Influence of Outlet Boundary Conditions on Cerebrovascular Aneurysm Hemodynamics

Computational fluid dynamic (CFD) studies of blood flow in cerebrovascular aneurysms have potential to improve patient treatment planning by enabling clinicians and engineers to model patient-specific geometries and compute predictors and risks prior to neurovascular intervention. However, the use of patient-specific computational models in clinical settings is unfeasible due to their complexity, computationally intensive and time-consuming nature. An important factor contributing to this challenge is the choice of outlet boundary conditions, which often involves a trade-off between physiological accuracy, patient-specificity, simplicity and speed. In this study, we analyze how resistance and impedance outlet boundary conditions affect blood flow velocities, wall shear stresses and pressure distributions in a patient-specific model of a cerebrovascular aneurysm. We also use geometrical manipulation techniques to obtain a model of the patient’s vasculature prior to aneurysm development, and study how forces and stresses may have been involved in the initiation of aneurysm growth. Our CFD results show that the nature of the prescribed outlet boundary conditions is not as important as the relative distributions of blood flow through each outlet branch. As long as the appropriate parameters are chosen to keep these flow distributions consistent with physiology, resistance boundary conditions, which are simpler, easier to use and more practical than their impedance counterparts, are sufficient to study aneurysm pathophysiology, since they predict very similar wall shear stresses, time-averaged wall shear stresses, time-averaged pressures, and blood flow patterns and velocities. The only situations where the use of impedance boundary conditions should be prioritized is if pressure waveforms are being analyzed, or if local pressure distributions are being evaluated at specific time points, especially at peak systole, where the use of resistance boundary conditions leads to unnaturally large pressure pulses. In addition, we show that in this specific patient, the region of the blood vessel where the neck of the aneurysm developed was subject to abnormally high wall shear stresses, and that regions surrounding blebs on the aneurysmal surface were subject to low, oscillatory wall shear stresses. Computational models using resistance outlet boundary conditions may be suitable to study patient-specific aneurysm progression in a clinical setting, although several other challenges must be addressed before these tools can be applied clinically.

Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system

Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light. © 2010 The American Physical Society.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Characterization of Image Quality for 3D Scatter Corrected Breast CT Images.

The goal of this study was to characterize the image quality of our dedicated, quasi-monochromatic spectrum, cone beam breast imaging system under scatter corrected and non-scatter corrected conditions for a variety of breast compositions. CT projections were acquired of a breast phantom containing two concentric sets of acrylic spheres that varied in size (1-8mm) based on their polar position. The breast phantom was filled with 3 different concentrations of methanol and water, simulating a range of breast densities (0.79-1.0g/cc); acrylic yarn was sometimes included to simulate connective tissue of a breast. For each phantom condition, 2D scatter was measured for all projection angles. Scatter-corrected and uncorrected projections were then reconstructed with an iterative ordered subsets convex algorithm. Reconstructed image quality was characterized using SNR and contrast analysis, and followed by a human observer detection task for the spheres in the different concentric rings. Results show that scatter correction effectively reduces the cupping artifact and improves image contrast and SNR. Results from the observer study indicate that there was no statistical difference in the number or sizes of lesions observed in the scatter versus non-scatter corrected images for all densities. Nonetheless, applying scatter correction for differing breast conditions improves overall image quality.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

An evaluation of remifentanil-sevoflurane response surface models in patients emerging from anesthesia: model improvement using effect-site sevoflurane concentrations.

INTRODUCTION: We previously reported models that characterized the synergistic interaction between remifentanil and sevoflurane in blunting responses to verbal and painful stimuli. This preliminary study evaluated the ability of these models to predict a return of responsiveness during emergence from anesthesia and a response to tibial pressure when patients required analgesics in the recovery room. We hypothesized that model predictions would be consistent with observed responses. We also hypothesized that under non-steady-state conditions, accounting for the lag time between sevoflurane effect-site concentration (Ce) and end-tidal (ET) concentration would improve predictions. METHODS: Twenty patients received a sevoflurane, remifentanil, and fentanyl anesthetic. Two model predictions of responsiveness were recorded at emergence: an ET-based and a Ce-based prediction. Similarly, 2 predictions of a response to noxious stimuli were recorded when patients first required analgesics in the recovery room. Model predictions were compared with observations with graphical and temporal analyses. RESULTS: While patients were anesthetized, model predictions indicated a high likelihood that patients would be unresponsive (> or = 99%). However, after termination of the anesthetic, models exhibited a wide range of predictions at emergence (1%-97%). Although wide, the Ce-based predictions of responsiveness were better distributed over a percentage ranking of observations than the ET-based predictions. For the ET-based model, 45% of the patients awoke within 2 min of the 50% model predicted probability of unresponsiveness and 65% awoke within 4 min. For the Ce-based model, 45% of the patients awoke within 1 min of the 50% model predicted probability of unresponsiveness and 85% awoke within 3.2 min. Predictions of a response to a painful stimulus in the recovery room were similar for the Ce- and ET-based models. DISCUSSION: Results confirmed, in part, our study hypothesis; accounting for the lag time between Ce and ET sevoflurane concentrations improved model predictions of responsiveness but had no effect on predicting a response to a noxious stimulus in the recovery room. These models may be useful in predicting events of clinical interest but large-scale evaluations with numerous patients are needed to better characterize model performance.

Monte Carlo Analysis and Physics Characterization of a Novel Nanoparticle Detector for Medical and Micro-dosimetry Applications

The outcomes for both (i) radiation therapy and (ii) preclinical small animal radio- biology studies are dependent on the delivery of a known quantity of radiation to a specific and intentional location. Adverse effects can result from these procedures if the dose to the target is too high or low, and can also result from an incorrect spatial distribution in which nearby normal healthy tissue can be undesirably damaged by poor radiation delivery techniques. Thus, in mice and humans alike, the spatial dose distributions from radiation sources should be well characterized in terms of the absolute dose quantity, and with pin-point accuracy. When dealing with the steep spatial dose gradients consequential to either (i) high dose rate (HDR) brachytherapy or (ii) within the small organs and tissue inhomogeneities of mice, obtaining accurate and highly precise dose results can be very challenging, considering commercially available radiation detection tools, such as ion chambers, are often too large for in-vivo use.

In this dissertation two tools are developed and applied for both clinical and preclinical radiation measurement. The first tool is a novel radiation detector for acquiring physical measurements, fabricated from an inorganic nano-crystalline scintillator that has been fixed on an optical fiber terminus. This dosimeter allows for the measurement of point doses to sub-millimeter resolution, and has the ability to be placed in-vivo in humans and small animals. Real-time data is displayed to the user to provide instant quality assurance and dose-rate information. The second tool utilizes an open source Monte Carlo particle transport code, and was applied for small animal dosimetry studies to calculate organ doses and recommend new techniques of dose prescription in mice, as well as to characterize dose to the murine bone marrow compartment with micron-scale resolution.

Hardware design changes were implemented to reduce the overall fiber diameter to <0.9 mm for the nano-crystalline scintillator based fiber optic detector (NanoFOD) system. Lower limits of device sensitivity were found to be approximately 0.05 cGy/s. Herein, this detector was demonstrated to perform quality assurance of clinical 192Ir HDR brachytherapy procedures, providing comparable dose measurements as thermo-luminescent dosimeters and accuracy within 20% of the treatment planning software (TPS) for 27 treatments conducted, with an inter-quartile range ratio to the TPS dose value of (1.02-0.94=0.08). After removing contaminant signals (Cerenkov and diode background), calibration of the detector enabled accurate dose measurements for vaginal applicator brachytherapy procedures. For 192Ir use, energy response changed by a factor of 2.25 over the SDD values of 3 to 9 cm; however a cap made of 0.2 mm thickness silver reduced energy dependence to a factor of 1.25 over the same SDD range, but had the consequence of reducing overall sensitivity by 33%.

For preclinical measurements, dose accuracy of the NanoFOD was within 1.3% of MOSFET measured dose values in a cylindrical mouse phantom at 225 kV for x-ray irradiation at angles of 0, 90, 180, and 270˝. The NanoFOD exhibited small changes in angular sensitivity, with a coefficient of variation (COV) of 3.6% at 120 kV and 1% at 225 kV. When the NanoFOD was placed alongside a MOSFET in the liver of a sacrificed mouse and treatment was delivered at 225 kV with 0.3 mm Cu filter, the dose difference was only 1.09% with use of the 4x4 cm collimator, and -0.03% with no collimation. Additionally, the NanoFOD utilized a scintillator of 11 µm thickness to measure small x-ray fields for microbeam radiation therapy (MRT) applications, and achieved 2.7% dose accuracy of the microbeam peak in comparison to radiochromic film. Modest differences between the full-width at half maximum measured lateral dimension of the MRT system were observed between the NanoFOD (420 µm) and radiochromic film (320 µm), but these differences have been explained mostly as an artifact due to the geometry used and volumetric effects in the scintillator material. Characterization of the energy dependence for the yttrium-oxide based scintillator material was performed in the range of 40-320 kV (2 mm Al filtration), and the maximum device sensitivity was achieved at 100 kV. Tissue maximum ratio data measurements were carried out on a small animal x-ray irradiator system at 320 kV and demonstrated an average difference of 0.9% as compared to a MOSFET dosimeter in the range of 2.5 to 33 cm depth in tissue equivalent plastic blocks. Irradiation of the NanoFOD fiber and scintillator material on a 137Cs gamma irradiator to 1600 Gy did not produce any measurable change in light output, suggesting that the NanoFOD system may be re-used without the need for replacement or recalibration over its lifetime.

For small animal irradiator systems, researchers can deliver a given dose to a target organ by controlling exposure time. Currently, researchers calculate this exposure time by dividing the total dose that they wish to deliver by a single provided dose rate value. This method is independent of the target organ. Studies conducted here used Monte Carlo particle transport codes to justify a new method of dose prescription in mice, that considers organ specific doses. Monte Carlo simulations were performed in the Geant4 Application for Tomographic Emission (GATE) toolkit using a MOBY mouse whole-body phantom. The non-homogeneous phantom was comprised of 256x256x800 voxels of size 0.145x0.145x0.145 mm3. Differences of up to 20-30% in dose to soft-tissue target organs was demonstrated, and methods for alleviating these errors were suggested during whole body radiation of mice by utilizing organ specific and x-ray tube filter specific dose rates for all irradiations.

Monte Carlo analysis was used on 1 µm resolution CT images of a mouse femur and a mouse vertebra to calculate the dose gradients within the bone marrow (BM) compartment of mice based on different radiation beam qualities relevant to x-ray and isotope type irradiators. Results and findings indicated that soft x-ray beams (160 kV at 0.62 mm Cu HVL and 320 kV at 1 mm Cu HVL) lead to substantially higher dose to BM within close proximity to mineral bone (within about 60 µm) as compared to hard x-ray beams (320 kV at 4 mm Cu HVL) and isotope based gamma irradiators (137Cs). The average dose increases to the BM in the vertebra for these four aforementioned radiation beam qualities were found to be 31%, 17%, 8%, and 1%, respectively. Both in-vitro and in-vivo experimental studies confirmed these simulation results, demonstrating that the 320 kV, 1 mm Cu HVL beam caused statistically significant increased killing to the BM cells at 6 Gy dose levels in comparison to both the 320 kV, 4 mm Cu HVL and the 662 keV, 137Cs beams.