Schizophrenia, Neurobiology and the

Schizophrenia, Neurobiology and the Methodology of Systemic Modeling Original Paper S26

F. Tretter1 J. Scherer2

Progress in the pharmacological treatment of schizophrenia is dependend on the extent of our understanding of the brain as the basis of this disease. Detailed examination of neurobiological data shows that only a systemic approach will integrate this

wealth of information. For this reason, the steps involved in model building should be clarified, as further progress will necessitate closer cooperation between neuropsychiatrists, neurobiologists and systems scientists.

Schizophrenia as a dynamic systems disorder of psychic functions

analysis, they showed that most patients improved within two weeks and reached a steady state after 4 weeks.

The complex symptomatology and time course of schizophrenia, already in the 1980 s, for the working group of Brenner, Böker and Ciompi (Univ. Bern) made a systemic perspective appear advisable [4]. Müller and Ciompi [30], for instance, who observed long-term courses of schizophrenia over years, found various patterns which cannot be easily explained by a common mechanism of symptom generation. In addition, Schiepek et al. [35] modeled the interaction of psychological variables like anxiety, stress, delusion etc., in a computer-based simulation and they were able to demonstrate these time courses by changing the coupling weights of these variables (Fig. 1). These patterns raised the question of wether some kind of `generator' of fractal patterns is involved. For this reason, the working group of Tschacher (Univ. Bern) later tried to identify latent patterns in the structure of the time course of symptoms during a schizophrenic episode [22]. They measured psychotic symptoms in patients by applying rating scales for 104 days. This group described fluctuations in the severity of symptoms and determined the average level of symptoms and the slope of their remission during the first response phase to treatment. The level of disorder in the stabilization phase and the fluctuations during this phase were also determined. By applying factor analysis combined with nonlinear

Within the context of systemic analysis, time-related patterns of intensity of any variable can be analyzed by various mathematical procedures, especially by non-linear techniques. This is one of the fields of methodology of systems science (an der Heiden, in this issue p. S36 and Schwegler, in this issue p. S43). The task involved ascertaining the mathematical properties of the biological ªgeneratorº of these symptoms.

Neuronal circuits in schizophrenia In the last few years, neurobiological methods have provided a large volume of data on brain dysfunction in schizophrenia [2]. The main macrocircuitry, being decisive for schizophrenia, was detected by Carlsson in the late 1980ies ([5]; Carlsson, in this issue p. S10). Additionally, the local micro-circuits on various levels of the brain must also be taken into consideration (Wang, in this issue p. S80 and Winterer, in this issue p. S68). These circuits are driven by various transmitters with excitatory or inhibitory effects on the subsequent neurons. For schizophrenia, several dysfunctional transmission processes have been proposed: besides hyperactivity of the subcortical dopamine system and hy-

Affiliation 1 Department of Addiction, District Hospital, Haar/Munich, Germany 2 District Hospital, Garmisch Partenkirchen, Germany Correspondence PD Dr. Dr. Dr. Felix Tretter ´ Department of Addiction ´ District Hospital ´ Ringstr. 9 ´ D-85529 Haar/Munich ´ Germany ´ E-Mail: [email protected] Bibliography Pharmacopsychiatry 2006; 39 Suppl 1: S26±S35 Georg Thieme Verlag KG Stuttgart ´ New York DOI 10.1055/s-2006-931486 ISSN 0936-9528

Fig. 1 Computer simulation of various long-term trends in courses of schizophrenic symptoms correspond to empirical findings (insert right above) [35]. A: The functional weight of withdrawal and delusion is elevated in the simulation, resulting in a persistently high level of pathology. B: The functional weight of stress and delusions is elevated, resulting in slowly progredient chronicity. C: Stress and delusions can easily evoke repetitive heavy psychotic episodes (From [35], with kind permission of Springer Sciences and Business Media).

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poactivity of the cortical networks, a hyperactive excitatory serotonin system as well as a hypoactive excitatory glutamate system and a hypoactive inhibitory GABA system have been discussed as alternatives [6]. These aspects can be integrated in the multiple-loop model designed by Carlsson (Carlsson, in this issue p. S10). These transmitters, especially glutamate and GABA, are also relevant for the local microcircuitry of the prefrontal cortex, which is supposed to be involved in working memory processes and their pathology (Wang, in this issue p. S80). In sensory systems, as well studied networks, the mechanism of ªlateral inhibitionº was detected (e. g. retina). It serves for enhancing contrasts and probably also to generate a gradient facilitating the detection of contours as the basis of pattern recognition and ªgestaltº detection (Fig. 2). The functional texture of these cellular networks represented by local activation and lateral inhibition is a widely used principle in biosystems [28]. It

might thus be a leading principle for constructing models of the central nervous system. Therefore, in order to understand cerebral neuronal networks, the interplay of activation and inhibition has to be considered (Carlsson, in this issue p. S10). The fact that the principle of local (selfreinforcing) excitation and lateral inhibition is also realized in the cortex must therefore also be taken in account (Wang, in this issue p. S80). Here we have evidence that the balance of excitation and inhibition might be deficient in schizophrenia, thus resulting in attenuated inhibition of lateral coupling. This could lead to an increased risk of attentional distraction by irrelevant stimuli and/or to overinclusive thinking (Wang, in this issue p. S80). Basically, pyramidal cells have excitatory couplings with nearby pyramidal cells, above all within a cortical column, and they also exert lateral inhibitions via interneurons (Fig. 3). However, local

Tretter F, Scherer J. Schizophrenia, Neurobiology and ¼ Pharmacopsychiatry 2006; 39 Suppl 1: S26 ± S35

Fig. 2 (A) When a light is shone on an array of retinal ganglion cells, there is local activation of the cells in the immediate neighborhood of the light with lateral inhibition of the cells further away from the light source. (B) This diagram illustrates the Hermann illusion. Here, cells have more illumination in their inhibitory surrounding regions than cells in other white regions and are thus more strongly inhibited and appear darker. (C) The result in the network is a landscape of local activation and surrounding inhibition (Mexican hat); (from [31]; with kind permission of Springer Sciences and Business Media).

Original Paper Fig. 3 Diagram of basic components of cortical networks with pyramidal cells, with local self-excitation and lateral inhibition by inhibitory interneurons (IN); (adapted from [41]).

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inhibition by local negative feedback loops and lateral excitation can also be identified within cortical networks, so that we do not know the conditions under which these components dominate the pattern of activation. Positive and negative feedback loops can be identified with respect to subcortical connections (Fig. 4). Dopamine neurons located in the upper brainstem (ventral tegmental area, VTA) project from there to areas of the prefrontal cortex (PFC) onto inhibitory neurons via inhibitory D3 and D4 receptors (Fig. 4, #2) and onto pyramidal cells via excitatory D1 receptors (Fig. 4, #1). Corticofugal projections from pyramidal cells to VTA constitute a self-reinforcing circuit (Fig. 4, # 4) and also an inhibitory feedback (Fig. 4, #3; from [16, 24]). Some D1 receptors that may be activated at high levels of dopamine were also found in GABA-containing neurons [16], a fact which is complicating the picture of the processes in cortical networks. Models of neuronal circuits usually use simple integrate-and-fire neurons without taking the dynamics of the synapse into account explicitly. This is important, as a cortical pyramidal cell, for instance, has about 10,000 synapses driven by glutamate,

norepinephrine and other transmitters. In nearly every transmitter system, except for glutamate and GABA, excitatory and inhibitory receptor subtypes are located on the respective cell. As far as pharmacotherapeutic options are concerned, the molecular mechanisms of these interneuronal connection sites, i. e. their synaptic molecular circuitry, is the most interesting issue. Some important properties of synapse dynamics will be considered therefore now.

Complexity of circuits of dopamine synapse The term ªsynaptic transmissionº means the transformation of presynaptic electrical signals into transmitter concentrations and receptor occupations resulting in electrical activity in the postsynaptic neuron [1]. Synaptic dynamics, measured as time-related fluctuations in transmitter concentrations (Dc/Dt), is basically determined by the production and release of transmitters minus the effects of the activity of the reuptake mechanism and the autoreceptors, which are acting as inhibitory feedback components. Finally, breakdown and diffusion must be taken into consideration.


Additionally, the dynamics induced in the binding of transmitters to receptors is of importance (Leuner and Müller, in this issue p. S15). It sould be mentioned here, that these variables cannot be measured simultaneously in-vivo, so that at present modeling of the synapse must use more or less constructed variables. With regard to the dopamine synapse, some relevant functional properties should be considered here, that are not yet clarified sufficiently and where, especially with respect to their quantification for modeling purposes, still inconsistent data are reported. This is mainly due to different experimental methods, which do not allow to integrate the available observations on-hand (Leuner and Müller, in this issue p. S15): a) Location in the brain: The dopamine system is a complex of several systems with various locations and different properties (Gründer et al., in this issue p. S21 and Leuner and Müller, in this issue p. S15). b) Location of synapse on the cell: We can distinguish between dendritic, somatic and axonal synapses with different effects on neuronal computation [34]. c) Location of the receptor around the synapse: Usually intrasynaptic, presynaptic and postynaptic receptors can be identified. Activation of the presynaptic D2 receptor, for instance, inhibits dopamine release and synthesis, but they are not present in every brain area [9]. Extrasynaptic receptors and also extrasynaptic release sites are now increasingly regarded as important sites of transmission [10], (Carlsson, in this issue p. S10). d) Subtypes of receptors: Basically, D1-type (D1 and D5) and D2type (D2, D3, D4) receptors are distinguished [9]. They exhibit an unequal distribution across the brain structures (e.g cortex vs. striatum). e) Activation and inhibition: According to transmission, it should be kept in mind that receptors can be classified according to antagonistically operating classes, with inhibitory and excitatory effects on the intracellular molecular transduction


Original Paper

Fig. 4 Diagram of the cortical microcircuits coupled with the dopamine system (adapted from [16]; s. text).

cascade and postsynaptic membrane potentials (Leuner and Müller, in this issue p. S15). Receptor activation thus has suppressing or facilitating effects on action potentials. Depending on the respective membrane potential the effects can be partially inverted [23]. Receptors of the D1-type stimulate several activating intracellular molecular cascades, whereas receptors of the D2-type inhibit some of these cascades ([9]; Leuner and Müller, in this issue p. S15). To a certain degree, this signaling pathway converges onto DA- and cyclic adenosine monophosphate (cAMP)-regulated phosphoprotein (DARPP-32). However, within a neuronal circuit, the final effect is determined by the cell type on which the respective receptor is located: Intensive cortical D2 receptor activation through high dopamine release levels may induce inhibition of inhibitory GABA neurons and thus will possibly evoke pathological disinhibitions of pyramidal cells (Winterer, in this issue p. S68). Pyramidal cells in slice preparations, thus show biphasic modulation by dopamine: first of all, suppression of inhibitory postsynaptic currents (IPSCs) occurs, followed by an increase in IPSCs [37, 38]. f) Dependence of receptor activation on dopamine concentration: Presynaptic D2 receptors show a high affinity for dopamine (range: nM) and also low concentrations of dopamine usually activate D1 receptors (low-pass filters); in contrast, high concentrations (range: mM) activate postsynaptic D2 receptors (high-pass filters, [43]). Seamans' group found that low doses of dopamine activate D1 receptors in the prefrontal cortex, whereas the D2 receptors are activated at high concentrations of dopamine. The dose-dependent effects of dopamine on the various receptors must therefore generally be taken into consideration. Consequently, on a network level, when dopamine input into the cortex is low, the resultant level of D1 receptor activation might not only lead to a low level of pyramidal-cell activation, but also to only a mild activation of inhibitory GABA neurons and thus to a low level of inhibition of pyramidal cells. Additionally, under this conditions only a very low activation of inhibitory D2-type receptors on GABA neurons is induced so that the inhibitory influence by these neurons onto pyramidal cells might be strong [37]. A low dopamine concentration thus would possibly diminish pyramidal-cell activity directly via D1 receptors and indirectly via D2 receptors. This indicates that dopamine receptors can play a synergistic role in the cortical network. Theoretically, the ratio of D1 to D2 type receptors (D3,D4) in inhibitory interneurons is crucial. The ratio of D1 receptors on pyramidal cells to those located on interneurons must also be considered (Winterer, in this issue p. S68). These components of the causal chain within the dopamine signaling network could cause that a low dopamine input into the PFC via the inhibitory interface probably inhibits cortical activity (possibly: ªhypofrontalityº), whereas a high level of dopamine input activates cortical activity. There are, however, some inconsistencies in the literature, suggesting cell-specific effects [15]. g) Discharge pattern: The distinction between (cortical) phasic and (subcortical) tonic activity of the various dopamine systems is of relevance for information processing [13,17, 30, 46]. VTA projections into cortex fire in a phasic, high-frequency bursting pattern (about 5 spikes with 15 Hz, about 70 ms inter-spike interval), whereas dopamine neurons projecting from the substantia nigra to the striatum fire with a low sustained-frequency pattern (4 Hz, about 250 ms inter-spike

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Original Paper S30

interval), as observed and analyzed by Grace and Bunney [17] and Schmitz et al. [36]. The activity patterns ± phasic (transient) or tonic (sustained) ± are relevant for the temporal pattern of receptor occupation by dopamine molecules and the subsequent effects on the postsynaptic neuron. However, the topographical distribution of these activity patterns in the brain is not so selective [46]. h) Time course of intrasynaptic dopamine concentration: Transmitter is released in microseconds, whereas the transmitter decay in intrasynaptic compartment is provided by activity of reuptake mechanisms within some milliseconds. In contrast, the autoinhibition of dopamine release by D2 autoreceptors has a latency of about 50 msec, a maximum at 500 msec and is terminated after 2 ± 5sec [3, 36]. Thus the activity level of the postsynaptic cell could be down-regulated. i) Several other findings with regard to dopamine transmission: Glutamate can be a co-transmitter of dopamine at various sites [7]. Furthermore, the very interesting finding of up-state and down-state activity conditions of neurons are largely neglected in theoretical neuropschiatry [21]. Finally, with regard to the action of antipsychotic substances, some authors distinguish between ªslow-offº (tight binding) and ªfast-offº (weak or loose binding) D2 receptor blockers. This might explain the mild side-effects of atypical neuroleptics, which exhibit a high dissociation constant (clozapine < 60 sec) compared to haloperidol with > 30 min [39, 40]. In summary, it is evident that the processes at the dopamine synapse and, in consequence, also the actions of antipsychotic drugs are not fully understood. For this reason, synaptic process modeling is not yet satisfactory. However, the wealth of experimental data and clinical observations of the mechanisms involved in schizophrenia raises the question of whether modern systems science can help us to achieve enhanced understanding of this huge volume of partially controversial data.

Understanding dynamic systems The study of natural systems, e.g. the weather, the climate, plant populations, animals, human beings, ecosystems etc., shows that the time course of states of the system can, in many cases, only be understood by concepts like selforganization, nonequilibrium, dynamics, nonlinearity, bifurcation, complexity, cooperativity, fractal generation of patterns etc. [26]. These phenomena are thought to be caused by feedback loops or other interaction mechanisms between various components of the system under study. In this context, the period since the 1940ies has witnessed a number of eras with systemic paradigms such as the cybernetic era, the era of catastrophe theory and finally the era of chaos theory and fractals. We are now passing through the era of complexity studies [26]. In this connection, the modeling of diseases can be found within the concept of ªdynamic diseasesº, as developed by Mackey, Glass and an der Heiden ([25]; cf an der Heiden, in this issue p. S36). The concepts of ªsynchronyº and ªcooperativityº, which are studied by ªsynergeticsº, are leading concepts in our approach to understanding brain dynamics (cf. [18]).

Like all sciences, which can be characterized by their subjects, concepts, theories, paradigms and, of course, methods, systems science, too, can be identified by its methodology.

Methodology of systems modeling In systems science, the procedure for analyzing systems and constructing models of such systems is described explicitly [32], (Fig. 5). From a systemic perspective, modeling means therefore means conceiving the subject of interest as a set of interrelated elements. These interrelations are first described in verbal form. The essential content of these descriptions defines the mode of action of the relation between the elements. For instance, it is necessary to clarify whether the action of element A on B activates or inhibits element B. Whether B also has a feedback action on element A has to be defined. Usually, if a complex system, consisting of several elements, has to be described, verbal descriptions become very complex. For describing the interrelations between of brain structures like those relevant for schizophrenia, for instance, a graphical representation is useful, as precise conceptualization of the system is required. This is demonstrated by Carlsson (Carlsson, in this issue p. S10). After having described the system structure in this qualitative (or semiquantitative) way, it is useful to achieve a quantification of the model. For this purpose, the use of mathematical language, especially differential or difference equations is necessary. Such formalization of the models makes computer-assisted experiments and model structure optimization possible. Such a procedure requires many empirical data. The relevant data very often are missing, however. Mathematical models are frequently also introduced without paying sufficient attention to assumptions regarding the empirical properties of the system being studied [12]. Systemic methodology, however, explicitly refers to the steps involved in modeling. This is due to communications between systems scientists and empirical researchers in the early stages of systems science, when the so-called `world models' were developed by Forrester, Meadows and others [27]. The problems of human ecology, arising in the 1960ies, were the main trigger of the development of a methodology of systemic thinking, as mathematicians, programmers, physicists and computer experts had to communicate with empirical researchers and even practitioners from various professions [14,19, 32, 33, 45, 47]. For this reason, systems science might provide a good basis for theoretical neuropsychiatry.

Computer-assisted modeling When dealing with mathematical equations, it is useful to make a computerized model, as this model can be tested and optimized by computer experiments. For non-mathematicians, i. e. most psychiatrists, such formalization is a difficult step. However, several icon-based computer programs that facilitate the modeling procedure are now available for simulations: Stella, Vensim, PowerSim etc. These programs help the user to build models based on differential or difference equations intuitively (Fig. 6).


Fig. 5 Methodology of systemic modeling with different theory building steps (from [45]).

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According to this strategy, the theoretical concept must be reconstructed within the framework of calculus. This means, for instance, that the relevant variable (e. g. transmitter concentration c in synaptic cleft) must be conceived as a level variable whose rate of the change (dc/dt) depends on the difference in transmitter inflows and transmitter outflows at a certain time: dc/dt = inflow (t) ± outflow (t)

Some elementary modular models Within the context of brain research, the fact that complex systems can be seen as being composed by paired elements should be taken into account. Such two-component systems are modules that exhibit typical behavior. If activation or inhibition represent the actions between the elements, three main types of interconnection structures can be distinguished (Fig. 7): I) Reciprocal activation. This is, in principle, a self-reinforcing, vicious cycle. II) Activation and inhibition. This system exhibits oscillations. III) Reciprocal inhibition. This system can exhibit periodical patterns (an der Heiden, in this issue p. S36). Depending on the initial value or external couplings, the system might also show divergent behavior courses. All three types of module are seen in the nervous system.

Steps involved in modeling the functional structure of macrocircuits Fig. 6 Basic module of icon-based modeling programs (cf. [20]). If the level variable has an influence on flows, it is coupled with the rate (e. g. outflow rate). The difference in flows at a certain time constitutes the rate of change.

In order to transform the graphical model of neuropsychiatry into a simulation program (Stella), the model can be animated and the behavior tested in relation to variations in the paramters. This will be demonstrated briefly.


Fig. 7 Circuit with two elements with activating (ACT) or inhibiting (INHIB) couplings. The activity of one element as a function of time depends on the mode of coupling (activity-time diagram). The co-variation of the state of both elements is illustrated in phase portraits, which permit classification of the system even at this stage (Schwegler, in this issue p. S43). I: Reciprocally activating couplings (ACTACT) II. Activating coupling and inhibiting coupling (ACT-INHIB) III: Reciprocally inhibiting couplings (INHIBINHIB)

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For modeling purposes, first a goal variable (i. g. acoustic hallucinations, as a state of neural hyperactivity) must be defined; this variable is to be ªexplainedº or ªexploredº by the structure of the model (Hoffman and McGlashan, in this issue p. S54). When defining such variables in our case, we must decide which biological measures should be used in the model ± single neuronal discharges, field potentials of neuron groups, transmitter concentrations etc. These measures must be correlated with any available psychological measures, e. g. scores of rating scales, as described above. This measurement problem is one of the most crucial ones in modeling and must sometimes be resolved by using estimations and dummy variables. With regard to this, the central core of any global macro-model of schizophrenia is the circuit that passes from cortex to striatum to thalamus and back to the cortex and is assumed to generate hallucinatory symptoms and or thought disorders by over-stimulating the cortex. We call this circuit C1. It has two excitatory glutamatergic connections and one inhibition. C1 is coupled with the inhibitory dopaminergic projection from substantia nigra (SN) onto the striatum and from there back to the SN by an inhibitory GABA projection (Fig. 8). This latter circuit is called C2. This model, consisting of C1 and C2, was mainly developed by Carlsson [5] (Fig. 8).

coupling parameters of the various components were estimated and normalized in line with the procedures of systems dynamics methodology [20, 33]. Self-inhibiting mechanisms (negative feedback) depending on the level of activity of the respective component, were also assumed to be able to generate rapid dynamic behaviour in the respective part of the system. The model was designed with the help of Stella simulation program (Fig. 9). In model tests it was shown that this system may oscillate under ªnormal conditionsº (Fig. 10). However, hyperactivity of the SN may result in elevated and also less modulated cortical activity (Fig. 11).

In a preliminary exploratory computerized version of this model by one of the authors (F.T.), the anatomical components were connected in an additive and multiplicative manner [44]. The Fig. 8 Functional structure of the basic model designed by Carlsson ([5]; cf. Carlsson, in this issue p. S10).

Fig. 9 Structure of the basic model represented by the Stella graphical modeling language (mod. from [44]). Boxes are the anatomical components, the inflows and outflows are depicted as tubes. Valves represent the speed of rise and fall of the activity level of the respective unit, the arrows between the boxes represent the coupling of the units.


Fig. 10 The simulation of the activity-time curves of the cortex (1), the striatum (2), the substantia nigra (3) and the thalamus (4, adapted from [44]).

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Fig. 11 Course of activity of the various components of the circuit when the activity of the substantia nigra is elevated. The system exhibits a higher level of cortical activity and reduced modulation (mod. from [44]).

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The main limitations of this computerized model are the following: the various components of the system, e. g. positive and negative growth rates of activity and strength and speed of the interconnections of each anatomical component, are selected arbitrarily. The main selection criterion for parameter estimation was the stability of the ªnormalº system. In order to achieve greater model validity, these parameters must be based on experimental data. For depicting symptom remission, the model should also be improved so as to show neurochemical self-organization in the course of time.

fire or be silent. Several models have been described also for schizophrenic information processing ([8, 41]; Hoffman and McGlashan, in this issue p. S54) and for working memory, as demonstrated by Wang (in this issue p. S80). In such models, the role of fast and slow synaptic action, phasic and tonic neuronal discharge activity, temporal and spatial range of inhibition and activation between neurons etc. should be taken into consideration additionally. These dynamic properties of signaling in the brain are very crucial for information processing [11].

Regardless of the validity of details such as state variables, time course and strength of component couplings etc., this model can help to explore system dynamics and promote not only more detailed modeling but also new empirical research. Modeling can thus help bridge the gap between neuropsychiatrists and theoreticians.

Conclusion

Such simple models are usually replaced by models based on the concept of ªartificial neural networksº (Hoffman and McGlashan, in this issue p. S54). In this approach, it is assumed that a set of several hundred artificial neurons are interconnected in various ways. The single neurons are summing up their inputs and will

The complexity of the temporal pattern of intensity of symptoms in schizophrenia in itself makes it difficult to recognize a basic symptom-generating rule. Over the last few years, neuropsychiatric research has produced a large amount of data on synaptic mechanisms and the peculiarities of cerebral networks in schizophrenia. The complexity of the brain, as a system of feedback loops, and the number of neurons make it difficult to understand the totality of the processes relevant for schizophrenia solely by imagination. The methods of systems science may therefore be useful tools for ªthinking in complexityº to use a concept from


Mainzer [26]. Computer simulations of models, as are currently being discussed, may be especially helpful for exploring such processes in the brain with regard to mental disorders. Further research should consider the interplay between neuropsychiatry and systems science more explicitly.

Remarks For exploratory modeling simulation programs are useful. In the context of the program Stella and in notation of System Dynamics methodology the equations of the model are as follows.

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CORTEX_(t) = CORTEX_(t ± dt) + (CORTIN ± CORTOUT) * dt INIT CORTEX_ = 40 INFLOWS: CORTIN = CORTINRATE*THALAMUS OUTFLOWS: CORTOUT = CORTOUTRATE STRIATUM(t) = STRIATUM(t ± dt) + (STRIATIN ± STRIATOUT) * dt INIT STRIATUM = 20 INFLOWS: STRIATIN = STRIATINRATE*CORTEX_*0.1 OUTFLOWS: STRIATOUT = STRIATOUTRATE*SUBNIGRA SUBNIGRA(t) = SUBNIGRA(t ± dt) + (SUBNIGRAIN ± SUBNIGRAOUT) * dt INIT SUBNIGRA = 10 INFLOWS: SUBNIGRAIN = SUBNIGRAINRATE OUTFLOWS: SUBNIGRAOUT = SUNIGRAOUTRATE*STRIATUM THALAMUS(t) = THALAMUS(t ± dt) + (THALIN ± THALOUT) * dt INIT THALAMUS = 30 INFLOWS: THALIN = THALOUT OUTFLOWS: THALOUT = THALOUTRATE*STRIATUM The initial value was 40 for cortex, 20 for striatum, 30 for thalamus and 10 for substanzia nigra. These values indicate the level of activity on a normalized scale. This scale represents a rating scale for the activity of the population of neurons.

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