Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality

Bibliography: pages 93-101.The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory

THE ECONOMIC IMPACTS OF A FOOT-AND-MOUTH DISEASE OUTBREAK: A REGIONAL ANALYSIS

Contagious animal diseases like foot-and-mouth disease (FMD) are often referred to as economic diseases because of the magnitude of economic harm they can cause to producers and to local communities. This study demonstrates the local economic impact of a hypothetical FMD outbreak in southwest Kansas, an area with high density of cattle feeding. The expected (most probable) economic impact of the disease hinges heavily on where the incidence of the disease occurs. If the disease were to occur in a cow-calf herd in the region economic impact is expected to be relatively small compared to if it were introduced simultaneously in five large feedlots in southwest Kansas. Disease surveillance, management strategies, mitigation investment, and overall diligence clearly need to be much greater in concentrated cattle feeding and processing areas at the large feeding operations in the region.Livestock Production/Industries,

Neurogenic Fever after Acute Traumatic Spinal Cord Injury: A Qualitative Systematic Review.

STUDY DESIGN: Systematic review. OBJECTIVE: To determine the incidence, pathogenesis, and clinical outcomes related to neurogenic fevers following traumatic spinal cord injury (SCI). METHODS: A systematic review of the literature was performed on thermodysregulation secondary to acute traumatic SCI in adult patients. A literature search was performed using PubMed (MEDLINE), Cochrane Central Register of Controlled Trials, and Scopus. Using strict inclusion and exclusion criteria, seven relevant articles were obtained. RESULTS: The incidence of fever of all origins (both known and unknown) after SCI ranged from 22.5 to 71.7% with a mean incidence of 50.6% and a median incidence of 50.0%. The incidence of fever of unknown origin (neurogenic fever) ranged from 2.6 to 27.8% with a mean incidence of 8.0% and a median incidence of 4.7%. Cervical and thoracic spinal injuries were more commonly associated with fever than lumbar injuries. In addition, complete injuries had a higher incidence of fever than incomplete injuries. The pathogenesis of neurogenic fever after acute SCI is not thoroughly understood. CONCLUSION: Neurogenic fevers are relatively common following an acute SCI; however, there is little in the scientific literature to help physicians prevent or treat this condition. The paucity of research underscored by this review demonstrates the need for further studies with larger sample sizes, focusing on incidence rate, clinical outcomes, and pathogenesis of neurogenic fever following acute traumatic SCI

The Use of Bone Morphogenetic Protein in the Intervertebral Disk Space in Minimally Invasive Transforaminal Lumbar Interbody Fusion

Study Design: Retrospective Cohort. Objective: The objective of this study was to characterize one surgeon’s experience over a 10-year period using rhBMP-2 in the disk space for minimally invasive transforaminal lumbar interbody fusion (MIS TLIF). Summary of Background Data: MIS TLIF has been utilized as a technique for decreasing patients’ immediate postoperative pain, decreasing blood loss, and shortened hospital stays. Effectiveness and complications of rhBMP-2’s use in the disk space is limited because of its off-label status. Methods: Retrospective analysis of consecutive MIS TLIFs performed by senior author between 2004 and 2014. rhBMP-2 was used in the disk space in all cases. Patients were stratified based on the dose of rhBMP-2 utilized. Patients had 9 to 12 month computerized tomography scan to evaluate for bony fusion and continued follow-up for 18 months. Results: A total of 688 patients underwent a MIS TLIF. A medium kit of rhBMP-2 was utilized in 97 patients, and small kit was used in 591 patients. Fusion rate was 97.9% and this was not different between the 2 groups with 96/97 patients fusing in the medium kit group and 577/591 patients fusing in the small kit group. Five patients taken back to the operating room for symptomatic pseudoarthrosis, 4 reoperated for bony hyperostosis, and 10 radiographic pseudoarthroses that did not require reoperation. A statistically significant difference in the rate of foraminal hyperostosis was found when using a medium sized kit of rhBMP-2 was 4.12% (4/97 patients), compared with a small kit (0/591 patients, P=0.0004). Conclusions: Utilization of rhBMP-2 in an MIS TLIF leads to high fusion rate (97.9%), with an acceptable complication profile. The development of foraminal hyperostosis is a rare complication that only affected 0.6% of patients, and seems to be a dose related complication, as this complication was eliminated when a lower dose of rhBMP-2 was utilized

Quantitative Assessment of the Anatomical Footprint of the C1 Pedicle Relative to the Lateral Mass: A Guide for C1 Lateral Mass Fixation

Study Design: Anatomic study. Objectives: To determine the relationship of the anatomical footprint of the C1 pedicle relative to the lateral mass (LM). Methods: Anatomic measurements were made on fresh frozen human cadaveric C1 specimens: pedicle width/height, LM width/height (minimum/maximum), LM depth, distance between LM’s medial aspect and pedicle’s medial border, distance between LM’s lateral aspect to pedicle’s lateral border, distance between pedicle’s inferior aspect and LM’s inferior border, distance between arch’s midline and pedicle’s medial border. The percentage of LM medial to the pedicle and the distance from the center of the LM to the pedicle’s medial wall were calculated. Results: A total of 42 LM were analyzed. The C1 pedicle’s lateral aspect was nearly confluent with the LM’s lateral border. Average pedicle width was 9.0 ± 1.1 mm, and average pedicle height was 5.0 ± 1.1 mm. Average LM width and depth were 17.0 ± 1.6 and 17.2 ± 1.6 mm, respectively. There was 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle, which constituted 41% ± 9% of the LM’s width. The distance from C1 arch’s midline to the medial pedicle was 13.5 ± 2.0 mm. The LM’s center was 1.6 ± 1 mm lateral to the medial pedicle wall. There was on average 3.5 ± 0.6 mm of the LM inferior to the pedicle inferior border. Conclusions: The center of the lateral mass is 1.6 ± 1 mm lateral to the medial wall of the C1 pedicle and approximately 15 mm from the midline. There is 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle. Thus, the medial aspect of C1 pedicle may be used as an anatomic reference for locating the center of the C1 LM for screw fixation

Clinical Outcomes After Four-Level Anterior Cervical Discectomy and Fusion.

Study Design: Retrospective cohort study. Objectives: Anterior cervical discectomy and fusion (ACDF) demonstrates reliable improvement in neurologic symptoms associated with anterior compression of the cervical spine. There is a paucity of data on outcomes following 4-level ACDFs. The purpose of this study was to evaluate clinical outcomes for patients undergoing 4-level ACDF. Methods: All 4-level ACDFs with at least 1-year clinical follow-up were identified. Clinical outcomes, including fusion rates, neurologic outcomes, and reoperation rates were determined. Results: Retrospective review of our institutional database revealed 25 patients who underwent 4-level ACDF with at least 1-year clinical follow-up. Average age was 57.5 years (range 38.2-75.0 years); 14 (56%) were male, and average body mass index was 30.2 kg/m Conclusions: Review of our institution\u27s experience demonstrated a low rate of revision cervical surgery for any reason of 8% at mean 19 months follow-up, and neurological examinations consistently improved, despite a high rate of radiographic nonunion (31%)

Using K-Means Clustering and Neural Net Analysis to Define and Predict Chicago Neighborhood Energy Consumption Trends

Energy markets worldwide are facing two primary issues: 1) meeting exponentially increasing demand and 2) satisfying external pressures to transition to clean energy sources. This report studies electricity consumption patterns in the City of Chicago through historical socioeconomic data. Using an unsupervised method of analysis (K-Means Cluster) together with a supervised method (Neural Net), our report provides three classifications of Chicago neighborhoods and identifies the strongest predictors of electricity consumption in each. Using this analysis framework, major cities can effectively devise long-term strategies for meeting energy demand while planning for a sustainable future