**1. Introduction**

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The majority of mental disorders (schizophrenia and other psychotic disorders, mood and anxiety disorders) have become treatable for the last several decades mostly due to development of the agents which modulate function of the brain dopaminergic, noradrenergic, and serotonergic system. The art of pharmacological healing in psychiatry consists actually in a great part in choice of the monoaminergic agent (i.e. antipsychotic or antidepressant) or their combinations which will modify the brainstem monoaminergic systems in an appropriate way. In other words, a daily problem in psychiatric practice could be realized as the task of estimation of the actual "neurochemical status" of the patient mostly in respect to the three brainstem monoamines. In clinical setting the task is still accomplished relying on the clinical picture and identifying the dominant symptoms that the patient manifests (e.g. Nutt, 2008; Nutt et al., 2007).

The search for biological correlates (biomarkers) of neurochemical processes associated with mental disorders has not yet resulted in convincing and applicable findings (Bartova et al., 2010; Mössner et al., 2007). A reason that may account for the fail could be that attempts that have been made had been focused on a single neurotransmitter activity (Mössner et al., 2007). On the other hand, "Models which postulate too little or too much of a single neurotransmitter are not consistent with the complex regulation of neurotransmitter systems… There are major functional interactions among different neurotransmitter and neuropeptide systems which make single neurotransmitter theories simplisti A task for future investigations… is to develop clinically applicable biological tests that can assess the functional interactions among different neurotransmitter and neuropeptide systems and specific brain structures. Successful development of such paradigms could result in improved diagnostic classification and prediction of treatment response…" (Charney et al., 1995).

In our interpretation of the task set by Charney & colleagues "functional interactions among different neurotransmitter and neuropeptide systems" are viewed as neurobiological signals in control system theory meaning of the word 'signal'. With this interpretation the task appear to be "to develop clinically applicable biological tests" which will allow insight into

Assessment of Brain Monoaminergic Signaling

continuous biological signal such as SCR.

system.1

**three feedback loops** 

Through Mathematical Modeling of Skin Conductance Response 85

respiration, electromyography) (Lader, 1980; O'Gorman, 1971). We suppose that dealing with weaker emotional stimuli put more lights on usual everyday-life emotional responding and arousal fluctuations, a range where individuals with a mental disorder (e.g. depression) are altered presumably due to the alterations in the brainstem monoaminergic systems' activity. The second reason for choosing SCR as a neurobiological mechanism for system identification is continuous nature of the SCR signal. From mathematical point of view, heart rate and respiration rate are derived variables that cannot be computed for time periods shorter than beat-to-beat and respiration-to-respiration period. Therefore, they are to greater extent discreet and so less convenient, since less informative for analysis than a

The goals of this chapter are: (1) to introduce the reader with the method of system identification of the SCR, (2) to point to the emerging metrics of the SCR process, and (3) to show how this metrics allow inferring about tonic and phasic functions of the brain monoaminergic signaling and about the central neural events – neural input for the SCR

**2. Mathematical model of the SCR process: A series of integrations with** 

signals with the activity of specific neurotransmitter systems.

**2.1 Solution for the "hidden input" problem in the SCR modeling** 

input to the SCR system, i.e. to solve the "hidden input" problem.

System identification approach enables to look into the process of the SCR in a neurophysiologically meaningful way. Through this method we approximate the whole arousal process (from the initial central neural event to the SCR output) as a series of integrators, with the integration constant of 100 ms, which corresponds to the temporal scale of brain neural integrations (Varela et al., 2001; Koch et al., 1996; Koch, 2005). Knowing the dynamic model of the SCR process enables further examination of the neurochemical meaning of the system parameters and eventually association of the identified regulatory

The prerequisite for the system identification procedure which is performed using the *System Identification Toolbox* included in the mathematical software MATLAB® is that both output and input signal of the system are known. But, while the output signal of the SCR system is observable and measurable, the input signal is not directly measurable. Therefore, a separate scientific task is to find an appropriate mathematical representation of the driving

A hint to visualize the initial forcing event in the SCR process came from mathematical dealing with differential equations with discontinuous forcing functions: the highest derivative of the solution appearing in the differential equation has jump discontinuities at

1 There is an aspect of the present approach which we want to point out. Many findings and concepts developed in neuroscience during the last two decades have not yet been operationalized for clinical use. The method which is presented here could contribute to lessen this gap translating some concepts of modern neuroscience and making them visible in everyday clinical work. The following concepts are involved: tonic and phasic function of neurotransmitters, gain modulation of neural activity by monoaminergic inervation, feedback regulation in the arousal process, resonance and frequency characteristics of neural systems, central neural code, and signal-to-noise ratio of neural signals.

the signal interactions among neurotransmitter systems. It means that we are interested in the signal properties of neurotransmission such as: strength of the signal, frequency of signal oscillations, signal amplification and integration, and feedback regulation of the neural signals. Although these signal properties are realized through chemical and electric neuronal activities our methodological approach is not based on the measurements at that level of the neurochemical events. Instead of direct measuring concentrations of released neurotransmitters, density, affinity, and activity of their membrane receptors and reuptake transporters we suggest a method that needs a shift in the perspective of looking at the brain neurochemistry. The twist is that we firstly examine signal processing and control system aspects of a relatively defined neurobiological mechanism. Then, informed with the system and the signals' properties we are able to infer about the underlying neurochemical activity of the involved neurotransmitter systems. In other words, we aim to estimate "interactions among different neurotransmitter and neuropeptide systems" looking at the signal processing in the examined neurobiological mechanism.

The method which enables to examine the underlying regulatory pattern and points to the way of signal processing during a neurobiological process is a mathematical tool, the system identification theory and technique (Ljung, 1999). As a neurobiological mechanism which is convenient for our task to reveal neurochemical signal processing involving the brain dopaminergic, noradrenergic, and serotonergic system we have employed an output of the process of emotional arousal, the phenomenon of emotional, palmar sweating measured as the skin conductance response (SCR), which is regarded as the most useful laboratory test for an autonomic response (Damasio, 1994).

The so-called electrodermal activity (EDA) was discovered at the end of the XIX century as two different phenomena which occur at the palmar and plantar skin surface. One is electrical resistance of the skin surface (Vigoroux, 1879, 1888) and its momentary decreases in response to variety of external stimuli (Féré, 1888). This phenomenon implies passing a small electrical current on the surface of the skin. The other phenomenon is a measurable electrical potential between two electrodes placed on the skin without applying an external current (Tarchanoff, 1890). Contemporary researchers use predominantly the first phenomenon as the method of choice whereby resistance is expressed as its reciprocal – conductance. From the earliest publications the tonic-phasic distinction in EDA has been implied. More about the phasic component speak other terms which have been used to refer to the EDA phenomena in the history, galvanic skin response (GSR), and psychogalvanic reflex (PGR). The phasic component of EDA is nowadays assigned as skin conductance response (SCR) as opposed to the tonic component of EDA which is referred to as skin conductance level (SCL).

Fluctuations in SCL occur at the time-scale of minutes while phasic SCRs appear at the timescale of seconds. Both SCL and SCR activity refer to the activity of palmar and plantar sweat glands and myoepithelial cells of their ducts which are under neural control of the sympathetic branch of the autonomic nervous system (Dementienko et al., 2000). Palmar and plantar sweat glands are not involved in the process of thermoregulation until the ambient temperature does not exceed 30C (Andreassi, 1989; Venables & Christie, 1980). On the other hand, palmar and plantar sweating is elicited by psychic, emotional stimuli.

The SCR is a sensitive measure, it could be evoked applying weaker psychic stimuli than it would be necessary for other physiological variables (e.g. heart rate, blood pressure,

the signal interactions among neurotransmitter systems. It means that we are interested in the signal properties of neurotransmission such as: strength of the signal, frequency of signal oscillations, signal amplification and integration, and feedback regulation of the neural signals. Although these signal properties are realized through chemical and electric neuronal activities our methodological approach is not based on the measurements at that level of the neurochemical events. Instead of direct measuring concentrations of released neurotransmitters, density, affinity, and activity of their membrane receptors and reuptake transporters we suggest a method that needs a shift in the perspective of looking at the brain neurochemistry. The twist is that we firstly examine signal processing and control system aspects of a relatively defined neurobiological mechanism. Then, informed with the system and the signals' properties we are able to infer about the underlying neurochemical activity of the involved neurotransmitter systems. In other words, we aim to estimate "interactions among different neurotransmitter and neuropeptide systems" looking at the signal

The method which enables to examine the underlying regulatory pattern and points to the way of signal processing during a neurobiological process is a mathematical tool, the system identification theory and technique (Ljung, 1999). As a neurobiological mechanism which is convenient for our task to reveal neurochemical signal processing involving the brain dopaminergic, noradrenergic, and serotonergic system we have employed an output of the process of emotional arousal, the phenomenon of emotional, palmar sweating measured as the skin conductance response (SCR), which is regarded as the most useful laboratory test

The so-called electrodermal activity (EDA) was discovered at the end of the XIX century as two different phenomena which occur at the palmar and plantar skin surface. One is electrical resistance of the skin surface (Vigoroux, 1879, 1888) and its momentary decreases in response to variety of external stimuli (Féré, 1888). This phenomenon implies passing a small electrical current on the surface of the skin. The other phenomenon is a measurable electrical potential between two electrodes placed on the skin without applying an external current (Tarchanoff, 1890). Contemporary researchers use predominantly the first phenomenon as the method of choice whereby resistance is expressed as its reciprocal – conductance. From the earliest publications the tonic-phasic distinction in EDA has been implied. More about the phasic component speak other terms which have been used to refer to the EDA phenomena in the history, galvanic skin response (GSR), and psychogalvanic reflex (PGR). The phasic component of EDA is nowadays assigned as skin conductance response (SCR) as opposed to

the tonic component of EDA which is referred to as skin conductance level (SCL).

Fluctuations in SCL occur at the time-scale of minutes while phasic SCRs appear at the timescale of seconds. Both SCL and SCR activity refer to the activity of palmar and plantar sweat glands and myoepithelial cells of their ducts which are under neural control of the sympathetic branch of the autonomic nervous system (Dementienko et al., 2000). Palmar and plantar sweat glands are not involved in the process of thermoregulation until the ambient temperature does not exceed 30C (Andreassi, 1989; Venables & Christie, 1980). On the other hand, palmar and plantar sweating is elicited by psychic, emotional stimuli.

The SCR is a sensitive measure, it could be evoked applying weaker psychic stimuli than it would be necessary for other physiological variables (e.g. heart rate, blood pressure,

processing in the examined neurobiological mechanism.

for an autonomic response (Damasio, 1994).

respiration, electromyography) (Lader, 1980; O'Gorman, 1971). We suppose that dealing with weaker emotional stimuli put more lights on usual everyday-life emotional responding and arousal fluctuations, a range where individuals with a mental disorder (e.g. depression) are altered presumably due to the alterations in the brainstem monoaminergic systems' activity. The second reason for choosing SCR as a neurobiological mechanism for system identification is continuous nature of the SCR signal. From mathematical point of view, heart rate and respiration rate are derived variables that cannot be computed for time periods shorter than beat-to-beat and respiration-to-respiration period. Therefore, they are to greater extent discreet and so less convenient, since less informative for analysis than a continuous biological signal such as SCR.

The goals of this chapter are: (1) to introduce the reader with the method of system identification of the SCR, (2) to point to the emerging metrics of the SCR process, and (3) to show how this metrics allow inferring about tonic and phasic functions of the brain monoaminergic signaling and about the central neural events – neural input for the SCR system.1
