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An Adaptive Network Model for a Possible Therapy
for the Effects of a Certain Type of Dementia
on Social Functioning
Charlotte Commu1, Jan Treur1,
Annemieke Dols2,3, Yolande A.L. Pijnenburg2
1Behavioural Informatics Group, Department of Computer Science,
Vrije Universiteit Amsterdam, The Netherlands.
2Ouderenpsychiatrie, GGZ inGeest, Amsterdam, The Netherlands
3Alzheimer Centre, VUmc, Amsterdam, The Netherlands
charlottecommu@gmail.com, j.treur@vu.nl,
A.Dols@ggzingeest.nl, YAL.Pijnenburg@vumc.nl
Abstract
This paper first describes a temporal-causal network model for recognition of
emotions shown by others. The model can show both normal functioning and cases of
dysfunctioning, such as can be the case with certain types of dementia. More specifically
the focus of the paper is on a specific type of therapy that has been incorporated in the
model (thus becoming adaptive) to study the effects and potentials of this therapy to
improve the dysfunctional behaviour. Simulations have been performed to test the model.
A mathematical analysis was done which gave evidence that the model as implemented
does what it is meant to do. The model can be applied to obtain a virtual patient model to
study the way in which recognition of emotions can deviate for certain types of persons,
and what a therapy can contribute to improve the situation.
Keywords: Adaptive network model, dementia, social functioning
1 Introduction
Computational methods are used more and more often to get further insight into human functioning
and dysfunctioning. By designing a human-like computational model for normal functioning of certain
mental and/or social processes, it can be established what alterations make the model show dysfunctional
behavior, and verify how that relates to the empirical literature. Such a computational model can be a
basis for a so-called virtual patient model. An important source of knowledge for the design of a human-
like computational model is found in the fields of Cognitive and Social Neuroscience, and in what is
encountered in the practice of medical clinics. The work reported in this paper results from a cooperation
between researchers in AI and in medical practice.
The focus of this study is on social functioning and dysfunctioning resulting from a certain type of
dementia, in particular the behavioral variant of frontotemporal dementia (bvFTD); see (Piguet et al.,
2011), and on the effect of a certain type of therapy. As will be explained in Section 2 in more detail,
one of the problems encountered is difficulty in recognizing emotions of others, in particular the
negative ones, even while emotion contagion can still function properly.
To model such human processes in a way that is justifiable from a neuroscientific perspective,
knowledge of the underlying mechanisms in the brain is necessary. Mainly, dynamics and cyclic
connections play an important role in such mechanisms, and therefore a modeling approach is needed
that can handle such cyclic dynamic processes. The Network-Oriented Modeling approach based on
temporal-causal networks used here is able to satisfy these needs (Treur, 2016; Treur, 2018).
In this paper, the first part focuses on creating the model, experimenting with the model and
verifying the model. First, Section 2 contains background knowledge on the processes addressed and on
the therapy that was addressed. In Section 3 the basic temporal-causal network model is introduced.
Section 4 describes the simulation experiments for the addressed case, both for normal functioning and
for dysfunctioning. Section 5 shows how the addition of a certain type of therapy (repetitive Transcranial
Magnetic Stimulation: rTMS) leads to an adaptive network model. Section 6 describes the simulation
experiments for the adaptive model with this therapy. Section 7 describes how the adaptive model was
verified by mathematical analysis. Section 8 is a discussion. Finally, Section 9 concludes the paper.
2 Neuropsychiatric Background of bvFTD and a Therapy
In the Netherlands, over 270.000 people have dementia. After cancer and heart- and vascular
diseases it is the most common cause of death. The majority of people that suffer from dementia (70%)
have the most common form: Alzheimer’s disease. No cures for the disease have been found yet, and
due to the aging of society its future perspective does not seem bright. Expectations are that over 500.000
people will have some form of dementia in 2040, in 2055 this number is expected to be over 690.000
(Alzheimer Nederland, 2017).
Alzheimer’s disease might be the most common form of dementia, but is certainly not the only one.
One other form of dementia that can be distinguished is Frontotemporal Dementia. Frontotemporal
dementia (FTD) is the second most common cause of early-onset dementia and exists in two forms: the
behavioral variant of frontotemporal dementia (bvFTD), which concerns progressive deterioration in
social function and personality, and primary progressive aphasia (PPA), which deals with a decline in
language skills (Piguet et al., 2011). This paper focusses on the behavioral variant of frontotemporal
dementia (bvFTD). The behavioral variant of frontotemporal dementia is a neurodegenerative disorder
associated with progressive degeneration of the frontal lobes, temporal lobes, or both (Piguet et al.,
2011, Rascovsky et al., 2011). These deal with the social functioning of a human and can be seen as the
social center of your brain. The control of your behaviour lies in those areas, when these areas are
damaged it affects your behaviour and personality.
The initial symptoms for someone that has bvFTD are not clearly present and only small changes
are shown at the early stages. Moreover, symptoms that are present at the early stages have often much
in common with other mental problems like depression, stress, adjustment problems or lapses of
judgment and self-control (Eslinger et al., 2012), which makes it hard to correctly connect the symptoms
with the correct disease. An important aspect to pinpoint the onset of the disease is interviewing a close
family member to evoke the start of the symptoms. Alterations in social cognitions represent the earliest
and core symptoms of bvFTD and this results in emotional disengagement and socially inappropriate
responses or activities (Ibanez and Manes, 2012; Kumfor, 2017). One of those symptoms that slightly
slips into the lives of someone that has bvFTD and his spouses is apathy and withdrawal from social
activities. Someone seems less goal-driven and has difficulties initiating conversations (Lanata and
Miller, 2016). Moreover, there is a lack of interest and progressive social isolation (Piguet and Hodges,
2013).
Another symptom is loss of empathy. Patients with bvFTD have difficulties interpreting and/or
processing the emotional states of self and others. This results in a lack of self-awareness, but also a
lack of empathy and sympathy towards others. Spouses of patients often report difficulties in connecting
with the patient on an emotional level since they show less sympathy, are not able to understand social
cues, and lack interpersonal warmth (Lanata, 2016; Piguet and Hodges, 2013).
One of the last core symptoms concerns disinhibition. Patients could show inappropriate behaviour
in public and towards strangers such as offensive jokes, cursing, telling stories, hugging, and kissing.
Also, behavioral acts such as impulsivity, gambling, excessive buying, criminal behaviour, or changes
in eating preferences are seen within patients (Piguet et al., 2011; Lanata, 2016; Piguet and Hodges,
2013). In this paper, the following case, experienced in the clinic, is used as an illustration.
The case is as follows:
Box 1. The case on which the model is based on
The case explains that in patients with bvFTD there may be a dissociation between emotion
contagion and facial emotion recognition. Specifically, the recognition of sadness shown by others is
particularly difficult. Some studies of social cognition in bvFTD have already shown that facial emotion
recognition is disturbed, with the exception of happiness. For example, damaged recognition of negative
emotions such as anger and disgust have been described (Gossink et al., 2018). As adopted from the
medical experts (Commu et al., 2018):
“Applying the animal model of empathy of Frans de Waal, emotional contagiousness is the most
inner layer, present from early evolution in most vertebrate animals (de Waal, 2009). Following
the hypothesis that empathy in humans, and more specific in bvFTD, will exhibit a ‘Recapitulati
in reverse’, the outlayers of the Russian Doll, symbolic for more advanced evolutionary social
cognitive abilities will be lost first and the inner layer of emotion contagion will be preserved
and even more prominent in advanced dementia: ‘Heightened emotional contagion in mild
cognitive impairment and Alzheimer's disease is associated with temporal lobe degeneration’, by
(Sturm, 2018), as is illustrated in this case.”
As explained above, one of the core symptoms of bvFTD are changes in social cognition which results
in inappropriate social behaviour and change of personality. For relatives of the patient, this symptom
strikes the most as the patient changes as a person and might not be recognized as himself anymore. As
of today, no cure has been found for bvFTD (Boxer and Boeve, 2007), while a delay of decline could
make a crucial difference for a patient and its relatives.
Repetitive Transcranial Magnetic Stimulation (rTMS) is a method which can improve network
efficacy in several neuropsychiatric disorders (Eldaief et al., 2013). It is a technique in which brain
Case:
A 55 year old man who was recently diagnosed with bvFTD visited our outpatient clinic
with his wife. While explaining the difficulties she met in the home situation, she started
crying. The patient followed the conversation, and at this point he looked at her, his own
eyes got watery, but he looked dazzled. Upon the question how he thought his wife was
feeling, he answered that his wife was probably feeling happy. On the Ekman 60 faces test,
he scored 43 out of 60 items correctly, which is below the cutoff of 46. His subscores were:
Anger 8/10, Disgust 9/10, Anxiousness 8/10, Happiness 8/10, Sadness 5/10, Surprise 5/10.
activity is changed by using a short magnetic pulse. A small coil of wire is placed on the scalp to pass
electrical energy across the scalp and skull. For example, when the coil is placed on the brain area that
is responsible for movement of the thumb, the magnetic pulse causes the thumb to move. By using it
repetitively, in this way, brain activity can be changed in the long term (Wassermann, 1998).
Repetitive TMS has been used successfully for many different subjects with psychiatric disorders
such as depression, auditory verbal hallucinations, schizophrenia, and obsessive-compulsive disorder
(Slotema et al., 2010). Unfortunately, research in the field of dementia is limited. However, research
that has been done has shown positive outcomes: improvements were found in alleviating
neuropsychiatric symptoms and cognitive deficits (Elder & Taylor, 2014). Consequently, research in
the field of rTMS with bvFTD is even more limited. As of today, one study has been performed in which
rTMS therapy has been used on patients with diagnosed bvFTD. Results showed that rTMS may
improve the cognitive performance and suggest that rTMS may also improve daytime functioning, but
no improvements of mood were found (Antczak et al., 2018). However, this does not directly imply that
social cognition improves as well.
The researchers in medical practice with whom a collaboration has been formed within this project have
set up a research program to use rTMS to improve social functioning in bvFTD. In this part, it is
hypothesised that for bvFTD patients rTMS will improve network efficacy of the social brain: when
used for stimulation of the relevant areas it will strengthen the connections that were weakened by
bvFTD. By designing a computational model including the rTMS therapy and its impacts, the effects of
this therapy can be analysed computationally by simulation and evaluated for future purposes.
3 The Temporal-Causal Network Model
This section describes the temporal-causal network model for the interpretation of emotions. The
model describes how interpretation of emotions takes place, focussing on recognizing emotions shown
by others. Patients with the behavioural variant of frontotemporal dementia (bvFTD) show emotional
disengagement and social responses or activities that are not suitable. In particular, this model focuses
on the part where people with bvFTD are unable to recognize and attribute emotional states to self and
others. This can lead to the effect that emotions are misinterpreted or even not recognized. The model
can both show how the process of recognizing and attributing emotional states works regularly and when
it is affected by bvFTD.
A conceptual representation of a temporal-causal network model represents in a declarative manner
states and connections between them that indicate (causal) impacts of states on each other, as assumed
to hold for the application domain addressed. The states have (activation) levels that vary over time. The
following three notions are main elements of a conceptual representation of a temporal-causal network
model:
Connection weight X,Y Each connection from a state X to a state Y has a connection weight value X,Y
representing the strength of the connection, between -1 and 1.
Combination function cY(..) For each state a combination function cY(..) to aggregate the causal impacts
of other states on state Y.
Speed factor Y For each state Y a speed factor Y to represent how fast a state is changing upon causal
impact.
The conceptual and numerical representation of the model introduced will be presented in this section.
The model is designed by integrating a number of theories some of which were discussed in Section 2,
and elements from Damasio (1994; 1999; 2018)’s view on emotions and feelings, and Iacoboni (2009)
on mirror neurons and social contagion.
The developed model shows the difficulties that persons with bvFTD can have regarding recognition
of emotions. Not only the recognition of emotions of others is included, but also the experience of own
emotional feelings which includes mirror links from observed emotions. Figure 1 gives an overview of
the conceptual representation of the model. The following notations are used for the state names:
ws world state
ss sensor state
srs sensory representation state
bs belief state
ps preparation state
cs control state
es execution state
For each state a label LPn refers to the corresponding numerical representation of the update equation of
the state, as described below. An overview of the states, their connections and weights can be found in
Table 1. States or weights with subscript h or s correspond to the emotional feelings happy or sad. An
example is ssh meaning the sensor state for the own emotional response for happy (sensing the own body
state, for example, the own smile). States indicated by a B correspond to the observation of emotional
expression(s) of another person B. For example, srsB,h means the sensory representation state of B having
a happy face. Finally, subscript e is used to indicate if someone is showing any emotion. Therefore, wsB,e
means the world state of person B showing an emotion, for example, an emotional face. Overall, the
upper part (the first three causal pathways) are used for recognizing the emotional state of someone else
(person B).
Figure 1. Overview of the conceptual representation of the model
The lower part (the other two causal pathways) is used to model feelings of own emotions using body
loops and as-if body loops as described by Damasio (1994, 1999, 2018). The model presented here
incorporates parts of the model described by (Treur, 2016, Ch. 9). The part that is included from this
model are the bottom two cycles of states with the body loops affecting the body state x of a person,
representing own emotional feeling according to the theory of Damasio (1994, 1999, 2018). In this
model, body state x can be either s (sad) or h (happy) corresponding to the emotion. This emotion can
also be expressed by another person B. Therefore, the communication of, for example, body state h
(happy) to B expresses that the person self knows that B feels h (happy). The connections from srsB,h and
srsB,s to psh and pss, respectively, provide mirroring functionality to the preparation states, following
Iacoboni’s (2009) findings. These connections make the person feel what the other person expresses.
Most connection weights have a positive value between 0 and 1 according to the strength of the effect
they have on consecutive states. However, suppressing effects are modeled by using a negative weight.
A few of those negative weights occur in the model. The connection weights with a negative value are
ω3,h,s, ω3,s,h, ω7,h,s, ω7,s,h, ω3,h, and ω3,s.
A conceptual representation of the temporal-causal network model can be transformed in a
systematic manner into a numerical representation of the model [32]:
• at each time point t each state X connected to state Y has an impact on Y defined as impactX,Y(t) =
X,Y X(t) where X,Y is the weight of the connection from X to Y
• Based on the combination function cY(…) the aggregated impact of multiple states Xi on Y at t is:
aggimpactY(t) = cY(impactX1,Y(t), …, impactXk,Y(t)) = cY(X1,YX1(t), …, Xk,YXk(t))
where Xi are the states with outgoing connections to state Y
Using the speed factor Y the effect of aggimpactY(t) on Y is exerted over time gradually:
Y(t+t) = Y(t) + Y [aggimpactY(t) - Y(t)] t or dY(t)/dt = Y [aggimpactY(t) - Y(t)]
• Thus, the following difference and differential equation for Y are obtained:
Y(t+t) = Y(t) + Y [cY(X1,YX1(t), …, Xk,YXk(t)) - Y(t)] t
dY(t)/dt = Y [cY(X1,YX1(t), …, Xk,YXk(t)) - Y(t)]
The states related to LP1, LP2, LP3, LP6, LP7, LP11, LP12, LP16, LP19, LP20, LP23, LP24, and LP25
make use of the identity combination function c(V) = id(V) = V. Those for LP8, LP9, LP13, LP14, LP17,
LP18, LP21, and LP22 make use of the scaled sum combination function, which is represented
numerically by:
c(V1, …, Vk) = ssumλ(V1, …, Vk) = (V1 + … + Vk) / λ
where λ is the scaling factor. Finally, states related to LP10 and LP15 make use of a logistic function to
get a binary all-or-nothing effect of these communications.
c(V1, …, Vk) = alogistic,(V1, …,Vk) = [(1/(1+e–σ(V1+ … + Vk -))) – 1/(1+eσ)] (1+e–σ)
Table 1. Overview of the connections, their weights, and their explanations; see also Fig. 1
from state
to state
weight
connection
LP
explanation
wsB,e
ssB,e
17,e
sensing e of B
LP1
Sensing body state e (emotional) of person B
ssB,e
srsB,e
19,e
representing e of B
LP2
Representing the stimulus: B showing emotional
srsB,e
csselfother,B,e
10,e
monitoring e of B
LP3
Control state for self-other distinction from represented
emotion of person B
wsB,h
ssB,h
17,h
sensing h of B
LP6
Sensing body state h (happy) of person B
ssB,h
srsB,h
19,h
representing h of B
LP7
Representing the stimulus of B showing happy
srsB,e
srsB,h
srsh
bsB,s
bsB,h
2,h
1,h,h
4,h
2,s,h
interpreting e of B
interpreting h of B
interpreting own h
suppressing belief of
s
LP8
Believing that B is feeling happy (h)
- from showing emotional by B
- from emotion h showed by B
- from own emotional feeling h
- decreases by belief state for emotion
s
csselfother,B,e
bsB,h
pscomm,B,s
pscomm,B,h
6,h
5,h
7,s,h
controlling
communication
believing h of B
suppressing
preparation state s of
B
LP9
Preparing for body state h: communicating that B feels
happy:
- controlled by self-other distinction
- from believing B has emotion h
- suppressed by preparation state that B has emotion s
csselfother,B,e
pscomm,B,h
escomm,B,h
9,h
8,h
controlling
communication
executing response
LP10
Expressing communication of body state h of B
(communicating that B feels happy)
- controlled by self-other distinction
- from preparation state for h
wsB,s
ssB,s
17,s
sensing s of B
LP11
Sensing body state s (sad) of person B
ssB,s
srsB,s
19,s
representing s of B
LP12
Representing the stimulus of B showing sad
srsB,e
srsB,n
srsB,s
srss
bsB,h
bsB,s
2,s
1,s,s
4,s
2,h,s
interpreting e of B
interpreting s of B
interpreting own s
suppressing belief of
h
LP13
Believing that B is feeling sad (s)
- from showing emotional by B
- from emotion s showed by B
- from own emotional feeling s
- decreases by belief state for emotion h
csselfother,B,e
bsB,s
pscomm,B,h
pscomm,B,s
6,s
5,s,h
7,h,s
controlling
communication
believing s of B
suppressing
preparation state h
of B
LP14
Preparing for body state s: communicating that B feels
sad
- controlled by self-other distinction
- from believing B has emotion s
- suppressed by preparation state that B has emotion h
csselfother,B,e
pscomm,B,s
escomm,B,s
9,s
8,s
controlling
communication
executing response
LP15
Expressing communication of body state s of B
(communicating that B feels sad)
- controlled by self-other distinction
- from preparation state for s
wsh
ssh
18,h
sensing own h
LP16
Sensing body state h (happy) for feeling happy
ssh
psh
srsh
13,h
14,h
representing h of B
predicting h
LP17
Representing a body map for h: emotion h felt (own
feeling of happy)
- from sensing own body state h
- via as-if body loop for body state h
srsh
srsB,h
psh
12,h
11,h
amplifying
mirroring h of B to
own emotional
feeling
LP18
Preparing for body state h: emotional response h (own
feeling h)
- via emotion integration from own emotion
- via mirroring of emotion that B shows
psh
esh
15,h
Executing emotional
response
LP19
Expressing emotional response of h
wss
sss
18,s
sensing own s
LP20
Sensing body state s (sad), own feeling of sad
sss
pss
srss
13,s
14,s
representing s of B
predicting s
LP21
Representing a body map for s: emotion s felt (own
feeling of sad)
- from sensing own body state s
- via as-if body loop for body state s
srss
srsB,s
pss
12,s
11,s
amplifying
mirroring s of B to
own emotional
feeling
LP22
Preparing for body state s: emotional response s (own
feeling s)
- via emotion integration from own emotion
- via mirroring of emotion that B shows
pss
ess
15,s
Executing emotional
response
LP23
Expressing emotional response of s
esh
wsh
16,h
Effectuating h
LP24
Effectuating actual body state
ess
wss
16,s
Effectuating s
LP25
Effectuating actual body state
4 Example Simulation Experiments for the Model without Therapy
To explore the behaviour of the designed temporal-causal network model, two scenarios were
simulated in Matlab. The first scenario describes the case of how a person normally would recognize
emotions shown by others. In this case, it is expected that when person B shows an emotion, the person
will correctly communicate this emotion at the communication states escomm,B,h or escomm,B,s. Also, the
own feeling of that specific observed emotion will be activated through mirror neurons. The second
scenario describes the specific case in which a person has difficulties recognizing the right emotions due
to bvFTD. It is expected that when person B shows the emotion sad, this emotion will be wrongly
interpreted by the patient with bvFTD as happy as explained by the case in Box 1. Therefore, the
communication states will yield activations that differ from the ones in the first scenario, although
through the mirroring system contagion still takes place through which the sadness is felt.
The weights for the connection strengths k are for most connections set to 1; the exceptions are
shown in the lower part of Table 2. For ω7,h,s and ω7,s,h a value of -0.2 has been chosen, since the
preparation states for communication that either it is a sad emotion that person B is showing or a happy
emotion normally will not have a high activation level at the same time. In this way, negative weights
will cause suppression between the states if one of them is activated. Similarly, for weights ω3,h,s and
ω3,s,h a value of -0.05 has been chosen, to express that the belief states for either believing person B
shows a happy emotion or a sad emotion will usually not have high activations at the same time. Note
that the values 0.7 and 0.05 for 2,h and 2,s, respectively, indicate that when no specific emotion is
recognized, usually an emotional face is more believed to indicate happiness than sadness.
The simulations have been performed with speed factor η = 0.5 for all states, Δt = 0.5, and the scaling
factors as displayed in the upper part of Table 2. Since LP10 and LP15 make use of a logistic function,
they have a threshold and steepness. Both states use a logistic function with steepness 200 and threshold
0.5. In the figures that show the results of the simulations, time can be seen on the horizontal axis of the
figures and the activation levels of the states are on the vertical axis.
Table 2 Settings for the scaling factors used and connection weights deviating from 1
LP8
LP9
LP13
LP14
LP17
LP18
LP21
LP22
λ
2.2
1.3
1.55
1.3
2
2
2
2
2,h
2,s
4,h
4,s
3,s,h
3,h,s
7,h,s
7,s,h
6,s
6,h
9,s
9,h
0.7
0.05
0.5
0.5
-0.05
-0.05
-0.2
-0.2
0.3
0.3
0.25
0.25
The graphs in Figures 2-4 display the results of the simulations that have been performed for both
scenarios. The graphs show a part of the results, to highlight the important states. A few of the states
have the same color, as they are overlapping and follow the exact same development over time. Scenario
1 is divided into two different simulations. Difference between both simulations is the input and expected
outcome. The first simulation describes a situation in which the input labeled as a sad emotion shown
by some person B, and the second simulation has an input labeled as a happy emotion shown by some
person B. The simulations are chosen to prove that the model works with different kinds of inputs.
Figure 2 shows the first simulation of Scenario 1. It can be seen that the states for a person showing
emotional (wsB,e) and for a person showing a sad face (wsB,s) are highly activated at the start (orange
lines). Naturally, the sensor states and sensory representation states are becoming active as well (srsB,e
and srsB,s) which can be seen by the yellow and black striped lines. The state for the representation of a
happy face (srsB,h) stays low, visible by the pink striped line. Furthermore, it can be seen that the belief
state for recognizing a happy face (bsB,h) shows some activation (purple line). This is caused by the fact
that the state for recognizing an emotional face is high, but when it becomes clear to the person that the
emotion is about a sad emotion, the feeling that it might be a happy emotion is quickly reduced and it
can be seen that the communication state for a happy emotion (escomm,B,s) stays low (dark blue line). In
the end, the person communicates that a sad face has been observed (escomm,B,s, red line). Also, the mirror
neuron system for the own sad feeling becomes active, showing that emotion contagion takes place for
the observed sadness. This can be seen by the activation of ess which is in the emotion contagion cycle
(light blue line). When performing the simulation with the activation of a happy face instead of a sad
face at the start, similar results are expected (with the activation of communication a happy face instead
of a sad face) as this is how people would normally react. This will be explored in the second simulation.
Figure 3 shows the second simulation of Scenario 1. It can be seen that the states for a person showing
emotional (wsB,e) and for a person showing a happy face (wsB,h) are highly activated at the start (orange
lines) while the state for a person showing a sad (wsB,s) face stays inactive (pink line). The process nearly
follows the same development over time as the simulation shown in Figure 2. It can be seen that as a
response to the input, the sensory response states become high as well (srsB,e and srsB,h). As a response,
the belief state that person B shows a happy emotion (bsB,h) gets highly activated as well. In the end, the
communication state for communicating that a happy emotion of person B has been experienced
(escomm,B,h). This simulation also confirms correct behaviour of the model, as it is expected that with an
input of emotional and happy, the output of communicating that a happy emotion has been experienced
will be activated for normal persons. Therefore, this model shows what is expected of how someone
without any impairment, affected by these processes, would interpret an emotion.
Figure 2. Simulation results for Scenario 1(1): normal functioning
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
010 20 30 40 50 60 70 80 90 100
States Value
Time
Scenario 1: Simulation without bvFTD (1)
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(s)
es(comm,B,s)
es(h)
srs(B,h)
ws(B.h)
es(comm,B,h)
ws(B,e)
Figure 3. Simulation results for Scenario 1(2): normal functioning
For the second scenario, the settings of four weights have been changed. The weights for ω1,h,h, ω1,s,s,
ω4,h, and ω4,s have been set to a connection weight of 0.05. These settings are chosen because the second
scenario illustrates the case of a person with bvFTD, which means that those links are damaged and
therefore have a low connection strength. Figure 4 displays the result of the second scenario. In the
graph, it can be seen that the external states for showing an emotional face (wsB,e) and showing a sad
face (wsB,s) are high from the start, and are kept high, to simulate their presence (orange lines). However,
due to the damaged links, the communication state for saying that a person shows a sad face (escomm,B,s,
red line) is not activated in the end. However, emotion contagion still causes the own sad feeling (ess) to
develop (activation of light blue line). This can be seen by the red line at the bottom of the graph that
stays low throughout the entire simulation, this implies that there is no communication of an observed
sad feeling while the light blue line indicates the own sad feeling to be active. In contrast, the
communication state for saying that a person shows a happy face (escomm,B,h, dark blue) does get activated
while the person never received an input of someone showing a happy face (wsB,h), and no contagion of
happiness took place (esh). This can be explained by the fact that the person does recognize that there is
an emotion visible (activation of srsB,e, yellow line). However, the interpretation of the specific kind of
emotion is disrupted. Therefore, the simulation shows the specific case that has been observed in
patients: how damaged links can cause someone with bvFTD to misinterpret emotions (Box 1).
0
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0,9
1
010 20 30 40 50 60 70 80 90 100
States Value
Time
Scenario 1: Simulation without bvFTD (2)
srs(B,e)
srs(B,h)
bs(B,h)
bs(B,s)
es(h)
es(comm,B,h)
es(s)
ws(B,s)
srs(B,s)
es(comm,B,s)
ws(B,e)
Figure 4. Simulation results for Scenario 2: the case with bvFTD
5 An Adaptive Network Model Incorporating a Therapy
This section describes the adaptive temporal-causal network model for therapy on people with
bvFTD. The model is an extension to the computational model proposed in the first part of the report
which describes how interpretation of emotions takes place, with a focus on recognizing emotions
showed by others. This model also showed how the recognition of emotions can be disturbed in people
with bvFTD. Damaged links can cause a patient to incorrectly classify emotions. The extension to the
model proposed in this section focuses on the possibility that people with bvFTD receive the rTMS
therapy that recovers the damaged links in the network. This could potentially lead to the effect that the
links are getting strong enough again to correctly classify emotions.
Figure 5 gives an overview of the conceptual representation of the model. The links that are marked
in red play an important role in the interpretation of emotions by a person, and are damaged (weakened)
in persons with bvFTD. When these links are not damaged the model behaves as someone without
bvFTD. When these links are damaged the model displays behaviour that has been seen by people with
bvFTD as was shown in Part 1.
0
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0,3
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0,6
0,7
0,8
0,9
1
010 20 30 40 50 60 70 80 90 100
States Value
Time
Scenario 2: Simulation with bvFTD
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(s)
es(comm,B,s)
es(comm,B,h)
es(h)
srs(B,h)
ws(B,h)
ws(B,s)
Figure 5. Overview of the conceptual representation of the model
To introduce the longer term effect of the therapy a Hebbian Learning Rule is applied to all damaged
links. With this rule, the weights become adaptive and can become stronger by the effect of learning.
The Hebbian Learning Rule used is numerically described as follows (Treur, 2016; Gerstner & Kistler,
2002):
(𝑡 + 𝑡) = (𝑡) + [c(𝑋1(𝑡), 𝑋2(𝑡), (𝑡)) − (𝑡)] 𝑡
with
c(𝑉1, 𝑉2, 𝑊) = 𝑉1𝑉2 (1 − 𝑊) + 𝑊
where V1 stands for X1(t), V2 for X2(t), and W for (t). Here η is a learning rate and a persistence factor,
and X1, X2 are the states connected by connection weight .
This is incorporated in the model by using the conceptual structure in Figure 6. The figure shows
one of the four places where the Hebbian Learning effect is applied to. An extra state has been added to
the model, namely X30 which represents the therapy. The therapy can have a state value of either zero
or one. Zero when the there is no therapy, one when there is therapy. When the therapy is on it will
stimulate the states in the brain area where the damaged parts are. When those get simultaneously
activated the connection will become stronger by the Hebbian learning. This will be paired with the
input to activate and stimulate the correct connections and areas during the same time. The therapy state
X30 and its connections is an addition to all the states and connections explained in Table 1.
Figure 6. Hebbian Learning incorporated in the model
This Hebbian learning principle is applied to all the areas in the brain where the damaged “red”
connections are, visible in Figure 5. Therefore, the model consists of four of these Hebbian learning
connections. By introducing a learning effect for these four connections, the network model becomes
an adaptive network model.
The choice for persistence factor and learning rate η for the Hebbian learning principle can have
big consequences for the simulations of the model and therefore must be chosen carefully and ideally in
relation to empirical observations. As such empirical information is not available yet, here it is analysed
how variation of these parameter values affects the outcomes of the therapy. The effects of different
values for these parameters can be seen in the three examples below. For all simulations, 1 is a weight
of which the connection is learned by the principle. Weight 4 is a connection to which the Hebbian
learning principle is applied, but no input is given for connections to which the learning principle never
takes place. The first example shows a simulation of one (very long) therapy session with persistence
= 1 and learning rate η = 0.01. The result can be seen in Figure 7. For connection 1, the learning effect
takes place and reaches a value of about 1 in the end. For the other weight, 4, nothing happens and the
value stays the same throughout the simulation.
Next, simulation example 2 in Figure 8 shows a simulation with persistence = 0.95 and learning
rate η = 0.01. The only difference to simulation 1 is the persistence factor which has decreased in this
simulation. As can be seen, this results in 1 increasing slightly less than the simulation in example 1.
Next to that, 4 shows slight decrease in value as can be explained by the persistence factor being 0.95
resulting in a decay of the connection weight when there is no input to increase by the Hebbian learning
effect.
Finally, simulation example 3 shows in Figure 9 shows a simulation with persistence = 0.95 and
learning rate η = 0.005. This example shows the influence of the learning rate η since this is the only
difference compared to simulation example 2. As can be seen, in the end the value for 1 turns out to be
about the same as for 1 in example 2. However, due to the lower learning rate, the increase of 1 is
slower than seen in example 1 and 2.
These examples show how different persistence factors and learning rates can affect the model.
Therefore, it shows how these parameters values affect the therapy and how they can and should be
chosen in such a manner that the therapy outcomes correspond to what is expected from empirical
literature.
Figure 7. Example simulation 1 with persistence = 1 and learning rate η = 0.01
Figure 8. Example simulation 2 with persistence = 0.95 and learning rate η = 0.01
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 100 200 300 400 500 600 700 800 900 1000
Example 1
w1 w4
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 100 200 300 400 500 600 700 800 900 1000
Example 2
w1 w4
Figure 9. Example simulation 3 with persistence = 0.95 and learning rate η = 0.005
6 Simulation Experiments for the Adaptive Model with Therapy
To explore the effects of the incorporated therapy by the adaptive temporal-causal network model
described above, again, simulations were performed in Matlab. The simulations show different states of
social functioning. First, it shows how damaged connections in the brain as a result of bvFTD cause a
dissociation between emotion contagion and facial emotion recognition. Specifically, this is shown by
a case in which a patient with bvFTD is confronted by an input that can be labeled as an emotionally
sad face. When the patient is asked to communicate the emotion that is experienced, the patient
communicates that these must be tears of joy. The incorrect labeling of emotions is an effect of bvFTD.
Second, the therapy will be applied to the patient in two different scenarios. The therapy consists of a
few sessions to the patient to enhance the damaged links and it is expected that by this therapy the
damaged links will become stronger. By the strengthening of these links the patient could be able to
correctly classify emotions shown by other persons again.
In this model, the strengths of ω1,s,s, ω1,h,h, ω4,s, and ω4,h are adapted using the Hebbian Learning rule.
The settings for the Hebbian learning rule are different for both scenarios to consider different cases. As
before, the simulations have been performed with speed factor η = 0.5 for all states, Δt = 1, and the
scaling factors as displayed in the upper part of Table 2. One change has been made to the model
considering the values displayed in Table 2. In this model, the scaling factor of LP13 has been increased
to a value of 2.05. This change has been made because connection ω4,s can become 1 due to the Hebbian
learning effect, while this was 0.5 in the model proposed in Part 1. Therefore, an increase of the scaling
factor is necessary. Again, LP10 and LP15 make use of a logistic function with steepness 200 and
threshold 0.5. The therapy is applied in sessions of 50 time units alternated by 500 time units rest period
in which no inputs are given and no therapy is applied. This process is repeated a number of times until
considered effective.
The graph in Figure 10 displays the result of a simulation that has been performed before any therapy
has been applied. The figure is identical to Figure 4. However, the graph is reproduced with a different
script that has the Hebbian Learning Principle implemented. Therefore, the results are evaluated once
again. In Figure 10, it can be seen that the states wsB,e for a person showing emotional and wsB,s for a
person showing a sad face are highly activated at the start and during the whole simulation (dark green
lines). This simulates a person B showing emotionally sad behaviour. After this, the sensory
representation states srsB,e and srsB,s for both observing an emotional face and a sad face become active
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 100 200 300 400 500 600 700 800 900 1000
Example 3
w1 w4
as well (black and yellow striped lines). The state srsB,h for observing a happy face stays inactive (red
line). Although there is no input for a happy face, the sensory representation state for happy and the
belief state for a happy face do not become highly active, the communication state escomm,B,h for saying
that a happy face is experienced becomes highly active (blue line) and the one escomm,B,s for a sad face
does not (red line). This simulation shows how damaged links can cause someone with bvFTD to
misinterpret emotions and shows the same behaviour as the simulation represented in Figure 4.
Therefore, the result of this simulation confirms that the adapted script also works as it should.
Figure 10. Simulation results for persons with bvFTD when no therapy is applied
The next step is to perform simulations where the therapy is applied to the patient. In this first
scenario the settings for the Hebbian learning rule are for all weights the same: a maximal connection
strength of 1, a learning rate η of 0.01 and a persistence factor µ of 1. Figure 11 shows the whole process.
The graph shows how there are three sessions of therapy (grey line) over a period of 1600 time units. It
can be seen that during each session the weights of damaged links with weights ω1,h,h and ω4,s become
stronger (orange and blue line). Damaged links with weights ω1,s,s and ω4,h are not included since they
will not become active during any of the simulation scenarios addressed here. However, the same effect
can be reached with these weights as well. After three sessions the weights ω1,h,h and ω4,s both reach a
value of about 0.8. More sessions to obtain a higher value are possible, but after testing, it is found that
these values already show the effect that is expected.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
010 20 30 40 50 60 70 80 90 100
States Value
Time
Simulation with bvFTD - before therapy
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(comm,B,h)
es(s)
es(comm,B,s)
srs(B,h)
es(h)
Therapy
ws(B,h)
ws(B,e)
Figure 11. Simulation results of the applied therapy (1)
These effects can be seen in the graph in Figure 12. The same input is given as the first simulation
that has been performed in Figure 10. Thus, the states wsB,e for a person showing emotional and wsB,s
for a person showing a sad face are highly activated at the start and during the whole simulation (dark
green lines). When comparing this graph to the graph in Figure 10 the effects can be seen clearly. The
most important difference is that now, after therapy, the communication state escomm,B,s for saying that a
person has been showing a sad emotion becomes active instead of the communication state escomm,B,h for
saying that a person has been showing a happy face as was the case before. This is the effect that is
expected of how persons normally would react to these stimuli. Therefore, the simulations show how
damaged links can be recovered by therapy. However, this case shows how the therapy could work in
theory but might not be realistic. The effect of the therapy might not be persistent, and the learning rate
might not be as high as is displayed here. Scenario 2 shows another simulation of how the therapy might
work, considering a decay and a lower learning rate.
Figure 12. Simulation results for persons with bvFTD after therapy is applied.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 200 400 600 800 1000 1200 1400 1600
Weights Value / Therapy State Value
Time
Hebbian Learning Effect
weight w1,s,s
weight w4,s
Therapy
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
020 40 60 80 100
States Value
Time
Simulation with bvFTD - after therapy
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(comm,B,h)
es(s)
es(comm,B,s)
srs(B,h)
es(h)
Therapy
ws(B,h)
In the second scenario, the settings for the Hebbian learning rule are for all weights the same: a maximal
connection strength of 1, a learning rate η of 0.003 and a persistence factor µ of 0.95. These values have
been chosen after testing the model multiple times with different configurations and by discussing this
with the medical experts who have experience with the patients and the techniques used with this
therapy. The graph in Figure 13 shows the whole process. The graph shows how there are sixteen
sessions of therapy over a period of about 8400 time units. When the therapy sessions are applied can
be seen by the orange line. It can be seen that during each session the weights of damaged links with
weights ω1,h,h and ω4,s become stronger (black and blue lines). As the black line shows almost the same
development over time as the blue line, it might be not always clearly visible. Each therapy session
causes the weights to strongly increase in value. After that, there are 500 time units of no therapy which
causes the weights to slowly decrease again due to the fact that the persistence of the learned connections
is not equal to 1. As can be seen, over time the effect of the therapy is decreasing in performance. In the
end, the gain of the therapy is almost equal to the loss in the period that follows of no therapy. This
suggests that after a certain amount of therapy sessions the therapy might become less efficient. If the
effect of the therapy is not sufficient yet at that point in time, this will require the sessions to be adapted.
This could possibly be accomplished by making the therapy sessions longer, to increase their effect,
make the periods between therapy sessions smaller, and if possible to make the decay smaller, or make
the sessions stronger, to create a higher learning rate in one session. Damaged links with weights ω1,s,s
and ω4,h are not included since they will not become active during any of the simulation scenarios
addressed here. However, the same effect can be reached with these connections as well. After sixteen
sessions of therapy the weights ω1,h,h and ω4,s both reach a value of about 0.65.
Figure 13. Simulation results of the applied therapy (2)
These effects can be seen in the graph in Figure 14. The same input is given as the first simulation
that has been performed in Figure 7. Thus, the states wsB,e for a person showing emotional and wsB,s for
a person showing a sad face are highly activated at the start and during the whole simulation (dark green
lines). When comparing this graph to the graph in Figure 10 the effects can be seen clearly. The most
important difference is that now, after therapy, the communication state escomm,B,s for saying that a person
has been showing a sad emotion (pink line) becomes active instead of the communication state escomm,B,h
for saying that a person has been showing a happy face (blue line) as was the case before. However, it
can be noted that both communication states become highly active. This can be explained by the fact
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 1000 2000 3000 4000 5000 6000 7000 8000
Hebbian Learning Effect
weight w1,s,s weight w4,s Therapy
that the connections have reached a weight of about 0.65, which in an ideal situation can be restored to
1 again. As a result, the person has some doubts about which emotion is shown in the beginning, causing
both communication states (escomm,B,s and escomm,B,h) to be high. However, in the end the person decides
this must be a sad emotion expressed by person B and this communication state stays high until the end
of the simulation (escomm,B,s). This is the effect that is expected of how persons normally would react to
these stimuli. Therefore, the simulations show how damaged links can be recovered by therapy.
As an addition, a simulation has been performed where the connection weights of the damaged links
reach a value of 0.85. This effect could not be reached with the settings of the simulation performed in
Figure 13 and 14. Therefore, the adaptations to the therapy in terms of therapy strength or interval
discussed earlier should be explored. This simulation is performed to show the effects when a higher
connection strength can be obtained with the therapy. The result can be seen in the graph displayed in
Figure 15. The graph shows that when a higher connection strength is obtained by the therapy, the belief
state that person B shows a sad emotion bsB,s becomes higher than shown in Figure 14, resulting in a
stronger connection of recognizing sad emotions and therefore also a better distinction of recognizing
happy and sad emotions. Therefore, a lower activation of the communication state for saying that it is a
happy emotion escomm,B,h is seen in comparison to the results shown in Figure 14. This concludes that a
connection strength of 0.65 can cause the patient to correctly identify emotions shown by others again
(as shown in Figure 14). However, it is more beneficial if a higher connection strength can be obtained
as this will significantly improve the patients’ abilities (as has been shown in Figure 15).
Figure 14. Simulation results for persons with bvFTD after therapy is applied (1)
0
0,1
0,2
0,3
0,4
0,5
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0,7
0,8
0,9
1
020 40 60 80 100
States Value
Time
After Therapy
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(comm,B,h)
es(s)
es(comm,B,s)
srs(B,h)
es(h)
Therapy
Figure 15. Simulation results for persons with bvFTD after therapy is applied (2)
7 Verification of the Network Model by Mathematical
Analysis
*
Dedicated methods have been developed for temporal-causal network models to verify whether an
implemented model shows behaviour as expected; see (Treur, 2016a; Treur, 2016b, Ch 12). In this
section equilibria of the designed model are addressed. By Mathematical Analysis their values are found
and by comparing them to simulated values the model is verified. Stationary points and equilibria are
defined as follows.
A state Y in a temporal-causal network model has a stationary point at t if dY(t)/dt = 0. A temporal-
causal network model is in an equilibrium state at t if all states have a stationary point at t. In that case
the above equations dY(t)/dt = 0 for all states Y are called the equilibrium equations. These are general
notions, for temporal network models the following simple criterion was obtained in terms of the basic
elements defining the network, in particular, the states Y, connection weights X,Y and the combination
functions cY(..); see (Treur, 2016a; 2016b, Ch 12).
Criterion for stationary points and equilibria in a temporal-causal network model
A state Y in an adaptive temporal-causal network model with nonzero speed factor has a stationary point
at t if and only if
cY(X1,Y(t) X1(t), …, Xk,Y(t) Xk(t)) = Y(t)
where X1, …, Xk are the states with outgoing connections to Y.
A temporal-causal network model is in an equilibrium state at t if and only if for all states with nonzero
speed factor the above criterion holds at t.
Equilibrium equations for an identity function id(.) or scaled sum combination function ssum(..) are
id(X,Y X(t)) = X,Y X(t) = Y(t)
*
Most parts of this section were adopted from: Commu, C., Treur, J., Dols, A. & Pijnenburg, Y. (2018) A Computational
Network Model for the Effects of Certain Types of Dementia on Social Functioning. Proc. of the 10th International Conference
on Computational Collective Intelligence, ICCCI’18. Springer Publishers, 2018
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
020 40 60 80 100
States Value
Time
After Therapy (potentially)
srs(B,s)
srs(B,e)
bs(B,h)
bs(B,s)
es(comm,B,h)
es(s)
es(comm,B,s)
srs(B,h)
es(h)
Therapy
ws(B,h)
cY(X1,Y X1(t), …, Xk,YXk(t)) = (X1,Y X1(t) + … + Xk,Y Xk(t)) / Y = Y(t)
So, they are linear equations in the state values involved with connection weights and scaling factors as
coefficients:
X,Y X(t) = Y(t)
X1,Y(t) X1(t) + … + Xk,Y(t) Xk(t) = Y Y(t)
In the presented model the scaling factors have been set as the sum of the positive weights of the
incoming connections; therefore all coefficients are built from connection weights. Using this, the
following equilibrium equations for the states were obtained for the presented network model here; to
simplify the notation the reference to t has been left out, and underlining is used to indicate that this
concerns equilibrium state values, not state names. Here the connection weights are named as shown in
Table 1, and A1 to A3 are constants.
srsB,h = A1 srsB,s = A2 srsB,e = A3
(1,X,X + 1,Y,X + 2,X + 4,X) bsB,X = 1,X,X srsB,X + 1,Y,X srsB,Y + 2,X srsB,e + 4,X srsX + 3,Y,X bsB,Y
(5,X + 6,X) pscomm,B,X = 5,X bsB,X + 6,X csselfother,B,e+ 7,Y,X pscomm,B,Y
(8,X + 9,X) escomm,B,X = 8,X pscomm,B,X + 9,X csselfother,B,e
csselfother,B,e = 10,e srsB,e
(11,X + 12,X) psX = 11,X srsB,X + 12,X srsX
(13,X + 14,X) srsX = 13,X ssX + 14,X psX
esX = 15,X psX
ssX = 16,X esX
Note that in the above equations in the equilibrium state values, variable names X and Y are used that
have multiple instances for h (happy) and s (sad). If these equilibrium state values are instantiated and
renamed as shown in Table 3, 19 linear equations in X1 to X19 are obtained with coefficients based on
the connection weights and the constants A1 to A3.
Table 3. State names used in the equilibrium equations.
X1
X2
X3
X4
X5
X6
X7
X8
X9
srsB,h
srsB,s
srsB,e
srsh
srss
bsB,h
bsB,s
Ps
comm,B,h
ps
comm,B,s
X10
X11
X12
X13
X14
X15
X16
X17
X18
escomm,B,h
es comm,B,s
csselfother,B,e
psh
pss
esh
ess
ssh
sss
These 19 linear equations can be solved symbolically, for example using the WIMS Linear Solver (see
[WIMS, 2018]), thereby obtaining complex algebraic expressions for the equilibrium values, linear in
the constants A1 to A3 with as coefficients rational (broken) functions in terms of the connection weights.
For verification all connection weights have been set as the simulation shown and Table 2. For these
connection weight values, the following solution was found in terms of A1 to A3:
X1 = A1 X2 = A2 X3 = A3 X4 = A1 X5 = A2
X6 = 0.3176815847395451 A3 - 0.02201027146001467 A2 + 0.682318415260455 A1
X7 = 0.02201027146001311 A3 + 0.9684519442406457 A2 - 0.02201027146001467 A1
X8 = 0.4476266702238825 A3 - 0.134729540452211 A2 + 0.5402521176549057 A1
X9 = 0.1788345672424897 A3 + 0.7656906556392985 A2 - 0.1000466884546121 A1
X10 = 0.558101336179106 A3 - 0.1077836323617688 A2 + 0.4322016941239245 A1
X11 = 0.3430676537939918 A3 + 0.6125525245114387 A2 - 0.08003735076368973 A1
X12 = A3 X13 = A1 X14 = A2 X15 = A1 X16 = A2 X17 = A1 X18 = A2
For the above connection weight values and values A1 = 1, A2 = 0, and A3 = 1, the solution was found
shown in the third and sixth row of Table 4.
Table 4. Results of the mathematical analysis.
X1
X2
X3
X4
X5
X6
X7
X8
X9
srsB,h
srsB,s
srsB,e
srsh
srss
bsB,h
bsB,s
pscomm,B,h
ps comm,B,s
1
0
1
1
0
1
0
0.987879
0.078788
X10
X11
X12
X13
X14
X15
X16
X17
X18
escomm,B,h
es comm,B,s
csselfother,B,e
psh
pss
esh
ess
ssh
sss
0.990303
0.263030
1
1
0
1
0
1
0
A logistic function with steepness 200 and threshold 0.625 applied to the communication execution
states X10 and X11 (multiplied by the scaling factor 1.25 to undo the scaling) provides X10 = 1, and X11 =
2.613 10-21. Similarly, for other values of A1 to A3, the equilibrium values have been found. For example,
for A1 = 0, A2 = 0, A3 = 1, it was found X6 = 0.3176815847395451, X7 = 0.02201027146001467, X8 =
0.4476266702238826, X9 = 0.1788345672424908, X10 = 0.5581013361791062, X11 =
0.3430676537939928 (a logistic function with steepness 200 and threshold 0.625 applied to the
communication execution states X10 and X11 multiplied by the scaling factor 1.25 to undo the scaling
provides X10 = 1, and X11 = 0), and for A1 = 0, A2 = 1, A3 = 1, X6 = 0.2956713132795305, X7=
0.9904622157006603, X8 = 0.3128971297716712, X9 = 0.9445252228817893, X10 =
0.4503177038173369, X11 = 0.9556201783054313 (a logistic function with steepness 200 and threshold
0.625 applied to the communication execution states X10 and X11 multiplied by the scaling factor 1.25 to
undo the scaling provides X10 = 1, and X11 = 0). All these values have been checked with the values of
the simulation scenarios and were found very accurate (deviations less than 0.001). This provides
evidence that the implemented model does what is expected.
Also the equilibria for the adaptive model have been analysed. Application of the stationary point
criterion on the Hebbian learning parts of the model is as follows. Recall that for that case the
combination function is
hebb(V1, V2, W) = V1V2(1-W) + W
where V1 refers to X1(t), V2 refers to X2(t), and W refers to X1,X2(t). Based on this, according to the
stationary point criterion in an equilibrium it holds
X1(t)X2(t) (1-X1,X2(t)) + X1,X2(t) = X1,X2(t)
X1(t)X2(t) (1-X1,X2(t)) = (1-) X1,X2(t)
X1(t)X2(t) - X1(t)X2(t) X1,X2(t)) = (1-) X1,X2(t)
X1(t)X2(t) = [X1(t)X2(t) + (1-)] X1,X2(t)
This provides the following relation for X1,X2(t):
X1,X2(t) = X1(t)X2(t) / [X1(t)X2(t) + (1-)]
= 1 / [1 + (1-)/(X1(t)X2(t))] (when X1(t)X2(t)> 0)
This is monotonically increasing in X1(t)X2(t); the maximal value occurs when X1(t) = 1 and X2(t)= 1,
and is
X1,X2(t) = 1/[2-]
Therefore, for example, in the simulations with = 0.95, it should be expected that the values of the
adaptive connections will never exceed 1/[2-0.95] = 0.95238. This can indeed be observed in the
simulations.
8 Discussion
In this paper, first a temporal-causal network model was introduced that describes the interpretation of
emotions shown by others. The model can also show cases in which the interpretation of emotions is
incorrect, as can be the case of persons with bvFTD; this is based on the assumption that it is at least
observed that there is an emotional face, although the specific type of emotion is not recognized
correctly. Several simulations have been performed to test the model in both these behaviours. In the
presented scenario for a person with bvFTD it was shown how an observed sad face led to contagion of
sadness by the mirror system in a correct way, but at the same time the emotional face was nevertheless
not recognized as sad, but instead as happy. A mathematical analysis was done confirming the simulation
outcomes; this gave evidence that the model as implemented does what it is meant to do.
By comparing the results of the model to the case it can be concluded that the model can correctly
simulate behaviour shown by the patient with bvFTD as described in the case in Box 1. Next to that, it
can also show how people without any damaged connections would respond to the input.
Next, the paper addresses an extension to the temporal-causal model by obtaining an adaptive
network model for the effects of a therapy. It addresses a therapy that might improve the damaged
connections in the brain that come with bvFTD. The extended model shows how Repetitive Transcranial
Magnetic Therapy (rTMS) can improve the network connections and, in the end, cause a patient to
(partly) retain the damaged connections. The two different scenarios show how after several therapy
sessions, the connections have improved in such a way that the patient will be able to correctly classify
experienced emotions by others again. The first scenario showed how the therapy could work best case
scenario. However, this scenario might be too optimistic and therefore a second scenario has been
performed. The second scenario also showed how the therapy can improve the connections but due to a
decay and a lower learning rate this would cost a lot more time. In the end, for all scenarios, differences
between before and after the therapy are clear: certain functions work again after therapy.
However, no real data is available yet to support the model. It could be that the rate of the learning
effect is not the exact same number as was used in the simulation scenario. This number can be higher,
when the learning effect is stronger, or lower, when the learning effect is slower. This also changes the
outcomes in terms of how many sessions are needed to get the desired effect, which means that a
different number of sessions are needed to get to the same effect. Also, this model assumes a persistence
of 1; meaning that when the improvement of the connection is obtained, it will be persistent, while it
might be the case that there is a small decay on the effect. When real data is obtained, all such changes
can be easily incorporated in the model as the model stands on its own and the parameters are easily
adjusted.
9 Conclusion
In the end, both models have proven to do what they were designed for. The model first introduced
shows a temporal-causal network model that describes how emotions shown by others are interpreted
by us. On top of that, it is shown that in people with bvFTD certain links within this process are damaged,
causing the patient to incorrectly interpret emotions of which an example case is explained in Box 1. A
paper on this model will be published as (Commu et al., 2018). The adaptive extension to the model
introduced shows how rTMS therapy can be used to restore the damaged connections and causing the
patient to interpret emotions correctly again.
Both models can be applied as the basis for human-like virtual agents, for example, to obtain a virtual
patient model to study the way in which recognition of emotions can deviate for certain types of persons.
Also, to study how to potentially enhance the recognition of emotions when damaged as was shown by
the second model. However, more therapies or techniques can be implemented in the model to explore
more possibilities. In further research real data can be used to test the model in more detail. Brain activity
could be measured to get real data to use as input for the model and get patterns of how states are
activated over time. This could help by tuning the parameters of the model to be even more human-like.
Furthermore, more scenarios or cases could be simulated to analyse more and different outcomes of the
model. In future extensions of the model, more emotions than sad and happy can also be addressed. This
report and model focuses specifically on the social cognition disturbances in people with bvFTD. Other
symptoms mentioned in Section 1 can also be potential subjects to extend the model or even create new
models within the subject of bvFTD. As a conclusion, the created model shows the process of emotion
recognition and is verified by not only interpreting the simulation results, but also mathematically. For
future work, the next step is to obtain real data that can be used to finetune the model and eventually
insert patient data into the model.
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