Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Second-Generation Orthopaedic Measurement Device for in-vivo Assessment of Bone Quality

There are two main types of bone in the human body, trabecular and cortical bone. Cortical bone is primarily found on the outer surface of most bones in the body while trabecular bone is found in vertebrae and at the end of long bones (Ross 2007). Osteoporosis is a condition that compromises the structural integrity of trabecular bone, greatly reducing the ability of the bone to absorb energy from falls. The current method for diagnosing osteoporosis and predicting fracture risk is measurement of bone mineral density. Limitations of this method include dependence on the bone density measurement device and dependence on type of test and measurement location (Rubin 2005). Each year there are approximately 250,000 hip fractures in the United States due to osteoporosis (Kleerekoper 2006). Currently, the most common method for repairing a hip fracture is a hip fixation surgery. During surgery, a temporary guide wire is inserted to guide the permanent screw into place and then removed. It is believed that directly measuring this screw pullout force may result in a better assessment of bone quality than current indirect measurement techniques (T. Bowen 2008-2010, pers. comm.). The objective of this project is to design a device that can measure the force required to extract this guide wire. It is believed that this would give the surgeon a direct, quantitative measurement of bone quality at the site of the fixation. A first generation device was designed by a Bucknell Biomedical Engineering Senior Design team during the 2008- 2009 Academic Year. The first step of this project was to examine the device, conduct a thorough design analysis, and brainstorm new concepts. The concept selected uses a translational screw to extract the guide wire. The device was fabricated and underwent validation testing to ensure that the device was functional and met the required engineering specifications. Two tests were conducted, one to test the functionality of the device by testing if the device gave repeatable results, and the other to test the sensitivity of the device to misalignment. Guide wires were extracted from 3 materials, low density polyethylene, ultra high molecular weight polyethylene, and polypropylene and the force of extraction was measured. During testing, it was discovered that the spring in the device did not have a high enough spring constant to reach the high forces necessary for extracting the wires without excessive deflection of the spring. The test procedure was modified slightly so the wires were not fully threaded into the material. The testing results indicate that there is significant variation in the screw pullout force, up to 30% of the average value. This significant variation was attributed to problems in the testing and data collection, and a revised set of tests was proposed to better evaluate the performance of the device. The fabricated device is a fully-functioning prototype and further refinements and testing of the device may lead to a 3rd generation version capable of measuring the screw pullout force during hip fixation surgery.

An Elaboration of the Psycho-Physiological Method and its Application on the Process of Socialization of Mentally Handicapped People

The socialisation of mentally handicapped people is a long-term process during which the disabled person learns new habits and abilities step by step through education and training. Anxiety and neuroses due to an inadequate social environment can place obstacles in the path of the disabled person's integration into society. A method of regulating the psycho-physiological condition of mentally handicapped people (MRPC) was developed in order to reduce anxiety and neuropsychological tension and to establish positive social attitudes. Both verbal and non-verbal means of manipulating the psycho-physiological condition were used and experimental and control groups were formed from among the clients of Israelian's institute. The experimental groups applied the new method for six months, leading to a significant shift in the response of the clients involved. Expressed anxiety and defensive responses to mental tasks were transformed into orienting responses after 30 psycho-regulative exercises. Cognitive functions such as attention and memory also improved significantly. EEG examinations of the actual process of psycho-regulation revealed a tendency towards a change of brain activity by increasing the fast pulse frequency values in the alpha zones. Israelian concludes that the application of the MRPC creates better functional conditions for the socialisation of mentally handicapped people.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

A three-dimensional histological atlas of the human basal ganglia. II. Atlas deformation strategy and evaluation in deep brain stimulation for Parkinson disease

OBJECT: The localization of any given target in the brain has become a challenging issue because of the increased use of deep brain stimulation to treat Parkinson disease, dystonia, and nonmotor diseases (for example, Tourette syndrome, obsessive compulsive disorders, and depression). The aim of this study was to develop an automated method of adapting an atlas of the human basal ganglia to the brains of individual patients. METHODS: Magnetic resonance images of the brain specimen were obtained before extraction from the skull and histological processing. Adaptation of the atlas to individual patient anatomy was performed by reshaping the atlas MR images to the images obtained in the individual patient using a hierarchical registration applied to a region of interest centered on the basal ganglia, and then applying the reshaping matrix to the atlas surfaces. RESULTS: Results were evaluated by direct visual inspection of the structures visible on MR images and atlas anatomy, by comparison with electrophysiological intraoperative data, and with previous atlas studies in patients with Parkinson disease. The method was both robust and accurate, never failing to provide an anatomically reliable atlas to patient registration. The registration obtained did not exceed a 1-mm mismatch with the electrophysiological signatures in the region of the subthalamic nucleus. CONCLUSIONS: This registration method applied to the basal ganglia atlas forms a powerful and reliable method for determining deep brain stimulation targets within the basal ganglia of individual patients.

A validated assay by liquid chromatography-tandem mass spectrometry for the simultaneous quantification of elvitegravir and rilpivirine in HIV positive patients

Because of the large variability in the pharmacokinetics of anti-HIV drugs, therapeutic drug monitoring in patients may contribute to optimize the overall efficacy and safety of antiretroviral therapy. An LC–MS/MS method for the simultaneous assay in plasma of the novel antiretroviral agents rilpivirine (RPV) and elvitegravir (EVG) has been developed to that endeavor. Plasma samples (100 μL) extraction is performed by protein precipitation with acetonitrile, and the supernatant is subsequently diluted 1:1 with 20-mM ammonium acetate/MeOH 50:50. After reverse-phase chromatography, quantification of RPV and EVG, using matrix-matched calibration samples, is performed by electrospray ionization–triple quadrupole mass spectrometry by selected reaction monitoring detection using the positive mode. The stable isotopic-labeled compounds RPV-13C6 and EVG-D6 were used as internal standards. The method was validated according to FDA recommendations, including assessment of extraction yield, matrix effects variability (<6.4%), as well as EVG and RPV short and long-term stability in plasma. Calibration curves were validated over the clinically relevant concentrations ranging from 5 to 2500 ng/ml for RPV and from 50 to 5000 ng/ml for EVG. The method is precise (inter-day CV%: 3–6.3%) and accurate (3.8–7.2%). Plasma samples were found to be stable (<15%) in all considered conditions (RT/48 h, +4°C/48 h, −20°C/3 months and 60°C/1 h). Selected metabolite profiles analysis in patients' samples revealed the presence of EVG glucuronide, that was well separated from parent EVG, allowing to exclude potential interferences through the in-source dissociation of glucuronide to parent drug. This new, rapid and robust LCMS/MS assay for the simultaneous quantification of plasma concentrations of these two major new anti-HIV drugs EVG and RPV offers an efficient analytical tool for clinical pharmacokinetics studies and routine therapeutic drug monitoring service.

Promises of cyclotron-produced 44Sc as a diagnostic match for trivalent β--emitters: in vitro and in vivo study of a 44Sc-DOTA-folate conjugate

In recent years, implementation of 68Ga-radiometalated peptides for PET imaging of cancer has attracted the attention of clinicians. Herein, we propose the use of 44Sc (half-life = 3.97 h, average β+ energy [Eβ+av] = 632 keV) as a valuable alternative to 68Ga (half-life = 68 min, Eβ+av = 830 keV) for imaging and dosimetry before 177Lu-based radionuclide therapy. The aim of the study was the preclinical evaluation of a folate conjugate labeled with cyclotron-produced 44Sc and its in vitro and in vivo comparison with the 177Lu-labeled pendant. Methods: 44Sc was produced via the 44Ca(p,n)44Sc nuclear reaction at a cyclotron (17.6 ± 1.8 MeV, 50 μA, 30 min) using an enriched 44Ca target (10 mg 44CaCO3, 97.00%). Separation from the target material was performed by a semiautomated process using extraction chromatography and cation exchange chromatography. Radiolabeling of a DOTA-folate conjugate (cm09) was performed at 95°C within 10 min. The stability of 44Sc-cm09 was tested in human plasma. 44Sc-cm09 was investigated in vitro using folate receptor–positive KB tumor cells and in vivo by PET/CT imaging of tumor-bearing mice Results: Under the given irradiation conditions, 44Sc was obtained in a maximum yield of 350 MBq at high radionuclide purity (>99%). Semiautomated isolation of 44Sc from 44Ca targets allowed formulation of up to 300 MBq of 44Sc in a volume of 200–400 μL of ammonium acetate/HCl solution (1 M, pH 3.5–4.0) within 10 min. Radiolabeling of cm09 was achieved with a radiochemical yield of greater than 96% at a specific activity of 5.2 MBq/nmol. In vitro, 44Sc-cm09 was stable in human plasma over the whole time of investigation and showed folate receptor–specific binding to KB tumor cells. PET/CT images of mice injected with 44Sc-cm09 allowed excellent visualization of tumor xenografts. Comparison of cm09 labeled with 44Sc and 177Lu revealed almost identical pharmacokinetics. Conclusion: This study presents a high-yield production and efficient separation method of 44Sc at a quality suitable for radiolabeling of DOTA-functionalized biomolecules. An in vivo proof-of-concept study using a DOTA-folate conjugate demonstrated the excellent features of 44Sc for PET imaging. Thus, 44Sc is a valid alternative to 68Ga for imaging and dosimetry before 177Lu-radionuclide tumor therapy.

Squeezing of Pore-water from Core Samples of DGR Boreholes: Feasibility Study

Three archived core samples from boreholes DGR-4, DGR-5 and DGR-6 from the Salina F Unit, Queenston Formation and the Georgian Bay Formation were subjected to squeezing tests at pressures of up to 500 MPa. Two samples did not yield any water, while a total of 0.88 g pore water was obtained from a clay-rich sample from the Blue Mountain Formation (water content = 2.8 wt.%, porosity = 8 %). This water mass was sufficient for a full chemical and water-isotope analysis – the first direct determination of pore-water composition in rocks from the DGR boreholes. The results are generally in reasonable agreement with those of independent methods, or the observed differences can be explained. Ancillary investigations included the determination of water content, densities and mineralogy, aqueous extraction of squeezed cores, and SEM investigations to characterise the microtexture of unsqueezed and squeezed rock materials. It is concluded that squeezing is a promising method of pore-water extraction and characterisation and is recommended as an alternative method for future studies. Selection criteria for potentially squeezable samples include high clay-mineral content (correlating in a high water content) and low carbonate content (low stiffness, limited cementation). Potential artefacts of the method, such as ion filtration or pressure solution, should be explored and quantified in future efforts.

Transferrin immunoextraction for determination of carbohydrate-deficient transferrin in human serum by capillary zone electrophoresis

CZE-based assays for carbohydrate-deficient transferrin (CDT) in which serum is mixed with an Fe(III) ion-containing solution prior to analysis are effective approaches for the determination of CDT in patient samples. Sera of patients with progressed diseases, however, are prone to interferences comigrating with transferrin (Tf) that prevent the proper determination of CDT by CZE in these samples. The need of a simple and economic approach to immunoextract Tf from human serum prompted us to investigate the use of a laboratory-made anti-Tf spin column containing polyclonal rabbit anti-human Tf antibodies linked to Sepharose 4 Fast Flow beads. This article reports extraction column manufacturing and column characterization with sera having normal and elevated CDT levels. The developed procedure was applied to a number of relevant hepatology and dialysis patient samples and could thereby be shown to represent an effective method for extraction and concentration of all Tf isoforms. Furthermore, lipemic sera were delipidated using a mixture of diisopropyl ether and butanol prior to immunoextraction. CDT could unambiguously be determined in all pretreated samples.

Effect of a Traditional Processing Method on the Chemical Composition of Local White Lupin (Lupinus albus L.) Seed in North-Western Ethiopia

The effect of a traditional Ethiopian lupin processing method on the chemical composition of lupin seed samples was studied. Two sampling districts, namely Mecha and Sekela, representing the mid- and high-altitude areas of north-western Ethiopia, respectively, were randomly selected. Different types of traditionally processed and marketed lupin seed samples (raw, roasted, and fi nished) were collected in six replications from each district. Raw samples are unprocessed, and roasted samples are roasted using fi rewood. Finished samples are those ready for human consumption as snack. Thousand seed weight for raw and roasted samples within a study district was similar (P > 0.05), but it was lower (P < 0.01) for fi nished samples compared to raw and roasted samples. The crude fi bre content of fi nished lupin seed sample from Mecha was lower (P < 0.01) than that of raw and roasted samples. However, the different lupin samples from Sekela had similar crude fi bre content (P > 0.05). The crude protein and crude fat contents of fi nished samples within a study district were higher (P < 0.01) than those of raw and roasted samples, respectively. Roasting had no effect on the crude protein content of lupin seed samples. The crude ash content of raw and roasted lupin samples within a study district was higher (P < 0.01) than that of fi nished lupin samples of the respective study districts. The content of quinolizidine alkaloids of fi nished lupin samples was lower than that of raw and roasted samples. There was also an interaction effect between location and lupin sample type. The traditional processing method of lupin seeds in Ethiopia has a positive contribution improving the crude protein and crude fat content, and lowering the alkaloid content of the fi nished product. The study showed the possibility of adopting the traditional processing method to process bitter white lupin for the use as protein supplement in livestock feed in Ethiopia, but further work has to be done on the processing method and animal evaluation.

Influence of unilateral maxillary first molar extraction treatment on second and third molar inclination in Class II subdivision patients.

OBJECTIVE To assess the maxillary second molar (M2) and third molar (M3) inclination following orthodontic treatment of Class II subdivision malocclusion with unilateral maxillary first molar (M1) extraction. MATERIALS AND METHODS Panoramic radiographs of 21 Class II subdivision adolescents (eight boys, 13 girls; mean age, 12.8 years; standard deviation, 1.7 years) before treatment, after treatment with extraction of one maxillary first molar and Begg appliances and after at least 1.8 years in retention were retrospectively collected from a private practice. M2 and M3 inclination angles (M2/ITP, M2/IOP, M3/ITP, M3/IOP), constructed by intertuberosity (ITP) and interorbital planes (IOP), were calculated for the extracted and nonextracted segments. Random effects regression analysis was performed to evaluate the effect on the molar angulation of extraction, time, and gender after adjusting for baseline measurements. RESULTS Time and extraction status were significant predictors for M2 angulation. M2/ITP and M2/IOP decreased by 4.04 (95% confidence interval [CI]: -6.93, 1.16; P  =  .001) and 3.67 (95% CI: -6.76, -0.58; P  =  .020) in the extraction group compared to the nonextraction group after adjusting for time and gender. The adjusted analysis showed that extraction was the only predictor for M3 angulation that reached statistical significance. M3 mesial inclination increased by 7.38° (95% CI: -11.2, -3.54; P < .001) and 7.33° (95% CI: -11.48, -3.19; P  =  .001). CONCLUSIONS M2 and M3 uprighting significantly improved in the extraction side after orthodontic treatment with unilateral maxillary M1 extraction. There was a significant increase in mesial tipping of maxillary second molar crowns over time.

A full pedigree based method for the statistical assessment of genetic anticipation

Genetic anticipation is defined as a decrease in age of onset or increase in severity as the disorder is transmitted through subsequent generations. Anticipation has been noted in the literature for over a century. Recently, anticipation in several diseases including Huntington's Disease, Myotonic Dystrophy and Fragile X Syndrome were shown to be caused by expansion of triplet repeats. Anticipation effects have also been observed in numerous mental disorders (e.g. Schizophrenia, Bipolar Disorder), cancers (Li-Fraumeni Syndrome, Leukemia) and other complex diseases. ^ Several statistical methods have been applied to determine whether anticipation is a true phenomenon in a particular disorder, including standard statistical tests and newly developed affected parent/affected child pair methods. These methods have been shown to be inappropriate for assessing anticipation for a variety of reasons, including familial correlation and low power. Therefore, we have developed family-based likelihood modeling approaches to model the underlying transmission of the disease gene and penetrance function and hence detect anticipation. These methods can be applied in extended families, thus improving the power to detect anticipation compared with existing methods based only upon parents and children. The first method we have proposed is based on the regressive logistic hazard model. This approach models anticipation by a generational covariate. The second method allows alleles to mutate as they are transmitted from parents to offspring and is appropriate for modeling the known triplet repeat diseases in which the disease alleles can become more deleterious as they are transmitted across generations. ^ To evaluate the new methods, we performed extensive simulation studies for data simulated under different conditions to evaluate the effectiveness of the algorithms to detect genetic anticipation. Results from analysis by the first method yielded empirical power greater than 87% based on the 5% type I error critical value identified in each simulation depending on the method of data generation and current age criteria. Analysis by the second method was not possible due to the current formulation of the software. The application of this method to Huntington's Disease and Li-Fraumeni Syndrome data sets revealed evidence for a generation effect in both cases. ^

Mutagenicity study of the urinary metabolites of 2-aminonaphthalene

The mutagenicity study of the urinary metabolites of 2-aminonaphthalene was conducted to determine whether differences in metabolism between different acetylator phenotypes could account for a proposed mechanism of bladder carcinogenesis. This required the use of fast and slow acetylator rabbits with phenotypic similarities to humans. In the absence of available slow acetylators, it was necessary to inhibit fast acetylators. The proposed mechanism was that slow acetylators were at greater potential risk of bladder carcinogenesis due to low rates of acetylation, a detoxification mechanism for certain aromatic amines. The alternate metabolic pathway will be hydroxylation. The fast acetylators were proposed to exhibit lower risk of bladder carcinogenicity as a result of higher acetylation rates and less mutagenic metabolites.^ This hypothesis was approached by determining from in vitro mutagenicity assays with Salmonella typhimurium strains TA98 and TA100 whether different metabolites were mutagenic. The acetylation rate of each rabbit and a suitable method of acetylation inhibition were determined through oral exposure to dapsone and the acetylation inhibitor, K-p-aminosalicylic acid. Residues of dapsone and its acetylated metabolite were extracted from blood samples and analyzed by ultra-violet spectrometry using standard curves for each metabolite. The urine samples were concentrated on XAD-2 resin and analyzed both as whole urine concentrates and as isolated metabolites from spots on high performance thin layer chromatography plates. The major isolated spots were identified and quantified through extraction and analysis by high performance liquid chromatography when possible.^ Acetylation rate determination and inhibition were successfully demonstrated in rabbits. Significant mutagenicity was noted for several critical metabolites. None of the mutagenic metabolites were detected in higher concentration in the inhibited acetylators and thus, no clear relationship of metabolite concentration to bladder carcinogenesis was evident for the compounds analyzed. There was some evidence that the inhibitor may have affected critical enzyme systems other than acetylation alone. This would account for the lower concentrations of mutagenic hydroxylated compounds observed. ^

A systematic review of the methods used to assess race and racial disparities in uterine fibroid research

Context: Black women are reported to have a higher prevalence of uterine fibroids, and a threefold higher incidence rate and relative risk for clinical uterine fibroid development as compared to women of other races. Uterine fibroid research has reported that black women experience greater uterine fibroid morbidity and disproportionate uterine fibroid disease burden. With increased interest in understanding uterine fibroid development, and race being a critical component of uterine fibroid assessment, it is imperative that the methods used to determine the race of research participants is defined and the operational definition of the use of race as a variable is reported for methodological guidance, and to enable the research community to compare statistical data and replicate studies. ^ Objectives: To systematically review and evaluate the methods used to assess race and racial disparities in uterine fibroid research. ^ Data Sources: Databases searched for this review include: OVID Medline, NML PubMed, Ebscohost Cumulative Index to Nursing and Allied Health Plus with Full Text, and Elsevier Scopus. ^ Review Methods: Articles published in English were retrieved from data sources between January 2011 and March 2011. Broad search terms, uterine fibroids and race, were employed to retrieve a comprehensive list of citations for review screening. The initial database yield included 947 articles, after duplicate extraction 485 articles remained. In addition, 771 bibliographic citations were reviewed to identify additional articles not found through the primary database search, of which 17 new articles were included. In the first screening, 502 titles and abstracts were screened against eligibility questions to determine citations of exclusion and to retrieve full text articles for review. In the second screening, 197 full texted articles were screened against eligibility questions to determine whether or not they met full inclusion/exclusion criteria. ^ Results: 100 articles met inclusion criteria and were used in the results of this systematic review. The evidence suggested that black women have a higher prevalence of uterine fibroids when compared to white women. None of the 14 studies reporting data on prevalence reported an operational definition or conceptual framework for the use of race. There were a limited number of studies reporting on the prevalence of risk factors among racial subgroups. Of the 3 studies, 2 studies reported prevalence of risk factors lower for black women than other races, which was contrary to hypothesis. And, of the three studies reporting on prevalence of risk factors among racial subgroups, none of them reported a conceptual framework for the use of race. ^ Conclusion: In the 100 uterine fibroid studies included in this review over half, 66%, reported a specific objective to assess and recruit study participants based upon their race and/or ethnicity, but most, 51%, failed to report a method of determining the actual race of the participants, and far fewer, 4% (only four South American studies), reported a conceptual framework and/or operational definition of race as a variable. However, most, 95%, of all studies reported race-based health outcomes. The inadequate methodological guidance on the use of race in uterine fibroid studies, purporting to assess race and racial disparities, may be a primary reason that uterine fibroid research continues to report racial disparities, but fails to understand the high prevalence and increased exposures among African-American women. A standardized method of assessing race throughout uterine fibroid research would appear to be helpful in elucidating what race is actually measuring, and the risk of exposures for that measurement. ^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^