Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Production of Iron-Tin Compacts by Powder Metallurgy and a Synopsis of their Principle Properties

This thesis is concerned primarily with the production of metal powder compacts of iron and tin. In producing these compacts, the effects of process­ing variables on some of the essential properties of the pellets made were investigated.

One-year outcomes of repeated adjunctive photodynamic therapy during periodontal maintenance: a proof-of-principle randomized-controlled clinical trial

BACKGROUND: Single photodynamic therapy (PDT) has been effective in initial periodontal therapy, but only improved bleeding on probing (BoP) in maintenance patients after a single use. Repeated PDT has not been addressed. OBJECTIVES: To study the possible added benefits of repeated adjunctive PDT to conventional treatment of residual pockets in patients enrolled in periodontal maintenance. MATERIAL AND METHODS: Ten maintenance patients with 70 residual pockets [probing pocket depth (PPD)>or=5 mm] were randomly assigned for treatment five times in 2 weeks (Days 0, 1, 2, 7, 14) with PDT (test) or non-activated laser (control) following debridement. The primary outcome variable was PPD, and the secondary variables were clinical attachment level (CAL) and BoP. These were assessed at 3, 6 and 12 months following the interventions. RESULTS: Greater PPD reductions were observed in the test (-0.67 +/- 0.34; p=0.01) compared with the control patients (-0.04 +/- 0.33; NS) after 6 months. Significant CAL gain (+0.52 +/- 0.31; p=0.01) was noted for the test, but not in the control (-0.27 +/- 0.52; NS) patients after 6 months. BoP percentages decreased significantly in test (97-64%, 67%, 77%), but not control patients after 3, 6 and 12 months. CONCLUSIONS: Repeated (five times) PDT adjunctive to debridement yielded improved clinical outcomes in residual pockets in maintenance patients. The effects were best documented after 6 months.

[Diagnostic pitfalls about a specific case of low back pain]

Diagnostic pitfalls about a specific case of low back pain Low back pain is classified into two principle categories: specific and non specific. This difference is important in terms of screening, medical care and treatment. Specific low back pain has various etiologies that imply specific treatment. This report describes one case of rare specific low back pain. The purpose of this article is to highlight the pitfalls that can represent such a common pathology, to show that obtaining an early diagnosis can be challenging, and finally to prevent care providers from stereotypes related to low back pain management.

In vitro accuracy evaluation of image-guided robot system for direct cochlear access

HYPOTHESIS A previously developed image-guided robot system can safely drill a tunnel from the lateral mastoid surface, through the facial recess, to the middle ear, as a viable alternative to conventional mastoidectomy for cochlear electrode insertion. BACKGROUND Direct cochlear access (DCA) provides a minimally invasive tunnel from the lateral surface of the mastoid through the facial recess to the middle ear for cochlear electrode insertion. A safe and effective tunnel drilled through the narrow facial recess requires a highly accurate image-guided surgical system. Previous attempts have relied on patient-specific templates and robotic systems to guide drilling tools. In this study, we report on improvements made to an image-guided surgical robot system developed specifically for this purpose and the resulting accuracy achieved in vitro. MATERIALS AND METHODS The proposed image-guided robotic DCA procedure was carried out bilaterally on 4 whole head cadaver specimens. Specimens were implanted with titanium fiducial markers and imaged with cone-beam CT. A preoperative plan was created using a custom software package wherein relevant anatomical structures of the facial recess were segmented, and a drill trajectory targeting the round window was defined. Patient-to-image registration was performed with the custom robot system to reference the preoperative plan, and the DCA tunnel was drilled in 3 stages with progressively longer drill bits. The position of the drilled tunnel was defined as a line fitted to a point cloud of the segmented tunnel using principle component analysis (PCA function in MatLab). The accuracy of the DCA was then assessed by coregistering preoperative and postoperative image data and measuring the deviation of the drilled tunnel from the plan. The final step of electrode insertion was also performed through the DCA tunnel after manual removal of the promontory through the external auditory canal. RESULTS Drilling error was defined as the lateral deviation of the tool in the plane perpendicular to the drill axis (excluding depth error). Errors of 0.08 ± 0.05 mm and 0.15 ± 0.08 mm were measured on the lateral mastoid surface and at the target on the round window, respectively (n =8). Full electrode insertion was possible for 7 cases. In 1 case, the electrode was partially inserted with 1 contact pair external to the cochlea. CONCLUSION The purpose-built robot system was able to perform a safe and reliable DCA for cochlear implantation. The workflow implemented in this study mimics the envisioned clinical procedure showing the feasibility of future clinical implementation.

Evaluation of a new six degrees of freedom couch for radiation therapy

Purpose: The aim of this work is to evaluate the geometric accuracy of a prerelease version of a new six degrees of freedom (6DoF) couch. Additionally, a quality assurance method for 6DoF couches is proposed. Methods: The main principle of the performance tests was to request a known shift for the 6DoF couch and to compare this requested shift with the actually applied shift by independently measuring the applied shift using different methods (graph paper, laser, inclinometer, and imaging system). The performance of each of the six axes was tested separately as well as in combination with the other axes. Functional cases as well as realistic clinical cases were analyzed. The tests were performed without a couch load and with a couch load of up to 200 kg and shifts in the range between −4 and +4 cm for the translational axes and between −3° and +3° for the rotational axes were applied. The quality assurance method of the new 6DoF couch was performed using a simple cube phantom and the imaging system. Results: The deviations (mean ± one standard deviation) accumulated over all performance tests between the requested shifts and the measurements of the applied shifts were −0.01 ± 0.02, 0.01 ± 0.02, and 0.01 ± 0.02 cm for the longitudinal, lateral, and vertical axes, respectively. The corresponding values for the three rotational axes couch rotation, pitch, and roll were 0.03° ± 0.06°, −0.04° ± 0.12°, and −0.01° ± 0.08°, respectively. There was no difference found between the tests with and without a couch load of up to 200 kg. Conclusions: The new 6DoF couch is able to apply requested shifts with high accuracy. It has the potential to be used for treatment techniques with the highest demands in patient setup accuracy such as those needed in stereotactic treatments. Shifts can be applied efficiently and automatically. Daily quality assurance of the 6DoF couch can be performed in an easy and efficient way. Long-term stability has to be evaluated in further tests.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Improving the accuracy of radiation pneumonitis dose response models

The prognosis for lung cancer patients remains poor. Five year survival rates have been reported to be 15%. Studies have shown that dose escalation to the tumor can lead to better local control and subsequently better overall survival. However, dose to lung tumor is limited by normal tissue toxicity. The most prevalent thoracic toxicity is radiation pneumonitis. In order to determine a safe dose that can be delivered to the healthy lung, researchers have turned to mathematical models predicting the rate of radiation pneumonitis. However, these models rely on simple metrics based on the dose-volume histogram and are not yet accurate enough to be used for dose escalation trials. The purpose of this work was to improve the fit of predictive risk models for radiation pneumonitis and to show the dosimetric benefit of using the models to guide patient treatment planning. The study was divided into 3 specific aims. The first two specifics aims were focused on improving the fit of the predictive model. In Specific Aim 1 we incorporated information about the spatial location of the lung dose distribution into a predictive model. In Specific Aim 2 we incorporated ventilation-based functional information into a predictive pneumonitis model. In the third specific aim a proof of principle virtual simulation was performed where a model-determined limit was used to scale the prescription dose. The data showed that for our patient cohort, the fit of the model to the data was not improved by incorporating spatial information. Although we were not able to achieve a significant improvement in model fit using pre-treatment ventilation, we show some promising results indicating that ventilation imaging can provide useful information about lung function in lung cancer patients. The virtual simulation trial demonstrated that using a personalized lung dose limit derived from a predictive model will result in a different prescription than what was achieved with the clinically used plan; thus demonstrating the utility of a normal tissue toxicity model in personalizing the prescription dose.