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## Über dieses Buch

This book presents the latest research in computational methods for modeling and simulating brain disorders. In particular, it shows how mathematical models can be used to study the relationship between a given disorder and the specific brain structure associated with that disorder. It also describes the emerging field of computational psychiatry, including the study of pathological behavior due to impaired functional connectivity, pathophysiological activity, and/or aberrant decision-making. Further, it discusses the data analysis techniques that will be required to analyze the increasing amount of data being generated about the brain. Lastly, the book offers some tips on the application of computational models in the field of quantitative systems pharmacology. Mainly written for computational scientists eager to discover new application fields for their model, this book also benefits neurologists and psychiatrists wanting to learn about new methods.

## Inhaltsverzeichnis

### Introduction

Abstract
Humans have endeavoured to understand the intricate ways of the brain and mind since several centuries, and yet, never has it been so much in the fore-front as the present. Powered by political support, a global endeavour is now ongoing to unravel the functioning of the brain, in health and disease. Computational models are playing an increasingly important role towards such an endeavour, resulting in the emergence of new fields of study. One such area is ‘Computational Neurology and Psychiatry’ comprising of theories and methodologies for studying neurological and psychiatric disorders. There is now a global consensus on the need for careful validation of computational model behaviour with physiological data. Equally important are the data processing and visualisation tools and techniques that are implemented for making hypotheses and predictions. In the first part of this chapter, the reader is introduced to neuroscience and the strategic importance of research on the brain in the present day and age. A brief historical perspective on the underlying mathematical models along with an overview of advancement in the field of computational neurology and psychiatry are discussed. The importance of physiological data and the difficulties and constraints faced are also mentioned. In the second part of this chapter, the reader is introduced to each ‘content-chapter’ of this book in context to the specific areas and themes that they cover in the general area of computational neurology and psychiatry.
Basabdatta Sen Bhattacharya, Amy L. Cochran, Péter Érdi

### Outgrowing Neurological Diseases: Microcircuits, Conduction Delay and Childhood Absence Epilepsy

Abstract
The study of familial disorders characterized by recurring changes in neurodynamics, such as epileptic seizures, paralysis and headaches, provide opportunities to identify the mechanisms for dynamic changes in the nervous system. Many of these diseases are channelopathies. The computational challenge is to understand how a constantly present molecular defect in an ion channel can give rise to paroxysmal changes in neurodynamics. The most common of these channelopathies is childhood absence epilepsy (CAE). Here we review the dynamical properties of three neural microcircuits thought to be important in epilepsy: counter inhibition, recurrent inhibition and recurrent excitation. Time delays, $$\tau$$, are an intrinsic property of these microcircuits since the time for a signal to travel between two neurons depends on the distance between them and the axonal conduction velocity. It is shown that all of these microcircuits can generate multistability provided that $$\tau$$ is large enough. The term “multistability” means that there can be the co-existence of two or more attractors. Attention is drawn to the transient dynamics which can be associated with transitions between attractors, such as delay-induced transient oscillations. In this way we link the paroxysmal nature of seizure recurrences in CAE with time-delayed multistable dynamical systems. The tendency of children with CAE to outgrow their epilepsy is linked to developmental changes in axonal myelination which decrease $$\tau$$.
John Milton, Jianhong Wu, Sue Ann Campbell, Jacques Bélair

### Extracellular Potassium and Focal Seizures—Insight from In Silico Study

Abstract
It is generally considered that epilepsy and seizures are related to alteration in neuronal excitation/inhibition balance. However, using in vitro isolated guinea pig brain model of focal seizures it has been shown that seizures were initiated with increased firing of inhibitory interneurons, neuronal silence of principal cells and increase of extracellular potassium concentration. Neuronal firing of principal cells was subsequently restored with an acceleration-deceleration firing pattern followed by rhythmic burst activity. In order to investigate the link between ionic dynamics and experimentally observed seizure pattern we developed a computational model of hippocampal cells embedded in the extracellular space with realistic dynamics of Na+, K+ and Cl ions, the glial uptake system and diffusion mechanisms. We show that ion concentration changes exert significant influence on the network behaviour. In particular, we show that in the model, strong discharge of inhibitory interneurons may result in long lasting accumulation of extracellular K+, which sustains depolarization of principal cells and causes their pathological discharges. This effect is not present in a reduced model with fixed ionic concentrations. Using computational model we also suggest novel antiepileptic therapies targeting potassium regulation system.
Piotr Suffczynski, Damiano Gentiletti, Vadym Gnatkovsky, Marco de Curtis

### Time Series and Interactions: Data Processing in Epilepsy Research

Abstract
Computational methods can have significant contribution to epilepsy research not only through modeling, but through data analysis as well. Vast amount of neural data has opened a new era of brain research, where new data analysis methods are needed to take full advantage of the available data. Seizure zones, for example, were traditionally localized manually, using the extremely good pattern matching or mismatch recognition skills of the human brain to identify the first pathological patterns at the initiation of the epileptic seizures. Today, mathematical methods can help automate this detection and examine possible markers of the epileptic tissue, either ictal and interictal. In this chapter, we start by discussing these detection methods, as well as open questions in the area of detection algorithms for interictal spikes and high frequency oscillations. We then continue by discussing methods for analyzing continuous signals, methods that include time-frequency analysis and entropy calculations. We finish this chapter with methods for determining causal interactions among signals and how these latter methods can be used to locate the epileptic foci.
Zsigmond Benkő, Dániel Fabó, Zoltán Somogyvári

### Connecting Epilepsy and Alzheimer’s Disease: Modeling of Normal and Pathological Rhythmicity and Synaptic Plasticity Related to Amyloid (A) Effects

Abstract
This chapter is motivated by the hidden links between neurodegeneration due to Alzheimer’s disease and temporal lobe epileptic activity. The following argument is based on the multiple effects of $$\beta$$-amyloid peptides (A$$\beta$$) forming these links potentially at molecular, cellular, synaptic, network, as well as system levels. To explore these links a computational framework was discussed, and two parts of the framework, i.e. pathological rhythm generation and altered bidirectional synaptic plasticity have been constructed and analyzed. By using a skeleton network model of the hippocampal rhythm generation it was demonstrated how A$$\beta$$ affects the ability of neurons in hippocampal networks to fire in unison at theta frequency resulting in reduced power of the theta rhythm. The dual qualitative effects of elevated A$$\beta$$ at the synaptic level, i.e. LTD facilitation and LTP impairment is studied by a modified calcium control hypothesis. The modification implemented the $$\beta$$-amyloid effects on the bidirectional synaptic plasticity and explained well the experimental findings of decreased LTP and increased LTD. The analysis of a kinetic model taking into account the phosphorylation and dephosphorylation pathways associated with potentiation and depression of the AMPA receptor activity supported the biological plausibility of the modification. Such kinds of models offer an integrative perspective to organize scattered data obtained by methods of anatomy, electrophysiology, brain imaging, neurochemistry, behavioral studies, etc. into a coherent picture.
Péter Érdi, Takumi Matsuzawa, Tibin John, Tamás Kiss, László Zalányi

### Dynamic Causal Modelling of Dynamic Dysfunction in NMDA-Receptor Antibody Encephalitis

Abstract
Using electroencephalography (EEG) dynamic brain function can be measured and its abnormalities identified and described. However, inferring pathological mechanisms from EEG recordings is an ill-posed, inverse problem. Here we illustrate the use of neural mass model based dynamic causal modelling to address this inverse problem. Using Bayesian model inversion and model comparison, DCM allows evaluation of different hypotheses regarding pathomechanisms leading to dynamic brain dysfunction in NMDA receptor encephalitis.
Richard E. Rosch, Gerald Cooray, Karl J. Friston

### Oscillatory Neural Models of the Basal Ganglia for Action Selection in Healthy and Parkinsonian Cases

Abstract
In this chapter we discuss various approaches to mathematical and computational modelling of the basal ganglia, particularly in the context of their most common pathology: Parkinson’s disease (PD). The chapter begins with a review of the basal ganglia and PD, which briefly describes the anatomical structure and connectivity as well as typical dynamics of neuronal activity which is mostly oscillatory. Also we provide a short review of computational models of the basal ganglia and PD. These reviews pay particular attention to the modelling of deep brain stimulation: a successful treatment for PD whose mechanism remains unknown. Following that, we present two different models that aim to demonstrate a physiological role of oscillations in the basal ganglia in the context of action selection. Through computational simulation and mathematical analysis of these models we demonstrate that a regime of partial activity synchronization can be considered as a potential mechanism for the action selection.
Robert Merrison-Hort, Nada Yousif, Andrea Ferrario, Roman Borisyuk

### Mathematical Models of Neuromodulation and Implications for Neurology and Psychiatry

Abstract
We use mathematical modeling to study how the electrophysiology and the pharmacology of the brain affect each other and brain function. Necessarily, this involves understanding volume transmission by which neurons in a brain nucleus project to distant nuclei and change the local biochemistry there. Examples include the serotonergic projection from the dorsal raphe nucleus to the striatum and the dopaminergic projection from the substantial nigra pars compacta to the striatum. The serotonin concentration in the striatum affects dopamine release in the striatum through receptors on the dopamine terminals. The concept of volume transmission is discussed and other examples of volume transmission are given. We describe how we construct our mathematical models based on known physiology and biochemistry. We describe model results that show how autoreceptors buffer the serotonin system against genetic polymorphisms and we explain why the brain serotonin concentration depends on diet but the dopamine concentration does not. We discuss the traditional hypotheses about the mechanism of action of selective sserotonin reuptake inhibitors (SSRIs), and introduce a new hypothesis about the mechanisms of SSRIs. We explain why the serotonin system has a large effect on the efficacy of levodopa treatment for Parkinson’s disease and why dyskinesias occur as the disease progresses. Finally, we study various aspects of the homeostasis of dopamine in the striatum. Volume transmission raises many new, interesting questions for the mathematical neuroscience community.
Janet A. Best, H. Frederik Nijhout, Michael C. Reed

### Attachment Modelling: From Observations to Scenarios to Designs

Abstract
The purpose of the research programme detailed in this paper is to update the attachment control system framework that John Bowlby set out in his formulation of Attachment Theory. It does this by reconceptualising it as a cognitive architecture that can operate within multi-agent simulations. This is relevant to computational psychiatry because attachment phenomena are broad in scope and range from healthy everyday interactions to psychopathology. The process of attachment modelling involves three stages and this paper makes contributions in each of these stages. Firstly, a survey of attachment research is presented which focuses on two important attachment behavioural measures: the Strange Situation Procedure and the Adult Attachment Interview (AAI). These studies are reviewed to draw out key behavioural patterns and dependencies. Secondly, the empirical observations that are to be explained in this research programme are abstracted into scenarios which capture key behavioural elements. The value of behavioural scenarios is that they can guide the simulation design process and help evaluate simulations which are produced. Thirdly, whilst the implementation of these scenarios is still a work in progress, several designs are described that have been created and implemented as simulations. These include normative and non-pathological infant behaviour patterns observed across the first year of life in naturalistic observations and ‘Strange Situation’ studies. Future work is described which includes simulating dysfunctional infant behaviour patterns and a range of adult attachment behaviour patterns observed in the Adult Attachment Interview. In conclusion, this modelling approach is distinguished from other approaches in computational psychiatry because of the psychologically high level at which it models phenomena of interest.
Dean Petters, Luc Beaudoin

### Self-attachment: A Holistic Approach to Computational Psychiatry

Abstract
There has been increasing evidence to suggest that the root cause of much mental illness lies in a sub-optimal capacity for affect regulation. Cognition and emotion are intricately linked and cognitive deficits, which are characteristic of many psychiatric conditions, are often driven by affect dysregulation, which itself can usually be traced back to sub-optimal childhood development. This view is supported by Attachment Theory, a scientific paradigm in developmental psychology, that classifies the type of relationship a child has with a primary care-giver to one of four types of insecure or secure attachments. Individuals with insecure attachment in their childhoods are prone to a variety of mental illness, whereas a secure attachment in childhood provides a secure base in life. We therefore propose, based on previous work, a holistic approach to Computational Psychiatry, which is informed by the development of the brain during infancy in social interaction with its primary care-givers. We identify the protocols governing the interaction of a securely attached child with its primary care-givers that produce the capacity for affect regulation in the child. We contend that these protocols can be self-administered to construct, by neuroplasticity and long term potentiation, new “optimal” neural pathways in the brains of adults with insecure attachment history. This procedure is called Self-attachment and aims to help individuals create their own attachment objects which has many parallels with Winnicott’s notion of transitional object, Bowlby’s comfort objects, Kohut’s empathetic self-object as well as religion as an attachment object. We describe some mathematical models for Self-attachment: a game-theoretic model, a model based on the notion of a strong pattern in an energy based associative neural network and several neural models of the human brain.
Abbas Edalat

### A Comparison of Mathematical Models of Mood in Bipolar Disorder

Abstract
We are far from a comprehensive understanding of the dynamics of mood in bipolar disorder. However, a number of models of mood have emerged to describe the pathological fluctuation in mood that is characteristic of this disorder. These models are surprisingly diverse in their dynamical principles, e.g. whether mood is periodic or whether mania and depression are stable points when ignoring external influences. This chapters presents a selective summary of existing models of mood in bipolar disorder and introduces two new models. We focus on a key question: how to differentiate between models when only time courses of mood are available. For each model we consider, time courses are evaluated through data transformations and statistical techniques, including estimating survival functions and spectral density. We then provide guidelines on how to decide whether a certain modeling assumption, e.g. periodicity, is appropriate.
Amy L. Cochran, André Schultz, Melvin G. McInnis, Daniel B. Forger

### Computational Neuroscience of Timing, Plasticity and Function in Cerebellum Microcircuits

Abstract
Cerebellum has been known to show homogeneity in circuit organization and hence the “modules” or various circuits in the cerebellum are attributed to the diversity of functions such as timing, pattern recognition, movement planning and dysfunctions such as ataxia related to the cerebellum. Ataxia-like conditions, induced by intrinsic excitability changes, disable spiking or bursts and thereby limit the quanta of downstream information. Understanding timing, plasticity and functional roles of cerebellum involve large-scale and microcircuit reconstructions validating molecular mechanisms in population activity. Using mathematical modelling, we attempted to reconstruct information transmission at the granular layer of the cerebellum, a circuit whose role in dysfunctions remain yet to be fully explored. We have employed spiking models to reconstruct timing roles and detailed biophysical models for extracellular activity and local field population response. The roles of inhibition, induced plasticity and their implications in information transmission were evaluated. Modulatory roles of Golgi inhibition and pattern abstraction via optimal storage were estimated. An abstraction of the granular and Purkinje layer circuit for neurorobotic roles such as pattern recognition and spike encoding via two new methods was developed. Simulations suggest plasticity at cerebellar relays may be an important element of tremendous storage capacity reliable in the learning of coordination of actions, sensorimotor or cognitive, in which the cerebellum participates.
Shyam Diwakar, Chaitanya Medini, Manjusha Nair, Harilal Parasuram, Asha Vijayan, Bipin Nair

### A Computational Model of Neural Synchronization in Striatum

Abstract
The role of basal ganglia circuits in voluntary motor movements has been known for decades, but its role in cognitive processes, especially in emotion-based action selection, has drawn recent attention. As more is discovered about the role of basal ganglia circuits in reward based learning for decision-making, it is increasingly recognized that deficits of this circuit give rise to psychiatric disorders besides neurodegenerative diseases. Striatum, the main input nuclei of basal ganglia, receives inputs not only from cortical areas but also from substantia nigra pars compacta and ventral tegmental area, which have dopamine neuron populations. Thus, the function of striatum, modulated by dopamine, has an important role in the motor and cognitive processes in which basal ganglia circuits are active. Here, a neurocomputational model will be given for investigating the role of dopamine level on the synchronized behavior of striatal medium spiny neurons.
Rahmi Elibol, Neslihan Serap Şengör

### A Neural Mass Computational Framework to Study Synaptic Mechanisms Underlying Alpha and Theta Rhythms

Abstract
Computational modelling in neuroscience is gaining in popularity towards investigating neurological and psychiatric disorders. One of the major obstacles in faster progress in this field has been the current state-of-the-art computational platforms and frameworks that struggle to simulate, in terms of time and memory, the complex brain structures and functions. Thus, modelling of neuronal population that are packed in dense spatial clusters and show local synchrony has been a popular methodology towards simulating higher level brain functions recorded via electroencephalogram (EEG); neural mass modelling has been one such paradigm. The drawback in these models of population level dynamics, however, is a lack of correlation with the underlying cellular mechanisms, which is crucial in investigating disease conditions. The neural mass model presented in this work approaches both these issues: first, kinetic models of synaptic information transfer replaces Rall’s alpha function that are traditionally used in these models, thus allowing correlation of model output simulating EEG-like dynamics with lower-level synaptic attributes; second, computational time for this modified approach in neural mass models is faster than the existing traditional approach and up to an order of ten. Here, the objective is to understand the underlying cellular mechanisms of alpha and theta rhythms that are EEG biomarkers in several neurological and psychiatric disorders. A biologically-inspired model of the thalamic Lateral Geniculate Nucleus using the modified neural mass modelling framework is tuned and parameterised to simulate EEG alpha and theta rhythms. The results suggest that low-levels of neurotransmitter concentration in the synaptic cleft along with a reduced GABA-ergic activity from the thalamic interneurons may play a role in alpha to theta band transition, a symptom implicated in several brain disorders. Furthermore, the model validates reports from experimental observations that similar thalamic mechanisms underlie alpha and theta band oscillations. In addition, the model predicts that the GABA-ergic pathways from the thalamic interneurons and the thalamic reticular nucleus may have distinct roles in EEG during cognitive state and state of sleep, and in both healthy and diseased brains.
Basabdatta Sen Bhattacharya, Simon J. Durrant

### The Role of Simulations in Neuropharmacology

Abstract
Computational models and simulations have evolved dramatically in the past decades, providing useful insights on neurological systems, their functions and dynamics. They successfully deepened our knowledge on systems ranging from biomolecular to neuronal network scale. In spite of these successes, Modeling and Simulation still represent a marginal contribution to the field of neuropharmacology. What may be the reasons behind this? These pages succinctly describe the current state of neuropharmacology, and provide arguments in favor of amplifying the role of Modeling and Simulation on the various phases of the drug discovery and development process for the nervous system. We provide examples illustrating how Modeling and Simulation can guide neuropharmacology. We then present a methodology for building multiscale models by reducing the computational complexity while maintaining predictability levels using computationally efficient input-output modeling. Finally, we deliver arguments in support of generalizing Modeling and Simulation in neuropharmacology to make it a cornerstone of the drug discovery and development process.
Jean-Marie C. Bouteiller, Theodore W. Berger
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