Computational Electromagnetic Methods for Transcranial Magnetic Stimulation.

Transcranial magnetic stimulation (TMS) is a noninvasive technique used both as a research tool for cognitive neuroscience and as a FDA approved treatment for depression. During TMS, coils positioned near the scalp generate electric fields and activate targeted brain regions. In this thesis, several computational electromagnetics methods that improve the analysis, design, and uncertainty quantification of TMS systems were developed. Analysis: A new fast direct technique for solving the large and sparse linear system of equations (LSEs) arising from the finite difference (FD) discretization of Maxwell’s quasi-static equations was developed. Following a factorization step, the solver permits computation of TMS fields inside realistic brain models in seconds, allowing for patient-specific real-time usage during TMS. The solver is an alternative to iterative methods for solving FD LSEs, often requiring run-times of minutes. A new integral equation (IE) method for analyzing TMS fields was developed. The human head is highly-heterogeneous and characterized by high-relative permittivities (10^7). IE techniques for analyzing electromagnetic interactions with such media suffer from high-contrast and low-frequency breakdowns. The novel high-permittivity and low-frequency stable internally combined volume-surface IE method developed. The method not only applies to the analysis of high-permittivity objects, but it is also the first IE tool that is stable when analyzing highly-inhomogeneous negative permittivity plasmas. Design: TMS applications call for electric fields to be sharply focused on regions that lie deep inside the brain. Unfortunately, fields generated by present-day Figure-8 coils stimulate relatively large regions near the brain surface. An optimization method for designing single feed TMS coil-arrays capable of producing more localized and deeper stimulation was developed. Results show that the coil-arrays stimulate 2.4 cm into the head while stimulating 3.0 times less volume than Figure-8 coils. Uncertainty quantification (UQ): The location/volume/depth of the stimulated region during TMS is often strongly affected by variability in the position and orientation of TMS coils, as well as anatomical differences between patients. A surrogate model-assisted UQ framework was developed and used to statistically characterize TMS depression therapy. The framework identifies key parameters that strongly affect TMS fields, and partially explains variations in TMS treatment responses.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111459/1/luisgo_1.pd

A survey for water maser emission towards planetary nebulae. New detection in IRAS 17347-3139

We report on a water maser survey towards a sample of 27 planetary nebulae (PNe) using the Robledo de Chavela and Medicina single-dish antennas, as well as the Very Large Array (VLA). Two detections have been obtained: the already known water maser emission in K 3-35, and a new cluster of masers in IRAS 17347-3139. This low rate of detections is compatible with the short life-time of water molecules in PNe (~100 yr). The water maser cluster at IRAS 17347-3139 are distributed on a ellipse of size ~ 0.2" x 0.1", spatially associated with compact 1.3 cm continuum emission (simultaneously observed with the VLA). From archive VLA continuum data at 4.9, 8.4, and 14.9 GHz, a spectral index alpha = 0.76 +- 0.03 is derived for this radio source, which is consistent with either a partially optically thick ionized region or with an ionized wind. However, the latter scenario can be ruled out on mass-loss considerations, thus indicating that this source is probably a young PN. The spatial distribution and the radial velocities of the water masers are suggestive of a rotating and expanding maser ring, tracing the innermost regions of a torus formed at the end of the AGB phase. Given that the 1.3 cm continuum emission peak is located near one of the tips of the major axis of the ellipse of masers, we speculate on a possible binary nature of IRAS 17347-3139, where the radio continuum emission could belong to one of the components and the water masers would be associated with a companion.Comment: Accepted by The Astrophysical Journal. 25 pages, 6 figure

A Cluster of Compact Radio Sources in NGC 2024 (Orion B)

We present deep 3.6 cm radio continuum observations of the H II region NGC 2024 in Orion B obtained using the Very Large Array in its A-configuration, with $0\rlap.{''}2$ angular resolution. We detect a total of 25 compact radio sources in a region of $4' \times 4'$. We discuss the nature of these sources and its relation with the infrared and X-ray objects in the region. At least two of the radio sources are obscured proplyds whose morphology can be used to restrict the location of the main ionizing source of the region. This cluster of radio sources is compared with others that have been found in regions of recent star formation.Comment: 21 pages, 7 figure

Finite temperature effective action, AdS_5 black holes, and 1/N expansion

We propose a phenomenological matrix model to study string theory in AdS_5 \times S_5 in the canonical ensemble. The model reproduces all the known qualitative features of the theory. In particular, it gives a simple effective potential description of Euclidean black hole nucleation and the tunnelling between thermal AdS and the big black hole. It also has some interesting predictions. We find that there exists a critical temperature at which the Euclidean small black hole undergoes a Gross-Witten phase transition. We identify the phase transition with the Horowitz-Polchinski point where the black hole horizon size becomes comparable to the string scale. The appearance of the Hagedorn divergence of thermal AdS is due to the merger of saddle points corresponding to the Euclidean small black hole and thermal AdS. The merger can be described in terms of a cusp (A_3) catastrophe and divergences at the perturbative string level are smoothed out at finite string coupling using standard techniques of catastrophe theory.Comment: 41 pages, 3 eps figures, uses harvma