Techn. University, Diss., 2003--Berlin.

Techn. Hochsch., Diss., 2005--Aachen.

Universiẗat, Diss., 2006--Frankfurt (Main).

University, Diss., 2005--Tübingen.

Techn. Universiẗat, Diss., 2005--Darmstadt.

A complete simulation system is proposed that can be used as an educational tool by physicians in training basic skills of Minimally Invasive Vascular Interventions. In the first part, a surface model is developed to assemble arteries having a planar segmentation. It is based on Sweep Surfaces and can be extended to T- and Y-like bifurcations. A continuous force vector field is described, representing the interaction between the catheter and the surface. The computation time of the force field is almost unaffected when the resolution of the artery is increased. The mechanical properties of arteries play an essential role in the study of the circulatory system dynamics, which has been becoming increasingly important in the treatment of cardiovascular diseases. In Virtual Reality Simulators, it is crucial to have a tissue model that responds in real time. In this work, the arteries are discretized by a two dimensional mesh and the nodes are connected by three kinds of linear springs. Three tissue layers (Intima, Media, Adventitia) are considered and, starting from the stretch-energy density, some of the elasticity tensor components are calculated. The physical model linearizes and homogenizes the material response, but it still contemplates the geometric nonlinearity. In general, if the arterial stretch varies by 1% or less, then the agreement between the linear and nonlinear models is trustworthy. In the last part, the physical model of the wire proposed by Konings is improved. As a result, a simpler and more stable method is obtained to calculate the equilibrium configuration of the wire. In addition, a geometrical method is developed to perform relaxations. It is particularly useful when the wire is hindered in the physical method because of the boundary conditions. The physical and the geometrical methods are merged, resulting in efficient relaxations. Tests show that the shape of the virtual wire agrees with the experiment. The proposed algorithm allows real-time executions and the hardware to assemble the simulator has a low cost. / Es wird ein vollständiges Simulationssystem entwickelt, das von Ärzten als Lehrmittel zur Ausbildung grundlegender Fertigkeiten bei Herzkathetereingriffen eingesetzt werden kann. Im ersten Teil wird ein Oberflächenmodell zur Erstellung von Arterien mit planarer Segmentierung entwickelt. Im zweiten Teil werden die Arterien durch ein zweidimensionales Netz diskretisiert, die Knoten werden durch drei Arten linearer Federn verbunden und ausgehend von einer Dehnungsenergie-Dichte-Funktion werden einige Komponenten des Elastizitätstensors berechnet. Im letzten Teil wird das von anderen Autoren vorgeschlagene physikalische Modell des Drahtes verbessert und eine neue geometrische Methode entwickelt. Der vorgeschlagene Algorithmus ermöglicht Echtzeit-Ausführungen. Die Hardware des Simulators hat geringe Herstellungskosten.

Light is one of the most advantageous stimuli to manipulate functional materials because it can be applied contactless and with high precision. A common strategy to prepare light-responsive physical systems is the embedding of photoswitchable groups such as the dye molecule azobenzene (azo). Upon irradiation with UV light, azobenzene undergoes photoisomerization from the trans to the cis isomer, whereas blue light triggers the inverse conversion. The two isomers differ with respect to their shape, solubility, and light absorption. Up to now, comparatively little research has been focusing on compounds that unite several photoswitchable groups. Such so-called multiphotochromes are promising multi-state molecular systems that can be controlled by light. In this thesis, the object of study is a star-shaped multiphotochromic molecule denoted TrisAzo. It is composed of three azo groups, which are centrally linked by a light-inert BTA group. The molecule has four photoisomers, ranging from the all-trans to the all-cis isomer. Furthermore, TrisAzo is the elementary building block of light-responsive supramolecular aggregates in solution. Previous experimental works report severe morphological changes of the aggregates under UV–Vis light but the underlying molecular mechanisms are still debated. The objective of this thesis is to elucidate the effects of light on TrisAzo – first, concerning its molecular properties and second, regarding the structure and stability of its supramolecular aggregates. In the presented work, the photoisomers of an azobenzene star with a BTA core are studied for the first time via computational methods, particularly using density functional theory and fully atomistic molecular dynamics (MD) simulations. The solvational and optical properties of TrisAzo are quantified as a function of its isomerization state. The solubility of TrisAzo in polar solvents improves with an increasing fraction of the cis-azo arms due to a redistribution of electron density. The absorption spectra of the TrisAzo isomers are nearly linear superpositions of the individual azo arm spectra but with slight deviations. These deviations indicate weak electronic coupling effects between the connected azo groups. Supramolecular aggregates of TrisAzo molecules in water are modeled using fully atomistic MD simulations for extensive investigations on the molecular scale. In equilibrium conditions, it is verified that randomly distributed TrisAzo molecules self-assemble into column-shaped stacks. Simulations of pre-assembled TrisAzo stacks provide detailed insights into their intermolecular interactions. The binding energies are dominated by π-π interactions between conjugated parts of the stacked molecules, especially the azo groups, while hydrogen bonds between the BTA cores play a subordinate but stabilizing role. To implement the effects of light into the simulations, a stochastic model of the repeated photoisomerization of azobenzene is developed. This model reproduces the photoisomerization kinetics of TrisAzo in good agreement with theory and previous experimental results. Based on this approach, light of various intensities and wavelengths is applied on an equilibrated TrisAzo stack. In contrast to prior assumptions, the simulations indicate that a stacked TrisAzo aggregate irradiated by light does not break or disassemble into separate fragments. The stack instead develops defects in the form of molecular shifts and reorientations. As a result, the aggregate eventually loses its columnar shape. The mechanism and driving forces behind these structural changes are clarified based on the simulation results. Thus, this work provides a new interpretation of the experimentally observed morphological changes. The obtained insights on the molecular scale may facilitate the design of light-responsive gels and supramolecular polymers.:Abstract v Kurzfassung vii 1 Introduction 1 2 Properties of Azobenzene and Azobenzene-Containing Materials 5 2.1 Azobenzene 5 2.1.1 Isomers and Photoisomerization 6 2.1.2 The Photostationary State 10 2.2 Multiphotochromic Molecules Based on Azobenzene 10 2.2.1 Azobenzene Stars 11 2.2.2 The Benzene-1,3,5-Tricarboxamide Linker Unit 11 3 Computational Methods and Models 15 3.1 Density Functional Theory 15 3.1.1 Functional and Basis Set 16 3.1.2 Implicit Solvation Models 17 3.1.3 Time-Dependent Density Functional Theory 17 3.2 Molecular Dynamics Simulations 18 3.2.1 All-Atom MD Simulations 18 3.2.2 Force Fields 19 4 Simulation Techniques 23 4.1 Thermodynamic Integration 23 4.1.1 Implementation in Atomistic Simulations 24 4.2 Modeling Photoisomerization in MD Simulations 27 4.2.1 Implementation of the Rotation Pathway 28 4.3 Modeling Light-Irradiated Azo-Materials in MD Simulations 30 4.3.1 The Cyclic Photoisomerization Model 31 5 Photoisomers of an Azobenzene Star 35 5.1 Object of Study: The Molecule TrisAzo 35 5.1.1 Isomers and Conformers 35 5.2 Ground State Properties in the Gas Phase and in Solvents 36 5.2.1 Energies and Standard Enthalpies of Formation 37 5.2.2 Geometry and Shape Properties 38 5.2.3 Dipole Moments 42 5.2.4 Molecular Properties Upon Hydration in Explicit Water 44 5.3 Solubility 47 5.3.1 Influence of Solvent Polarity 48 5.3.2 Influence of Isomerization State 48 5.3.3 Hydration Free Energy 49 5.4 Absorption Spectra and Intramolecular Coupling 51 5.4.1 Influence of the Number of Azo Groups and Their Isomerization State 52 5.4.2 Effect of the Solvent Polarity 54 5.5 Summary 56 6 Equilibrium Properties of TrisAzo Clusters 59 6.1 Supramolecules of Azobenzene Stars in the Experiment 60 6.1.1 Light-Induced Morphological Transition 60 6.2 Self-Assembly Starting from a Random Distribution 62 6.2.1 Radial Distribution Function 63 6.2.2 Cluster Analysis 65 6.3 Intermolecular Energy of a TrisAzo Dimer 69 6.3.1 Total Intermolecular Energy 70 6.3.2 Energy Decomposition 71 6.4 Structural Properties of Columnar TrisAzo Clusters 75 6.4.1 Considered Cluster Arrangements (Cluster Types) 75 6.4.2 Inner Structure of the Clusters 79 6.4.3 Effect of Cluster Size 79 6.5 Intermolecular Energy of Columnar TrisAzo Clusters 82 6.5.1 Total Intermolecular Energy 82 6.5.2 Energy Decomposition 83 6.5.3 The Role of Hydrogen Bonding 88 6.5.4 Rationalizing the Structural Differences of the Considered Cluster Types 91 6.6 Summary 93 7 Columnar TrisAzo Clusters Under UV–Vis Light 97 7.1 TrisAzo Stacks in the Full Photoisomerization Model 97 7.1.1 Cluster Structure Before and After Irradiation 98 7.1.2 Intermolecular Energy 101 7.2 TrisAzo Stacks in the Cyclic Photosomerization Model 104 7.2.1 Photoisomerization Kinetics 104 7.2.2 Cluster Structure Under Irradiation 108 7.2.3 Intermolecular Energy of TrisAzo Stacks Under Irradiation 112 7.2.4 Mechanism of Defect Formation 116 7.2.5 Comparison with Simulations of Comparable Systems 118 7.3 Summary 118 8 Summary and Outlook 121 8.1 Summary 121 8.2 Outlook 123 A Functional Form of the Force Fields 125 A.1 DREIDING Force Field 125 A.2 Polymer Consistent Force Field (PCFF) 129 B Additional Details about Thermodynamic Integration 133 B.1 Derivation of the Formalism 133 B.2 Avoiding Singularities and Instabilities 134 C Details of the Computational Models 137 C.1 DFT and TD-DFT Calculations 137 C.1.1 DFT Calculations 137 C.1.2 TD-DFT Calculations 138 C.2 MD Simulations of TrisAzo Molecules in PCFF 138 C.2.1 Parametrization 139 C.2.2 Preparation of Initial Configurations 139 C.2.3 Simulation Settings 140 C.3 MD Simulations of TrisAzo Molecules in DREIDING 140 C.3.1 Parametrization 141 C.3.2 Preparation of Initial Configurations 141 C.3.3 Simulation Settings 141 C.4 Intermolecular Energy Calculations of TrisAzo Dimers in PCFF and DREIDING 142 C.5 Visualization of Molecular Structures 142 D Equilibrium Properties of TrisAzo Clusters: Additional Material 143 D.1 From Experiments to Simulations 143 D.2 Cluster Analysis for TrisAzo Self-Assembly: Additional Material 144 D.3 Intermolecular Energy of a TrisAzo Dimer: PCFF Results 145 D.3.1 Total Intermolecular Energy 145 D.3.2 Energy Decomposition 145 D.3.3 Estimated Total Intermolecular Energy of TrisAzo-H 148 D.4 Structural Properties of Columnar TrisAzo Clusters: Additional Material 149 D.5 Intermolecular Energy of Columnar TrisAzo Clusters: Additional Material 150 D.5.1 Defect Detection Algorithm 151 D.6 The Role of Hydrogen Bonds: Additional Material 152 E Columnar TrisAzo Clusters Under UV–Vis Light: Additional Material 155 E.1 TrisAzo Stacks in the Full Photoisomerization Model: Additional Material 155 E.2 TrisAzo Stacks in the Cyclic Photosomerization Model: Additional Material 156 F Code Availability 161 Bibliography 163 List of Publications 183 Copyright of Published Articles 187 Acknowledgements / Danksagung 189 List of Abbreviations 191 List of Symbols 193 List of Physical Constants and Unit Conversions 195 Eidesstattliche Erklärung 197 / Licht ist einer der vorteilhaftesten Stimuli für die Manipulation responsiver Funktionsmaterialien, da es berührungslos und mit hoher Präzision angewendet werden kann. Ein weit verbreiteter Ansatz zur Herstellung lichtresponsiver physikalische Systeme ist der Einbau lichtschaltbarer Gruppen wie das Farbstoffmolekül Azobenzol (Azo). Unter UV-Licht vollzieht Azobenzol eine Photoisomerisation vom trans- zum cis-Isomer, während blaues Licht die umgekehrte Umwandlung auslöst. Die beiden Isomere unterscheiden sich vor allem durch ihre räumliche Gestalt, Löslichkeit und Lichtabsorption. Noch unzureichend erforscht sind Moleküle, die mehrere lichtschaltbare Gruppen in sich vereinen. Solche sogenannten Multiphotochrome sind vielversprechende molekulare Mehrzustandssysteme, die durch Licht geschaltet werden können. Untersuchungsobjekt dieser Arbeit ist ein sternförmiges multiphotochromes Molekül namens TrisAzo. Es besteht aus drei Azogruppen, die zentral über eine gegenüber Licht inerte BTA-Gruppe verknüpft sind. Dementsprechend existieren vier Photoisomere dieses Moleküls, vom all-trans- bis zum all-cis-Isomer. Des Weiteren ist TrisAzo der elementare Baustein lichtempfindlicher supramolekularer Aggregate in Lösung. Frühere experimentelle Arbeiten berichten starke morphologische Strukturänderungen der Aggregate unter Lichteinfluss, jedoch sind die zugrundeliegenden molekularen Mechanismen bisher ungeklärt. Ziel dieser Arbeit ist es, die Auswirkungen von Licht auf TrisAzo aufzuklären, erstens in Bezug auf dessen molekulare Eigenschaften und zweitens hinsichtlich der Struktur und Stabilität der supramolekularen Aggregate. In der vorgestellten Arbeit werden erstmals die Photoisomere eines Azosterns mit BTA-Kern auf Basis computerbasierter Methoden untersucht. Eingesetzt werden dabei Dichtefunktionaltheorie und atomistische Molekulardynamiksimulationen (MD). Insbesondere wird die Löslichkeit und das Lichtabsorptionsverhalten von TrisAzo in Abhängigkeit seines Isomerisationszustands analysiert. Die Löslichkeit von TrisAzo verbessert sich mit steigendem Anteil der cis-Azogruppen aufgrund einer damit einhergehenden Umverteilung der Elektronendichte. Die Absorptionsspektren der TrisAzo-Isomere sind in erster Näherung lineare Superpositionen der Einzelspektren jedes Molekülarms, jedoch mit geringen Abweichungen. Diese Abweichungen deuten auf schwache elektronische Kopplungseffekte zwischen den Azogruppen hin. Supramolekularen Aggregate von TrisAzo-Molekülen in Wasser werden für umfangreiche Untersuchungen auf molekularer Ebene in atomistischen MD-Simulationen modelliert. Im thermodynamischen Gleichgewicht bestätigt sich, dass sich zufällig verteilte TrisAzo-Moleküle in säulenförmig gestapelten Aggregaten zusammenfinden. Weitere Simulationen vorgestapelter TrisAzo-Aggregate liefern detaillierte Rückschlüsse auf deren intermolekulare Wechselwirkungen. Die Bindungsenergien werden von π-π-Wechselwirkungen zwischen den konjugierten Bereichen der aufeinanderliegenden Moleküle dominiert. Wasserstoffbrücken zwischen den BTA-Gruppen haben eine untergeordnete, aber stabilisierende Rolle. Um den Effekt von Licht in die Simulationen einzubauen, ist ein stochastisches Modell für die wiederholte Photoisomerisation der Azogruppen entwickelt worden. Dieses Modell reproduziert die Photoisomerisationskinetik von TrisAzo in guter Übereinstimmung mit Theorie und vorigen Experimenten. Basierend auf diesem Ansatz wird Licht verschiedener Intensitäten und Wellenlängen auf die gestapelten TrisAzo-Aggregate angewandt. Entgegen früherer Annahmen zerfallen die Aggregate daraufhin nicht in Einzelfragmente. Stattdessen entwickeln sie Defekte in Form von Molekülumordnungen sowie -reorientierungen und verlieren dadurch ihre säulenartige Form. Der Mechanismus und die Ursachen dieser Strukturänderungen werden anhand der Simulationen aufgeklärt. Damit liefert diese Arbeit eine neue Interpretation der experimentell beobachteten morphologischen Veränderungen. Die gewonnenen Erkenntnisse können die Entwicklung lichtresponsiver Gele und supramolekularer Polymere unterstützen.:Abstract v Kurzfassung vii 1 Introduction 1 2 Properties of Azobenzene and Azobenzene-Containing Materials 5 2.1 Azobenzene 5 2.1.1 Isomers and Photoisomerization 6 2.1.2 The Photostationary State 10 2.2 Multiphotochromic Molecules Based on Azobenzene 10 2.2.1 Azobenzene Stars 11 2.2.2 The Benzene-1,3,5-Tricarboxamide Linker Unit 11 3 Computational Methods and Models 15 3.1 Density Functional Theory 15 3.1.1 Functional and Basis Set 16 3.1.2 Implicit Solvation Models 17 3.1.3 Time-Dependent Density Functional Theory 17 3.2 Molecular Dynamics Simulations 18 3.2.1 All-Atom MD Simulations 18 3.2.2 Force Fields 19 4 Simulation Techniques 23 4.1 Thermodynamic Integration 23 4.1.1 Implementation in Atomistic Simulations 24 4.2 Modeling Photoisomerization in MD Simulations 27 4.2.1 Implementation of the Rotation Pathway 28 4.3 Modeling Light-Irradiated Azo-Materials in MD Simulations 30 4.3.1 The Cyclic Photoisomerization Model 31 5 Photoisomers of an Azobenzene Star 35 5.1 Object of Study: The Molecule TrisAzo 35 5.1.1 Isomers and Conformers 35 5.2 Ground State Properties in the Gas Phase and in Solvents 36 5.2.1 Energies and Standard Enthalpies of Formation 37 5.2.2 Geometry and Shape Properties 38 5.2.3 Dipole Moments 42 5.2.4 Molecular Properties Upon Hydration in Explicit Water 44 5.3 Solubility 47 5.3.1 Influence of Solvent Polarity 48 5.3.2 Influence of Isomerization State 48 5.3.3 Hydration Free Energy 49 5.4 Absorption Spectra and Intramolecular Coupling 51 5.4.1 Influence of the Number of Azo Groups and Their Isomerization State 52 5.4.2 Effect of the Solvent Polarity 54 5.5 Summary 56 6 Equilibrium Properties of TrisAzo Clusters 59 6.1 Supramolecules of Azobenzene Stars in the Experiment 60 6.1.1 Light-Induced Morphological Transition 60 6.2 Self-Assembly Starting from a Random Distribution 62 6.2.1 Radial Distribution Function 63 6.2.2 Cluster Analysis 65 6.3 Intermolecular Energy of a TrisAzo Dimer 69 6.3.1 Total Intermolecular Energy 70 6.3.2 Energy Decomposition 71 6.4 Structural Properties of Columnar TrisAzo Clusters 75 6.4.1 Considered Cluster Arrangements (Cluster Types) 75 6.4.2 Inner Structure of the Clusters 79 6.4.3 Effect of Cluster Size 79 6.5 Intermolecular Energy of Columnar TrisAzo Clusters 82 6.5.1 Total Intermolecular Energy 82 6.5.2 Energy Decomposition 83 6.5.3 The Role of Hydrogen Bonding 88 6.5.4 Rationalizing the Structural Differences of the Considered Cluster Types 91 6.6 Summary 93 7 Columnar TrisAzo Clusters Under UV–Vis Light 97 7.1 TrisAzo Stacks in the Full Photoisomerization Model 97 7.1.1 Cluster Structure Before and After Irradiation 98 7.1.2 Intermolecular Energy 101 7.2 TrisAzo Stacks in the Cyclic Photosomerization Model 104 7.2.1 Photoisomerization Kinetics 104 7.2.2 Cluster Structure Under Irradiation 108 7.2.3 Intermolecular Energy of TrisAzo Stacks Under Irradiation 112 7.2.4 Mechanism of Defect Formation 116 7.2.5 Comparison with Simulations of Comparable Systems 118 7.3 Summary 118 8 Summary and Outlook 121 8.1 Summary 121 8.2 Outlook 123 A Functional Form of the Force Fields 125 A.1 DREIDING Force Field 125 A.2 Polymer Consistent Force Field (PCFF) 129 B Additional Details about Thermodynamic Integration 133 B.1 Derivation of the Formalism 133 B.2 Avoiding Singularities and Instabilities 134 C Details of the Computational Models 137 C.1 DFT and TD-DFT Calculations 137 C.1.1 DFT Calculations 137 C.1.2 TD-DFT Calculations 138 C.2 MD Simulations of TrisAzo Molecules in PCFF 138 C.2.1 Parametrization 139 C.2.2 Preparation of Initial Configurations 139 C.2.3 Simulation Settings 140 C.3 MD Simulations of TrisAzo Molecules in DREIDING 140 C.3.1 Parametrization 141 C.3.2 Preparation of Initial Configurations 141 C.3.3 Simulation Settings 141 C.4 Intermolecular Energy Calculations of TrisAzo Dimers in PCFF and DREIDING 142 C.5 Visualization of Molecular Structures 142 D Equilibrium Properties of TrisAzo Clusters: Additional Material 143 D.1 From Experiments to Simulations 143 D.2 Cluster Analysis for TrisAzo Self-Assembly: Additional Material 144 D.3 Intermolecular Energy of a TrisAzo Dimer: PCFF Results 145 D.3.1 Total Intermolecular Energy 145 D.3.2 Energy Decomposition 145 D.3.3 Estimated Total Intermolecular Energy of TrisAzo-H 148 D.4 Structural Properties of Columnar TrisAzo Clusters: Additional Material 149 D.5 Intermolecular Energy of Columnar TrisAzo Clusters: Additional Material 150 D.5.1 Defect Detection Algorithm 151 D.6 The Role of Hydrogen Bonds: Additional Material 152 E Columnar TrisAzo Clusters Under UV–Vis Light: Additional Material 155 E.1 TrisAzo Stacks in the Full Photoisomerization Model: Additional Material 155 E.2 TrisAzo Stacks in the Cyclic Photosomerization Model: Additional Material 156 F Code Availability 161 Bibliography 163 List of Publications 183 Copyright of Published Articles 187 Acknowledgements / Danksagung 189 List of Abbreviations 191 List of Symbols 193 List of Physical Constants and Unit Conversions 195 Eidesstattliche Erklärung 197

Embryonic development depends on the precise coordination of cell fate specification, patterning and morphogenesis. Although great strides have been made in the molecular understanding of each of these processes, how their interplay governs the formation of complex tissues remains poorly understood. New techniques for experimental manipulation and image quantification enable the study of development in unprecedented detail, resulting in new hypotheses on the interactions between known components. By expressing these hypotheses in terms of rules and equations, computational modeling and simulation allows one to test their consistency against experimental data. However, new computational methods are required to represent and integrate the network of interactions between gene regulation, signaling and biomechanics that extend over the molecular, cellular and tissue scales. In this thesis, I present a framework that facilitates computational modeling of multiscale multicellular systems and apply it to investigate pancreatic development and the formation of vascular networks. This framework is based on the integration of discrete cell-based models with continuous models for intracellular regulation and intercellular signaling. Specifically, gene regulatory networks are represented by differential equations to analyze cell fate regulation; interactions and distributions of signaling molecules are modeled by reaction-diffusion systems to study pattern formation; and cell-cell interactions are represented in cell-based models to investigate morphogenetic processes. A cell-centered approach is adopted that facilitates the integration of processes across the scales and simultaneously constrains model complexity. The computational methods that are required for this modeling framework have been implemented in the software platform Morpheus. This modeling and simulation environment enables the development, execution and analysis of multi-scale models of multicellular systems. These models are represented in a new domain-specific markup language that separates the biological model from the computational methods and facilitates model storage and exchange. Together with a user-friendly graphical interface, Morpheus enables computational modeling of complex developmental processes without programming and thereby widens its accessibility for biologists. To demonstrate the applicability of the framework to problems in developmental biology, two case studies are presented that address different aspects of the interplay between cell fate specification, patterning and morphogenesis. In the first, I focus on the interplay between cell fate stability and intercellular signaling. Specifically, two studies are presented that investigate how mechanisms of cell-cell communication affect cell fate regulation and spatial patterning in the pancreatic epithelium. Using bifurcation analysis and simulations of spatially coupled differential equations, it is shown that intercellular communication results in a multistability of gene expression states that can explain the scattered spatial distribution and low cell type ratio of nascent islet cells. Moreover, model analysis shows that disruption of intercellular communication induces a transition between gene expression states that can explain observations of in vitro transdifferentiation from adult acinar cells into new islet cells. These results emphasize the role of the multicellular context in cell fate regulation during development and may be used to optimize protocols for cellular reprogramming. The second case study focuses on the feedback between patterning and morphogenesis in the context of the formation of vascular networks. Integrating a cell-based model of endothelial chemotaxis with a reaction-diffusion model representing signaling molecules and extracellular matrix, it is shown that vascular network patterns with realistic morphometry can arise when signaling factors are retained by cell-modified matrix molecules. Through the validation of this model using in vitro assays, quantitative estimates are obtained for kinetic parameters that, when used in quantitative model simulations, confirm the formation of vascular networks under measured biophysical conditions. These results demonstrate the key role of the extracellular matrix in providing spatial guidance cues, a fact that may be exploited to enhance vascularization of engineered tissues. Together, the modeling framework, software platform and case studies presented in this thesis demonstrate how cell-centered computational modeling of multi-scale and multicellular systems provide powerful tools to help disentangle the complex interplay between cell fate specification, patterning and morphogenesis during embryonic development.

The human motor system is adaptive in two senses. It adapts to the properties of the body to enable effective control. It also adapts to different situational requirements and constraints. This thesis proposes a new neural network model of both kinds of adaptivity for the motor cortical control of human reaching movements, called SURE_REACH (sensorimotor unsupervised learning redundancy resolving control architecture). In this neural network approach, the kinematic and sensorimotor redundancy of a three-joint planar arm is encoded in task-independent internal models by an unsupervised learning scheme. Before a movement is executed, the neural networks prepare a movement plan from the task-independent internal models, which flexibly incorporates external, task-specific constraints. The movement plan is then implemented by proprioceptive or visual closed-loop control. This structure enables SURE_REACH to reach hand targets while incorporating task-specific contraints, for example adhering to kinematic constraints, anticipating the demands of subsequent movements, avoiding obstacles, or reducing the motion of impaired joints. Besides this functionality, the model accounts for temporal aspects of human reaching movements or for data from priming experiments. Additionally, the neural network structure reflects properties of motor cortical networks like interdependent population encoded body space representations, recurrent connectivity, or associative learning schemes. This thesis introduces and describes the new model, relates it to current computational models, evaluates its functionality, relates it to human behavior and neurophysiology, and finally discusses potential extensions as well as the validity of the model. In conclusion, the proposed model grounds highly flexible task-dependent behavior in a neural network framework and unsupervised sensorimotor learning. / Das motorische System des Menschen ist in zweierlei Hinsicht anpassungsfähig. Es passt sich den Eigenschaften des Körpers an, um diesen effektiv zu kontrollieren. Es passt sich aber auch unterschiedlichen situationsabhängigen Erfordernissen und Beschränkungen an. Diese Dissertation stellt ein neues neuronales Netzwerk Modell der motor-kortikalen Steuerung von menschlichen Zeigebewegungen vor, das beide Arten von Anpassungsfähigkeit integriert (SURE_REACH, Sensumotorische, unüberwacht lernende, redundanzauflösende Kontrollarchitektur). Das neuronale Netzwerk speichert kinematische und sensumotorische Redundanz eines planaren, dreigelenkigen Armes in aufgabenunabhängigen internen Modellen mittels unüberwachter Lernverfahrenen. Vor der Ausführung einer Bewegung bereitet das neuronale Netzwerk einen Bewegungsplan vor. Dieser basiert auf den aufgabenunabhängigen internen Modells und passt sich flexibel äu"seren, aufgabenabhängigen Erfordernissen an. Der Bewegungsplan wird dann durch propriozeptive oder visuelle Regelung umgesetzt. Auf diese Weise erklärt SURE_REACH Bewegungen zu Handzielen die aufgabenabhängige Erfordernisse berücksichtigen, zum Beispiel werden kinematische Beschränkungen miteinbezogen, Erfordernisse nachfolgender Aufgaben antizipiert, Hindernisse vermieden oder Bewegungen verletzter Gelenke reduziert. Desweiteren werden zeitliche Eigenschaften menschlicher Bewegungen oder die Ergebnisse von Primingexperimenten erklärt. Die neuronalen Netzwerke bilden zudem Eigenschaften motor-kortikaler Netzwerke ab, zum Beispiel wechselseitig abhängige Raumrepräsentationen, rekurrente Verbindungen oder assoziative Lernverfahren. Diese Dissertation beschreibt das neue Modell, vergleicht es mit anderen Modellen, untersucht seine Funktionalität, stellt Verbindungen zu menschlichem Verhalten und menschlicher Neurophysiologie her und erörtert schlie"slich mögliche Erweiterungen und die Validität des Models. Zusammenfassend stellt das vorgeschlagene Model eine Erklärung für flexibles aufgabenbezogenes Verhalten auf ein Fundament aus neuronalen Netzwerken und unüberwachten sensumotorischen Lernen.

Die elektrophysiologischen Vorgänge während der Depolarisation und Repolarisation des Myokards können mittels der Signale des 12-Kanal EKGs selbst bei Vorliegen großen Expertenwissens nur unzureichend beobachtet bzw. interpretiert werden. Grund hierfür sind vor allen Dingen Inhomogenitäten in der kardialen und thorakalen elektrischen Leitfähigkeit sowie die starke Signalabschwächung in den durchlaufenen Geweben. Intrakardiale Verfahren der Signalableitung sind ein Ansatz zu Lösung dieses Problems; sie sind jedoch aufwändig und risikobehaftet. In dem in dieser Arbeit eingesetzten Verfahren hingegen konnte, durch patientenindividuelle Modellierung der Herz- und Thoraxanatomie sowie der Leitfähigkeitsverhältnisse, mittels numerischer Verfahren aus einer Vielzahl von Oberflächen-EKG Ableitungen auf die elektrophysiologischen Vorgänge im Myokard in ihrem zeitlichen und örtlichen Verlauf geschlossen werden (Inverses Problem der Elektrokardiographie). Es konnten bei gesunden Probanden sowie bei Patienten mit verschiedenen kardialen Pathologien zeitlich und örtlich hochaufgelöste Rekonstruktionen von epikardialen- und Transmembranpotentialverteilungen angefertigt werden. Es zeigte sich, dass insbesondere im Bereich großer Infarktnarben der Herzvorder- sowie der Herzhinterwand elektrophysiologische Auffälligkeiten nachweisbar waren. So zeigten sich während der Depolarisationsphase Myokardareale mit einer verminderten Aktivität und Polarisationsumkehr, Bezirke mit verzögerter Depolarisationsaktivität sowie Areale mit atypisch verlaufender Repolarisationsaktivität. Anhand der vorliegenden Ergebnisse konnte gezeigt werden, dass eine Rekonstruktion der physiologischen Abläufe im Myokard während der Depolarisation und der Repolarisation mit dem hierzu implementierten Verfahren möglich ist. Anhand von elektroanatomischen Modellen konnten darüber hinaus die physiologische sowie die pathologisch veränderte Erregungsausbreitung im Myokard simuliert werden. Durch Verbesserung der Rekonstruktionsalgorithmen, der Methoden der Signalverarbeitung und der Regularisierung der Lösungsverfahren ist zukünftig eine weitere Verbesserung der Rekonstruktionsergebnisse zu erwarten. Vor dem klinischen Einsatz der Methode muss eine eingehende Validation erfolgen. / The electrophysiological processes that occur during cardiac depolarization and repolarization can be interpreted via 12-channel ECG only in a limited manner. This is due to inhomogeneities in the cardiac and thoracic electric conductivity and the attenuation of the electric signals in the body. Invasive cardiac measurements can avoid these problems but are expensive and not free of risk for the patient. In this work therefore a method of non-invasive electrocardiographic imaging was established which permits the reconstruction of cardiac electrophysiological processes using exclusively information obtained by non-invasive methods (MR-imaging, electrocardiographic mapping). Using anatomic information from MR-images of the patient’s heart and chest, a patient-individual model of electric conductivity could be created (finite-element method). Numerical algorithms were used to solve the inverse problem of electrocardiography, i.e. finding cardiac potential distributions that explain the measured surface potential distribution. In two healthy volunteers as well as in 7 patients with different cardiac pathologies, reconstructions of epicardial potentials and transmembrane voltages were performed. Specific electrophysiological abnormalities (decreased electric activity, polarization reversal, delayed depolarization and atypical repolarization patterns) could be detected in the proximity of myocardial scars. To optimize reconstruction algorithms and regularization methods, cardiac potentials were also simulated using a cellular automaton and the patient individual conductivity model. This study shows that the reconstruction of cardiac electrophysiology is feasible with this method and that myocardial scars and atypical patterns of depolarization and repolarization can be detected. By further improving the method and after a process of validation, clinically relevant data might be obtained.