Simulation of epiretinal prostheses - Evaluation of geometrical factors affecting stimulation thresholds

Background An accurate understanding of the electrical interaction between retinal prostheses and retinal tissue is important to design effective devices. Previous studies have used modelling approaches to simulate electric fields generated by epiretinal prostheses in saline and to simulate retinal ganglion cell (RGC) activation using passive or/and active biophysical models of the retina. These models have limited scope for studying an implanted human retinal prosthesis as they often do not account for real geometry and composition of the prosthesis-retina interface. This interface consists of real dimensions and location of stimulation and ground electrodes that are separated by the retinal tissue and surrounded by physiological fluids. Methods In this study, we combined the prosthesis-retina interface elements into a framework to evaluate the geometrical factors affecting stimulation thresholds for epiretinal prostheses used in clinical human trials, as described by Balthasar et al. in their Investigative Ophthalmology and Visual Science (IOVS) paper published in 2008 using the Argus I epiretinal implants. Finite element method (FEM) based computations were used to estimate threshold currents based on a threshold criterion employing a passive electric model of the retina. Results Threshold currents and impedances were estimated for different electrode-retina distances. The profiles and the values for thresholds and impedances obtained from our simulation framework are within the range of measured values in the only elaborate published clinical trial until now using Argus I epiretinal implants. An estimation of resolution for the electrodes used in these trials was provided. Our results reiterate the importance of close proximity between electrodes and retina for safe and efficient retinal stimulation. Conclusions The validation of our simulation framework being relevant for epiretinal prosthesis research is derived from the good agreement of the computed trends and values of the current study with measurements demonstrated in existing clinical trials on humans (Argus I). The proposed simulation framework could be used to generate the relationship between threshold and impedance for any electrode geometry and consequently be an effective tool for design engineers, surgeons and electrophysiologists.

Modelling of high temperature superconductors for AC power applications

This Ph.D. thesis is focused on the development of novel models for calculation of AC losses, current and magnetic field profiles in high-temperature superconductors (HTS). The thesis is concentrated on the modelling of Bi-2223 conductors at 77 K, which for the moment have the most advanced manufacturing technology and will be primarily used in the first large-scale power applications of high-temperature superconductors. The analysis of AC losses in Bi-2223 conductors is the leading thread in the structure of the thesis. An introduction to high-temperature superconductivity is made with special emphasis on the mechanisms of AC losses in HTS. Presented are some of the most promising power applications of HTS materials together with a discussion on the required improvements in their performance. A model for dissociating the hysteresis, eddy-current and resistive flux-creep loss contributions, based on relatively broad-range frequency measurements on Bi-2223 tapes has been used for analysis of the frequency behaviour of the transport-current loss in self-field. The hysteresis, eddy-current and flux-creep loss components have been separated due to their different frequency dependence. The study of eddy current loss in the silver sheath and matrix has been complimented by numerical simulations using a simple electromagnetic model of HTS tapes. Described is an original method for estimating the performance of Bi-2223 tapes in typical power grid perturbations by experiments and analysis of over-critical current excursions of various waveform, frequency and current amplitude up to 20×Ic. For precise calculation of the AC losses and studying the electromagnetic properties of HTS with smooth current-voltage characteristics and complex geometry, the finite element method (FEM) has been used. The implementation of the power-law model of the E-J characteristic of HTS into the FEM software package Flux2D is presented. The Flux2D implementation has been validated by means of comparison with results from theoretical predictions, electrical measurements, and other numerical methods. The significance of the power index n and the lateral distribution of the critical current density Jc in multifilamentary HTS tapes has been evaluated by FEM simulations. New anisotropic models of Jc(B) and n(B) for textured Bi-2223 materials have been developed. The models are based on experimental data; they are fairly simple and take into account the orientation of the local magnetic field. These models have been used in FEM simulations on monofilamentary and multifilamentary Bi-2223 conductors with different geometry and filament arrangement. In conductors with given Jc(B) dependence, the notion of effective AC critical current has been defined. The AC losses in Bi-2223 multifilamentary flat tapes and wires of round and square geometry in various operating conditions have been calculated and compared. The AC loss analysis has been supported and complimented by current density and magnetic flux distributions in the different conductors. The influence of the shape factor of the geometry and the filament orientation with respect to the local magnetic field has been thoroughly investigated. The optimal geometry and filament arrangement have been determined for each application.

EPFL2002

Numerical modelling of high temperature superconducting tapes and cables

Francesco Grilli

This Ph.D. thesis is focused on the numerical modelling of high-Tc superconductors (HTS) at the operating temperature of 77 K (liquid nitrogen). The purpose of numerical modelling is to precisely calculate the current and field distributions inside HTS devices (tapes, cables) and the corresponding AC losses, which are one of the most important limiting factors for a large-scale application of such materials. From the electrical point of view, superconductors are characterized by a strongly non-linear voltage-current relation, which defines the transition from superconducting to normal state. In the case of HTS, the steepness of this transition is smoother than for low-Tc superconductors (LTS), so that the commonly used critical state model (CSM) gives a too simplified representation of their electromagnetic behaviour and can be used for a qualitative description only. In this thesis the finite element method (FEM) has been used for precisely computing the current and field distributions as well as for evaluating the AC losses in HTS devices. The superconducting transition is modelled with a power-law relation, E(J) = Ec(J/Jc)n, which is derived from the fit of transport measurements. Firstly, the results obtained with the software package FLUX3D on multi-filamentary tapes have been validated by means of a comparison with the ones obtained by another software package (FLUX2D). The results from FLUX2D, having already been successfully compared with experimental measurements within the framework of two previous Ph.D. theses at LANOS, have been used as reference. Secondly, two power-law models, which take into account the spatial variation of the critical current density inside HTS tapes and its strongly anisotropic dependence on the magnetic field, have been implemented in FLUX3D. In most cases, this latter dependence is extremely important, since the transport capacity of the superconductor is considerably reduced (and its power loss sensibly increased) by the presence of a magnetic field. Afterwards, FEM modelling of HTS tapes has been extended to cables. HTS cables are in general composed by different layers of several tapes and have a quite complex three-dimensional structure: in fact, the layers are wound around a central cylindrical support with different pitch lengths and relative winding orientations, in order to obtain a uniform repartition of the transport current among the layers, which minimizes the total AC losses. For overcoming the difficulties of a direct 3D FEM simulation, a simple electrical model, which allows to find the optimal pitch lengths and whose results are the input data for a 2D FEM evaluation of the AC losses, has been developed. FEM computations have also been used to investigate the influence of the non-uniformity of the tape properties (contact resistance, critical current, power index) on the global loss performance of a single-layer HTS cable. As an alternative to FEM computations, an equivalent circuit model of HTS cables has been utilized. It describes the cable from the macroscopic point of view and allows to compute the current repartition among the layers and the corresponding AC losses, without the necessity of having detailed information about individual tapes. In the framework of the European project BIG-POWA, I have collaborated to the assembling process of a HTS power-link at the Pirelli Labs, in the Milan region, Italy. Finally, 3D simulations have been performed to extensively study the coupling effect between two superconducting filaments via the resistive matrix, which is a typical case where analytical solutions exist for very peculiar geometries and physical conditions only. FEM simulations have been utilized to study the dependence of the filament coupling on the physical and geometrical parameters of the conductors.

EPFL2004

Electromagnetic radiation from lightning return strokes to tall structures

Davide Pavanello

The study of the interaction of lightning electromagnetic fields with electrical systems and the design of appropriate protection strategies are generally based on statistical distributions of the lightning current measured at the channel base using either instrumented towers or artificial initiation of lightning using rockets. Recent studies based both on numerical modeling and experimental observations have shown that the presence of the structure struck by (or used to initiate) lightning does affect the current measurement in a way depending upon the geometry of the structure itself, compromising therefore the reliability of the statistics adopted so far for lightning data. The aim of this thesis is to provide new elements (from both theoretical and experimental investigations) to improve the understanding of the electromagnetic consequences of the impact of lightning return strokes to tall structures. Chapter 2 introduces to the phenomenology of cloud-to-ground lightning and the importance of lightning return-stroke modeling. Among the different classes of return-stroke models existing in the literature, the attention is focused in this thesis on the so-called engineering models, which allow describing the current distribution along the channel as a function of the current at the channel base and the return-stroke speed, two quantities for which data can be obtained experimentally. After presenting a review of five engineering return-stroke models describing lightning strikes to ground, the extension of the engineering models to take into account the presence of an elevated strike object is presented and discussed. The original contributions of this thesis, consisting of both theoretical and experimental works, are presented in Chapters 3 through 6. Chapter 3 is devoted to the computation of the electromagnetic field produced by lightning return strokes to elevated strike objects, using the extension of the engineering models to include an elevated strike object presented in the previous chapter. It is shown, for the first time, that the current distribution associated with these extended models exhibits a discontinuity at the return-stroke wavefront which (although not physically conceivable) needs to be taken into account by an additional term in the equations for the electromagnetic field, the so-called "turn-on" term. A general analytical formula describing the "turn-on" term associated with this discontinuity for various engineering models is derived and simulation results illustrating the effect of the "turn-on" term on the radiated electric and magnetic fields are also presented. In the second part of the chapter, dedicated to the investigation of the propagation effects on lightning electromagnetic field traveling along a finitely-conducting ground, the commonly-used assumption of an idealized perfectly-conducting ground is relaxed in order to analyze, for the first time, how the electromagnetic field radiated by a tower-initiated strike is affected while propagating along a soil characterized by a finite conductivity. The results showed that the attenuation of the initial peak of the field radiated by a tower-initiated strike, resulting from the propagation over finitely conducting ground, depends strongly on the risetime of the current, the tower height and the ground conductivity and is, in general, much more important than the attenuation experienced, while propagating along the same finite ground, by the field produced by ground-initiated strikes. Chapter 4 presents a comparison among the predictions obtained using the five extended engineering return-stroke models for lightning strikes to tall structures described in Chapter 2. The spatial-temporal current profiles along the tower-channel axis predicted by the engineering models, as well as the respective predictions for the radiated electric and magnetic fields, calculated at different distances, are compared and discussed. It is shown that the computed electromagnetic fields associated with a strike to a tall tower are generally less model-dependent than those corresponding to a strike to ground, especially as far as the first-peak value is concerned, which is nearly model-insensitive in case of tall-tower strikes. A theoretical analysis is performed in the last part of the chapter with the aim to provide, for the same five engineering models extended to take into account the presence of the tower, expressions relating the return-stroke current and the associated distant radiated electric and magnetic fields. It is demonstrated, in addition, that only one model among the five presented is characterized by simple analytical formulas relating current-peak and far-field peak values, which (being the electromagnetic field peak value nearly independent of the adopted model) become general expressions applicable for any engineering return-stroke model in case of tower-initiated lightning. It was also shown that the peak amplitude of the electromagnetic field radiated by a lightning strike to a tall structure is relatively insensitive to both the values of the top reflection coefficient and the return-stroke speed. This latter result is important, in particular, because, unlike ground-initiated strikes, for which the far-field peak is strongly dependent on the return-stroke speed, far field peaks associated with strikes to tall structures are little sensitive to the return stroke speed. Since in most practical cases the value of the return-stroke speed is unknown, this interesting result suggests a possible calibration procedure for lightning detection systems by means of direct measurement of lightning currents on instrumented towers. Chapter 5 reports on the simultaneous measurements of the return-stroke current and of the electric and magnetic fields at three distances associated with lightning strikes to the Toronto CN Tower (553 m) that have been carried out during the summer of 2005. This is the first time ever that simultaneous records of lightning current and associated electric and magnetic fields at three distances have been obtained. Two propagation paths for the electromagnetic field to the first and to the second field measurement stations (located, respectively, 2.0 km and 16.8 km away from the CN Tower) were along the soil and through the Toronto city, whereas for the third location (50.9 km away) the propagation path was nearly entirely across the fresh water of Lake Ontario. It is shown that the waveforms of the electric and magnetic fields at 16.8 km and 50.9 km exhibit a first zero-crossing about 5 microseconds after the onset of the return-stroke, which is part of a narrow undershoot and which may be attributed to the transient processes along the tower. Effects of propagation (decrease of field amplitude and increase of its risetime) could also be observed in experimental records. It is shown that the fields at 50.9 km are less affected by such attenuation, compared to those at 16.8 km, presumably because the path of propagation was mostly across Lake Ontario. The measured waveforms are compared with the theoretical predictions obtained using five engineering return-stroke models, extended to include the presence of the strike object, finding a reasonable agreement for the magnetic field waveforms at the three considered distances. The overall agreement between the theoretically predicted and the experimentally observed field-peak-to-current-peak ratio is reasonable, although the theoretical expression appears to underestimate the experimentally measured ratio (by about 25 %). This may be due, at least in part, to the enhancement effect of the buildings on which the field measurement antennas were installed. Finally, the directly-measured lightning currents at the tower were correlated and compared with the current-peak estimations provided by the US National Lightning Detection Network (NLDN). It is shown that the NLDN-inferred values overestimate the actual current peaks because the presence of the tall struck object produces an enhanced radiated field at far distances (with respect to strikes to flat ground), which is not included in the algorithm used to infer lightning current peaks from remote field measurements. It is shown in this thesis that correcting the NLDN estimates using the correction factor introduced by the tower results in an excellent estimation of lightning current peaks. This is an important conclusion of this study showing that the estimation of lightning peak currents for tall towers can be greatly improved by considering the tower correction factor. Chapter 6 is devoted to the measurement of electromagnetic fields radiated by lightning. In its first part, the need for guidelines for reporting lightning data obtained experimentally is emphasized. The second part of the chapter presents the design, the construction and preliminary tests of a low-cost, multi-channel lightning field measuring system for the simultaneous measurement of three components of the electromagnetic field radiated by lightning. The proposed system uses one single optical link for the transmission of the three signals, appropriately digitized and multiplexed, lowering considerably the overall cost of the system itself.

EPFL2007