Bio-electromagnetic model of deep brain stimulation

Functional stimulation is one of the most fascinating applications of bioelectromagnetism. It deals with the stimulation of excitable biological tissues by electromagnetic fields. One of its most impressive medical applications is the subthalamic nucleus deep brain stimulation (DBS). It consists in the insertion of an electrode into the deep brain, delivering electric pulses to treat Parkinson's disease and other movement disorders. But despite its wide use throughout the world for almost twenty years, the understanding of the mechanisms of action remains unclear. To help clinicians to better understand the mechanisms of DBS, its limitations and implications from an electrical point of view, electrical models of the head can be used to predict the electric potential distribution generated by the electric pulse. With the development of medical imaging techniques, the information on biological tissues that can be used to build these electrical models has never been so detailed. The diffusion tensor magnetic imaging (DT-MRI) is able to provide the orientation of the fibers within the cerebral tissues. Thus, the high inhomogeneity and anisotropy of the head can be modeled through anisotropic electrical conductivity tensors to set up realistic models of the patient's head. This thesis aims to provide to clinicians an accurate prediction of the potential distribution generated by the electric pulse. With this purpose, a finite element (FE) model is set up using electric conductivity values based on DT-MRI data. Special care has been taken to model more realistic boundary conditions than the ones commonly encountered in literature. A great effort has also been put to model the tissues surrounding the stimulation. The results show that these two aspects are impacting significantly the potential distribution. To predict the neural extent of the stimulation, electrical equivalent models of axons are combined with the obtained potentials. Volume of tissues activated (VTA) are thus obtained. Results show that the VTA are also impacted by the decision on how to model the boundary conditions. They show that the usual choice assumed in literature up to now leads to an overestimation of 30% of the VTA.

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

Modelling of 2G HTS Coated Conductors for Fault Current Limiter Applications

Daniele Colangelo

Thanks to recent scientific achievements, second generation high-temperature superconductor coated conductors (HTS-CCs) can carry enormous current densities with reduced losses. In addition, they are able to switch from a negligible resistivity state to a high resistivity state (quench) in a very fast time. The most promising application for this technology is represented by resistive superconducting fault current limiters (SFCLs). These devices enable us to operate the grid at larger power flows without the need of expensive upgrading interventions. One of the crucial challenge for the design of SFCLs is to deal with the inhomogeneous properties the superconducting materials present. The inhomogeneity of the material properties causes a non uniform transition to the high resistivity state. The consequence is a local heat generation. As HTS-CCs are characterized by low thermal conductivity, the heat does not diffuse longitudinally and the conductors are exposed to local thermal runaway. This Ph.D. thesis focuses on the numerical modelling of (RE)BaCuO-based HTS-CCs for resistive fault current limiter applications. The purpose of numerical modelling is to improve the HTS-CCs thermal stability and to optimize the design of resistive SFCLs. First, we develop a thermal-electrical coupled model that describes the transient response of long length (hundreds of meters) inhomogeneous HTS-CC candidates. The implementation of the inhomogeneous properties is based on Gaussian distributions derived from commercial wires. The electrical part of the model has been tuned to fit experimental measurements made on commercial coated conductors. The thermal part of the model has been validated with the support of finite element methods (FEMs). Then, we extended the modelling of HTS-CCs to SFCL modules. The model of a resistive SFCL has been interfaced with the characteristic parameters of two real medium voltage grids. The effect of the tape inhomogeneity has been analyzed under real fault scenarios. Afterwards, we used FEM calculations to investigate the possibility of improving the thermal stability of commercial HTS-CCs. In this respect, we analyzed the effects of a medium inserted between a HTS-CC and the cooling bath. The benefits of the concept idea has been demonstrated through a simplified 2D electro-thermal model (2D ET). In its turn, the assumptions used to develop the 2D ET model have been validated with a 2D magneto-thermal model (2D MT) and a 3D electro-thermal model (3D ET). The 2D MT model has been used to compare the magnetic and the thermal dynamics of a HTS-CC, whereas the 3D ET model has been used to study the quench propagation across the width and along the length of a HTS-CC.

EPFL2013

Finite-element modelling of superconductors in over-critical regime with temperature dependent resistivity

Joseph Duron, Bertrand Dutoit, Francesco Grilli

In this paper, we present a new numerical model, in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite-element-method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the superconductor when the current exceeds

I_{c}

. This model has been applied for studying the behaviour of strip lines of an YBCO/Au FCL with a sapphire substrate. Simulations with currents largely exceeding

I_{c}

have been performed, showing that the total current limitation occurs only when the temperature dependence of the electrical parameters is taken into consideration. Such modelling can replace experiments with currents far exceeding

I_{c}

which may damage or destroy the studied sample or HTS device.

2006