Addiction assignment

Instructions attached as well as i have already included journal entries. Make sure proper APA format and guidlines are done and read instructions carefully!! This is due tomorrow no later then noon.

Complete a 3–5-page in current APA format about cocaine addiction. The paper should address possible causes of the addiction as well as the prevalence and potential treatments. The paper must include at least 3 outside sources (not including the textbooks) from current professional journals (published within the last 5 years) which I have attached. Make sure all correct APA format is followed with any web site address and page numbers so I can verify all information.

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Expanding Treatment Options for Cocaine Dependence
Brady, Kathleen T, MD, PHD
The American Journal of Psychiatry; Nov 2009; 166, 11; ProQuest
pg. 1209

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Cocaine addiction and personality:
A mathematical model

Antonio Caselles1*, Joan C. Micó2 and Salvador Amigó3
1Departament de Matemàtica Aplicada, Universitat de València, Spain
2Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de
València, Spain

3Departament de Personalitat, Avaluació i Tractaments Psicològics, Universitat de
València, Spain

The existence of a close relation between personality and drug consumption is
recognized, but the corresponding causal connection is not well known. Neither is it
well known whether personality exercises an influence predominantly at the beginning
and

development of addiction, nor whether drug consumption produces changes in

personality. This paper presents a dynamic mathematical model of personality and
addiction based on the unique personality trait theory (UPTT) and the general
modelling methodology. This model attempts to integrate personality, the acute effect
of drugs, and addiction. The UPTT states the existence of a unique trait of personality
called extraversion, understood as a dimension that ranges from impulsive behaviour
and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert
pole). As a consequence of drug consumption, the model provides the main patterns
of extraversion dynamics through a system of five coupled differential equations.
It combines genetic extraversion, as a steady state, and dynamic extraversion in

unique variable measured on the hedonic scale. The dynamics of this variable describes
the effects of stimulant drugs on a short-term time scale (typical of the acute effect);
while its mean time value describes the effects of stimulant drugs on a long-term
time scale (typical of the addiction effect). This understanding may help to develop
programmes of prevention and intervention in drug misuse.

1. Introduction

Personality is a major explanatory factor in understanding the start and development

of drug addiction. Various personality factors have been considered as precedents
for addiction, such as impulsiveness and nonconformism (Kandel, 1978) and

sensation-seeking (Zuckerman, 1994), or as factors related to addiction itself, such as

* Correspondence should be addressed to Professor Antonio Caselles, Departament de Matemàtica Aplicada,
Universitat de València, Dr Moliner 50, 46100 Burjassot, Valencia, Spain (e-mail: antonio.caselles@uv.es).

The
British
Psychological
Society

449

British Journal of Mathematical and Statistical Psychology (2010), 63, 449–480

q 2010 The British Psychological Society

www.bpsjournals.co.uk

DOI:10.1348/000711009X470768

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neuroticism and psychoticism (King, Enrico, & Parsons, 1995; Nishith, Mueser, &

Gupta, 1994). There are also signs that drug consumption can change personality

(Trull & Sher,

1994).

A set of studies show the existence of a broad latent factor with a large genetic

component called labelled externalizing, which would explain the co-occurrence of

antisocial conduct disorders and drug dependence, and the disinhibitory personality
trait (Dick, Viken, Kaprio, Pulkkinen, & Rose, 2005; Jang, Vernon, & Livesley, 2000;

Krueger et al., 2002; Young, Stallings, Corley, Krauter, & Hewitt, 2000). This is a

hierarchical model that defines the externalizing spectrum, which links normal

personality with psychopathology.

Other studies also established the relationships between normal personality and

psychopathology (Trull & Sher, 1994). Since they deal with cross-sectional studies of

unrelated persons, however, it is not possible to state causal connections between

personality and psychopathology (Nathan, 1988; Tarter, 1988).
The existence of a close relationship between personality and drug consumption

is recognized, but the corresponding causal connection is not well known. None of

the aforementioned studies clarifies this relationship. Neither is it well known

whether personality exercises an influence predominantly at the beginning and

development of addiction, nor whether drug consumption produces changes in

personality. Thus, studying in depth the connection between personality and

addiction is an important challenge in understanding the phenomenon of addiction.

This understanding may help to develop programmes of prevention and intervention
in drug misuse.

System-inspired models of personality – such as the individuality theory (Royce

& Powell, 1983) and Pelechano’s parameter model (Pelechano, 1973, 2000) – can

be found in the specialized literature. On the other hand, mathematical models

based on the systems dynamics to explain alcohol consumption (Warren, Hawkins,

& Sprott, 2003), nicotine addiction (Fan & Elketroussi, 1989; Gutkin, Dehaene, &

Changeaux, 2006), biochemical effects of cocaine (Nicolaysen & Justice, 1988),

addiction as a neuropharmacological and learning process (Redish, 2004), and the
economic models of addiction (Becker & Murphy, 1988; O’Donoghue & Rabin,

1999) can also be found. These models involve psychological variables such as

decision-making or self-control, but they do not use personality traits. Thus, a

dynamic model that integrates the effects of personality and addiction has yet to be

presented in the specialized literature.

In this paper, a dynamic model that studies the relationship between personality

and drug addiction is presented, based on the unique personality trait theory (UPTT;

Amigó, 2005). The UPTTattempts to integrate personality, the acute effect of drugs, and
addiction and, therefore, appears to offer a way forward in the study of the

aforementioned relation between personality and drugs. Following empirical studies

(Amigó, 2002; Amigó & Seshadri, 1999) on the relation between personality and drug

consumption, Amigó (2005) revises the principal theories about temperamental

personality traits (of biological nature), and the empirical, theoretical, and

neurobiological evidence of Eysenck’s and Gray’s approach (Eysenck & Eysenck,

1985; Gray, 1972, 1981, 1982). As a consequence of this review, Amigó proposes that

anxiety and impulsivity are the two poles of a single dimension called extraversion
which is the most basic and fundamental trait of the hierarchy of personality traits.

This trait of extraversion (with its poles of impulsivity, extraversion and high

psychoticism on the one hand and anxiety, introversion and low psychoticism on the

450 Antonio Caselles et al.

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other) is a unique (understood as the most basic and fundamental) personality trait.

Thus, the word extraversion is used to denote a continuous extraversion–introversion

dimension, following a convention proposed by Eysenck which is widely accepted

today. Thus, extraversion is a similar factor to the above-mentioned labelled

externalizing factor, although it is an integrator factor of complete personality, which

in its own definition, considers both the externalizing component and the internalizing
one (on the internalizing spectrum, see Blonigen, Hicks, Krueger, Patrick, & Iacono,

2005; Widiger & Clark, 2000).

Amigó, Caselles, and Micó (2008) study the relationship between personality

dynamics and the acute effect of a single stimulant drug (cocaine) intake. Thus, the

model presented herein is an extension of that study that considers repeated drug

consumption leading to addiction.

Stimulant drug addiction requires repeated consumption. A different effect of

sensitization or drug habituation can be observed depending on the consumption
pattern. For instance, Dalia et al. (1998) administered intermittent cocaine injections

(40mg kg21 at 3-day intervals) to rats, observing a sensitization response to a challenge

dose (7.5mg kg21). Later, they implanted an osmotic pump into the rats that released

cocaine continuously (80mg kg21 day21) for 7 days. Habituation was observed as a

consequence of a challenge dose 1 day after removing the pump.

With respect to the simulations carried out with the suggested model and

reported in this paper, a hypothetical (and, obviously, very atypical) strong cocaine

addiction with a constant drug consumption per week is simulated in order to
confirm that the model reproduces the three classical phases of the addictive process

independently of the drug intake pattern. Finally, the following time pattern

with three separate phases is simulated in the context of our model: (1) a

progressive and intermittent increase of doses which produces sensitizing; (2) a large

and continuous increase of doses which produces habituation; and (3) a slow return

to genetic extraversion due to the abandonment of the drug consumption or, in the

context of a ‘limit’ consumption pattern, due to the null effect caused by the

cocaine consumption. The results of such simulations are expected to be in
accordance with those described in the cited literature (which is the case and is

demonstrated below).

Drug-seeking behaviour has not been modelled at this stage. This is another problem

that merits a specific study. Thus, we restrict the objectives of the modelling process

to try to reproduce the excitation dynamics described in the literature, that is, to build

a model explaining sensitization as a result of discontinuous drug intake in the

first stages of the addiction process and, habituation as a result of continuous drug

intake in the late stages of the addition process (for a review, see Gawin, 1991; Goudie &
Emmett-Oglesby, 1991; Johanson & Fischman, 1989; Martin-Iverson & Burger, 1995;

Morgan & Roberts, 2004).

In the context of the UPTT, the tonic activation level (or basal activation level),

which is the genetic activation level and takes place in the organism in a repose state, is

distinguished from the phasic activation level, which occurs as the response to a

determined stimulus such as a drug unit dose. On the short-term time scale (typical of

the acute effect of a stimulant drug), the extravert presents a lower tonic activation

level

and a stronger (longer in time and higher in activation level) phasic activation level than
the introvert, whose tonic activation level is higher and who has a weaker phasic

activation level (Amigó, 2005; Amigó et al., 2008). On the long-term time scale (typical

of addiction), the pattern of consumption is such that a lower and intermittent

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consumption precedes a higher and continuous consumption. The first intakes in the

first phases of this consumption pattern (lower and intermittent) produce a high phasic

activation level which makes the return to the tonic activation level easy; whereas the

last phases of this consumption pattern (higher and continuous) produce a high tonic

activation level, before each intake, which makes the return to the initial value before

consumption difficult (see Grace, 1995, 2000). Thus, an evolution from extraversion to
introversion occurs. In other words, a change of personality happens as the

consumption pattern develops in time, in such a way that a change in the consumption

habits generates a change of personality, and at the same time a change of personality

generates a change in the consumption habits, as Trull and Sher (1994) point out (but

without considering dynamics). The main goal of this paper is to present a dynamic

mathematical model of personality and addiction that mathematically describes such an

interrelation and co-evolution, and to use this model to simulate different seemingly

realistic scenarios, which include a possible strategy for intervention in drug misuse.
The dynamic model (referred to henceforth as DBRAIN), has been obtained by

following the general modelling methodology (GMM) (Caselles 1992, 1993, 1994,

1995) within the general systems theory context that he also developed. This

methodology consists of 10 stages (Caselles, 1994) which do not run sequentially, rather

natural feedback processes take place among them. With these 10 steps, Caselles

generalized the scientific method, or the hypothetico-deductive method, with a view to

adapting it to complex systems modelling. Generally, an interdisciplinary approach is

needed to understand such systems, which also applies to our case, and the model
validation in these systems may prove difficult, or even impossible, given the design of

experiments within the real system that are needed. Furthermore, a model may only

come about through differences in experts’ opinions (which often come to light in

the scientific literature). In this way, once the model has been validated and computer-

programmed, it may be used to perform the simulations required to solve the problems

raised (this may be interpreted as the model being used to design experiments).

The basic structure of variables and interrelations of the dynamic model of

personality and addiction presented in this paper arises from the UPTT. Following the
GMM, DBRAIN has been obtained as a system of five coupled differential equations for

five state variables: the non-absorbed drug in the body, the drug level in the body, the

power of the excitation effect, the power of the inhibitor effect, and the

activation level.

In addition, extraversion and activator effect are dynamic variables involved in

DBRAIN and are computed, respectively, as the mean values for each time instant of

the activation level and of the drug level in the body. The simulations performed using

DBRAIN demonstrate that the time patterns reported by the UPTT (previously

described) to explain the dynamics of extraversion hold, i.e. these simulations
reproduce such dynamics.

Finally, the dynamic model presented by Amigó et al. (2008) is a simplification of

the model presented herein, being restricted to the case in which a single drug unit

dose is considered (so that addiction is not studied). Moreover, this work can be

considered the closest work to that presented herein.

The proposed model (DBRAIN) has the following intuitive structure:

(1) Cocaine intake remains in the nose for a period while it is distributed and enters
the blood.

(2) Then it produces a stimulant effect that depends on the extraversion of the

individual and on the stimulant power of the drug.

452 Antonio Caselles et al.

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(3) The stimulant effect increases the excitation of the brain.

(4) The excitation of the brain induces a short-term homeostatic effect, a long-term

(delayed) depressive effect, and modifies the instantaneous extraversion of the

individual.

(5) The depressive effect also depends on the depressive power of the drug.

(6) The stimulant power, the depressive power, and the delay of the depressive

power

vary depending on the past history of drug intakes.

Figure 1 shows the proposed structure in a little more detail, and Figure 2 will complete

the necessary details when variables, equations, and parameters are introduced.

Such a structure is inspired by the works of Amigó et al. (2008), Grossberg (2000),

Solomon and Corbit (1974), and by the literature on the genetic regulation of brain

activity (see, for instance, Beretta, Robertson, & Graybiel, 1992; Colby, Whisler, Steffen,

Nestler, & Self, 2003; Hiroi et al., 1998; Hyman, 1996; Torres & Rivier, 1993; Werme
et al., 2002; Young, Porrino, & Iadarola, 1991), and is obtained after a long trial and error

process proceeding from the idea that the model reproduces the three phases of the

addiction process (sensitization, habituation, and return) suggested by Amigó (2005),

Gutkin et al. (2006), and Redish (2004) after repeated drug intakes and stopping. The

parameters of the model have to be able to be adjusted to a given individual, and the

model has to be useful to determine the optimal dose and delay between consecutive

doses of cocaine (or alternative drug) that make the return phase as short and

comfortable as possible for the drug addict.
The rest of this paper is organized as follows. The stimulus is modelled in

Section 2 by integrating the two coupled differential equations corresponding to the

variables non-absorbed drug in the body and drug level in the body. The time

function of the stimulus corresponds to the second of these variables. Therefore,

this function is the so-called input variable of the addiction module formed by

three coupled differential equations which correspond to the rest of the variables

involved. These equations are determined in Section 3. The results of the

simulations carried out with the model, designed to validate the model by contrast

Figure 1. Structure implicit in the proposed model (dashed arrows denote influence).

Cocaine addiction and personality 453

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with the existing literature and to try out a strategy of intervention, are shown in

Section 4, as are the conclusions reached from the simulations. A general discussion

is provided in Section 5.

2. Stimulus equation

Before presenting a complete description of DBRAIN in Section 3, we focus on the

dynamics of the stimulus produced by a stimulant drug. Two state variables are involved

in the dynamics of the stimulus (Amigó et al., 2008): non-absorbed drug in the body,

c(t), or the amount of drug present that is not distributed at instant t in the organism (for

instance, cocaine powder in the nose); and drug level in the body, s(t), or the amount of
drug in plasma being consumed by cells at the same instant t (see Figure 2 for the

structure of relations between these variables). We suppose that the variable s(t)

produces the organism’s acute response to the drug, and is therefore representative of

the stimulus. Previous studies on the effect of different stimulant drugs in animals and

humans (see, for instance, Fowler et al., 2008; Kufahl, Rowe, & Li, 2007; Tsibulsky &

Norman, 2005) suggest that the time needed for cocaine to reach the brain is very short

(about 4min to the highest concentration). Thus, given that our study is concerned with

addiction, and addiction is a matter of months, such an elapsed time may be considered
negligible. Furthermore, Javaid, Musa, Fischman, Schuster, and Davis (1983) confirm

that ‘After intranasal administration, cocaine kinetics conform to a one-compartment

model with first-order absorption and first-order elimination’. Consequently, and in

order to simplify the model, we assume that the difference in drug concentration

between plasma and brain is not significant at the time scale considered, and adopt a

one-compartment pharmacokinetic model.

Let us assume that a number N of repeated drug unit doses occur with doses

M1;M2; : : : ;MN , respectively, at instants t1; t2; : : : ; tN , after an initial instant t0 $ 0, so
that ti21 , ti, i ¼ 1; 2; : : : ;N . The variation of c(t) with time is caused by a flow that
makes c increase A(t), produced by the repeated drug unit dose, and also by a flow that

makes c decrease produced by the drug being distributed in plasma, C(t), that is:

dcðtÞ
dt

¼ AðtÞ2 CðtÞ;

cðt0Þ ¼ c0;
ð1Þ

where c0 is the amount of non-absorbed drug at the initial instant t0.
On the one hand, A(t) has the following structure:

AðtÞ ¼
Mi; t ¼ ti;
0; t – ti;

(
i ¼ 1; 2; : : : ;N : ð2Þ

On the other hand, if we assume that the drug distribution occurs at a constant rate

(the absorption rate constant), a . 0, for each instant we obtain:

CðtÞ ¼ acðtÞ: ð3Þ

The absorption rate constant is a parameter that depends on each individual. The

variation of s(t) over time is given by the same distribution flow in plasma C(t), which is

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now a growth flow, and by another reducing flow which would represent the drug

elimination, R(t), that is:

dsðtÞ
dt

¼ CðtÞ2 RðtÞ;

sðt0Þ ¼ s0:

ð4Þ

Let us assume that there is a level s0 of drug in the body at the initial instant, just as the

initial condition of (4) indicates. Let us furthermore assume that the elimination from

plasma is proportional to the level of the drug in the body with an elimination rate
constant b . 0. Then

RðtÞ ¼ bsðtÞ: ð5Þ

The elimination rate constant is also a parameter that depends on each individual. By

substituting (2) in (1) and (5) in (4), we obtain a system of two coupled differential

equations:

dcðtÞ
dt

¼ AðtÞ2 acðtÞ;

dsðtÞ
dt

¼ acðtÞ2 bsðtÞ;

sðt0Þ ¼ s0;
cðt0Þ ¼ c0:

ð6Þ

In (6), function A(t) is structured as in (2). In order to obtain the solution s(t) (which

represents the desired time function of the drug level in the body), we can break down

system (6) into N þ 1 subsystems which correspond to each of the intervals ½ti; tiþ1�,
0 # i # N . At each initial instant of every interval, the initial condition for c(t) will be
the amount of non-absorbed drug present in the organism at this instant, c(ti), plus the
new drug dose intake at instant ti, Mi. Specifically, for the initial interval ½t0; t1�, which
has no new intake (M0 ¼ 0), the corresponding subsystem is:

dcðtÞ
dt

¼ 2acðtÞ;

cðt0Þ ¼ c0;
dsðtÞ
dt

¼ acðtÞ2 bsðtÞ;
sðt0Þ ¼ s0:

ð7Þ

The solution of (7) for c(t) and s(t) with t [ ½t0; t1� is:

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ; ð8Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ; ð9Þ

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where

vðtÞ ¼

b2 a
ðexpð2atÞ2 expð2btÞÞ b – a;

at expð2atÞ b ¼ a:

8>< >: ð10Þ

The intake, M1, of a new dose (the first intake after the initial situation) is produced at
instant t ¼ t1. The amount of still non-absorbed drug present in the organism at this
instant is cðt1Þ ¼ c0 expð2aðt1 2 t0ÞÞ plus the first intake dose M1, while the amount of
drug level in the body and that being consumed by the cells is

sðt1Þ ¼ s0 expð2bðt1 2 t0ÞÞ þ c0vðt1 2 t0Þ. Both values represent the initial conditions
of c(t) and s(t), respectively, in the following subsystem, valid for interval ½t1; t2�, as
shown by the following equations:

dcðtÞ
dt
¼ 2acðtÞ;

cðt1Þ ¼ c0 expð2aðt1 2 t0ÞÞ þ M1;
dsðtÞ
dt

¼ acðtÞ2 bsðtÞ;

sðt1Þ ¼ s0 exp ð2bðt1 2 t0ÞÞ þ c0vðt1 2 t0Þ;

ð11Þ

whose solution for t [ ½t1; t2� is

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ þ M1 expð2aðt 2 t1ÞÞ; ð12Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ þ M1vðt 2 t1Þ: ð13Þ

If we reason by induction for the drug intake 1 # j # N with t [ ½t0; tjþ1�, we obtain
the time functions c(t) and s(t) we were looking for:

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ þ
Xj
i¼

Mi expð2aðt 2 tiÞÞ; ð14Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ þ
Xj
i¼1

Mivðt 2 tiÞ: ð15Þ

Solutions (14) and (15) are valid for any t $ tN, that is, for the last consumption intake if
j ¼ N , and they represent the corresponding time functions after the drug addict stops

consuming permanently.

Let us go on to specify a consumption intake pattern that is more closely linked to a
real consumer. For this purpose, we first have to consider a simple case in which the

consumer takes a constant drug dose M with a certain frequency T . 0 as from the
initial instant t0. If he/she takes the drug N times, he/she will do so at the instants

tj ¼ t0 þ jT , 1 # j # N , and for time lasting NT starting from the instant of the first
intake. In this case, the time functions (14) and (15) corresponding to intake 1 # j # N ,

456 Antonio Caselles et al.

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are rewritten with t [ ½t0; t0 þ ð j þ 1ÞT �, as

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ þ M
Xj
i¼1

expð2aðt 2 tiÞÞ; ð16Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ þ M
Xj
i¼1

vðt 2 tiÞ: ð17Þ

For the final intake, that is if j ¼ N, solutions (16) and (17) are valid for any t $ t0 þ TN.
They also represent the corresponding time functions after the drug addict stops

consuming permanently.

An even more realistic case is obtained by generalizing the final intake. Under normal

circumstances, the drug taker takes a constant M0 dose N0 times, with a frequency of

T 0 . 0, for a period of duration N0T0. In a second subsequent period of N1T1 duration,
the drug taker consumes a constant M1 dose which is equal to or greater than the former

with a lower consumption frequency (T 1 , T 0). Then he/she continues with a similar
consumption pattern for n different periods of NjTj duration, with Mj $ Mjþ1 and
T j , T jþ1, j ¼ 0; 1; 2; : : : ;n 2 1, n . 0. This way, the drug taker will improve the
agreeable effects of the first intakes during a first phase (the sensitization phase),

although he/she will unsuccessfully attempt to reproduce these first phase agreeable

effects at a second phase. At the habituation phase, the drug taker will even notice

a progressive worsening of such effects in relation to the first phase. Finally, this
individual will become an addict after a period of NnTn duration, during which he or

she will hardly reproduce any agreeable effect no matter how much the dose or

frequency is increased.

Let us thus assume that we are in period j ¼ 0; 1; : : : ;n 2 1, characterized by a
number Nj of intakes, with a Tj frequency and constant Mj doses. Let us consider any

arbitrary ij consumption in this period (ij ¼ 1; 2; : : : ;Nj). Suppose we have defined
Hj21, the time which has elapsed from t0 to the beginning of period j:

Hj21 ¼
0 j ¼ 0;Pj21
r¼0 NrTr j . 0:

(
ð18Þ

Then the time functions c(t) and s(t) for t [ ½t0 þ Hj21 þ ijT j; t0 þ Hj21 þ ðij þ 1ÞT j�
will be expressed as

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ þ
Xj
k¼0

Mk
Xij
ik¼0

expð2aðt 2 ikTk 2 Hk21 2 t0ÞÞ; ð19Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ þ
Xj
k¼0

Mk
Xij
ik¼0

vðt 2 ikTk 2 Hk21 2 t0Þ: ð20Þ

For the final intake (if j ¼ n 2 1 and in21 ¼ Nn21), solutions (19) and (20) are valid
for any t $ t0 þ

Pn21
j¼0 T jNj, and represent the corresponding time functions after the

drug taker, now considered an addict, stops consuming permanently (the return phase).

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3. The dynamic addiction module

The UPTT asserts that the stress system is the biological basis for the unique trait

extraversion. Let the activation level variable and the extraversion variable be the
dynamic variables representative of extraversion as a trait. Both variables are measured

on the hedonic scale. (The ranges assumed for these and other variables of the model are

shown in Table 1.) Why two variables and not one? Because each plays its own role at

Table 1. Model variables: State variables in bold along with their initial conditions

Parameters, input variables,

and output variables

Value attributed

to characteristics of Symbol Dimensions

Range

(assumed)

Drug unit dose Individual M M [0,120]

Resistance time Drug and individual tm T [0,10
5]

Delay reducing rate Drug and individual w T21 [0,20]
Absorption rate constant Drug and individual a T21 [0,1]

Elimination rate constant Drug and individual b T21 [0,1]
Tonic or basal activation level Individual b AU [0,20]

Homeostatic control rate Drug and individual a T21 [0,1]

Rate of increase of the

excitation

effect power

Drug and individual g AU2 T22 M22 [0,20]

Rate of decrease of the

excitation effect power

Drug and individual d T21 [0,20]

Rate of increase of the inhibitor

effect power

Drug and individual 1 AU21 T22 M22 [0,1]

Rate of decrease of the inhibitor

effect power

Drug and individual h T21 [0,1]

Consumption rate Individual decision A(t) MT21 [0,1500]

Absorption rate Equations C(t) MT21 [0,1500]

Ingested and non-absorbed
drug

Equations,

individual decision

c(t), c0 M [0,1500]

Elimination rate Equations R(t) MT21 [0,1500]

Drug level in the body Equations. initial value s(t), s0 M [0,1500]
Activator effect Equations S(t) M [0,20]

Homeostatic control Equations B(t) AUT21 [0,20]

Excitation effect Equations X(t) AUT21 [0,20]

Inhibitor effect Equations D(t) AUT21 [0,20]

Excitation–inhibitor balance Equations X(t) 2 D(t) AUT21 ½210; 10�
Activation level Equations, initial value y(t), y0 AU [0,20]
Extraversion Equations E(t) AU [0,20]

Increase of the excitation

effect power

Equations IP(t) AUM21 T22 [0,20]

Reduction of the excitation

effect power

Equations RP(t) AUM21 T22 [0,20]

Excitation effect power Equations, initial value p(t), p0 AUM
21 T21 [0,20]

Delay Equations, initial value t(t), t0 T [0,50]
Increase of the inhibitor

effect power

Equations IQ(t) AU21 M21 T22 [0,20]

Reduction of the inhibitor

effect power

Equations RQ(t) AU21 M21 T22 [0,20]

Inhibitor effect power Equations, initial value q(t), q0 AU
21 M21 T21 [0,1]

Note. AU, activation units on the hedonic scale; M, drug unit dose; T, time.

458 Antonio Caselles et al.

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each time scale: the activation level on the short-term time scale (typical of the acute

effect of a drug unit dose), and extraversion on the long-term time scale (typical of

addiction), although both are involved in the dynamics of the two time scales.

Biologically, the activation level variable represents the instantaneous state of the brain

(on the hedonic scale). The extraversion variable is defined as the mean value, at each

time instant, of the activation level variable, and thus has a cumulative sense. In other
words, the extraversion variable is interpreted here as the ‘mean perception’ of the

activation level over time. In addition, the extraversion variable, thus defined, behaves

by the UPTT for the extraversion dynamics as expected.

The UPTT states the existence of a genetic extraversion particular to each individual

that characterizes his or her natural personality, in the absence of any stimuli that can

change it. To put it quantitatively, the activation level variable must have a value that is a

steady state. This steady state is the so-called tonic (or basal ) activation level. Due to

the definition of the extraversion variable as the mean value that takes into account all
the past history at each time instant of the activation level variable, the tonic level is also

a steady state of the extraversion variable.

Given that two variables are defined as mean instantaneous values that take into

account all the corresponding past history (the extraversion variable and the activator

effect presented below), let kz(t)l be an arbitrary mean value of a generic z(t) variable.
This is given by

zðtÞh i ¼ lim
tm!þ1

t þ tm

ðt
2tm

zðxÞdx: ð21Þ

In equation (21), tm is called the memory time and, although theoretically it recovers all

the history of the z(t) variable, in practice it is represented by a finite value (the value

tm ¼ 1 year has been obtained as a result of the calibration of the model). In addition, if
t0 is the initial time, the values that z(t) takes before this time depend on its own nature.
If z(t) is the mean value of the amount of drug in the blood (the activator effect),

zðt , t0Þ will be zero, because we assume that the individual has never consumed
cocaine before, and he/she does not have any history of cocaine in blood. If z(t) is the

mean value of the activation level (the extraversion variable), zðt , t0Þ will be its tonic
value, because we assume that the individual has never consumed cocaine or other

drugs before, and its activation level remains around its tonic level. From a physiological

point of view, our hypothesis is that the finite value given to tm represents the time that

brain recalls when faced with the effects of new drug unit doses. This is why we have
named tm the memory time.

Let y(t) be the activation level, such that t [ ½t0;þ1½, and let yðt0Þ ¼ y0
be its initial condition, i.e. the activation level prior to the stimulus produced by

the first stimulant drug unit dose. Therefore, the extraversion, E(t), is defined

according to (21) as EðtÞ ¼ yðtÞh i, with yðtÞ ¼ b when t , t0 and b . 0 the tonic level
of y(t).

The UPTT states that extraversion can vary with time due to the effect of drug

consumption. The variation of extraversion with time as a consequence of drug
stimulus is examined here by studying the flows that influence the derivative of

the activation level variable with respect to time. Three flows have been considered

(Amigó et al., 2008) in the variation process of the activation level once a stimulus

is produced: the excitation effect, X(t), considered as a growth flow; the inhibitor

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effect, D(t), considered as a reducing flow; and the homeostatic control, B(t),

considered as a neutral flow. We have

dyðtÞ
dt

¼ BðtÞ þ XðtÞ2 DðtÞ;

yðt0Þ ¼ y0:

ð22Þ

Following the UPTT, the dynamics of extraversion depends on its genetic value, that

is, on the tonic level. Let b . 0 be the parameter that represents it. Its value on the
hedonic scale depends on each individual’s biology, and it determines the individual’s

personality in the absence of drug use. Furthermore, the initial value of the activation

level y0 must coincide with the tonic level b in repose conditions, or in the absence

of stimuli that are specific to a substantial change of the brain’s state. The

dependence on the tonic level is present in our approach in the mathematical
structure of the homeostatic control:

BðtÞ ¼ aðb 2 yðtÞÞ: ð23Þ

Equation (23) has been taken directly from Grossberg (2000). Its mathematical structure

shows that, in the absence of the other two flows, a small variation of y(t) in (22) with

respect to the tonic level y ¼ b produces a response that tends asymptotically to the
steady state. Thus, in absence of the other two flows, the tonic level behaves as a real

steady state. However, we observe in the simulations that, also in the presence of the

other flows, the tonic level behaves as a steady state. In (23), the positive parameter a,
known as the homeostatic control rate, depends on each individual’s biological

characteristics, exactly as the b value does.

In relation to the excitation effect, we assume the following functional dependence:

XðtÞ ¼ pðtÞsðtÞ
EðtÞ : ð24Þ

In (24), s(t) is the stimulus, the drug level in the body obtained in (20). The p(t) variable

is called the excitation effect power. Therefore, on the one hand, we are assuming that

the excitation effect is directly proportional to the stimulus, with p(t) as proportionality
variable, since the greater the stimulus, the greater the excitation. On the other hand,

the inverse dependence of X(t) on E(t) in (24) must be explained. On the short-term

time scale, the most representative variable of extraversion is the activation level. The

dynamics of this time scale has to be reproduced, i.e. if the effects on the activation level

have to be higher for smaller values of the tonic level and vice versa then an inverse

dependence on the tonic level should occur. That could be explained from the

tonic/phasic model of the dopamine regulation system (Grace, 1995, 2000). Thus, the

functional dependence should be XðtÞ ¼ pðtÞsðtÞ=b. Nevertheless, the real activation
after some drug unit doses is not given by the genetic activation, but by the mean

activation E(t), and then (24) holds.

The time-dependence of the proportionality variable, the excitation effect power

p(t), must also be explained. We suppose that the variation with time of p(t) depends

on two flows: IP(t), or increase of the excitation effect power, and RP(t), or reduction

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of the excitation effect power, expressed as

dpðtÞ
dt

¼ IPðtÞ2 RPðtÞ;

pðt0Þ ¼ p0:
ð25Þ

The initial value p0 should depend on each individual’s biology. On the other hand, and

in order to model sensitization, IP(t) has been considered to be proportional to the so-

called activator effect S(t), defined as the mean instantaneous value of the drug level in

the body. So, IP(t) and S(t) would be

IPðtÞ ¼ gSðtÞ;
SðtÞ ¼ sðtÞh i;
SðtÞ ¼ sðtÞ ¼ 0; t , t0;

ð26Þ

where g is the elevating rate of the excitation effect power. Otherwise, RP(t) is
assumed proportional to p(t), which means it loses part of the excitation effect power at

each instant, contributing to model the habituation phase:

RPðtÞ ¼ dpðtÞ; ð27Þ

where d is the reducing rate of the excitation effect power. If we substitute (26) and (27)
in (25), we obtain

dpðtÞ
dt

¼ gSðtÞ2 dpðtÞ;

pðt0Þ ¼ p0:
ð28Þ

Both g and d are parameters whose values also depend on the biology of
each individual. The previous assumptions are based on well-known genetic regulation

mechanisms. Thus, p(t) would represent the number of D1, AMPA, and NMDA synaptic

receptors, the increase of such receptors IP is proportional to the activator effect S

(comparable with dopamine and glutamate, which increase is a consequence of the

average drug level in the body), the decrease of such receptors RP comes from feedback
loops implying the regulator genes Fos and GluR2 among others. The delays implied in

the starting of such mechanisms are represented in the model by t(t) and tm. (See, for
instance, Beretta et al., 1992; Hyman, 1996; Torres & Rivier, 1993; Young et al., 1991).

For the inhibitor effect, D(t), we assume the following functional dependence:

D ðtÞ ¼
qðtÞEðt 2 tðtÞÞsðt 2 tðtÞÞyðt 2 tðtÞÞ t . t0 þ tðtÞ;

0 t # t0 þ tðtÞ:

(
ð29Þ

Equation (29) is a generalization of the equatioin proposed by Grossberg (2000), which
supposes that the inhibitor effect D(t) is equal to the product of the drug level in the

body s(t) and the activation level y(t). Note that our proposal is more complex. We have

considered the inhibitor effect D(t) to be directly proportional to the product of the

mean activation E(t), the activation level y(t), and the drug level in the body s(t). The

proportionality variable, q(t), is called the inhibitor effect power. In addition,

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the functional dependence of the inhibitor effect appears with a delay variable, t(t),
such as the opposing process theory by Solomon and Corbit (1974) proposes.

The reason for introducing the direct mean activation dependence is similar to

the reason used in the excitation effect case: following the UPTT, if the effects on

the activation level have to be higher for smaller values of the tonic level and vice

versa, a direct dependence on the tonic level should occur. Thus, in the present
case, the functional dependence should be DðtÞ ¼ qðtÞbsðtÞyðtÞ. Nevertheless, the
real activation after some drug unit doses is not given by the genetic activation b,

but by the mean activation E(t), so that DðtÞ ¼ qðtÞEðtÞsðtÞyðtÞ. This assumption
lends stranger support to the mathematical role of the memory time, tm: again,

tm allows E(t) to behave as the tonic activation b does in the first intake.

Furthermore, in the context of the opposing process theory of Solomon and Corbit

(1974), the inhibitor effect appears with a delay after a drug unit dose. Biologically,

this delay represents the time that long-term regulator genes need to produce
regulation effects and it may differ from person to person (Nestler, 2001). This

delay, t(t), is a variable that depends on time because we assume that it depends
on the mean amount of drug present in plasma in each instant, i.e. on the activator

effect S(t). If we consider this delay in the time-dependence on E(t), s(t), and y(t)

then equation (29) holds.

The variation of the delay variable with time must be such that, on the one hand,

it remains equal to its initial value, t0, while the activator effect is close to zero, and,
on the other hand, for very high values of the activator effect (i.e. after many
repeated intakes) it tends to zero. This last idea is taken from Solomon and Corbit

(1974), and states that one way in which the organism becomes accustomed to drug

consumption is by responding earlier with the inhibitor effect after each drug unit

dose. An equation which provides this dynamics for t(t) is

tðtÞ ¼ t0 expð2wSðtÞÞ; ð30Þ

where w is the delay reducing rate. Both parameters, t0 and w, depend on the
biology of each individual.

The time-dependence of the proportionality variable, the inhibitor effect power q(t),

must be also explained. Variation with time of q(t) has been considered to depend on

two flows: IQ(t), or increasing inhibitor effect power, and RQ(t), or reducing inhibitor

effect power. In addition, because it is involved in the computation of the inhibitor
effect, its effects have been considered to take place with a delay, that is, from the time

value t0 þ tðtÞ, which leads to

dqðtÞ
dt

¼ IQðtÞ2 RQðtÞ;

qðtÞ ¼ q0; t # t0 þ t0:
ð31Þ

The initial value q0 will depend on each individual’s biology. IQ(t) has been considered

to be proportional to the delayed activator effect, that is

IQðtÞ ¼ 1Sðt 2 tðtÞÞ; ð32Þ

where 1 has been called the elevating rate of the inhibitor effect power, and in
coherence with equation (21), Sðt 2 tðtÞÞ ¼ sðt 2 tðtÞÞh i.

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On the other hand, RQ(t), which contributes to the model for the return phase, is

considered to be proportional to q(t), that is, it loses a part of the

inhibitor effect power

at each instant

RQðtÞ ¼ hqðtÞ; ð33Þ

where h is the reducing rate of the inhibitor effect power. Both 1 and h are parameters
whose values depend also on the biology of each individual. The previous assumptions

are also based on the well-known gene regulation mechanisms, some of them already

considered in equation (28). Biologically, q(t) would be represented by the gene

products FosB, DfosB, 33 kDa, DfosB, 35–37 kDa; these are the technical names of some
proteins and genes implied in the referred regulation processes. To describe the function

of each one is beyond the scope of the paper; (for instance, see Colby et al., 2003;
Hiroi et al., 1998; Werme et al., 2002). If we substitute (32) and (33) in (31), we obtain

dqðtÞ
dt

¼ 1Sðt 2 tðtÞÞ2 hqðtÞ;

qðtÞ ¼ q0; t # t0 þ t0:
ð34Þ

If we substitute (23), (24), and (29) in (22), we obtain the following equation for the

dynamics of y(t)

dyðtÞ
dt

¼
aðb 2 yðtÞÞ þ pðtÞs tð Þ

EðtÞ t0 , t # t0 þ t0;

aðb 2 yðtÞÞ þ pðtÞs tð Þ
EðtÞ 2 qðtÞEðt 2 tðtÞÞsðt 2 tðtÞÞyðt 2 tðtÞÞ t . t0 þ t0;

8>>>< >>>:

yðt0Þ ¼ y0:

ð35Þ
Equation (35) is a non-linear delayed integro-differential equation which reproduces the

activation level dynamics measured on the hedonic scale as a representative variable of

the global brain state of an individual submitted to repeated stimulant drug unit doses.
This equation, along with the differential equations (28) and (34), and with the

extraversion variable and the activator effect variable, provides the desired dynamic

addiction model, which we have called DBRAIN. The hydrodynamic diagram of this

model may be seen in Figure 2, and represents the structure of the relations among all its

variables. The names, dimensions and symbols of these variables are shown in Table 1.

Now, let us see how the model of Amigó et al. (2008) can be derived as a particular

case of the model presented in this paper. This is done by introducing the following

restrictions in the model:

(1) Only one drug unit dose is considered; thus, (19) and (20) become

cðtÞ ¼ c0 expð2aðt 2 t0ÞÞ; ð36Þ

sðtÞ ¼ s0 expð2bðt 2 t0ÞÞ þ c0vðt 2 t0Þ: ð37Þ

(2) Extraversion, excitation effect power, inhibitor effect power, and delay variables

are assumed constant:

EðtÞ ¼ b; pðtÞ ¼ p0; qðtÞ ¼ q0; tðtÞ ¼ t0: ð38Þ

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If the results (36), (37), and (38) are inserted in (35), the outcome is:

dyðtÞ
dt

¼
aðb 2 yðtÞÞ þ p0sðtÞ

b
t0 , t # t0 þ t0;

aðb 2 yðtÞÞ þ p0sðtÞ
b

2 q0bsðt 2 t0Þyðt 2 t0Þyðt0Þ ¼ y0 t . t0 þ t0:

8>>< >>: ð39Þ

The delay differential equation (39) along with (37) has an analytical solution and

describes the dynamics of the activation level, such as Grossberg (2000) and Solomon
and Corbit (1974) previewed; see Amigó et al. (2008) for these results. In addition,

Figure 2. Hydrodynamic diagram (Forrester, 1961, 1970) of the DBRAIN model. For the name of

each variable and its dimensions, see Table 1.

464 Antonio Caselles et al.

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the simulations on the short-term time scale, typical of the acute effect of each

intake, reproduce similar results for the activation level dynamics to those obtained

by Amigó et al. (2008). The comparison of both models provides a theoretical

confirmation of the outcomes provided herein.

4. Simulations performed with the DBRAIN model

The system of coupled differential equations (28), (34), and (35) completed with (15),

or by (20) (depending on the considered intake pattern) to calculate the concentration

of the drug in the blood after the last drug intake, does not have a complete analytical

solution (that is, for all the variables). For this purpose, results are obtained by an

approximation to finite differences programmed in the Visual Basic language in the

environment provided by the expert SIGEM system designed by Caselles (1992, 1993,

1994).

The characteristics of the simulations to be performed are the same as those

considered by Amigó et al. (2008), namely:

(1) Cocaine is assumed to be consumed intranasally (sniffed).

(2) The time unit for computation is the minute. A week has 10,080min. In the
context of these simulations, a ‘month’ has 4 weeks (40,320min) and a ‘year’ has

13 months. Within a given month, cocaine intake is assumed to have constant

frequency and elapsed time. A week before consuming is computed in all

simulations in order to present the graphics in a clearer manner.

(3) The measurement units for the activation level and the extraversion variables are

the ‘activation units’ (AU) on a psychological hedonic scale [a,b ]. In future

research, with this scale, the model can be verified experimentally using data

obtained from questionnaires filled by experimental subjects.
(4) The model has been calibrated using the hedonic scale [0,20]. The formula

to convert the model outcomes into outcomes belonging to another arbitrary

hedonic scale [h, k ] is x ¼ ðk 2 hÞy=20þ h, where y [ ½0; 20� and x [ ½h; k�.
(5) On the [0, 20] scale, the tonic activation level b ¼ 10:0AU corresponds to an

ambiverted individual. The values of b situated close to the minimum of this

scale correspond to the most extraverted individuals. A zero or negative value of

the activation level y would represent the collapse of the individual. The values

of b situated close to the maximum on this scale correspond to the most
introverted individuals. Nevertheless, this maximum can be exceeded by the

model results in some simulations. Such results would correspond to extreme

cases such as cocaine binges. For these extreme cases, the values exceeding the

maximum have to be considered as being equal to the maximum value when

the model is verified using a hedonic scale.

(6) The values of the parameters in the calibrated model, as well as estimated ranges

of possible values, are shown in Table 2. The value of b ¼ 0:013min21
(elimination rate) is estimated from data in Winhusen et al. (2006; 0:014^
0:001min21 for 20mg injected and 0:012^ 0:002min21 for 40mg injected). The
value of a ¼ 0:059min21 (distribution rate) is estimated from data in Jeffcoat,
Perez-Reyes, Hill, Sadler, and Cook (1989; 11.7min half-life for intranasal

cocaine).

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(7) Cocaine intake (M) is measured in milligrams. A common cocaine unit for abusers

may be between 10 and 120mg and a cocaine line may contain between 10 and

30mg (Kleankids page). Thus, we will consider it to vary in the range [0, 120].

(8) Three typical personalities have been considered, distinguished by the

corresponding value of b [ ½0; 20�, the tonic activation level value (while the
other parameter values remain constant and equal to the calibrated values, provided

by Table 2): the extraverted personality (with b ¼ 7:0AU or b ¼ 5:0AU for binge
simulations), the ambiverted personality (with b ¼ 10:0AU), and the introverted
personality (with b ¼ 13:0AU or b ¼ 15:0AU to simulate the individual collapse).
The value provided for the initial activation level – for all the simulations carried out

– is the same as that given to the tonic level. This means that the individual starts

his/her addiction process in rest conditions and not influenced by other stimulants.

The goals of the simulations are as follows:

(1) To demonstrate that the model predicts the three phases of sensitization,

habituation, and return (Simulations 1-1, 1-2, 1-3, 1-4, 1-5).

(2) To show the co-influence between personality and addiction, that is, to show how

personality influences the addiction process and how the addiction process

influences personality (Simulations 2-1, 2-2, 2-3).

Table 2. Parameters and values taken for the calibrated model

Parameter Symbol Value Units Range

Drug unit dose M 30mg mg [0,120]

Memory time tm 10,080 £ 4 £ 13min
(a year)

min [0,105]

Initial delay t0 30min min [0,50]
Reducing delay rate w 15min21 min21 [0,20]
Initial drug level in

the body

s0 0 units mg [0,1500]

Absorption rate constant a 0:059min21 min21 [0,1]
Elimination rate constant b 0:013min21 min21 [0,1]
Tonic or basal activation

level

b 5, 7, 10, 13, 15AU AU [0,20]

Initial activation level y0 5, 7, 10, 13, 15AU AU [0,20]

Homeostatic control rate a 0:001min21 min21 [0,1]
Initial excitation effect

power

p0 10 AU
2 min21 mg21 AU2 min21 mg21 [0,20]

Increasing rate of the

excitation effect power

g 9:0AU2 min22 mg22 AU2 min22 mg22 [0,20]

Reducing rate of the

excitation effect power

d 1:5min21 min21 [0,20]

Initial inhibitor effect

power

q0 0:00001AU
21

min21 mg21
AU21 min21 M21 [0,1]

Increasing rate of the
inhibitor effect power

1 0:0000001AU21

min22 mg22
AU21 min22 mg22 [0,1]

Reducing rate of the
inhibitor effect power

h 0:00001min21 min21 [0,1]

Note. AU: activation units on the hedonic scale.

466 Antonio Caselles et al.

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(3) To show that the short-term dynamics of the addiction process in its different

phases (Simulations 3-1, 3-2, 3-3) are the same as forecast by Amigó et al. (2008),

Grossberg (2000), and Solomon and Corbit (1974).

(4) To suggest a possible use of the model to determine the way to conduct the return

phase (controlling dose and elapsed time between doses) in order that the addict

reaches a comfortable state (Simulations 4-1, 4-2). Observe that we do not attempt
to return the addict to his/her tonic level. The tonic level can represent either an

impulsive state that would return the extraverted individual to consumption, or an

anxious state that would close the introverted individual to new experiences

representative of happiness.

We now describe the simulations and the conclusions that can be obtained from them.

4.1. Simulation 1-1: Constant intake and frequency
The three phases of sensitization, habituation, and return take place. This non-realistic

simulation is performed in order to check that the model reproduces the three phases

independently of possible variations of dose and frequency. An ambiverted individual

with a constant drug unit dose (M ¼ 30:0mg) and a constant elapsed time between
intakes (every 10,080min, i.e. once a week), for 1 year, is simulated. Observe in Figure 3
that after a short period where the sensitization and habituation phases – for both

activation level and extraversion variables – are quickly reached, a long period with an

approximately oscillating effect around the tonic level follows, ending with the return

phase.

Simulation 1-1 was carried out to demonstrate that the model presented here can

reproduce the same phases as, on one hand, the model of Gutkin et al. (2006)

reproduces for the nicotine addiction process, and on the other hand, the model of

Amigó et al. (2008) reproduces for the phasic response of a unique intake of cocaine.
Simulation 1-2 considers a more suitable consumption pattern for a person who may

become an addict, likewise reproducing the three phases.

4.2. Simulation 1-2: A realistic addiction process
Simulations 1-2, 1-3, and 1-4 represent the three common consumption patterns

(the diary pattern, the episodic pattern, and the combined pattern) described by
American Psychiatric Association (2000). Doses and frequencies are obtained from the

Figure 3. Activation level (left) and extraversion (right) versus time for Simulation 1-1, for an

ambivert (b ¼ y0 ¼ 10:0AU).

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clinical experience of the authors in the Drug Detoxification Centre (Centro de

Desintoxicación de Drogas) of Bétera (Valencia, Spain) and from the literature (for a

review, see Goudie & Emmett-Oglesby, 1991). The probable addiction process for an

ambiverted individual over a period of 13 months may be the following: constant drug

unit doses of 30mg, with equally time elapsed frequencies of 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9,

9, 10 times each month. This consumption pattern is more realistic than the

consumption pattern of Simulation 1-1 because an increase in frequencies is observed in
addicts and, on the other hand, the final frequency can be related to the financial

limitations of the consumer. Observe in Figure 4 that this consumption pattern

reproduces the sensitization, habituation, and return phases more clearly than that

obtained in Simulation 1-1. Such phases are observed both in the activation level variable

and in the average perception represented by the extraversion variable.

4.3. Simulation 1-3: Weekend binges
An extraverted individual binges on cocaines on Saturday nights between midnight and

noon. An extreme extraverted personality (b ¼ 5:0AU) is considered in this simulation
because he/she has more inclination to binges (Amigó et al., 2008). He/she consumes

30mg of cocaine every two hours (amount related to what he/she can afford), that is, six

times in 12 h, and non-consumption for the rest of the week, for a year, plus a week of

non-consumption after the last binge. Figure 5 shows that this consumption pattern
reproduces the sensitization, habituation, and return phases. Observe that, with binge

consumption, the maximum of the scale can be exceeded, and the short time responses

are higher than the ones provided by Simulations 1-1 and 1-2. In addition, the individual’s

personality, characterized by

the extraversion variable, undergoes a great change.

Figure 4. Activation level (left) and extraversion (right) versus time for Simulation 1-2, for an

ambivert (b ¼ y0 ¼ 10:0AU).

Figure 5. Activation level with all outcomes (left), activation level on the [0,20] scale

(middle), and extraversion (right) versus time for Simulation 1-3, for an extreme extrovert

(b ¼ y0 ¼ 5:0AU).

468 Antonio Caselles et al.

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4.4. Simulation 1-4: Weekend binges plus regular consumption pattern
The consumption pattern of weekend binges is the same as in Simulation 1-3,
but the individual regularly once a week takes an additional 30mg. Figure 6 shows that

this consumption pattern reproduces the sensitization, habituation, and return phases.

As in Simulation 1-3, the maximum of the scale can be exceeded and, the short time

responses are higher than those provided by Simulation 1-3 due to the additional

consumption during the week. Besides, the individual’s personality, characterized by

the extraversion variable, undergoes a great change.

4.5. Simulation 1-5: A consumption pattern leading to collapse
The consumption pattern of an introverted individual considered in Simulation 1-2 is

used to study the possibility of individual collapse (i.e. he/she either suffers a coma or

dies). The collapse can be observed in an extreme introvert (b ¼ 15AU) approximately
3 months, 3 weeks, and 1 day after starting the consumption pattern (without stopping

the supply of drug). The conclusion of this simulation is the equivalence between an
extreme individual’s introversion and an extreme consumption pattern. The collapse

(see Figure 7) is represented by the fall to zero of the activation level variable (observe

that the model continues to run, in spite of collapse, until the simulation time ends; that

is an option in the modelling process).

The general conclusions from Simulations 1-1 to 1-5 are that the model

reproduces the three phases of sensitization, habituation, and return, firstly, when the

consumption pattern is characterized by a constant drug unit dose and a constant

elapsed time between intakes (Simulation 1-1); secondly, with a more realistic

Figure 6. Activation level with all outcomes (left), activation level in the [0, 20] scale (middle) and

extraversion (right) versus time for Simulation 1-4, for an extreme extrovert (b ¼ y0 ¼ 5:0AU).

Figure 7. Activation level (left) and extraversion (right) versus time for Simulation 1-5, for an

introvert (b ¼ y0 ¼ 15:0AU).

Cocaine addiction and personality 469

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consumption pattern characterized by a progressive increase in drug doses and
frequencies until reaching a physiologically limit constant dose (Simulation 1-2); and,

finally, with two patterns of binging (Simulations 1-3 and 1-4). The model also

predicts that a common consumption pattern in an extreme introvert drives the

individual to collapse (Simulation 1-5).

4.6. Simulation 2-1: Personality and addiction, the extravert case
Let us suppose that an extraverted individual (b ¼ 7:0AU) becomes addicted by
following the consumption pattern of Simulation 1-2 for 13 months, with a constant

intake of 30mg. Let us also suppose that the consumer stops consumption for a year.

The development of the activation level and the extraversion is shown in Figure 8.
Observe the three phases of sensitization, habituation, and return (especially the

part of the last phase after the abandonment of consumption) for the activation

level variable. The dynamics of this variable shows that no values below the tonic

level are observed. Nevertheless, the dynamics of the extraversion variable shows

a slow tendency to its tonic level (which should come as no surprise because it is

an average).

4.7. Simulation 2-2: Personality and addiction, the ambivert case
Let us consider an ambiverted individual (b ¼ 10:0AU) consuming cocaine for a year
with the same consumption pattern considered in Simulation 2-1, also with a second

Figure 8. Activation level (left) and extraversion (right) versus time for Simulation 2-1, for an

extravert (b ¼ y0 ¼ 7:0AU).

Figure 9. Activation level (left) and extraversion (right) versus time for Simulation 2-2, for an

ambivert (b ¼ y0 ¼ 10:0AU).

470 Antonio Caselles et al.

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year without consumption. Figure 9 reproduces the three phases of sensitization,

habituation, and return (especially after the abandonment of consumption) for the

activation level variable. The dynamics of this variable shows that the maximum

increase of the sensitization phase with respect to its tonic value is not as high as for

an extraverted individual (Simulation 2-1) and the values below the tonic level are

strengthened in this phase. The habituation phase is larger than that for an
extraverted individual (Simulation 2-1). Again the dynamics of the extraversion

variable shows a very slow tendency to its tonic level.

4.8. Simulation 2-3: Personality and addiction, the introvert case
Let us consider an introverted individual (b ¼ 13:0AU) consuming cocaine for a year
with the same consumption pattern as considered for Simulations 2-1 and 2-2, and also a

year more without consumption. Figure 10 reproduces the three phases of sensitization,
habituation, and return (especially after the abandonment of consumption) for the

activation level variable. The dynamics of this variable shows that, for the first dose,

the negative effect is greater than the positive effect; the sensitization phase is shorter

and smaller than in Simulation 2-2; the habituation phase continues being very large and

high under its tonic level but more than in Simulation 2-2. In this case, the dynamics of

the extraversion variable shows a large decrease under its tonic level, followed by a slow

tendency to the tonic level. The relatively high first dose decrease of activation is due to

the negative effects that a stimulant drug produces on an introverted individual.
This decrease is not observed in the extraverted and in the ambiverted individuals

(Simulations 2-1 and 2-2).

The general conclusion from simulations 2-1, 2-2, and 2-3 is that they show

the co-dependence between personality and addiction. On the one hand, the

tonic (genetic) activation level – which describes the personality before the addiction

process – influences the dynamics of addiction: the lower the tonic (genetic) activation

level is, the higher the sensitization phase is (the maximum reached over its tonic level is

higher) and the lower the habituation phase is (theminimum reachedunder its tonic level
keeps near its tonic value or is negligible). And vice versa: the higher the tonic (genetic)

activation level is, the lower the sensitizing phase is (the maximum reached over its tonic

level is lower) and the higher the habituation phase is (the minimum reached under its

tonic level reachespoints far from its tonic level). These conclusions are similar to those of

Amigó et al. (2008) for the dynamic patterns of different individual personalities as a

consequence of a single stimulant drug unit dose. Moreover, the addiction process

changes the personality of individuals: the addiction process converts extraverts

Figure 10. Activation level (left) and extraversion (right) versus time for Simulation 2-3, for an

introvert (b ¼ y0 ¼ 13:0AU).

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(low tonic or genetic level) into introverts (high mean activation perception given by the

extraversion variable) and introverts (high tonic or genetic level) into extraverts (low

mean activation perception given by the extraversion variable). Furthermore, this change

of personality is characterized by a great inertia: the dynamics of the extraversion variable

shows that, when drug consumption stops, this variable tends to recover its tonic

(genetic) value very slowly (no surprise, because E(t) is an average over time). Thus, the
newpersonality of an individual, obtained as a consequence of his/her addiction process,

remains different from his/her tonic (genetic) level during an appreciable and long time.

The next three simulations try to detail what happens in the next 100min following

three chosen points of the addiction process that would correspond, respectively, to the

sensitization, habituation, and return phases. So, let us consider the case studied in

Simulation 1-2 of an ambivert individual (b ¼ 10:0AU) and the dynamics of the
activation level, y(t).

4.9. Simulation 3-1: The short-term dynamics following an intake in the sensitization
phase
Let us consider a moment of the sensitization phase, for instance the beginning of the

third month after starting to consume, when the individual starts to consume every

8,064min (five times per month). From this moment, the evolution of y(t) is shown for

100min in Figure 11 (left).

4.10. Simulation 3-2: The short-term dynamics following an intake in the habituation
phase
Let us consider a moment of the habituation phase, for instance the beginning of the

seventh month after starting to consume, when the individual starts to consume every

5,760min (seven times per month). From this moment, the evolution of y(t) is shown

for 100min in Figure 11 (middle).

4.11. Simulation 3-3: The short-term dynamics following an intake in the return phase
Let us consider a moment of the return phase, for instance the beginning of the 13th

month when the individual starts to consume every 4,032min (10 times per month).

From this moment, the evolution of y(t) is shown for 100min in Figure 11 (right).

Figure 11. Activation level versus time for Simulations 3-1 (left), 3-2 (middle), and 3-3 (right).

These correspond, respectively, to an intake of the sensitization, habituation, and return phases of

Simulation 1-2, in an ambivert (b ¼ y0 ¼ 10:0AU).

472 Antonio Caselles et al.

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Observe that the evolution of y(t) is in correspondence with what has been

predicted by Amigó et al. (2008), Grossberg (2000), and Solomon and Corbit (1974).

A rise in the curve represents the pleasant sensation felt by the consumer, and the part

of the curve under the tonic activation level represents the craving sensation. The curve

tends finally to recover asymptotically the tonic activation level until the next intake.

Observe also that, the more advanced in phase the intake is the lesser the part of the
curve over its tonic level is and the greater the part of the curve under its tonic level is.

Thus, the more advanced in phase the intake is the lesser the pleasant sensation for the

individual is and the greater the unpleasant sensation (craving) is. In other words, in

general, the pleasant sensation evolves from more to less and the unpleasant sensation

evolves from less to more in the addiction process.

The final two simulations attempt to determine how to manage the return phase,

controlling dose, and elapsed time between doses, in order to reach and maintain a

comfortable state. Comfortableness means avoiding excessive extroversion or
introversion. Excessive extroversion implies impulsiveness towards drug consumption.

Excessive introversion implies anxiety and tendency to avoid new experiences. Thus,

with the next two simulations, we aim to keep extroverts and introverts as close as

possible to ambiversion.

4.12. Simulation 4-1: Trying to conduct extraverts towards ambiversion
This simulation is the result of testing several doses and elapsed times between doses,

over a second year, on the extraverted individual of Simulation 2-1, trying to minimize

the

number of intakes, to maximize the elapsed time between them and to keep the

activation level as high as possible. Figure 12 shows the evolution of the activation level

and the extraversion in the second year with a dose of 30mg every 10,080min, i.e. once

per week. Observe that, in spite of the larger elapsed time between doses, the activation

level tends to keep a constant dynamic pattern and the extraversion variable tends to

keep closer to its maximum value, 7.8 AU (of Simulation 2-1), and thus, closer to the

value 10.0 AU corresponding to an ambivert.

4.13. Simulation 4-2: Trying to conduct introverts towards ambiversion
This simulation is the result of testing several doses and elapsed times between doses,

for a second year, on the introverted individual of Simulation 2-3, trying to minimize the

number of intakes, to maximize the elapsed time between them and to keep the

Figure 12. Activation level (left) and extraversion (right) versus time for Simulation 4-1, for

an extravert (b ¼ y0 ¼ 7:0AU).

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activation level as low as possible. Figure 13 shows the evolution of the activation level

and the extraversion in the second year with a dose of 30mg every 10,080min, i.e. once
per week. Observe that, in spite of the larger elapsed time between doses, the activation
level tends to keep a constant dynamic pattern and the extraversion variable tends to

decrease under its minimum value 12.25 AU (in Simulation 2-3), and thus, under the

value 10.0 AU corresponding to an ambivert.

A conclusion of Simulations 4-1 and 4-2 is that a possible programme of intervention

in cocaine misuse is to consider the administration with a lesser dose or a larger elapsed
time between doses of the same drug or an alternative drug that, having similar effects to

cocaine, minimizes the shock to the organism of the consumer.

5. Discussion

The UPTT presented in this work attempts to integrate personality, the acute effect of

drugs and addiction. The main innovating assertions of the UPTT are the consideration

of a unique trait of personality, called extraversion, and the existence of a genetic
extraversion that influences the dynamic nature of this trait.

A dynamic mathematical model of a stimulant drug addiction (cocaine), based on the

UPTT, is presented in this paper. The model has been named DBRAIN. By using DBRAIN

it is possible to reproduce, via the simulations performed, the dynamics of extraversion

on a short-term time scale, typical of the acute effect of a drug unit dose, and on a long-

term time scale, typical of addiction.

DBRAIN has been obtained by following the GMM. The two representative variables

of extraversion are: the activation level, which plays a role on the short-term time scale,
and the extraversion variable, which plays a role on the long-term time scale. The

conclusions of the simulations with DBRAIN involve these two variables. Let us

summarize them.

On the one hand, the extraversion variable, typical of addiction, on the long-term

time scale changes in time as a consequence of the drug stimulus, leading to the typical

phases of sensitization and habituation, and return to the tonic level (the steady state

representative of the genetic extraversion) when the individual stops consuming or

enters a limited consumption pattern where the dynamic evolution of the activation
level tends to be uniform. The dynamics of the extraversion variable allows for the

evaluation of an individual’s predisposition to drug misuse: extraverts are more

predisposed to this misuse than introverts. On the other hand, the dynamics of the

activation level variable, typical of the acute effect of a drug unit dose, on the short-term

Figure 13. Activation level (left) and extraversion (right) versus time for Simulation 4-2, for an

introvert (b ¼ y0 ¼ 13:0).

474 Antonio Caselles et al.

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time scale leads to the first agreeable phase as opposed to the disagreeable or craving

phase, which finally tends to vanish as time passes, unless another drug unit dose is

taken. The results of the simulations on this time scale show a time pattern for the

activation level similar to that obtained by Amigó et al. (2008), Grossberg (2000), and

Solomon and Corbit (1974). In short, the time-dependence manner of both activation

level and extraversion shows that the sensitization, habituation, and return phases
are reproduced on two time scales, although the tendency towards genetic extraversion

on the short-term time scale is slower for the extraversion variable than for the

activation level.

These simulation results indicate that, on the one hand, the model is an excellent fit

to the process of addiction, and, on the other hand, the model can help explain the

interaction between personality and addiction. Thus, this model may act as a

springboard for latter developments. These developments could include proposals for

intervention in addiction processes by considering personality as a significant factor. Let
us summarize the outcomes obtained from the simulations performed.

Simulations 1-1 to 1-5 demonstrate that the model predicts the three phases of

sensitization, habituation, and return, which the model of Gutkin et al. (2006)

reproduces for the nicotine addiction process, and the model of Amigó et al. (2008)

reproduces for the phasic response to a unique intake of cocaine.

Simulations 2-1 to 2-3 show the co-influence between personality and addiction.

Extraverted individuals, characterized by a low tonic (genetic) activation level,

reproduce longer and higher sensitization and habituation phases than introverted
individuals, characterized by a high tonic (genetic) activation level. Therefore, an

important conclusion obtained from this work by observing the results of these

simulations is that high extraversion means a predisposition to stimulant drug intake and

abuse, particularly to stimulants such as cocaine.

Simulations 3-1 to 3-3 reproduce, respectively, the short-term time scale dynamics of

the three phases of the addiction process, and they prove that their predictions are the

same as those forecast by Amigó et al. (2008), Grossberg (2000), and Solomon and

Corbit (1974).
Finally, Simulations 4-1 and 4-2 suggest a possible programme of intervention in the

addiction process. Assuming robustness of the model with respect to parameters (not

yet checked), a drug consumption pattern that tries to minimize the frequency of

intakes (or tries to maximize the elapsed time between intakes) has been tested in order

to keep the addict away from the extreme values of extraversion. Bear in mind that

cocaine can be substituted by an alternative drug that, having the same effects of

cocaine, minimizes the shock on the organism of the consumer.

DBRAIN receives indirect experimental confirmation through the corroboration of
the theories by Eysenck and Gray, which have been integrated into the UPTT. For

example, Gray (1972, 1981, 1982) presents evidence that neuroticism amplifies both

extraversion and introversion. In DBRAIN, neurotic extraversion would correspond to

the upward curve section at which the extravert’s versus the introvert’s greatest

hedonic response to cocaine would be responsible for the sensitization process. This is

so because the repeated stimulant drug intake progressively produces an increased

internal excitability, the equivalent to an increase of neuroticism. In this way, the

neurotic extravert would show a gradually increased response to the drug, and the
opposite would occur with the introvert. The downward curve section would represent

the neurotic introvert’s response, and therefore the habituation phase, with a

decreasing hedonic response to cocaine. Unlike Gray’s theory, these two factors

Cocaine addiction and personality 475

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(neurotic extraversion and neurotic introversion) are clearly related in DBRAIN.

Furthermore, the scores corresponding to neurotic extraversion obtained by an

individual progressively evolve towards scores in neurotic introversion from a specific

stimulation level (frequency and quantity of intake). This is also deduced from a large

amount of empirical evidence which, in relation to both theories by Eysenck and

Gray, is also presented in the work by De Juan and Garcı́a (2004). On the other hand,
DBRAIN predicts the acquisition process of pathology: addiction, from a personality

variable (extraversion) and from a repeated stimulant drug intake. A relation between

personality and psychopathology has been confirmed in various studies. Thus, a

profile of disorders has been observed from the DSM I-axis (such as anxiety,

depression, and substance abuse) and the five-factor model (NEO-FFI, Costa &

McCrae, 1992). Therefore, Trull and Sher (1994) obtained the following triad of traits

as characteristics of different pathologies, including drug abuse: high neuroticism,

introversion, and low concordance. If, as some research work has shown, such as
Goldsberg and Rosolack (1994), low concordance and conformity to the five-factor

model corresponds to the psychoticism of Eysenck’s model, then we may conclude

that it is common practice to find the pattern of both neurotic introversion and high

psychoticism in the I-axis clinical disorders. Indeed, psychoticism allows for an

explanation of the differences in seriousness among people diagnosed with the same

disorder (Rachman & Eysenck, 1978). These same results were found in a Spanish

sample from EPQ-R and CAQ (Forns et al., 1998; Sandin et al., 2002), except for

externalizing disorders such as psychopathic deviation. This is consistent with
Millon’s (1985) opinion that this type of people (diagnosed with an antisocial

personality disorder) resists chronic stress, which would be the equivalent to high

neuroticism, in accordance with our proposal.

As previously stated, given that the scientific literature insists that those subjects

who gain high scores in sensation-seeking and psychoticism (see for example, Kandel,

1978; Rydelius, 1983), who are therefore extraverts according to our criteria, have a

greater predisposition to drug abuse, and that an extended pattern of drug abuse is that

of neurotic introversion (as seen in Trull & Sher, 1994), it is then thought that addicts
have modified their personality (from the extraversion to the introversion pole), which

is further indirect empiric evidence in favour of DBRAIN.

DBRAIN suggests and permits important application and development possibilities

for future research. For instance, new simulations could explore the stationary values

of extraversion obtained with different consumption schedules and different values of

the tonic extraversion b, or could explore the stability of the model. Moreover, DBRAIN

may prove useful in designing experimental studies which may not only directly

confirm the aforementioned predictions (receiving direct experimental confirmation,
that is, directly verifying experimentally the model), but also (now using the model)

helping in the diagnosis and prognosis of cocaine addicts from knowledge of their

activation level (by means of an EEG or a brain image assessment) and their stage of

addiction. On the other hand, it may also prove useful, after sensitivity analysis over the

parameters, to assay different ways of drug intake (varying parameters) and different

stimulant drugs, as well as to design therapies which permit the recovery of optimum

activation levels with no drug intake, and also to predict their therapeutic success

rates. In short, DBRAIN may be of great use in solving into the profound knowledge of
the biological mechanisms involved in addiction, human personality, psychopathology,

and integrating all these aspects in a unique comprehension model, which has been

our intention in this study.

476 Antonio Caselles et al.

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Received 3 April 2008; revised version received 21 July 2009

480 Antonio Caselles et al.

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individual use.

Warm

Low
density

Cool

High
density

Warm

Platinum
film

Spin
current

Electric field

Chemical
potential m

m↓

m↑

Ferromagnet

Magnetic
field (’spin-up’)

Ferromagnet

Metal bar

Cool

Warm Cool

process. In the rest frame of the electron, the
charged impurity rushing towards it consti-
tutes a current filament, so the electron ‘sees’ a
weak magnetic field circling the filament. This
non-uniform magnetic field imparts a force
on the electron along a direction that depends
on its spin orientation3,4. The net result is that
spin-up electrons are pushed to the right of
the impurity whereas spin-down electrons are
pushed to its left.

In effect, each impurity acts like a spin filter
that selectively kicks electrons to one side or
the other, depending on their spin. As shown
in Figure 1c, the excess spin-up population
in the incident beam results in more charge
accumulating on the far face than on the near
face of the platinum film. The voltage differ-
ence between the two faces is observable as
a Hall signal. The asymmetric scattering of
electrons is especially large in materials with
a high atomic number, such as platinum. Fol-
lowing its prediction3,4, the spin Hall effect was
first observed by applying purely optical tech-
niques to semiconductors5,6, and was later
detected electrically in metals7,8.

In a series of tests, Uchida et al.2 convincingly
show that the Hall voltage in the platinum film
arises from the spin voltage. The Hall signal in

the platinum film tracks both the magnitude
and the direction of the magnetization in the
nickel–iron film. Moreover, by moving the
platinum film along the length of the nickel–
iron film, they show that the spin voltage varies
linearly over the 6-mm length of the sample.
In demonstrating that the spin Seebeck effect
can produce a large, calibrated spin-voltage
source that can be ‘tapped’ anywhere along
the length of the ferromagnet, Uchida and
colleagues have added an important tool to the
spintronics toolbox. ■
N. P. Ong is in the Department of Physics,
Princeton University, Princeton, New Jersey
08544, USA.
e-mail: npo@princeton.edu

1. Gregg, J. F. in Spin Electronics (eds Ziese, M. & Thornton,
M. J.) 3–31 (Springer, 2001).

2. Uchida, K. et al. Nature 455, 778–781 (2008).
3. D’yakonov, M. I. & Perel, V. I. Phys. Lett. A 35, 459–460

(1971).
4. Hirsch, J. E. Phys. Rev. Lett. 83, 1834–1837 (1999).
5. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D.

Science 306, 1910–1913 (2004).
6. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T.

Phys. Rev. Lett. 94, 047204 (2005).
7. Valenzuela, S. O. & Tinkham, M. Nature 442, 176–179

(2006).
8. Kimura, T., Otani, Y., Sato, T., Takahashi, S. & Maekawa, S.

Phys. Rev. Lett. 98, 156601 (2007).

Figure 1 | The spin Seebeck effect. a, In
the ordinary Seebeck effect, a temperature
gradient in a metal bar causes more electrons to
accumulate at the cool end, producing a tilt in the
chemical potential (μ), which is observable as an
electric field. b, Uchida et al.2 extend the Seebeck
effect to spins. In a ferromagnet, the temperature
gradient results in an excess of spin-up electrons
at the cool end, and an excess of spin-down
electrons at the warm end. Their respective spin-
chemical potentials, μ and μ , have tilt profiles
of opposite signs (solid lines), the average
(dashed line) giving the electric field. c, The
spin Hall effect. The excess of spin-up electrons
(red arrows) at the cool end of the ferromagnet
drives a spin current that flows vertically into
the platinum film (yellow arrow). Here, spin-up
means that the direction of the spin is parallel to
the magnetic field, and thus points to the right.
By spin–orbit coupling, electrons ‘see’ a weak
magnetic field circulating around a charged
impurity (circles around blue dot). Scattering
from the charged impurity causes spin-up
electrons to accumulate preferentially on the far
face of the platinum film, whereas spin-down
electrons (blue arrows) end up on the near face.
The imbalance is observed as a Hall voltage
difference between the two faces.

NEUROSCIENCE

Brain’s defence against cocaine
L. Judson Chandler and Peter W. Kalivas

Long-term exposure to cocaine changes the organization of synaptic
connections within the addiction circuitry of the brain. This process
might protect against the development and persistence of addiction.

Neurons modify their structure and communi-
cation with other neurons in response to
experiences. Such experience-dependent
neuro plasticity is crucial for survival because
it allows learning from, and responses to,
changes in the environment. But the cellular
mechanisms that mediate this process can also
be co-opted by drugs of abuse. Reporting in
Neuron, Pulipparacharuvil et al.1 describe how
some of the chemical, structural and behav-
ioural changes in neurons that are induced by
repeated exposure to cocaine are regulated at
a molecular level.

Drug addiction is characterized by com-
pulsive drug seeking. It resembles a chronic
relapsing disorder in which the addict resumes
taking drugs after a period or periods of absti-
nence. Human and animal studies indicate that
the recalcitrant nature of addiction results from
drug-induced stimulation of reward-related
learning processes in the brain. The pleasure-
producing effects of the drug trigger cellular
and molecular processes that are normally
activated by natural rewards such as food and
sex. Repeated exposure to an addictive drug

leads to a long-lasting associative memory of
its rewarding properties through experience-
dependent neuroplasticity. In effect, drug-
seeking behaviour becomes hard-wired in
the addict’s brain, and the persistent memory
trace is easily reactivated by drug-associated
environmental stimuli, such as the sight of
drug paraphernalia.

Along the dendritic processes of a neuron,
morphologically specialized structures called
dendritic spines receive most of the excitatory
signals from other neurons through synap-
tic junctions. These spines are considered to
be a primary cellular site for mediating the
synaptic plasticity that is thought to under-
pin memory formation2. One regulator of
the density of excitatory signals on dendritic
spines is the gene transcription factor MEF2
(ref. 3). When active (dephosphorylated),
MEF2 favours elimination of dendritic spines,
and when inactive (phosphorylated) it allows
spine formation3,4.

Repeated exposure to cocaine and other
psychostimulants increases the number of
dendritic spines on medium spiny neurons

drives a spin current into the platinum film.
The decay of this spin current leads to the
appearance of an electrical signal through the
spin Hall effect3,4, which enables spin currents
to be detected using a sensitive voltmeter.

To understand the spin Hall effect, one can
track an electron as it enters the platinum film
and scatters off a charged impurity (Fig. 1c).
The spin–orbit interaction — the interaction
between an electron’s spin and its motion —
imparts a left–right asymmetry to the scattering

743

NATURE|Vol 455|9 October 2008 N E WS & V I E WS

in the nucleus accumbens — a primary brain
region in the addiction neurocircuitry. So Pulip-
paracharuvil and colleagues1 hypothesized that
such cocaine-induced structural neuro plasticity
might also be regulated by MEF2. Indeed, they
demonstrate that this transcription factor,
which is highly expressed in medium spiny
neurons and is predominantly active under
normal conditions1, is affected by chronic
cocaine administration. Specifically, long-term
exposure to cocaine seems to prevent MEF2
dephosphorylation by a calcium/calmodu-
lin-dependent phosphatase enzyme known as
calcineurin, thereby suppressing its activation.

Cocaine-induced MEF2 inhibition also
seems to involve enhanced phosphorylation
of this transcription factor by a kinase known
as Cdk5. In the nucleus accumbens, Cdk5
activity — which modulates behavioural
responses to cocaine, such as motivation to
consume the drug5 — increases after chronic
exposure to cocaine6. Together with Pulippa-
racharuvil and colleagues’ data, these observa-
tions4–6 strongly suggest that repeated exposure
to cocaine inhibits MEF2 activity through
both enhanced phosphorylation by Cdk5 and
attenuation of dephosphorylation by calci-
neurin. The reduction in MEF2’s transcriptional
activity in turn promotes increases in the
number of dendritic spines.

The basic mechanism underlying experi-
ence-dependent synaptic plasticity is often
described by the phrase “Neurons that fire
together, wire together”7. Reward-related
associative learning is a form of such ‘Hebbian
plasticity’, in which synaptic connections are
enhanced by the improved strength of existing

synapses and/or by an increase in the number
of such connections. So a logical conclusion
would be that cocaine-induced increases in
spine density reflect an activity-dependent
strengthening of synaptic connectivity, which
presumably underlies addictive behaviour.
Surprisingly, however, Pulipparacharuvil and
colleagues’ observations1 do not support this
inference. By manipulating MEF2 activity,
they inhibited cocaine-induced increases in
spine density. However, this did not seem to
prevent increases in the behavioural response
to this drug, and might even promote it. So
increases in spine density resulting from MEF2
inhibition seem to be associated with reduced
behavioural sensitivity to cocaine.

If bulk increase in spine density within
the nucleus accumbens does not contribute to
enhanced behavioural responses to cocaine,
then what is its function, and how can it be
reconciled with the processes of experience-
dependent associative learning? One con-
founding aspect of Hebbian plasticity is that,
when allowed to proceed unchecked, activity-
dependent changes in synaptic connections
can destabilize neural networks8. In self-
defence, the brain uses homeostatic-plasticity
mechanisms to oppose such destabilizing
effects.

Homeostatic plasticity tends to occur on a
large scale to maintain the overall firing activ-
ity of a neuron. This allows synapse-specific
remodelling of neuronal circuits to proceed
through Hebbian mechanisms while maintain-
ing stability of the overall neural network. A
major excitatory input reaching medium spiny
neurons originates from the prefrontal cortex,

but chronic exposure to cocaine markedly
alters the output of prefrontal cortical neurons
projecting to the nucleus accumbens9. So, as
Pulipparacharuvil et al. suggest, an intriguing
possibility is that cocaine-induced increases
in spine density in the nucleus accumbens,
which are mediated by MEF2 inhibition, may
represent a homeostatic response to altered
excitatory input from the prefrontal cortex.

These findings1 provide a direct challenge to
the view that increased spine density induced
by repeated exposure to psychostimulants
underlies maladaptive plasticity. More over,
they agree with previous observations10 that
identified compensatory drug-induced neuro-
adaptations. Future research into the neuroplas-
ticity induced by addictive drugs must therefore
consider competition between activity-depend-
ent remodelling of synaptic connections and
homeostatic adaptations that maintain overall
stability in neuronal networks. ■
L. Judson Chandler and Peter W. Kalivas are
in the Department of Neurosciences, Medical
University of South Carolina, Charleston,
South Carolina 29425, USA.
e-mails: chandj@musc.edu; kalivasp@musc.edu

1. Pulipparacharuvil, S. et al. Neuron 59, 621–633 (2008).
2. Alvarez, V. A. & Sabatini, B. L. Annu. Rev. Neurosci. 30,

79–97 (2007).
3. Flavell, S. W. et al. Science 311, 1008–1012 (2006).
4. Gong, X. et al. Neuron 38, 33–46 (2003).
5. Benavides, D. R. et al. J. Neurosci. 27, 12967–12976 (2007).
6. Bibb, J. A. et al. Nature 410, 376–380 (2001).
7. Bi, G. & Poo, M. Annu. Rev. Neurosci. 24, 139–166 (2001).
8. Abbott, L. F. & Nelson, S. B. Nature Neurosci. 3, 1178–1183

(2000).
9. Kalivas, P. W., Volkow, N. & Seamans, J. Neuron 45,

647–650 (2005).
10. Toda, S. et al. J. Neurosci. 26, 1579–1587 (2006).

With high oil prices sparking a surge
of interest in alternative energy
sources, solar cells have become
the subject of intense research.
Much of this effort focuses on
finding new designs that open up
fresh applications. John Rogers and
colleagues now report just such a
development (J. Yoon et al. Nature
Mater. doi:10.1038/nmat2287;
2008) — tiny, ultrathin cells made
of silicon that, when fixed in arrays
on a flexible substrate, create large,
bendy solar cells (pictured).

The authors carve their microcell
arrays from a rectangular block of
silicon. They begin by etching the
outlines of the microcells (the tops
and sides) onto the upper surface
of the silicon block. They then make
electronic junctions and electrical
contacts by ‘doping’ the silicon,

adding boron and phosphorus, and
using an inert mask to define the
regions to be doped. A further round
of etching exposes the final three-
dimensional shape of the microcells,
retaining a thin sliver of silicon to
anchor the cells to the block. Finally,
the base of the wafer is doped with
boron, to yield functioning solar
microcells.

To make bendable, large-scale
solar cells, Rogers and colleagues
use a printing technique. They
press a flat stamp onto the
arrays of microcells on the silicon
block, breaking the anchors that
tether them to the silicon. The
microcells stick to the soft surface of
the stamp, and are transferred to a
flexible substrate simply by pressing
the stamp onto the substrate. The
authors then construct electrodes to

connect the microcells
to each other, using one
of various established
methods.

The resulting devices
have several desirable
properties. First, they
are remarkably light,
which, along with their
flexibility, allows them
to be transported and
installed more easily
than existing solar
cells. Second, they
work just as efficiently
when bent as they do
when flat, so they
could be fixed to
curved or irregular
surfaces. Furthermore,
they can be made to be
transparent, which would allow
them to be used on windows.
And because the microcells are
so thin, less silicon is used,
minimizing costs.
Andrew Mitchinson

MATERIALS SCIENCE

Solar cells go round the bend

J.
Y

O
O

N
E

T
A

744

NATURE|Vol 455|9 October 2008N E WS & V I E WS

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