this, causal modeling becomes applicable to modeling of dynamic and
adaptive processes that otherwise would be out of reach for causal modeling.
The introduced second-order adaptive network model provides a good basis to develop
a patient model (based on a virtual agent) for virtual training of therapists. In future, the
author aims at extending the model by incorporating more neurological states for both
the negative and positive metaplasticity and the neurological states involved in MBCT.

References

1. Allen, N.B., Blashki, G., Gullone, E.: Mindfulness-based psychotherapies: a review of conceptual foundations, empirical evidence and practical considerations. Australian and New Zealand Journal of Psychiatry 40(2), 285–294 (2006). doi:10.1111/j.1440-1614.2006.01794.x

2. Butler, E.A., Egloff, B., Wlhelm, F.H., Smith, N.C., Erickson, E.A., Gross, J.J.: The social consequences of expressive suppression. Emotion 3(1), 48–67 (2003). doi:10.1037/1528-3542.3.1.48

3. Charles, S.T.: Strength and vulnerability integration: A model of emotional well-being across adulthood. Psychological Bulletin 136(6), 1068–1091 (2010). doi:10.1037/a0021232

4. Coffey, K.A., Hartman, M., Fredrickson, B.L.: Deconstructing Mindfulness and Constructing Mental Health: Understanding Mindfulness and its Mechanisms of Action. Mindfulness 1(4), 235–253 (2010). doi:10.1007/s12671-010-0033-2

5. Foster, T.C.: Involvement of hippocampal synaptic plasticity in age-related memory decline. Brain research reviews 30(3), 236–49 (1999). doi:10.1016/s0165-0173(99)00017-x

6. Fuchs, E., Gould, E.: In vivo neurogenesis in the adult brain: regulation and functional implications. European Journal of Neuroscience 12(7), 2211–2214 (2000).

7. Garcia, R.: Stress, Metaplasticity, and Antidepressants. Current Molecular Medicine 2(7), 629–638 (2002). doi:10.2174/1566524023362023

8. Garland, E., Gaylord, S., Park, J.: The role of mindfulness in positive reappraisal. Explore 5(1), 37–44 (2009). doi:10.1016/j.explor.2008.10.001

9. Garland, E.L., Gaylord, S.A., Fredrickson, B.L.: Positive Reappraisal Mediates the Stress-Reductive Effects of Mindfulness: An Upward Spiral Process. Mindfulness 2(1), 59–67 (2011). doi:10.1007/s12671-011-0043-8

10. Gross, J.J., John, O.P.: Individual differences in two emotion regulation processes: Implications for affect, relationships, and well-being. Journal of Personality and Social Psychology 85(2), 348–362 (2003). doi:10.1037/0022-3514.85.2.348

11. Jha, A.P., Krompinger, J., Baime, M.J.: Mindfulness training modifies subsystems of attention. Cognitive, Affective, & Behavioral Neuroscience 7(2), 109–119 (2007).

12. John, O.P., Gross, J.J.: Healthy and Unhealthy Emotion Regulation: Personality Processes, Individual Differences, and Life Span Development. Journal of Personality 72(6), 1301–1334 (2004). doi:10.1111/j.1467-6494.2004.00298.x

13. Kabat-Zinn, J.: Full Catastrophe Living: Using the Wisdom of Your Body and Mind to Face Stress, Pain and Illness. 1st edn. Delta, New York (1990).

14. Kim, J.J., Yoon, K.S.: Stress: metaplastic effects in the hippocampus. Trends in neurosciences 21(12), 505–9 (1998). doi:10.1016/s0166-2236(98)01322-8
15. Kuipers, B.: Commonsense reasoning about causality: Deriving behavior from structure. Artif. Intell. 24, 169–203 (1984). doi:10.1016/0004-3702(84)90039-0

16. Kuipers, B., Kassirer, J.P.: How To Discover a Knowledge Representation for Casual REasoning by Studying an Expert Pysician. In: Proc. IJCAI’83 (1983).

17. Lupien, S.J., Gaudreau, S., Tchiteya, B.M., Maheu, F., Sharma, S., Nair, N.P., Hauger, R.L., McEwen, B.S., Meaney, M.J.: Stress-induced declarative memory impairment in healthy elderly subjects: relationship to cortisol reactivity. The Journal of clinical endocrinology and metabolism 82(7), 2070–2075 (1997). doi:10.1210/jcem.82.7.4075

18. Mazure, C.M., Maciejewski, P.K., Jacobs, S.C., Bruce, M.L.: Stressful life events interacting with cognitive/personality styles to predict late-onset major depression. The American journal of geriatric psychiatry 10(3), 297–304 (2002)

19. Mizoguchi, K., Yuzurihara, M., Ishige, A., Sasaki, H., Chui, D.H., Tabira, T.: Chronic stress induces impairment of spatial working memory because of prefrontal dopaminergic dysfunction. The Journal of neuroscience 20(4), 1568–1574 (2000).

20. Mocchetti, I., Spiga, G., Hayes, V., Isackson, P., Colangelo, A.: Glucocorticoids differentially increase nerve growth factor and basic fibroblast growth factor expression in the rat brain. The Journal of Neuroscience 16(6), 2141–2148 (1996). doi:10.1523/JNEUROSCI.16-06-02141.1996

21. Mohammadi Ziabari, S.S., Treur, J.: Cognitive Modeling of Mindfulness Therapy by Autogenic Training. In: Satapathy, S.C., Bhateja, V., Somanah, R., Yang, X.-S., and Senkerik, R. (eds.) Proceedings of 5th International Conference on Information Systems Design and Intelligent Applications INDIA 2018, vol. 2, pp. 53–66. Springer, Singapore (2019). doi: 10.1007/978-981-13-3338-5_6

22. Pearl, J.: Causality. Cambridge University Press. (2009).

23. Sapolsky, R.M.: Glucocorticoids, stress, and their adverse neurological effects: relevance to aging. Experimental gerontology 34(6), 721–732 (1999). doi:10.1016/S0531-5565(99)00047-9

24. Smith, M.A., Makino, S., Kvetnansky, R., Post, R.M.: Stress and glucocorticoids affect the expression of brain-derived neurotrophic factor and neurotrophin-3 mRNAs in the hippocampus. The Journal of neuroscience 15(3), 1768–1777 (1995).

25. Tennant, C.: Work-related stress and depressive disorders. Journal of psychosomatic research 51(5), 697–704 (2001). doi:10.1016/S0022-3999(01)00255-0

26. Treur, J.: Network- Oriented Modeling: Addressing Complexity of Cognitive, Affective and Social Interactions. Springer, Cham (2016). doi: 10.1007/978-3-319-45213-5.

27. Treur, J.: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Springer International Publishing, Cham (2020). doi: 10.1007/978-3-030-31445-3

28. Troy, A.S., Shallcross, A.J., Davis, T.S., Mauss, I.B.: History of Mindfulness-Based Cognitive Therapy Is Associated with Increased Cognitive Reappraisal Ability. Mindfulness 4(3), 213–222 (2013). doi:10.1007/s12671-012-0114-5

29. Ullah, N., Treur, J.: The Choice Between Bad and Worse: A Cognitive Agent Model for Desire Regulation Under Stress. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., and Zalila Wenkstern, R. (eds.) Principles and Practice of Multi-Agent Systems PRIMA 2019, Lecture Notes in Computer Science, vol. 11873, pp. 496–504. Springer International Publishing, Cham (2019). doi: 10.1007/978-3-030-33792-6_34

30. Ullah, N., Treur, J.: Better Late than Never: A Multilayer Network Model Using Metaplasticity for Emotion Regulation Strategies. In: Cherifi, H., Gaito, S., Mendes, J.F., Moro, E., and Rocha, L.M. (eds.) Complex Networks and Their Applications VIII COMPLEX NETWORKS 2019, Studies in Computational Intelligence, vol. 882, pp. 697–708. Springer International Publishing, Cham (2020). doi:10.1007/978-3-030-36683-4_56

31. Verhaeghen, P.: Cognitive processes and ageing. In: Stuart-Hamilton, I. (ed.) An Introduction to Gerontology. pp. 159–193. Cambridge University Press, Cambridge (2011). doi/10.1017/CBO9780511973697.006.