Title from first page of PDF document. Includes bibliographical references (p. 22-31).

Στην παρούσα εργασία μελετάμε τη μοντελοποίηση του υποθαλαμικού πυρήνα των βασικών γαγγλίων με χρήση του μαθηματικού νευρωνικού μοντέλου Izhikevich. Βάση της μελέτης μας αποτελούν μικροηλεκτροδιακές καταγραφές, που έχουν ληφθεί κατά τη διάρκεια νευροχειρουργικών επεμβάσεων εν τω βάθει εγκεφαλικής διέγερσης, για τη συμπτωματική θεραπεία της νόσου Πάρκινσον. Θα ξεκινήσουμε με μια εισαγωγή στην φυσιολογία του νευρικού κυττάρου και στην ανατομία των βασικών γαγγλίων. Θα αναλύσουμε τα βασικά ποιοτικά μοντέλα που ερμηνεύουν τη συμμετοχή των τελευταίων σε κινητικές διεργασίες, αλλά και την εμπλοκή τους στη νόσο Πάρκινσον. Μετά από μια σύντομη αναφορά στη μέθοδο της εν τω βάθει διέγερσης και στις μικροηλεκτροδιακές καταγραφές, θα εστιάσουμε στα δυναμικά τοπικού πεδίου και στη νευροφυσιολογική σημασία τους. Συνεχίζοντας, θα κάνουμε μια περιεκτική ανασκόπηση των βασικότερων μαθηματικών μοντέλων νευρώνων και ύστερα θα επικεντρωθούμε στον υποθαλαμικό πυρήνα, περιγράφοντας δύο πρόσφατα μοντέλα που έχουν κατασκευαστεί για την προσομοίωση των νευρώνων αυτού. Έπειτα, θα περάσουμε στην περιγραφή του μοντέλου Izhikevich και στην τροποποίησή του για την αναπαραγωγή των χαρακτηριστικών του νευρώνα του υποθαλαμικού πυρήνα. Κατόπιν, θα αναλύσουμε τη μεθοδολογία που ακολουθήσαμε στην παρούσα υλοποίηση και τις βασικές θεωρήσεις της μοντελοποίησης μας. Θα ολοκληρώσουμε με την παρουσίαση των αποτελεσμάτων, το σχολιασμό αυτών και τις ιδέες για μελλοντική επέκταση της μεθόδου μας. / The main objective of this MSc thesis is the study of subthalamic nucleus, by using the Izhikevich neuron model. Microelectrode recordings, taken during deep brain stimulation operations for Parkinson’s disease, have been used for that purpose. In chapters 1-2, there is an introduction to the physiology of the neuron and the basal ganglia anatomy. In the two following chapters, we are analyzing the basic qualitative models that describe the involvement of the basal ganglia in movements and the pathophysiology of Parkinson’s disease. We are briefly discussing the method of deep brain stimulation, microelectrode recordings processing and the extraction of local field potentials. In chapter 5, the basic mathematical neuron models are discussed. We are focusing on the subthalamic nucleus and we are describing two recently developed mathematical models of the subthalamic neuron. In chapter 6, we are outlining Izhikevich neuron model and its modification in order to describe the subthalamic neuron. In addition, we are analyzing the methodology developed for the implementation of the modeling process and our basic considerations. In chapter 7, the results of the simulation are presented and discussed, so that our conclusions provide ideas for further research.

Les potentiels de champs locaux (LFP) sont des événements de fréquence inférieure à 200-500 Hz, résultant de l'activité cérébrale. Leur signification et les mécanismes contribuant à leur formation sont encore très débattus. Ainsi, l'existence et l'importance d'un filtrage des courants ioniques par le tissu cérébral est controversée. Certains auteurs concluent que le milieu est résistif, alors que d'autres suggèrent que le tissu cérébral pourrait exercer un filtrage passe-bas significatif sur les courants électriques. Une méthode de mesure nouvelle est présentée ici, s'appuyant sur le concept d'impédance naturelle, mesurée en utilisant un neurone comme " électrode " . Ceci permet d'obtenir l'impédance la plus pertinente d'un point de vue physiologique, en termes d'interface électrode-milieu, d'intensité des courants et d'échelle spatiale. L'impédance mesurée est stable, reproductible, plus forte que celle mesurée traditionnellement, et possède une dépendance en fréquence en 1/vf. Un modèle physique prenant en compte la diffusion ionique dans le milieu est capable de reproduire cette impédance. Une méthode similaire permet de calculer la fonction de transfert entre les potentiels intra- et extracellulaire d'un neurone. Des modèles sont proposés pour expliquer sa forme, prédire les LFP d'après l'activité cellulaire et vice-versa. Ces résultats pourraient aider à l'interprétation des signaux de LFP et d'électroencéphalographie, permettant une compréhension plus profonde du fonctionnement cérébral physiologique et pathologique. / Local field potentials (LFPs) are low-frequency (< 200-500 Hz) events resulting from brain activity. Their meaning and the mechanisms shaping them have been highly debated for decades. The existence and importance of a frequency-dependant filtering of ionic currents by brain tissue is controversial. Some authors conclude that the medium is resistive, while others suggest that brain tissue may exert significative low-pass filtering on electrical currents. A new measurement method is presented here, relying on the concept of natural impedance, which is measured using a neuron as an ''electrode''. This allows to obtain the most relevant impedance from a physiological point of view, in terms of electrode-medium interface, current intensity and spatial scale. The measured impedance is stable, reproducible, stronger than what is traditionally measured, and has a 1/\√f frequency dependance. A physical model, taking into account ionic diffusion in the medium, is able to reproduce this impedance. A similar method allows to compute the transfer function between the intra- and extracellular potentials of a neuron. Models are proposed to explain its structure, predict LFPs from cell activity and vice-versa. These results may help interpreting LFP and electroencephalography signals, yielding a deeper understanding of the physiological and pathological brain function.

L’irradiation des matériaux par des impulsions laser ultrabrèves déclenche un agencement anisotrope de la matière à l’échelle nanométrique: des structures de surface périodiques induites par laser (LIPSS). L'énergie laser déposée et distribuée de manière inhomogène dans le matériau induit des contraintes thermiques locales et des changements de phase transitoires entraînant ainsi des modifications microstructurales. Cette thèse porte sur le rôle de l'altération de la surface irradiée ainsi que les modifications microstructurales en profondeur dans la contribution à la formation des LIPSS, en établissant une corrélation entre l'auto-organisation de la matière et la génération de défauts en tenant en compte de l'orientation cristalline. Comme les LIPSS sont générés au seuil de transition de phase, l’étude de la corrélation avec les défauts induits est alors pertinente. Une étude expérimentale couplée à des simulations de dynamique moléculaire effectuées à l’Université de Virginie suggère que l'altération de surface générée par une irradiation d'échantillons monocristallins de Chrome dans le régime de spallation est susceptible de jouer un rôle majeur dans le déclenchement de génération de LIPSS de haute fréquence spatiale. La microscopie à force atomique ainsi que les résultats de simulations attestent que les caractéristiques de rugosité de surface à l'échelle nanométrique dépendent de l'orientation cristalline. La forte rugosité de surface générée par la première impulsion laser active la diffusion de la lumière laser et l’exaltation du champ local lors des irradiations ultérieures, ce qui génère des structures LIPSS de haute fréquence plus prononcés du côté (100) que celle du (110). Une étude expérimentale approfondie, utilisant la microscopie électronique rétrodiffusés et transmission, a révélé que le Cr (110) est plus susceptible d'être endommagé que les autres orientations cristallines de surface. On constate que les défauts induits par le laser peuvent altérer la topographie de surface et la région sous-jacente, ce qui peut avoir un impact sur les caractéristiques des centres de rugosité favorisant la formation de structures de fréquence spatiale élevée. Afin d’accéder à la transition de phase subie dans la région de formation des LIPSS, une approche d'analyse microstructurale à haute résolution couplée à des calculs hydrodynamiques est utilisée, comprenant la croissance épitaxiale et la nanocavitation. La formation de structures de fréquence spatiale élevée est le résultat de nanocavités périodiques piégés sous la surface, ainsi que des nanocavités apparues à la surface des matériaux cubiques faces centrées.De plus, étant donné que le feedback dans la formation des LIPSS est souvent évoquée, le comportement dynamique des surfaces a été sondé par microscopie électronique à photoémission et étayé par des calculs électromagnétiques. Un caractère périodique des photoélectrons émis par les creux des LIPSS a été mis en évidence, ce qui a permis de vérifier la modulation du dépôt d'énergie.Le travail effectué contribue non seulement à progresser vers l'objectif général d’élucider le phénomène complexe multi-échelles de la formation des LIPSS, mais ouvre une nouvelle voie expérimentale pour générer des structures non conventionnelles avec des périodicités extrêmes (~60nm), offrant ainsi de nouvelles opportunités pour le traitement laser ultrarapide des métaux. / Irradiation of materials by ultrashort laser pulses triggers anisotropically structured arrangement of matter on the nanoscale, the so-called laser-induced periodic surface structures (LIPSS), or ‘ripples’. Ultrashort laser energy deposited and distributed inhomogeneously in the material launches local thermal stresses and transient phase changes yielding microstructural modifications. This thesis focuses on the role of irradiated surface alteration as well as in-depth microstructural modifications in promoting LIPSS formation, by establishing a correlation between self-organization of matter and defect generation taking into account crystalline orientation. Since LIPSS are generated at the threshold of phase transition, then the correlation with defects formation is relevant. An experimental study coupled with molecular dynamic MD simulations performed in the University of Virginia suggest that surface alteration generated by a single pulse irradiation of monocrystalline Cr samples in the spallation regime is likely to play a main role in triggering high-spatial frequency LIPSS generation upon irradiation by multiple laser pulses. Atomic force microscopy as well as computational results suggested that the nanoscale surface features are crystalline orientation dependent. The higher surface roughness generated by the first laser pulse activates scattering of the laser light and the local field enhancement upon irradiation by the second laser pulse, leading to the formation of much more pronounced high-spatial frequency structures on the (100) surface as compared to (110) one. An extended in-depth experimental study, using electron backscattered and transmission microscopy, combined with large-scale two-temperature model TTM-MD simulations revealed that Cr (110) is more likely to get damaged. It is found that laser-induced defects can alter the surface topography and the region beneath it which can impact in turn the roughness center features promoting high-spatial frequency structures formation. In order to infer the phase transition undergone in the LIPSS region, a high resolution microstructural analysis approach coupled with hydrodynamic calculations is employed, including epitaxial regrowth and nanocavitation. High-spatial frequency structures formation is found to be the result of periodic nanovoids trapped beneath the surface as well as nanocavities emerged at the surface on fcc materials. Furthermore, since optical feedback in LIPSS is often evoked, the behavior of dynamical surfaces was probed by photoemission electron microscopy and supported by electromagnetic calculations. A periodic character of photoelectrons emitted from nanoholes was unveiled, which in turn verified a modulated energy deposition. The performed work not only contributes to the progress towards the general goal of untangling the complex multiscale phenomenon of the LIPSS formation, but unlocks a new experimental setup to generate unconventional structures with extreme periodicities (~60 nm), which offers new opportunities in ultrafast laser processing of metals.

Signals recorded from the brain often show rhythmic patterns at different frequencies, which are tightly coupled to the external stimuli as well as the internal state of the subject. These signals also have transient structures related to spiking or sudden onset of a stimulus, which have a duration not exceeding tens of milliseconds. Further, brain signals are highly non-stationary because both behavioral state and external stimuli can change over a short time scale. It is therefore essential to study brain signals using techniques that can represent both rhythmic and transient components of the signal. In Chapter 2, we describe a multi-scale decomposition technique based on an over-complete dictionary called matching pursuit (MP), and show that it is able to capture both sharp stimulus-onset transient and sustained gamma rhythm in local field potential recorded from the primary visual cortex. Gamma rhythm (30 to 80 Hz), often associated with high-level cortical functions, has been proposed to provide a temporal reference frame (“clock”) for spiking activity, for which it should have least center frequency variation and consistent phase for extended durations. However, recent studies have proposed that gamma occurs in short bursts and it cannot act as a reference. In Chapter 3, we propose another gamma duration estimator based on matching pursuit (MP) algorithm, which is tested with synthetic brain signals and found to be estimating the gamma duration efficiently. Applying this algorithm to real data from awake monkeys, we show that the median gamma duration is more than 330 ms, which could be long enough to support some cortical computations.

The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity. / <p>The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.</p><p></p><p>QC 20170209</p>

Na epilepsia do lobo temporal (ELT), alterações morfofuncionais em estruturas límbicas são classicamente acompanhadas de déficits cognitivos. Estudos anteriores revelaram que disfunções eletrofisiológicas em circuitos hipocampo-corticais são observadas durante o sono NREM (non rapid eye movement), onde eventos patológicos como fast ripples e IEDs (interictal epileptiform discharges) substituem gradativamente eventos fisiológicos, como as sharp-wave ripples (SWR). Tal substituição pode estar por trás dos prejuízos cognitivos observados tanto nos modelos animais como em pacientes, já que as SWRs são fundamentais para a transferência de informação do hipocampo ao córtex durante a consolidação de memórias. De maneira complementar, o sono REM também parece exercer um papel fundamental em processos mnemônicos, facilitando eventos de plasticidade sináptica e coordenando regiões encefálicas distantes por meio de acoplamento entre diferentes frequências oscilatórias, tais como teta e gama. Entretanto, as alterações no sono REM durante os processos de epileptogênese ainda foram pouco exploradas. Neste trabalho testamos a hipótese de que disfunções na coordenação rítmica durante o sono REM estariam associadas a prejuízos de memória que se manifestam na epileptogênese. Para isso, submetemos ratos Wistar adultos machos a protocolo de abrasamento rápido da amígdala basolateral, possibilitando a avaliação de alterações eletrofisiológicas gradativas durante o processo de epileptogênese. Foram realizados implantes crônicos de eletrodos para registro do potencial local de campo (LFP, Local Field Potential) nas regiões de CA1 e do córtex pré-frontal medial (mPFC, medial prefrontal cortex), além de eletrodos bipolares para estímulo na amígdala basolateral. Os protocolos de abrasamento foram realizados durante um período de 3 dias, aplicando-se diariamente 10 trens de estímulos a 50 Hz com duração de 10 segundos. Para avaliarmos os prejuízos cognitivos, os animais foram submetidos a testes de reconhecimento de objetos antes do início a após o término dos protocolos de abrasamento. O sonosubsequente às sessões de reconhecimento de objetos e aos protocolos de estimulações foram registrados diariamente. Além do prejuízo no reconhecimento de objetos e alterações eletrofisiológicas durante o sono NREM, como a substituição gradativa de ripples por IEDs, os animais submetidos ao abrasamento elétrico apresentaram um aumento na comodulação fase-amplitude entre oscilações teta e gama durante o sono REM após as estimulações, exibindo também uma correlação negativa entre a comodulação e a duração das pós-descargas induzidas pelos estímulos elétricos do abrasamento durante o sono subsequente a aplicação dos protocolos. Nossos achados ampliam a compreensão vigente sobre como alterações de oscilações cerebrais durante o sono, especialmente da fase REM, poderiam estar subjacentes a prejuízos de memória que ocorrem na ELT. / Morphofunctional changes in limbic structures are classically followed by cognitive deficits in Temporal Lobe Epilepsy (TLE) patients. Previous studies revealed that electrophysiological dysfunctions in hippocampal-cortical circuits are observed during NREM (non-rapid eye movement) sleep, where pathological events such as fast ripples and IEDs (interictal epileptiform discharges) gradually replace physiological events, such as Sharpwave Ripples (SWR). This replacement seems to describe the cognitive impairments observed in animal models and TLE patients since SWRs are fundamental for information transfer from the hippocampus to cortex during memory consolidation. Complementary, REM sleep also plays a significant role in mnemonic processes, facilitating synaptic plasticity events and coordinating distant brain regions by coupling different frequencies, such as theta and gamma. However, alterations in REM sleep during the epileptogenesis processes are poorly investigated. In this study, we tested the hypothesis that dysfunctions on rhythmic coordination during REM sleep would be associated with memory deficits showed during epileptogenesis. For this, we submitted adult Wistar rats to a rapid kindling protocol on basolateral amygdala (BLA), allowing the evaluation of progressive electrophysiological changes during the epileptogenic process. Chronic electrodes were implanted for the local field potentials (LFP) recording in the CA1 and medial prefrontal cortex (mPFC), as well as bipolar electrodes for BLA stimulation. The kindling protocols were performed during three days, applying ten trains of 50 Hz stimulations with ten seconds duration. Object recognition tasks were performed before and after the kindling protocol to evaluate cognitive impairment. Sleep recordings were performed daily after the object recognition or kindling application. Along with object recognition impairment and electrophysiological changes during NREM sleep, such as progressive SWR substitution by IEDs, kindled rats presented an increase in phase-amplitude comodulation between theta and gamma oscillations during REM sleep after stimulation sessions, which also correlates negatively with after-discharges (AD) duration induced by the kindling stimulation. Our findingsexpand the comprehension about how changes in brain oscillations during REM sleep underlies observed memory deficits in TLE.

Dipolar couplings are one of the major source of structural information. Due to their dependence on the distance between the nuclei and the angle of orientation of the dipolar vector with respect to the magnetic field, they provide significant insight into the geometry and topology of molecules. As the dipolar interactions are in general present in the solid phase of the compounds, solid state NMR experiments have gained significant popularity and is widely used. Separated Local Field NMR spectroscopy based on cross-polarization technique has been used to measure the heteronuclear dipolar couplings in solid state. However, the technique undergoes many experimental challenges and requires further development. This thesis is concerned mainly with the development of techniques to measure the dipolar couplings accurately in oriented molecules. In this regard, a method for fast data acquisition is also proposed. The first chapter briefly introduces the basics of NMR spectroscopy, methodologies applied for obtaining a high resolution NMR spectrum in the solid state. An introduction to liquid crystals is presented and the nature of NMR interaction in the liquid crystalline phases is described. In chapter-2, a new pulse scheme has been proposed that includes the X-nucleus polarization in the SLF experiments and is shown to provide better sensitivity and resolution. A quantitative analysis with simulation and experimental results are also presented. In chapter-3, the performance of various homonuclear decoupling pulse schemes incorporated into SLF experiments tested on oriented systems are compared. The proposed pulse schemes are shown to provide high resolution spectrum with accurate dipolar coupling measurement for natural abundant samples and for uniformly labeled compounds as well. Theoretical description with simulation and experimental results shown here are found to provide optimum results under several technical complications seen with respect to the conventional methods used for SLF experiments. Chapter-4, an attempt is made to reconstruct 2D J-resolved and 2D- SLF spectra from several 1D experimental data. This is achieved with the help of projection reconstruction method and is shown to provide high resolution 2D spectrum with saving of experimental time by an order of two. Chapter-5, high resolution spectra from SLF experiments under phase alternating pulses and using amplitude and time averaged nutation techniques are shown for accurate dipolar coupling measurement with a dramatic reduction in rf power. This is important as the use of low rf power leads to low sample heating and can be applied suitably for the study of liquid crystals and salty biomolecules. Chapter-6, attempts are made to characterize two novel thiophene based liquid crystals using both solution and solid state NMR spectroscopy. C-H dipolar couplings measured from SLF experiments are mainly used to find the order parameters and geometry of the molecules.

The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups, and those obtained for two-dimensional electron gas systems whenever it is possible. It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities. Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values, which may be observed experimentally, are found.

Effective focusing of electromagnetic (EM) energy to nanoscale regions is one of the major challenges in nano-photonics and plasmonics. The strong localization of the optical energy into regions much smaller than allowed by the diffraction limit, also called nanofocusing, offers promising applications in nano-sensor technology, nanofabrication, near-field optics or spectroscopy. One of the most promising solutions to the problem of efficient nanofocusing is related to surface plasmon propagation in metallic structures. Metallic tapered rods, commonly used as probes in near field microscopy and spectroscopy, are of a particular interest. They can provide very strong EM field enhancement at the tip due to surface plasmons (SP’s) propagating towards the tip of the tapered metal rod. A large number of studies have been devoted to the manufacturing process of tapered rods or tapered fibers coated by a metal film. On the other hand, structures such as metallic V-grooves or metal wedges can also provide strong electric field enhancements but manufacturing of these structures is still a challenge. It has been shown, however, that the attainable electric field enhancement at the apex in the V-groove is higher than at the tip of a metal tapered rod when the dissipation level in the metal is strong. Metallic V-grooves also have very promising characteristics as plasmonic waveguides. This thesis will present a thorough theoretical and numerical investigation of nanofocusing during plasmon propagation along a metal tapered rod and into a metallic V-groove. Optimal structural parameters including optimal taper angle, taper length and shape of the taper are determined in order to achieve maximum field enhancement factors at the tip of the nanofocusing structure. An analytical investigation of plasmon nanofocusing by metal tapered rods is carried out by means of the geometric optics approximation (GOA), which is also called adiabatic nanofocusing. However, GOA is applicable only for analysing tapered structures with small taper angles and without considering a terminating tip structure in order to neglect reflections. Rigorous numerical methods are employed for analysing non-adiabatic nanofocusing, by tapered rod and V-grooves with larger taper angles and with a rounded tip. These structures cannot be studied by analytical methods due to the presence of reflected waves from the taper section, the tip and also from (artificial) computational boundaries. A new method is introduced to combine the advantages of GOA and rigorous numerical methods in order to reduce significantly the use of computational resources and yet achieve accurate results for the analysis of large tapered structures, within reasonable calculation time. Detailed comparison between GOA and rigorous numerical methods will be carried out in order to find the critical taper angle of the tapered structures at which GOA is still applicable. It will be demonstrated that optimal taper angles, at which maximum field enhancements occur, coincide with the critical angles, at which GOA is still applicable. It will be shown that the applicability of GOA can be substantially expanded to include structures which could be analysed previously by numerical methods only. The influence of the rounded tip, the taper angle and the role of dissipation onto the plasmon field distribution along the tapered rod and near the tip will be analysed analytically and numerically in detail. It will be demonstrated that electric field enhancement factors of up to ~ 2500 within nanoscale regions are predicted. These are sufficient, for instance, to detect single molecules using surface enhanced Raman spectroscopy (SERS) with the tip of a tapered rod, an approach also known as tip enhanced Raman spectroscopy or TERS. The results obtained in this project will be important for applications for which strong local field enhancement factors are crucial for the performance of devices such as near field microscopes or spectroscopy. The optimal design of nanofocusing structures, at which the delivery of electromagnetic energy to the nanometer region is most efficient, will lead to new applications in near field sensors, near field measuring technology, or generation of nanometer sized energy sources. This includes: applications in tip enhanced Raman spectroscopy (TERS); manipulation of nanoparticles and molecules; efficient coupling of optical energy into and out of plasmonic circuits; second harmonic generation in non-linear optics; or delivery of energy to quantum dots, for instance, for quantum computations.