DRUG ADDICTION: A COMPUTATIONAL MULTISCALE

MODEL COMBINING NEUROPSYCHOLOGY,

COGNITION AND BEHAVIOR

Yariv Z. Levy

1,∗

, Dino Levy

2,∗

, Jerrold S. Meyer

and Hava T. Siegelmann

Laboratory of Biologically Inspired Neural and Dynamical Systems (BINDS), University of Massachusetts Amherst, U.S.A.

Department of Neurobiology, The Weizmann Institute of Science, Rehovot, Israel

Laboratory of Developmental Neuropharmacology, University of Massachusetts Amherst, U.S.A.

Keywords:

Addiction, Multiscale Modeling, Bio-signal Modeling, Behavioral Processes, Cognitive Processes, Neuro-

physiological Processes.

Abstract:

According to the United Nations, approximately 24.7 million people used amphetamines, 16 million used

cocaine, and 12 million used heroin in 2006/07 (Costa, 2008). Full recovery from drug addiction by chemical

treatment and/or social and psychological support is uncertain. The present investigation was undertaken to

expand our understanding of the factors that drive the dynamics of addiction. A new multiscale computational

model is presented which integrates current theories of addiction, unlike previous models, considers addiction

as a reversible process (Siegelmann, 2008). Explicit time dependency is added to the inhibition and the

compulsion processes. Preliminary computational predictions of drug-seeking behavior are presented and

potential correlation with experimental data is discussed. Validation of the model appears promising, however

additional investigation is required.

1 INTRODUCTION

Drug addiction is a global problem. Historically, ad-

dicted people have been simply considered to be lack-

ing the willpower to quit. But the prevailing view has

changed in response to scientiﬁc studies which show

that addiction correlates with social, psychological,

and physiological factors. Addiction is now classi-

ﬁed as a disease, a “bio-psycho-social-spiritual disor-

der” (Interlandi, 2008), but the underling causes and

prospects for full recovery remain uncertain. Compu-

tational models for addictive behavior could assist in

this quest for understanding.

Many computational models of addiction have

been proposed and applied in order to provide a bet-

ter understanding of factors which affect the nature

of the addictive process. The relevant literature in-

cludes two types of models: one deals with either be-

havior acquisition or behavior maintenance of drug

self-administration, and the other integrates both ac-

quisition and maintenance based on machine learning

or neuronal network dynamical approaches (Ahmed

et al., 2007). Both model types share the common

∗

Authors with equal contributions.

assumption that addiction is a non-reversible process,

and hence can not describe experimental observations

which support possible recovery (Winick, 1962; So-

bell et al., 2000). A new model of addiction, the

“dynamical addict”, takes into account both relapse

and rehabilitation processes (Siegelmann, 2008). This

approach considers addiction as a dynamical system

where actual addiction behavior and processes of in-

hibition and compulsion are separated. Unlike other

computational and mathematical models, it does not

condemn the addict to a monotonic worsening of the

addictive condition. Moreover, temporal parameters

are introduced to quantify the virtual subject’s level

of cognitive rationality and levels of feedback param-

eters that make addiction so difﬁcult to defeat.

The present investigation was undertaken to de-

scribe this new model in terms of neuropsychological,

cognitive, and behavioral observations, to incorporate

the temporal dimension within the processes of inhi-

bition and compulsion, and to present a preliminary

correlation between synthetic data presented in this

work and empirical data found in the literature.

Levy Y., Levy D., Meyer J. and T. Siegelmann H. (2009).

DRUG ADDICTION: A COMPUTATIONAL MULTISCALE MODEL COMBINING NEUROPSYCHOLOGY, COGNITION AND BEHAVIOR.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 87-94

DOI: 10.5220/0001539100870094

 SciTePress

Figure 1: Addiction model combining neuropsychological (NepS), cognitive (CogS), and behavioral (BehS) scales. The

output G(t) is the likelihood of drug-seeking behavior.

2 DESCRIPTION OF THE MODEL

This section describes the multiscale framework for

formulating this new addiction model (Siegelmann,

2008). The model can be considered to comprise

three resolution scales: neuropsychological (NepS),

cognitive (CogS), and behavioral (BehS) scales as

shown in Figure 1. The original formulation of the

model’s output is the likelihood of drug-seeking

behavior G(t):

G(t) = (1 − r(t)) · (−C) + r(t) · I (1)

where r(t) is a cognitive parameter deﬁned below in

Section 2.2, and C and I are behavioral processes with

longer time scales than r which are approximated by

constants.

The output of the model, G(t), is generated at the

BehS. The BehS is composed of inhibition I and com-

pulsion C signals that respectively prevent and en-

courage drug-seeking behavior. The balance between

I and C is modulated by the CogS, which is mainly

intended to integrate the information coming from the

NepS where internal and external processes are com-

puted and weighted.

The remainder of this section presents further details

of the model parameters. The following two sub-

sections 2.1 and 2.2 present a brief review of the

original model from a multi-scale viewpoint. This is

followed by a sub-section 2.3 which introduces inhi-

bition and compulsion as dynamical time-dependent

processes.

2.1 Neuropsychological Scale (NepS)

The NepS consists of effects which are dependent on

the internal state of the virtual subject as well as acute

external effects. How these internal and external pro-

cesses behave is summarized in Table 1 with corre-

sponding mathematical details in the Appendix.

Internal processes are considered to include P(t),

S(t), D(t) and q(t). P(t) denotes the level of pain

or negative consequences, in areas such as health or

social relations; which are increased by drug intake

(De Alba et al., 2004). S(t) denotes the level of stress

or the negative emotional state of the virtual subject.

S(t) increases during withdrawal periods (Hodgins

et al., 1995; Koob and Le Moal, 2001; Aston-Jones

and Harris, 2004) and may trigger craving (Stewart,

2000). D(t) denotes the level of current craving which

depends on dopamine transmission in the nucleus ac-

cumbens (NAc). Finally, q(t) denotes the saliency

of drug-associated cues that increase with repeated

drug consumption. When considering drug addic-

tion as a disease of the learning and memory mech-

anism (Hyman, 2005), repeated learning results in a

stronger association between the stimuli and the re-

wards, causing a sensitized saliency for drug associ-

ated cues (Robinson and Berridge, 2003). The sig-

nal q(t) deﬁnes the initial value of the drug-associated

cue Q(t) when it is encountered, as described below.

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

Table 1: Effects of G(t), the likelihood of drug-seeking behavior, on internal and external processes for NepS.

Processes behavior when G(t) > 0 behavior when G(t) < 0

Internals

S(t) exponentially increases exponentially decreases

P(t) exponentially decreases exponentially increases

D(t)

starting from the change in the sign of G(t),

exponentially increases

from negative to positive,

D(t) exponentially increases for a ﬁxed

number of time steps, then exponentially decreases

q(t)

starting from the change in the sign of G(t),

exponentially increases

from negative to positive,

q(t) stays constant for a ﬁxed

number of time steps, then exponentially decreases

Externals

(t) can be triggered can NOT be triggered

(t) can NOT be triggered can be triggered

(t) can be triggered can NOT be triggered

Q(t) can be triggered - its initial value depends on q(t)

External processes are considered to include

(t), A

(t) and Q(t). A

(t) denotes a

painful trauma that may cause an addict to stop tak-

ing drugs immediately (Bradby and Williams, 2006;

Barth et al., 2006); A

(t) denotes a stressful episode

that leads to immediate drug use (Erb et al., 1996;

Sinha et al., 2000); A

(t) denotes drug priming that

could reinstate drug use again (de Wit and Stewart,

1983; Spealman et al., 1999); and Q(t) denotes a

drug-associated cue that may be triggered, for ex-

ample, by visiting a particular friend who uses that

drug (See, 2002). If an event Q(t) is encountered, the

saliency of this signal is deﬁned by the value of q(t).

When any of these external processes is triggered, its

value jumps to a ﬁxed value, stays constant for a num-

ber of time steps, and then decreases exponentially. If

this external process is triggered again before its pre-

vious effect disappears, it reverts to its initial value,

stays constant for a number of time steps and then de-

creases exponentially.

2.2 Cognitive Scale (CogS)

The CogS mediates between low and high level con-

trols of behavior. As such, it computes the cognitive

rationality factor r(t) and the input to the cognitive

rationality f (t) (Siegelmann, 2008). The parameter

r(t) characterizes the activity of the addiction-related

neuronal patterns: low levels cause compulsion to

dominate and the value of G(t) to decrease, and

high levels cause inhibition to dominate and G(t)

to increase. The value of r(t) at any instant is a

combination of the previous value of the cognitive

process r(t −1) and the input to the cognitive process

f (t):

r(t) =

tanh



α · r(t − 1) + β · f (t) + γ



(2)

where r ∈ [0, 1], and α, β, and γ are constants.

The input to the cognitive process f (t) can be ex-

pressed as a weighted sum of the internal processes,

that make addiction so difﬁcult to overcome, and the

external processes that have a strong but temporary

effect:

f (t) =

P(t) − ω

S(t) − ω

D(t)

+ (3)



(t) − A

(t)



− ω

Q(t)

where ω

, ω

, and ω

are the constants weighting

factors for S(t), P(t), and D(t), respectively; ω

is the

constant weighting factor for A

(t), A

(t), and A

(t);

and ω

is the constants weighting factor for Q(t).

2.3 Behavioral Scale (BehS)

The global output from the model G(t) computed in

the BehS is the likelihood of drug-seeking behavior.

G(t) indicates whether the virtual subject is more

or less likely to manifest behavior inducing drug

intake at time t according to Equation 1, which can

be readily modiﬁed to include time dependence:

G(t) = (1 − r(t)) · (−C(t)) + r(t) · I(t) (4)

Here G(t) ∈ [−1, 1], I(t) represents the time-

dependant inhibition, and C(t) the time-dependant

DRUG ADDICTION: A COMPUTATIONAL MULTISCALE MODEL COMBINING NEUROPSYCHOLOGY,

COGNITION AND BEHAVIOR

compulsion as deﬁned below. For G(t) > 0 the

virtual subject is less likely to have an episode of

drug-seeking behavior (healthy behavior), whereas

for G(t) < 0 the virtual subject is more likely to ex-

hibit drug-seeking behavior (maladaptive behavior).

The overall inhibition I(t) is the arithmetical

mean of inhibitions i

(t) and i

(t). Inhibition i

(t) is

related to the virtual subject’s neural development

of the frontal lobes of the cortex (Durston et al.,

2002; Leon-Carrion et al., 2004; Blakemore and

Choudhury, 2006), given by:

(t) =











1 − e

· i

max,s

if t < s

(t − 1) + (2d − 1)δ

if t < s

max

− (i

max

− i

−β

if t < s

(t − 1) else

(5)

where s

, s

and s

correspond to developmental

changes age from birth to childhood (s

), to puberty

), to adulthood (s

); β

and β

are constants; i

max,s

is the maximum value of i

(t) for age stage s

; i

max

is the maximal value of i

(t); δ

is the maximal

increase of i

(t) during age stage s

; d is the number

of time steps after a change in the age stage s

, s

and

; and i

is the value i

(d).

The inhibition i

(t) is ascribable to social rules

governing the society in which the virtual subject is

living. We assume i

(t) a sinusoidal function bounded

by two exponential functions:

(t) =

1 − e

−χ

[(χ

− χ

)sin(χ

t) + χ

+ χ

] (6)

where χ

is a constant, χ

is the asymptote of the

higher exponential function that bounds i

(t), χ

the asymptote of the lower exponential function that

bounds i

(t) and χ

is the angular frequency whose

value is changed randomly. Random noise is added to

(t) and i

(t).

The compulsion C(t) is the arithmetical mean

of c

(t) and c

(t) which are computed according

to the “incentive-sensitization theory of addiction”

(Robinson and Berridge, 1993). This theory assumes

that the neural substrate of the subject using drugs for

the ﬁrst few times becomes more sensitive to the drug

by assigning high saliency to drug-related inputs,

and this saliency alteration is then the instigator to

the compulsive behavior to repetitive drug intakes.

According to this theory, the ﬁrst step is the pleasure

phase, during which the subject increasingly enjoys

drug effects. The second step is the wanting phase

during which the subject changes behavior in order

to obtain more and more of the drug. The parameter

(t) describes the sensitization (liking) process and

the parameter c

(t) describes the incentive (wanting)

process:

(t) =











− (c

− c

−γd

if G(t) < 0

and τ

= 0



− c



−β

if G(t) < 0

and τ

= 1



− c



−β

if G(t) > 0

and τ

= 1

(t − 1) else

(7)

and

(t) =











− (c

− c

−γ

if G(t) < 0

and τ

= 0

− (c

− c

−γ

if G(t) < 0

and τ

= 1

+ |c

− c

−βd

if G(t) > 0

and τ

= 1

(t − 1) else

(8)

where c

, c

and c

are maximal and

minimal values of respectively c

(t) and c

(t); γ, γ

, β, β

and β

are constants; τ

is a binary value set

to 1 when G(t) < 0 for a number of time steps; d is

the number of time steps after a change in the sign of

G(t) or the value of τ

; c

= c

(d) and c

= c

(d).

Random noise is added to both signals.

3 EXPERIMENTAL EVALUATION

Drinking, smoking, and drug use are serious prob-

lems among college students and can cause addiction.

A preliminary experimental evaluation of our model

has been performed in order to characterize such be-

havior. We begin by describing the onset and main-

tenance of addictive behavior in G.D., a college-age

virtual male subject who had a healthy physical and

mental development.

The evolution of G.D.’s inhibition I(t) up to age

25 is shown in Figure 2. Here i

(t) is the inhibi-

tion related to his neural development, and i

(t) is

the inhibition related to the social rules present in his

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

environment. Note that the neural related inhibition

(t) undergoes an abrupt transformation after age 10,

whereas the inhibition i

(t) ﬂuctuates between two

exponential curves that represent the minimum and

maximum inhibitions in G.D.’s social environment.

Figure 2: Evolution of G.D.’s inhibition I(t) from birth to

age 25: i

(t) is the inhibition related to neural development,

and i

(t) is the inhibition related to the social environment.

G.D. had his ﬁrst encounter with drugs at age 17.

The evolution of his drug-seeking behavior G(t) and

his compulsion C(t), between the ages of 16 and 18,

are shown in Figure 3. Note that the sign of G(t)

changes form positive to negative at age 17, and how

the incentive and sensitization processes c

(t) and

(t) change their trajectories.

Figure 3: G(t) (upper curve) and C(t) (lower curve) for

G.D. from age 16 to 18. Also included are incentive

(t) and the sensitization c

(t) processes (Robinson and

Berridge, 1993).

As a further check of the model, we used the same

I(t) and C(t) signals and performed 10 different sim-

ulations to compute G(t) and also the other signals.

Figures 4 to 6 show the means of these signals as well

as the standard errors of the mean (SEM). The evolu-

tion of G.D.’s internal processes S(t), P(t) and D(t)

at the age of 17 when he begins to take drugs and be-

comes addicted is shown in Figure 4. The level of

negative consequences in areas such as health or so-

cial relations P(t) and the dopamine-related craving

D(t) have low values at the beginning of the addictive

experience, and then progressively increase to steady

values.

Figure 4: Means and SEMs of the internal processes S(t),

P(t), and D(t) for G.D. from age 17 to 18 (10 simulations).

In the years following his encounter with addic-

tion, G.D. exempliﬁes the drug-seeking behavior of

someone who is unsuccessfully trying to quit using

drugs. This relapse pattern, which is a fundamental

characteristic of addiction, is apparent in Figure 5,

which shows the mean values of G(t) over 10 sim-

ulations and the corresponding SEM, from age 19 to

21.

Figure 5: G(t) mean and SEM for 10 simulations. Between

ages 19 to 21, G.D. shows a continuous relapse pattern of

a person unsuccessfully trying to escape from drug-seeking

behavior.

G.D.’s internal processes for this same period are

shown in Figure 6. Acute traumas A

(t) bring him

towards a healthy behavior, but he is unable to over-

come addiction because of the drug-associated cues

Q(t). As G(t) < 0 the value of q(t) increases, and

(t) and A

(t) can not occur.

This particular case exempliﬁes a college-age stu-

dent who has his ﬁrst encounter with drugs at the age

of 17. Initially G.D. enjoyed the drug, but his enjoy-

ment progressively decreased as his desire increased.

This dynamic behavior is due to the negative effect of

Q(t) being stronger than the positive effect of A

(t).

Our model is not limited to monotonic non-

reversible processes. Another example with a health-

ier dynamic is shown in Figure 7. In this case, the

virtual male subject, we call V.R. has job-related dif-

ﬁculties following his 36th birthday. The acute stress

episodes he experiences at his workplace makes V.R.

more vulnerable to addiction. Over a period of several

DRUG ADDICTION: A COMPUTATIONAL MULTISCALE MODEL COMBINING NEUROPSYCHOLOGY,

COGNITION AND BEHAVIOR

Figure 6: Acute pain A

(t) (upper curve), and drug-

associated cues Q(t) and their saliency value q(t) (lower

curves) mean and SEM over 10 simulations for G.D. be-

tween ages 19 to 21.

days, his G(t) value decreases and becomes negative,

but acute episodes of pain make his G(t) value posi-

tive again and his behavior is healthy again.

Figure 7: G(t) mean and SEM over 10 simulations for V.R.

for 5 months following his 36th birthday. His drug-seeking

behavior changes from healthy to maladaptive and back to

healthy.

4 DISCUSSION

The present paper introduces a multi-scale approach

to the modeling of addiction while also incorporat-

ing time dependence to the inhibition and the com-

pulsion processes. A fundamental issue is evaluating

the model’s ability to mimic experimental data. The

ﬁrst step in this endeavor is to assess whether the cal-

culated likelihood of drug-seeking behavior G(t) is

suitable for describing actual addictive behavior.

Computed values for the likelihood of drug-

seeking G(t) give rise to speciﬁc patterns or trajecto-

ries of behavior. For example, it was shown that over

4 years, a group of college-age occasional smokers

is likely to evolve into three categories: 45% of the

subjects are likely to become nonsmokers, 35% oc-

casional smokers, and 20% daily smokers (Kenford

et al., 2005). Another investigation classiﬁes drink-

ing trajectories of ﬁrst year college students into ﬁve

groups: light drinkers the whole year (light-stable),

light drinkers the whole year but with a considerable

increase during holidays (light-stable plus high hol-

iday), initial moderate drinkers who increased their

consumption during the year (medium-increasing),

initial heavy drinkers who decreased their consump-

tion during the year (high-decreasing), and ﬁnally

heavy drinkers during the whole year (heavy-stable)

(Greenbaum et al., 2005).

The drug-seeking behavior proﬁle of virtual sub-

ject G.D. presented in Figure 5 suggests a person in

the “light-stable plus high holiday” group cited above.

This parallelism can be made under the assumption

that G.D.’s birthday is in September. Within this con-

text, associations between local minima of G(t) and

holiday periods seem reasonable with respect to time

and the absolute values of G(t). The two local minima

prior to G.D.’s 20

and 21

birthdays may be consid-

ered to occur in the summer, and the two local minima

around ages 19.5 and 20.5 during winter breaks. Also

associations between local maxima of G(t) and par-

ticularly intense periods of the school year seem rea-

sonable. Local maxima prior to G.D.’s 20

and 21

birthdays may be considered to occur during exam-

ination periods. It is reasonable to associate G.D.’s

proﬁle with the proﬁle of a student which tends to

decrease his drinking consumption during periods re-

quiring more responsibility, and to increase consump-

tion during more serene periods.

Preliminary results presented in this paper suggest

that the “dynamical addict” model could provide a

complementary view to existing computational mod-

els toward a better understanding of addiction and its

dynamical properties. Future work will concentrate

on more extensive comparisons with real data as well

as the integration of an additional neurophysiological

scale.

ACKNOWLEDGEMENTS

We thank Jung Yi, Kun Tu, and Gal Niv for their

valuable assistance, and also the paper reviewers for

their constructive comments. Scientiﬁc suggestions

by Pascal Steiner and Lisa Scott were incorporated in

this paper, and we are thankful for their advice. This

research was sponsored in part by Ofﬁce of Naval Re-

search Grant #N00014-07-1-0009.

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APPENDIX

This Appendix contains the mathematical details for

the internal and external processes in Section 2.1.

The bounding function σ is deﬁned as:

σ(x) =







0 if x < 0

x if x ∈ [0, 1]

1 if x > 1

In the following, ν(∈ [−0.05, 0.05]) denotes the

uniform noise that is different for every signal at each

time step t.

The internal processes in the NepS are computed as

follows:

S - stress

S(t) =











σ[1 − (1 − S

) · e

−β

·d

+ ν] if G > 0

σ[S(t − 1) + ν] if G = 0

σ[S

· e

−γ

·d

+ ν] if G < 0

DRUG ADDICTION: A COMPUTATIONAL MULTISCALE MODEL COMBINING NEUROPSYCHOLOGY,

COGNITION AND BEHAVIOR

where t

is the time of last change of sign of G; S

is the value of S(t

); β

is the exponential constant

of S when G > 0; γ

is the exponential constant of S

when G < 0; d is the number of steps after t

; d ∈ N;

S ∈ [0, 1].

P - pain

P(t) =











σ[P

· e

−β

·d

+ ν] if G > 0

σ[P(t − 1) + ν] if G = 0

σ[1 − (1 − P

) · e

−γ

·d

+ ν] if G < 0

where t

is the time of last change of sign of G; P

is the value of P(t

); β

is the exponential constant

of P when G > 0; γ

is the exponential constant of P

when G < 0; d is the number of steps after t

; d ∈ N;

P ∈ [0, 1].

D - dopamine related craving

D(t) =











σ[1 − (1 − D

) · e

−β

·d

+ ν] if G > 0

and d ∈ [1, τ]

σ[D

· e

−β

·d

+ ν] if G > 0

and d > τ

σ[D(t − 1) + ν] if G = 0

σ[1 − (1 − D

) · e

−γ

·d

+ ν] if G < 0

where t

is the time of last change of sign of G; D

is the value of D(t

); τ is the number of time steps

in which the dopamine related craving increases after

there is no drug consumption; D

is the value of D(t)

at t = τ; β

is the exponential constant of D when G >

0; γ

is the exponential constant of D when G < 0; d

is the number of steps after t

; d ∈ N; D ∈ [0, 1].

q - saliency to drug cues

q(t) =











σ[q(t − 1) + ν] if {G > 0

and d ∈ [1, τ]}

or if G = 0

σ[q

· e

−β

·d

+ ν] if G > 0

and d > τ

σ[1 − (1 − q

) · e

−γ

·d

+ ν] if G < 0

where t

is the time of last change of sign of G; q

is the value of q(t

); τ is the number of time steps in

which saliency to drug cues does not decrease even

that there is no drug consumption; q

is the value of

q(t) when t = τ; β

is the exponential constant of

q when G > 0; γ

is the exponential constant of q

when G < 0; d is the number of steps after t

; d ∈ N;

q ∈ [0, 1].

The external processes in the NepS are computed as

follows:

- acute shock

(t) =











if {G > 0

and b

(t) = 1}

or t

∈ [1, τ

]

· A

(t − 1) if t

∈ [τ

, τ

]

0 else

where b

(t) is a Boolean variable ∈ {0, 1}; b

(t) = 1

means that a shock begins at time t; A

is a constant;

is a constant < 1; t

is the starting time of a shock;

∈ N is the number of steps after t

; τ

is the number

of time steps in which the shock effect is constant; τ

is the number of time steps in which the shock effect

is decreasing (τ

> τ

); A

∈ [0, A

and A

- acute trauma and acute priming to

drugs

The signals A

, A

, and A

are mathematically very

similar. The main difference is that an event A

can

start only when G < 0, but events A

and A

can start

only when G > 0.

Q - encountering drug cues

Q(t) =











q(t) if b

(t) = 1

Q(t − 1) if t

∈ [1, τ

]

· Q(t − 1) if t

∈ [τ

, τ

]

0 else

where b

(t) is a Boolean variable ∈ {0, 1}; b

(t) = 1

means that a cue begins at time t; ρ

is a constant > 1;

is the starting time of a cue; t

∈ N is the number of

steps after t

; τ

is the number of time steps in which

the cue effect is constant; τ

is the number of time

steps in which the cue effect is decreasing (τ

> τ

);

Q ∈ [0, ρ

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing