On the Efficient Evaluation of the Azimuthal Fourier Components of the Green\u27s Function for the Helmholtz\u27s Equation in Cylindrical Coordinates

In this dissertation, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green’s function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green’s function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green’s function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most of the state of the art methods cannot easily be parallelized. In this work, we present an algorithm for evaluating the modal Green’s function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as O(m). Furthermore, our algorithm is embarrassingly parallelizable

On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates

In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most state of the art methods cannot be easily parallelized. In this manuscript, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as $O(m)$, where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly parallelizable.Comment: 58 pages, 9 tables, 11 figure

THz and mm-Wave Sensing of Corneal Tissue Water Content: Electromagnetic Modeling and Analysis.

Terahertz (THz) spectral properties of human cornea are explored as a function of central corneal thickness (CCT) and corneal water content, and the clinical utility of THz-based corneal water content sensing is discussed. Three candidate corneal tissue water content (CTWC) perturbations, based on corneal physiology, are investigated that affect the axial water distribution and total thickness. The THz frequency reflectivity properties of the three CTWC perturbations were simulated and explored with varying system center frequency and bandwidths (Q-factors). The modeling showed that at effective optical path lengths on the order of a wavelength the cornea presents a lossy etalon bordered by air at the anterior and the aqueous humor at the posterior. The simulated standing wave peak-to-valley ratio is pronounced at lower frequencies and its effect on acquired data can be modulated by adjusting the bandwidth of the sensing system. These observations are supported with experimental spectroscopic data. The results suggest that a priori knowledge of corneal thickness can be utilized for accurate assessments of corneal tissue water content. The physiologic variation of corneal thickness with respect to the wavelengths spanned by the THz band is extremely limited compared to all other structures in the body making CTWC sensing unique amongst all proposed applications of THz medical imaging

A system for evaluating magnetic resonance imaging of prostate cancer using patient-specific 3D printed molds.

We have developed a system for evaluating magnetic resonance imaging of prostate cancer, using patient-specific 3D printed molds to facilitate MR-histology correlation. Prior to radical prostatectomy a patient receives a multiparametric MRI, which an expert genitourinary radiologist uses to identify and contour regions suspicious for disease. The same MR series is used to generate a prostate contour, which is the basis for design of a patient-specific mold. The 3D printed mold contains a series of evenly spaced parallel slits, each of which corresponds to a known MRI slice. After surgery, the patient's specimen is enclosed within the mold, and all whole-mount levels are obtained simultaneously through use of a multi-bladed slicing device. The levels are then formalin fixed, processed, and delivered to an expert pathologist, who identifies and grades all lesions within the slides. Finally, the lesion contours are loaded into custom software, which elastically warps them to fit the MR prostate contour. The suspicious regions on MR can then be directly compared to lesions on histology. Furthermore, the false-negative and false-positive regions on MR can be retrospectively examined, with the ultimate goal of developing methods for improving the predictive accuracy of MRI. This work presents the details of our analysis method, following a patient from diagnosis through the MR-histology correlation process. For this patient MRI successfully predicted the presence of cancer, but true lesion volume and extent were underestimated. Most cancer-positive regions missed on MR were observed to have patterns of low T2 signal, suggesting that there is potential to improve sensitivity

THz and mm-Wave Sensing of Corneal Tissue Water Content: Electromagnetic Modeling and Analysis.

Terahertz (THz) spectral properties of human cornea are explored as a function of central corneal thickness (CCT) and corneal water content, and the clinical utility of THz-based corneal water content sensing is discussed. Three candidate corneal tissue water content (CTWC) perturbations, based on corneal physiology, are investigated that affect the axial water distribution and total thickness. The THz frequency reflectivity properties of the three CTWC perturbations were simulated and explored with varying system center frequency and bandwidths (Q-factors). The modeling showed that at effective optical path lengths on the order of a wavelength the cornea presents a lossy etalon bordered by air at the anterior and the aqueous humor at the posterior. The simulated standing wave peak-to-valley ratio is pronounced at lower frequencies and its effect on acquired data can be modulated by adjusting the bandwidth of the sensing system. These observations are supported with experimental spectroscopic data. The results suggest that a priori knowledge of corneal thickness can be utilized for accurate assessments of corneal tissue water content. The physiologic variation of corneal thickness with respect to the wavelengths spanned by the THz band is extremely limited compared to all other structures in the body making CTWC sensing unique amongst all proposed applications of THz medical imaging

THz and MM-Wave Sensing of Corneal Tissue Water Content: In Vivo Sensing and Imaging Results

A pulsed terahertz (THz) imaging system and millimeter-wave reflectometer were used to acquire images and point measurements, respectively, of five rabbit cornea in vivo. These imaging results are the first ever produced of in vivo cornea. A modified version of a standard protocol using a gentle stream of air and a Mylar window was employed to slightly dehydrate healthy cornea. The sensor data and companion central corneal thickness (CCT) measurements were acquired every 10-15 min over the course of two hours using ultrasound pachymmetry. Statistically significant positive correlations were established between CCT measurements and millimeter wave reflectivity. Local shifts in reflectivity contrast were observed in the THz imagery; however, the THz reflectivity did not display a significant correlation with thickness in the region probed by the 100 GHz and CCT measurements. This is explained in part by a thickness sensitivity at least 10 × higher in the mm-wave than the THz systems. Stratified media and effective media modeling suggest that the protocol perturbed the thickness and not the corneal tissue water content (CTWC). To further explore possible etalon effects, an additional rabbit was euthanized and millimeter wave measurements were obtained during death induced edema. These observations represent the first time that the uncoupled sensing of CTWC and CCT have been achieved in vivo

THz and mm-Wave Sensing of Corneal Tissue Water Content: In Vivo Sensing and Imaging Results

A pulsed terahertz (THz) imaging system and millimeter-wave reflectometer were used to acquire images and point measurements, respectively, of five rabbit cornea in vivo. These imaging results are the first ever produced of in vivo cornea. A modified version of a standard protocol using a gentle stream of air and a Mylar window was employed to slightly dehydrate healthy cornea. The sensor data and companion central corneal thickness (CCT) measurements were acquired every 10–15 min over the course of two hours using ultrasound pachymmetry.. Statistically significant positive correlations were established between CCT measurements and millimeter wave reflectivity. Local shifts in reflectivity contrast were observed in the THz imagery; however, the THz reflectivity did not display a significant correlation with thickness in the region probed by the 100 GHz and CCT measurements. This is explained in part by a thickness sensitivity at least 10× higher in the mm-wave than the THz systems. Stratified media and effective media modeling suggest that the protocol perturbed the thickness and not the corneal tissue water content (CTWC). To further explore possible etalon effects, an additional rabbit was euthanized and millimeter wave measurements were obtained during death induced edema. These observations represent the first time that the uncoupled sensing of CTWC and CCT have been achieved in vivo