Interval approximation of higher order to the ranges of functions

AbstractThe Bernstein and B-spline forms are generalized to multivariate polynomials. These forms are combined with a type of Taylor form for multivariate functions to generate realizable forms for multivariate functions

Extrusion properties of a Zr-based bulk metallic glass

The extrusion behavior of Zr41.2Ti13.8Cu12.5Ni10Be22.5 metallic glasses in the supercooled liquid region was investigated. Good extrusion formability was observed under low strain rates at temperatures higher than 395 &deg;C. The metallic glasses were fully extruded without crystallization and failure within the range of T=395&ndash;415 &deg;C under strain rates from 5&times;10&minus;3 s&minus;1 to 5&times;10&minus;2 s&minus;1, and the deformation behavior of the metallic glasses during the extrusion was found to be in a Newtonian viscous flow mode by a strain rate sensitivity of 1.0.<br /

A Fast and Accurate Diagnostic Test for Severe Sepsis Using Kernel Classifiers

Severe sepsis occurs frequently in the intensive care unit (ICU) and is a leading cause of admission, mortality, and cost. Treatment guidelines recommend early intervention, however gold standard blood culture test results may return in up to 48 hours. Insulin sensitivity (SI) is known to decrease with worsening condition and inflammatory response, and could thus be used to aid clinical treatment decisions. Some glycemic control protocols are able to accurately identify SI in real-time. A biomarker for severe sepsis was developed from retrospective SI and concurrent temperature, heart rate, respiratory rate, blood pressure, and SIRS score from 36 adult patients with sepsis. Patients were identified as having sepsis based on a clinically validated sepsis score (ss) of 2 or higher (ss = 0–4 for increasing severity). Kernel density estimates were used for the development of joint probability density profiles for ss = 2 and ss < 2 data hours (213 and 5858 respectively of 6071 total hours) and for classification. From the receiver operator characteristic (ROC) curve, the optimal probability cutoff values for classification were determined for in-sample and out-of-sample estimates. A biomarker including concurrent insulin sensitivity and clinical data for the diagnosis of severe sepsis (ss = 2) achieves 69–94% sensitivity, 75–94% specificity, 0.78–0.99 AUC, 3–17 LHR+, 0.06–0.4 LHR-, 9–38% PPV, 99–100% NPV, and a diagnostic odds ratio of 7–260 for optimal probability cutoff values of 0.32 and 0.27 for in-sample and out-of-sample data, respectively. The overall result lies between these minimum and maximum error bounds. Thus, the clinical biomarker shows good to high accuracy and may provide useful information as a real-time diagnostic test for severe sepsis

Comprehensive Phylogenetic Reconstruction of Amoebozoa Based on Concatenated Analyses of SSU-rDNA and Actin Genes

Evolutionary relationships within Amoebozoa have been the subject of controversy for two reasons: 1) paucity of morphological characters in traditional surveys and 2) haphazard taxonomic sampling in modern molecular reconstructions. These along with other factors have prevented the erection of a definitive system that resolves confidently both higher and lower-level relationships. Additionally, the recent recognition that many protosteloid amoebae are in fact scattered throughout the Amoebozoa suggests that phylogenetic reconstructions have been excluding an extensive and integral group of organisms. Here we provide a comprehensive phylogenetic reconstruction based on 139 taxa using molecular information from both SSU-rDNA and actin genes. We provide molecular data for 13 of those taxa, 12 of which had not been previously characterized. We explored the dataset extensively by generating 18 alternative reconstructions that assess the effect of missing data, long-branched taxa, unstable taxa, fast evolving sites and inclusion of environmental sequences. We compared reconstructions with each other as well as against previously published phylogenies. Our analyses show that many of the morphologically established lower-level relationships (defined here as relationships roughly equivalent to Order level or below) are congruent with molecular data. However, the data are insufficient to corroborate or reject the large majority of proposed higher-level relationships (above the Order-level), with the exception of Tubulinea, Archamoebae and Myxogastrea, which are consistently recovered. Moreover, contrary to previous expectations, the inclusion of available environmental sequences does not significantly improve the Amoebozoa reconstruction. This is probably because key amoebozoan taxa are not easily amplified by environmental sequencing methodology due to high rates of molecular evolution and regular occurrence of large indels and introns. Finally, in an effort to facilitate future sampling of key amoebozoan taxa, we provide a novel methodology for genome amplification and cDNA extraction from single or a few cells, a method that is culture-independent and allows both photodocumentation and extraction of multiple genes from natural samples

Long term verification of glucose-insulin regulatory system model dynamics

doi: 10.1109/IEMBS.2004.1403269Hyperglycaemia in critically ill patients increases the risk of further complications and mortality. A long-term verification of a model that captures the essential glucose- and insulin-kinetics is presented, using retrospective data gathered in an Intensive Care Unit (ICU). The model uses only two patient specific parameters, for glucose clearance and insulin sensitivity. The optimization of these parameters is accomplished through a novel integration-based fitting approach, and a piecewise linearization of the parameters. This approach reduces the non-linear, non-convex optimization problem to a simple linear equation system. The method was tested on long-term blood glucose recordings from 17 ICU-patients, resulting in an average error of 7%, which is in the range of the sensor error. One-hour predictions of blood glucose data proved acceptable with an error range between 7- 11%. These results verify the model’s ability to capture longterm observed glucose-insulin dynamics in hyperglycaemic ICU patients

Impact of glucocorticoids on insulin resistance in the critically ill

Glucocorticoids (GCs) have been shown to reduce insulin sensitivity in healthy individuals. Widely used in critical care to treat a variety of inflammatory and allergic disorders, they may inadvertently exacerbate stress-hyperglycaemia. This research uses model-based methods to quantify the reduction of insulin sensitivity from GCs in critically ill patients, and thus their impact on glycaemic control. A clinically validated model-based measure of insulin sensitivity (SI) was used to quantify changes between two matched cohorts of 40 intensive care unit (ICU) patients who received GCs and a control cohort who did not. All patients were admitted to the Christchurch hospital ICU between 2005 and 2007 and spent at least 24 hours on the SPRINT glycaemic control protocol. A 31% reduction in whole-cohort median insulin sensitivity was seen between the control cohort and patients receiving glucocorticoids with a median dose equivalent to 200mg/day of hydrocortisone per patient. Comparing percentile-patients as a surrogate for matched patients, reductions in median insulin sensitivity of 20, 25, and 21% were observed for the 25th, 50th and 75th-percentile patients. All these cohort and per-patient reductions are less than or equivalent to the 30-62% reductions reported in healthy subjects especially when considering the fact that the GC doses in this study are 1.3-4 times larger than those in studies of healthy subjects. This reduced suppression of insulin sensitivity in critically ill patients could be a result of saturation due to already increased levels of catecholamines and cortisol common in critically illness. Virtual trial simulation showed that reductions in insulin sensitivity of 20-30% associated with glucocorticoid treatment in the ICU have limited impact on glycaemic control levels within the context of the SPRINT protocol

Development of a Clinical Type 1 Diabetes Metabolic System Model and in Silico Simulation Tool

Invited journal symposium paperObjectives: To develop a safe and effective protocol for the clinical control of Type 1 diabetes using conventional self-monitoring blood glucose (SMBG) measurements, and multiple daily injection (MDI) with insulin analogues. To develop an in silico simulation tool of Type 1 diabetes to predict long-term glycaemic control outcomes of clinical interventions. Methods: The virtual patient method is used to develop a simulation tool for Type 1 diabetes using data from a Type 1 diabetes patient cohort (n=40). The tool is used to test the adaptive protocol (AC) and a conventional intensive insulin therapy (CC) against results from a representative control cohort. Optimal and suboptimal basal insulin replacement are evaluated as a function of self-monitoring blood glucose (SMBG) frequency in conjunction with the (AC and CC) prandial control protocols. Results: In long-term glycaemic control, the AC protocol significantly decreases HbA1c in conditions of suboptimal basal insulin replacement for SMBG frequencies =6/day, and reduced the occurrence of mild and severe hypoglycaemia by 86-100% over controls over all SMBG frequencies in conditions of optimal basal insulin. Conclusions: A simulation tool to predict long-term glycaemic control outcomes from clinical interventions is developed to test a novel, adaptive control protocol for Type 1 diabetes. The protocol is effective and safe compared to conventional intensive insulin therapy and controls. As fear of hypoglycaemia is a large psychological barrier to glycaemic control, the AC protocol may represent the next evolution of intensive insulin therapy to deliver increased glycaemic control with increased safety. Further clinical or experimental validation is needed to fully prove the concept

Integral-based filtering of continuous glucose sensor measurements for glycaemic control in critical care

Hyperglycaemia is prevalent in critical illness and increases the risk of further complications and mortality, while tight control can reduce mortality up to 43%. Adaptive control methods are capable of highly accurate, targeted blood glucose regulation using limited numbers of manual measurements due to patient discomfort and labour intensity. Therefore, the option to obtain greater data density using emerging continuous glucose sensing devices is attractive. However, the few such systems currently available can have errors in excess of 20-30%. In contrast, typical bedside testing kits have errors of approximately 7-10%. Despite greater measurement frequency larger errors significantly impact the resulting glucose and patient specific parameter estimates, and thus the control actions determined creating an important safety and performance issue. This paper models the impact of the Continuous Glucose Monitoring System (CGMS, Medtronic, Northridge, CA) on model-based parameter identification and glucose prediction. An integral-based fitting and filtering method is developed to reduce the effect of these errors. A noise model is developed based on CGMS data reported in the literature, and is slightly conservative with a mean Clarke Error Grid (CEG) correlation of R=0.81 (range: 0.68-0.88) as compared to a reported value of R=0.82 in a critical care study. Using 17 virtual patient profiles developed from retrospective clinical data, this noise model was used to test the methods developed. Monte-Carlo simulation for each patient resulted in an average absolute one-hour glucose prediction error of 6.20% (range: 4.97-8.06%) with an average standard deviation per patient of 5.22% (range: 3.26-8.55%). Note that all the methods and results are generalisable to similar applications outside of critical care, such as less acute wards and eventually ambulatory individuals. Clinically, the results show one possible computational method for managing the larger errors encountered in emerging continuous blood glucose sensors, thus enabling their more effective use in clinical glucose regulation studies

Dichromatic polynomials and Potts models summed over rooted maps

We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the $q$-state Potts model randomized over such maps. Like the regular ferromagnetic lattice models, it has a first-order transition when $q$ is greater than a critical value $q_c$, but $q_c$ is much larger - about 72 instead of 4.Comment: 29 pages, three figures changes in App D, introduction and acknowledgement

Overview of Glycemic Control in Critical Care - Relating Performance and Clinical Results

Inagural review article invited for inaugural journalBackground: Hyperglycemia is prevalent in critical care and tight control can save lives. Current ad-hoc clinical protocols require significant clinical effort and produce highly variable results. Model-based methods can provide tight, patient specific control, while addressing practical clinical difficulties and dynamic patient evolution. However, tight control remains elusive as there is not enough understanding of the relationship between control performance and clinical outcome. Methods: The general problem and performance criteria are defined. The clinical studies performed to date using both ad-hoc titration and model-based methods are reviewed. Studies reporting mortality outcome are analysed in terms of standardized mortality ratio (SMR) and a 95th percentile (±2 ) standard error (SE95%) to enable better comparison across cohorts. Results: Model-based control trials lower blood glucose into a 72-110mg/dL band within 10 hours, have target accuracy over 90%, produce fewer hypoglycemic episodes, and require no additional clinical intervention. Plotting SMR versus SE95% shows potentially high correlation (r=0.84) between ICU mortality and tightness of control. Summary: Model-based methods provide tighter, more adaptable “one method fits all” solutions, using methods that enable patient-specific modeling and control. Correlation between tightness of control and clinical outcome suggests that performance metrics, such as time in a relevant glycemic band, may provide better guidelines. Overall, compared to current “one size fits all” sliding scale and ad-hoc regimens, patient-specific pharmacodynamic and pharmacokinetic model-based, or “one method fits all”, control, utilizing computational and emerging sensor technologies, offers improved treatment and better potential outcomes when treating hyperglycemia in the highly dynamic critically ill patient