Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion.

Graph-based structural analysis of planar mechanisms.

Kinematic structure of planar mechanisms addresses the study of attributes determined exclusively by the joining pattern among the links forming a mechanism. The system group classification is central to the kinematic structure and consists of determining a sequence of kinematically and statically independent-simple chains which represent a modular basis for the kinematics and force analysis of the mechanism. This article presents a novel graph-based algorithm for structural analysis of planar mechanisms with closed-loop kinematic structure which determines a sequence of modules (Assur groups) representing the topology of the mechanism. The computational complexity analysis and proof of correctness of the implemented algorithm are provided. A case study is presented to illustrate the results of the devised method.

Implementation of an enhanced planar processing protocol in clinical practice

Introdução: A cintigrafia óssea é um dos exames mais frequentes em Medicina Nuclear. Esta modalidade de imagem médica requere um balanço apropriado entre a qualidade de imagem e a dose de radiação, ou seja, as imagens obtidas devem conter o número mínimo de contagem necessárias, para que apresentem qualidade considerada suficiente para fins diagnósticos. Objetivo: Este estudo tem como principal objetivo, a aplicação do software Enhanced Planar Processing (EPP), nos exames de cintigrafia óssea em doentes com carcinoma da mama e próstata que apresentam metástases ósseas. Desta forma, pretende-se avaliar a performance do algoritmo EPP na prática clínica em termos de qualidade e confiança diagnóstica quando o tempo de aquisição é reduzido em 50%. Material e Métodos: Esta investigação teve lugar no departamento de Radiologia e Medicina Nuclear do Radboud University Nijmegen Medical Centre. Cinquenta e um doentes com suspeita de metástases ósseas foram administrados com 500MBq de metilenodifosfonato marcado com tecnécio-99m. Cada doente foi submetido a duas aquisições de imagem, sendo que na primeira foi seguido o protocolo standard do departamento (scan speed=8 cm/min) e na segunda, o tempo de aquisição foi reduzido para metade (scan speed=16 cm/min). As imagens adquiridas com o segundo protocolo foram processadas com o algoritmo EPP. Todas as imagens foram submetidas a uma avaliação objetiva e subjetiva. Relativamente à análise subjetiva, três médicos especialistas em Medicina Nuclear avaliaram as imagens em termos da detetabilidade das lesões, qualidade de imagem, aceitabilidade diagnóstica, localização das lesões e confiança diagnóstica. No que respeita à avaliação objetiva, foram selecionadas duas regiões de interesse, uma localizada no terço médio do fémur e outra localizada nos tecidos moles adjacentes, de modo a obter os valores de relação sinal-ruído, relação contraste-ruído e coeficiente de variação. Resultados: Os resultados obtidos evidenciam que as imagens processadas com o software EPP oferecem aos médicos suficiente informação diagnóstica na deteção de metástases, uma vez que não foram encontradas diferenças estatisticamente significativas (p>0.05). Para além disso, a concordância entre os observadores, comparando essas imagens e as imagens adquiridas com o protocolo standard foi de 95% (k=0.88). Por outro lado, no que respeita à qualidade de imagem, foram encontradas diferenças estatisticamente significativas quando se compararam as modalidades de imagem entre si (p≤0.05). Relativamente à aceitabilidade diagnóstica, não foram encontradas diferenças estatisticamente significativas entre as imagens adquiridas com o protocolo standard e as imagens processadas com o EPP software (p>0.05), verificando-se uma concordância entre os observadores de 70.6%. Todavia, foram encontradas diferenças estatisticamente significativas entre as imagens adquiridas com o protocolo standard e as imagens adquiridas com o segundo protocolo e não processadas com o software EPP (p≤0.05). Para além disso, não foram encontradas diferenças estatisticamente significativas (p>0.05) em termos de relação sinal-ruído, relação contraste-ruído e coeficiente de variação entre as imagens adquiridas com o protocolo standard e as imagens processadas com o EPP. Conclusão: Com os resultados obtidos através deste estudo, é possível concluir que o algoritmo EPP, desenvolvido pela Siemens, oferece a possibilidade de reduzir o tempo de aquisição em 50%, mantendo ao mesmo tempo uma qualidade de imagem considerada suficiente para fins de diagnóstico. A utilização desta tecnologia, para além de aumentar a satisfação por parte dos doentes, é bastante vantajosa no que respeita ao workflow do departamento.

Assessment of the performance of an enhanced planar processing algorithm for whole-body bone scintigraphy : a phantom study

A cintigrafia óssea de corpo inteiro representa um dos exames imagiológicos mais frequentes realizados em medicina nuclear. Para além de outras aplicações, este procedimento é capaz de fornecer o diagnóstico de metástases ósseas. Em doentes oncológicos, a presença de metástases ósseas representa um forte indicador prognóstico da longevidade do doente. Para além disso, a presença ou ausência de metástases ósseas irá influenciar o planeamento do tratamento, requerendo para isso uma interpretação precisa dos resultados imagiológicos. Problema: Tendo em conta que a metastização óssea é considerada uma complicação severa relacionada com aumento da morbilidade e diminuição de sobrevivência dos doentes, o conceito de patient care torna-se ainda mais imperativo nestas situações. Assim, devem ser implementadas as melhores práticas imagiológicas de forma a obter o melhor resultado possível do procedimento efetuado, associado ao desconforto mínimo do doente. Uma técnica provável para atingir este objetivo no caso específico da cintigrafia óssea de corpo inteiro é a redução do tempo de aquisição, contudo, as imagens obtidas por si só teriam qualidade de tal forma reduzida que os resultados poderiam ser enviesados. Atualmente, surgiram novas técnicas, nomeadamente relativas a processamento de imagem, através das quais é possível gerar imagens cintigráficas com contagem reduzida de qualidade comparável àquela obtida com o protocolo considerado como standard. Ainda assim, alguns desses métodos continuam associados a algumas incertezas, particularmente no que respeita a sustentação da confiança diagnóstica após a modificação dos protocolos de rotina. Objetivos: O presente trabalho pretende avaliar a performance do algoritmo Pixon para processamento de imagem por meio de um estudo com fantoma. O objetivo será comparar a qualidade de imagem e a detetabilidade fornecidas por imagens não processadas com aquelas submetidas à referida técnica de processamento. Para além disso, pretende-se também avaliar o efeito deste algoritmo na redução do tempo de aquisição. De forma a atingir este objetivo, irá ser feita uma comparação entre as imagens obtidas com o protocolo standard e aquelas adquiridas usando protocolos mais rápidos, posteriormente submetidas ao método de processamento referido. Material e Métodos: Esta investigação for realizada no departamento de Radiologia e Medicina Nuclear do Radboud University Nijmegen Medical Centre, situado na Holanda. Foi utilizado um fantoma cilíndrico contendo um conjunto de seis esferas de diferentes tamanhos, adequado à técnica de imagem planar. O fantoma foi preparado com diferentes rácios de atividade entre as esferas e o background (4:1, 8:1, 17:1, 22:1, 32:1 e 71:1). Posteriormente, para cada teste experimental, o fantoma foi submetido a vários protocolos de aquisição de imagem, nomeadamente com diferentes velocidades de aquisição: 8 cm/min, 12 cm/min, 16 cm/min e 20 cm/min. Todas as imagens foram adquiridas na mesma câmara gama - e.cam Signature Dual Detector System (Siemens Medical Solutions USA, Inc.) - utilizando os mesmos parâmetros técnicos de aquisição, à exceção da velocidade. Foram adquiridas 24 imagens, todas elas submetidas a pós-processamento com recurso a um software da Siemens (Siemens Medical Solutions USA, Inc.) que inclui a ferramenta necessária ao processamento de imagens cintigráficas de corpo inteiro. Os parâmetros de reconstrução utilizados foram os mesmos para cada série de imagens, estando estabelecidos em modo automático. A análise da informação recolhida foi realizada com recurso a uma avaliação objetiva (utilizando parâmetros físicos de qualidade de imagem) e outra subjetiva (através de dois observadores). A análise estatística foi efetuada recorrendo ao software SPSS versão 22 para Windows. Resultados: Através da análise subjetiva de cada rácio de atividade foi demonstrado que, no geral, a detetabilidade das esferas aumentou após as imagens serem processadas. A concordância entre observadores para a distribuição desta análise foi substancial, tanto para imagens não processadas como imagens processadas. Foi igualmente demonstrado que os parâmetros físicos de qualidade de imagem progrediram depois de o algoritmo de processamento ter sido aplicado. Para além disso, observou-se ao comparar as imagens standard (adquiridas com 8 cm/min) e aquelas processadas e adquiridas com protocolos mais rápidos que: imagens adquiridas com uma velocidade de aquisição de 12 cm/min podem fornecer resultados melhorados, com parâmetros de qualidade de imagem e detetabilidade superiores; imagens adquiridas com uma velocidade de 16 cm/min fornecem resultados comparáveis aos standard, com valores aproximados de qualidade de imagem e detetabilidade; e imagens adquiridas com uma velocidade de 20 cm/min resultam em valores diminuídos de qualidade de imagem, bem como redução a nível da detetabilidade. Discussão: Os resultados obtidos foram igualmente estabelecidos por meio de um estudo clínico numa investigação independente, no mesmo departamento. Foram incluídos cinquenta e um doentes referidos com carcinomas da mama e da próstata, com o objetivo de estudar o impacto desta técnica na prática clínica. Os doentes foram, assim, submetidos ao protocolo standard e posteriormente a uma aquisição adicional com uma velocidade de aquisição de 16 cm/min. Depois de as imagens terem sido cegamente avaliadas por três médicos especialistas, concluiu-se que a qualidade de imagem bem como a detetabilidade entre imagens era comparável, corroborando os resultados desta investigação. Conclusão: Com o objetivo de reduzir o tempo de aquisição aplicando um algoritmo de processamento de imagem, foi demonstrado que o protocolo com 16 cm/min de velocidade de aquisição será o limite para o aumento dessa mesma velocidade. Após processar a informação, este protocolo fornece os resultados mais equivalentes àqueles obtidos com o protocolo standard. Tendo em conta que esta técnica foi estabelecida com sucesso na prática clínica, pode-se concluir que, pelo menos em doentes referidos com carcinomas da mama e da próstata, o tempo de aquisição pode ser reduzido para metade, duplicando a velocidade de aquisição de 8 para 16 cm/min.

Design of Mm-Wave RLSA with lossy waveguides by slot coupling control techniques

This paper discusses how to design a Radial Line Slot Antenna (RLSA) whose waveguide is filled with high loss dielectric materials. We introduce a new design for the aperture slot coupling synthesis to restrain the dielectric losses and improve the antenna gain. Based on a newly defined slot coupling, a number of RLSAs with different sizes and loss factors are analyzed and their performances are predicted. Theoretical calculations suggest that the gain is sensitive to the material losses in the radial lines. The gain enhancement by using the new coupling formula is notable for larger antenna size and higher loss factor of the dielectric material. Three prototype RLSAs are designed and fabricated at 60GHz following different slot coupling syntheses, and their measured performances consolidate our theory.

Subwavelength Index Engineering for SOI Waveguides

Photonic structures with a sub-wavelength pitch, small enough to suppress diffraction, can behave as equivalent homogenous materials that can be engineered to exhibit a specific refractive index and dispersion. Here we discuss the design of a variety of integrated photonic devices, ranging from grating couplers to multimode interference couplers, for which the use of sub-wavelength structures enables unique characteristics. We will place special emphasis on the design and experimental demonstration of multi-mode interference couplers with an unprecedented bandwidth beyond 200nm at telecom wavelengths.

Packaging and Deployment of Large Planar Spacecraft Structures

This thesis presents a set of novel methods to biaxially package planar structures by folding and wrapping. The structure is divided into strips connected by folds that can slip during wrapping to accommodate material thickness. These packaging schemes are highly efficient, with theoretical packaging efficiencies approaching 100%. Packaging tests on meter-scale physical models have demonstrated packaging efficiencies of up to 83%. These methods avoid permanent deformation of the structure, allowing an initially flat structure to be deployed to a flat state.

Also presented are structural architectures and deployment schemes that are compatible with these packaging methods. These structural architectures use either in-plane pretension -- suitable for membrane structures -- or out-of-plane bending stiffness to resist loading. Physical models are constructed to realize these structural architectures. The deployment of these types of structures is shown to be controllable and repeatable by conducting experiments on lab-scale models.

These packaging methods, structural architectures, and deployment schemes are applicable to a variety of spacecraft structures such as solar power arrays, solar sails, antenna arrays, and drag sails; they have the potential to enable larger variants of these structures while reducing the packaging volume required. In this thesis, these methods are applied to the preliminary structural design of a space solar power satellite. This deployable spacecraft, measuring 60 m x 60 m, can be packaged into a cylinder measuring 1.5 m in height and 1 m in diameter. It can be deployed to a flat configuration, where it acts as a stiff lightweight support framework for multifunctional tiles that collect sunlight, generate electric power, and transmit it to a ground station on Earth.

Optical Waveguides and Structures for Short Haul Optical Communication Channels within Printed Circuit Boards

Optical waveguides have shown promising results for use within printed circuit boards. These optical waveguides have higher bandwidth than traditional copper transmission systems and are immune to electromagnetic interference. Design parameters for these optical waveguides are needed to ensure an optimal link budget. Modeling and simulation methods are used to determine the optimal design parameters needed in designing the waveguides. As a result, optical structures necessary for incorporating optical waveguides into printed circuit boards are designed and optimized. Embedded siloxane polymer waveguides are investigated for their use in optical printed circuit boards. This material was chosen because it has low absorption, high temperature stability, and can be deposited using common processing techniques. Two sizes of waveguides are investigated, 50 $unit{mu m}$ multimode and 4 - 9 $unit{mu m}$ single mode waveguides. A beam propagation method is developed for simulating the multimode and single mode waveguide parameters. The attenuation of simulated multimode waveguides are able to match the attenuation of fabricated waveguides with a root mean square error of 0.192 dB. Using the same process as the multimode waveguides, parameters needed to ensure a low link loss are found for single mode waveguides including maximum size, minimum cladding thickness, minimum waveguide separation, and minimum bend radius. To couple light out-of-plane to a transmitter or receiver, a structure such as a vertical interconnect assembly (VIA) is required. For multimode waveguides the optimal placement of a total internal reflection mirror can be found without prior knowledge of the waveguide length. The optimal placement is found to be either 60 µm or 150 µm away from the end of the waveguide depending on which metric a designer wants to optimize the average output power, the output power variance, or the maximum possible power loss. For single mode waveguides a volume grating coupler is designed to couple light from a silicon waveguide to a polymer single mode waveguide. A focusing grating coupler is compared to a perpendicular grating coupler that is focused by a micro-molded lens. The focusing grating coupler had an optical loss of over -14 dB, while the grating coupler with a lens had an optical loss of -6.26 dB.

Direct Write Fabrication of Waveguides and Interconnects for Optical Printed Wiring Boards

Current copper based circuit technology is becoming a limiting factor in high speed data transfer applications as processors are improving at a faster rate than are developments to increase on board data transfer. One solution is to utilize optical waveguide technology to overcome these bandwidth and loss restrictions. The use of this technology virtually eliminates the heat and cross-talk loss seen in copper circuitry, while also operating at a higher bandwidth. Transitioning current fabrication techniques from small scale laboratory environments to large scale manufacturing presents significant challenges. Optical-to-electrical connections and out-of-plane coupling are significant hurdles in the advancement of optical interconnects. The main goals of this research are the development of direct write material deposition and patterning tools for the fabrication of waveguide systems on large substrates, and the development of out-of-plane coupler components compatible with standard fiber optic cabling. Combining these elements with standard printed circuit boards allows for the fabrication of fully functional optical-electrical-printed-wiring-boards (OEPWBs). A direct dispense tool was designed, assembled, and characterized for the repeatable dispensing of blanket waveguide layers over a range of thicknesses (25-225 µm), eliminating waste material and affording the ability to utilize large substrates. This tool was used to directly dispense multimode waveguide cores which required no UV definition or development. These cores had circular cross sections and were comparable in optical performance to lithographically fabricated square waveguides. Laser direct writing is a non-contact process that allows for the dynamic UV patterning of waveguide material on large substrates, eliminating the need for high resolution masks. A laser direct write tool was designed, assembled, and characterized for direct write patterning waveguides that were comparable in quality to those produced using standard lithographic practices (0.047 dB/cm loss for laser written waveguides compared to 0.043 dB/cm for lithographic waveguides). Straight waveguides, and waveguide turns were patterned at multimode and single mode sizes, and the process was characterized and documented. Support structures such as angled reflectors and vertical posts were produced, showing the versatility of the laser direct write tool. Commercially available components were implanted into the optical layer for out-of-plane routing of the optical signals. These devices featured spherical lenses on the input and output sides of a total internal reflection (TIR) mirror, as well as alignment pins compatible with standard MT design. Fully functional OEPWBs were fabricated featuring input and output out-of-plane optical signal routing with total optical losses not exceeding 10 dB. These prototypes survived thermal cycling (-40°C to 85°C) and humidity exposure (95±4% humidity), showing minimal degradation in optical performance. Operational failure occurred after environmental aging life testing at 110°C for 216 hours.

Tunable single- and dual-wavelength SHG from diode-pumped PPKTP waveguides

A compact, all-room-temperature, widely tunable, continuous wave laser source in the green spectral region (502.1–544.2 nm) with a maximum output power of 14.7 mW is demonstrated. This was made possible by utilizing second-harmonic generation (SHG) in a periodically poled potassium titanyl phosphate (PPKTP) crystal waveguide pumped by a quantum-well external-cavity fiber-coupled diode laser and exploiting the multimode-matching approach in nonlinear crystal waveguides. The dual-wavelength SHG in the wavelength region between 505.4 and 537.7 nm (with a wavelength difference ranging from 1.8 to 32.3 nm) and sum-frequency generation in a PPKTP waveguide is also demonstrated.

Development and validation of a computationally efficient pseudo 3D model for planar SOFC integrated with a heating furnace

Efficient numerical models facilitate the study and design of solid oxide fuel cells (SOFCs), stacks, and systems. Whilst the accuracy and reliability of the computed results are usually sought by researchers, the corresponding modelling complexities could result in practical difficulties regarding the implementation flexibility and computational costs. The main objective of this article is to adapt a simple but viable numerical tool for evaluation of our experimental rig. Accordingly, a model for a multi-layer SOFC surrounded by a constant temperature furnace is presented, trained and validated against experimental data. The model consists of a four-layer structure including stand, two interconnects, and PEN (Positive electrode-Electrolyte-Negative electrode); each being approximated by a lumped parameter model. The heating process through the surrounding chamber is also considered. We used a set of V-I characteristics data for parameter adjustment followed by model verification against two independent sets of data. The model results show a good agreement with practical data, offering a significant improvement compared to reduced models in which the impact of external heat loss is neglected. Furthermore, thermal analysis for adiabatic and non-adiabatic process is carried out to capture the thermal behaviour of a single cell followed by a polarisation loss assessment. Finally, model-based design of experiment is demonstrated for a case study.

Planar solid oxide fuel cell modeling and optimization targeting the stack's temperature gradient minimization

Minimization of undesirable temperature gradients in all dimensions of a planar solid oxide fuel cell (SOFC) is central to the thermal management and commercialization of this electrochemical reactor. This article explores the effective operating variables on the temperature gradient in a multilayer SOFC stack and presents a trade-off optimization. Three promising approaches are numerically tested via a model-based sensitivity analysis. The numerically efficient thermo-chemical model that had already been developed by the authors for the cell scale investigations (Tang et al. Chem. Eng. J. 2016, 290, 252-262) is integrated and extended in this work to allow further thermal studies at commercial scales. Initially, the most common approach for the minimization of stack's thermal inhomogeneity, i.e., usage of the excess air, is critically assessed. Subsequently, the adjustment of inlet gas temperatures is introduced as a complementary methodology to reduce the efficiency loss due to application of excess air. As another practical approach, regulation of the oxygen fraction in the cathode coolant stream is examined from both technical and economic viewpoints. Finally, a multiobjective optimization calculation is conducted to find an operating condition in which stack's efficiency and temperature gradient are maximum and minimum, respectively.

Patterning optically clear films: co-planar transparent and color-contrasted thin films from interdiffused electrodeposited and solution-processed metal oxides

Transparent thin films can now be site-selectively patterned and positioned on surface using mask-defined electrodeposition of one oxide and overcoating with a different solution-processed oxide, followed by thermal annealing. Annealing allows an interdiffusion process to create a new oxide that is entirely transparent. A primary electrodeposited oxide can be patterned and the secondary oxide coated over the entire substrate to form high color contrast coplanar thin film tertiary oxide. The authors also detail the phase formation and chemical state of the oxide and how the nature of the electrodeposited layer and the overlayer influence the optical clearing of the patterned oxide film.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.