Prediction of postprandial blood glucose under intra-patient variability and uncertainty and its use in the design of insulin dosing strategies for type 1 diabetic patients

In this thesis I propose a novel method to estimate the dose and injection-to-meal time for low-risk intensive insulin therapy. This dosage-aid system uses an optimization algorithm to determine the insulin dose and injection-to-meal time that minimizes the risk of postprandial hyper- and hypoglycaemia in type 1 diabetic patients. To this end, the algorithm applies a methodology that quantifies the risk of experiencing different grades of hypo- or hyperglycaemia in the postprandial state induced by insulin therapy according to an individual patient’s parameters. This methodology is based on modal interval analysis (MIA). Applying MIA, the postprandial glucose level is predicted with consideration of intra-patient variability and other sources of uncertainty. A worst-case approach is then used to calculate the risk index. In this way, a safer prediction of possible hyper- and hypoglycaemic episodes induced by the insulin therapy tested can be calculated in terms of these uncertainties.

Application of modal interval analysis to the simulation of the behaviour of dynamic systems with uncertain parameters

Els models matemàtics quantitatius són simplificacions de la realitat i per tant el comportament obtingut per simulació d'aquests models difereix dels reals. L'ús de models quantitatius complexes no és una solució perquè en la majoria dels casos hi ha alguna incertesa en el sistema real que no pot ser representada amb aquests models. Una forma de representar aquesta incertesa és mitjançant models qualitatius o semiqualitatius. Un model d'aquest tipus de fet representa un conjunt de models. La simulació del comportament de models quantitatius genera una trajectòria en el temps per a cada variable de sortida. Aquest no pot ser el resultat de la simulació d'un conjunt de models. Una forma de representar el comportament en aquest cas és mitjançant envolupants. L'envolupant exacta és complete, és a dir, inclou tots els possibles comportaments del model, i correcta, és a dir, tots els punts dins de l'envolupant pertanyen a la sortida de, com a mínim, una instància del model. La generació d'una envolupant així normalment és una tasca molt dura que es pot abordar, per exemple, mitjançant algorismes d'optimització global o comprovació de consistència. Per aquesta raó, en molts casos s'obtenen aproximacions a l'envolupant exacta. Una aproximació completa però no correcta a l'envolupant exacta és una envolupant sobredimensionada, mentre que una envolupant correcta però no completa és subdimensionada. Aquestes propietats s'han estudiat per diferents simuladors per a sistemes incerts.

Cost effectiveness of shortening screening interval or extending age range of NHS breast screening programme: computer simulation study

Objective: To compare the cost effectiveness of two possible modifications to the current UK screening programme: shortening the screening interval from three to two years and extending the age of invitation to a final screen from 64 to 69.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - III. The integrated wheat model (I_WHEAT)

Previous work has identified several short-comings in the ability of four spring wheat and one barley model to simulate crop processes and resource utilization. This can have important implications when such models are used within systems models where final soil water and nitrogen conditions of one crop define the starting conditions of the following crop. In an attempt to overcome these limitations and to reconcile a range of modelling approaches, existing model components that worked demonstrably well were combined with new components for aspects where existing capabilities were inadequate. This resulted in the Integrated Wheat Model (I_WHEAT), which was developed as a module of the cropping systems model APSIM. To increase predictive capability of the model, process detail was reduced, where possible, by replacing groups of processes with conservative, biologically meaningful parameters. I_WHEAT does not contain a soil water or soil nitrogen balance. These are present as other modules of APSIM. In I_WHEAT, yield is simulated using a linear increase in harvest index whereby nitrogen or water limitations can lead to early termination of grainfilling and hence cessation of harvest index increase. Dry matter increase is calculated either from the amount of intercepted radiation and radiation conversion efficiency or from the amount of water transpired and transpiration efficiency, depending on the most limiting resource. Leaf area and tiller formation are calculated from thermal time and a cultivar specific phyllochron interval. Nitrogen limitation first reduces leaf area and then affects radiation conversion efficiency as it becomes more severe. Water or nitrogen limitations result in reduced leaf expansion, accelerated leaf senescence or tiller death. This reduces the radiation load on the crop canopy (i.e. demand for water) and can make nitrogen available for translocation to other organs. Sensitive feedbacks between light interception and dry matter accumulation are avoided by having environmental effects acting directly on leaf area development, rather than via biomass production. This makes the model more stable across environments without losing the interactions between the different external influences. When comparing model output with models tested previously using data from a wide range of agro-climatic conditions, yield and biomass predictions were equal to the best of those models, but improvements could be demonstrated for simulating leaf area dynamics in response to water and nitrogen supply, kernel nitrogen content, and total water and nitrogen use. I_WHEAT does not require calibration for any of the environments tested. Further model improvement should concentrate on improving phenology simulations, a more thorough derivation of coefficients to describe leaf area development and a better quantification of some processes related to nitrogen dynamics. (C) 1998 Elsevier Science B.V.

Monte Carlo simulation of the basic features of the GE Millennium MG single photon emission computed tomography gamma camera

Objective - To describe and validate the simulation of the basic features of GE Millennium MG gamma camera using the GATE Monte Carlo platform. Material and methods - Crystal size and thickness, parallel-hole collimation and a realistic energy acquisition window were simulated in the GATE platform. GATE results were compared to experimental data in the following imaging conditions: a point source of 99mTc at different positions during static imaging and tomographic acquisitions using two different energy windows. The accuracy between the events expected and detected by simulation was obtained with the Mann–Whitney–Wilcoxon test. Comparisons were made regarding the measurement of sensitivity and spatial resolution, static and tomographic. Simulated and experimental spatial resolutions for tomographic data were compared with the Kruskal–Wallis test to assess simulation accuracy for this parameter. Results - There was good agreement between simulated and experimental data. The number of decays expected when compared with the number of decays registered, showed small deviation (≤0.007%). The sensitivity comparisons between static acquisitions for different distances from source to collimator (1, 5, 10, 20, 30cm) with energy windows of 126–154 keV and 130–158 keV showed differences of 4.4%, 5.5%, 4.2%, 5.5%, 4.5% and 5.4%, 6.3%, 6.3%, 5.8%, 5.3%, respectively. For the tomographic acquisitions, the mean differences were 7.5% and 9.8% for the energy window 126–154 keV and 130–158 keV. Comparison of simulated and experimental spatial resolutions for tomographic data showed no statistically significant differences with 95% confidence interval. Conclusions - Adequate simulation of the system basic features using GATE Monte Carlo simulation platform was achieved and validated.

Sequencing cutting patterns with colored interval graphs

The problem addressed here originates in the industry of flat glass cutting and wood panel sawing, where smaller items are cut from larger items accordingly to predefined cutting patterns. In this type of industry the smaller pieces that are cut from the patterns are piled around the machine in stacks according to the size of the pieces, which are moved to the warehouse only when all items of the same size have been cut. If the cutting machine can process only one pattern at a time, and the workspace is limited, it is desirable to set the sequence in which the cutting patterns are processed in a way to minimize the maximum number of open stacks around the machine. This problem is known in literature as the minimization of open stacks (MOSP). To find the best sequence of the cutting patterns, we propose an integer programming model, based on interval graphs, that searches for an appropriate edge completion of the given graph of the problem, while defining a suitable coloring of its vertices.

Simulation-based systematic review of imatinib population pharmacokinetics and PK-PD relationships in chronic myeloid leukemia (CML) patients

Objectives: Several population pharmacokinetic (PPK) and pharmacokinetic-pharmacodynamic (PK-PD) analyses have been performed with the anticancer drug imatinib. Inspired by the approach of meta-analysis, we aimed to compare and combine results from published studies in a useful way - in particular for improving the clinical interpretation of imatinib concentration measurements in the scope of therapeutic drug monitoring (TDM). Methods: Original PPK analyses and PK-PD studies (PK surrogate: trough concentration Cmin; PD outcomes: optimal early response and specific adverse events) were searched systematically on MEDLINE. From each identified PPK model, a predicted concentration distribution under standard dosage was derived through 1000 simulations (NONMEM), after standardizing model parameters to common covariates. A "reference range" was calculated from pooled simulated concentrations in a semi-quantitative approach (without specific weighting) over the whole dosing interval. Meta-regression summarized relationships between Cmin and optimal/suboptimal early treatment response. Results: 9 PPK models and 6 relevant PK-PD reports in CML patients were identified. Model-based predicted median Cmin ranged from 555 to 1388 ng/ml (grand median: 870 ng/ml and inter-quartile range: 520-1390 ng/ml). The probability to achieve optimal early response was predicted to increase from 60 to 85% from 520 to 1390 ng/ml across PK-PD studies (odds ratio for doubling Cmin: 2.7). Reporting of specific adverse events was too heterogeneous to perform a regression analysis. The general frequency of anemia, rash and fluid retention increased however consistently with Cmin, but less than response probability. Conclusions: Predicted drug exposure may differ substantially between various PPK analyses. In this review, heterogeneity was mainly attributed to 2 "outlying" models. The established reference range seems to cover the range where both good efficacy and acceptable tolerance are expected for most patients. TDM guided dose adjustment appears therefore justified for imatinib in CML patients. Its usefulness remains now to be prospectively validated in a randomized trial.

An Interval Intelligent-based Approach for Fault Detection and Modelling

Not considered in the analytical model of the plant, uncertainties always dramatically decrease the performance of the fault detection task in the practice. To cope better with this prevalent problem, in this paper we develop a methodology using Modal Interval Analysis which takes into account those uncertainties in the plant model. A fault detection method is developed based on this model which is quite robust to uncertainty and results in no false alarm. As soon as a fault is detected, an ANFIS model is trained in online to capture the major behavior of the occurred fault which can be used for fault accommodation. The simulation results understandably demonstrate the capability of the proposed method for accomplishing both tasks appropriately

Sex differences in urinary levels of several biological indicators of exposure: a simulation study using a compartmental based toxicokinetic model

Toxicokinetic modeling is a useful tool to describe or predict the behavior of a chemical agent in the human or animal organism. A general model based on four compartments was developed in a previous study in order to quantify the effect of human variability on a wide range of biological exposure indicators. The aim of this study was to adapt this existing general toxicokinetic model to three organic solvents, which were methyl ethyl ketone, 1-methoxy-2-propanol and 1,1,1,-trichloroethane, and to take into account sex differences. We assessed in a previous human volunteer study the impact of sex on different biomarkers of exposure corresponding to the three organic solvents mentioned above. Results from that study suggested that not only physiological differences between men and women but also differences due to sex hormones levels could influence the toxicokinetics of the solvents. In fact the use of hormonal contraceptive had an effect on the urinary levels of several biomarkers, suggesting that exogenous sex hormones could influence CYP2E1 enzyme activity. These experimental data were used to calibrate the toxicokinetic models developed in this study. Our results showed that it was possible to use an existing general toxicokinetic model for other compounds. In fact, most of the simulation results showed good agreement with the experimental data obtained for the studied solvents, with a percentage of model predictions that lies within the 95% confidence interval varying from 44.4 to 90%. Results pointed out that for same exposure conditions, men and women can show important differences in urinary levels of biological indicators of exposure. Moreover, when running the models by simulating industrial working conditions, these differences could even be more pronounced. In conclusion, a general and simple toxicokinetic model, adapted for three well known organic solvents, allowed us to show that metabolic parameters can have an important impact on the urinary levels of the corresponding biomarkers. These observations give evidence of an interindividual variablity, an aspect that should have its place in the approaches for setting limits of occupational exposure.

Méthode de simulation avec les variables antithétiques

Les fichiers qui accompagnent mon document ont été réalisés avec le logiciel Latex et les simulations ont été réalisés par Splus(R).

An Interval Intelligent-based Approach for Fault Detection and Modelling

Not considered in the analytical model of the plant, uncertainties always dramatically decrease the performance of the fault detection task in the practice. To cope better with this prevalent problem, in this paper we develop a methodology using Modal Interval Analysis which takes into account those uncertainties in the plant model. A fault detection method is developed based on this model which is quite robust to uncertainty and results in no false alarm. As soon as a fault is detected, an ANFIS model is trained in online to capture the major behavior of the occurred fault which can be used for fault accommodation. The simulation results understandably demonstrate the capability of the proposed method for accomplishing both tasks appropriately

Experimental measurement and numerical simulation of horizontal-coupled slinky ground source heat exchangers

Results from both experimental measurements and 3D numerical simulations of Ground Source Heat Pump systems (GSHP) at a UK climate are presented. Experimental measurements of a horizontal-coupled slinky GSHP were undertaken in Talbot Cottage at Drayton St Leonard site, Oxfordshire, UK. The measured thermophysical properties of in situ soil were used in the CFD model. The thermal performance of slinky heat exchangers for the horizontal-coupled GSHP system for different coil diameters and slinky interval distances was investigated using a validated 3D model. Results from a two month period of monitoring the performance of the GSHP system showed that the COP decreased with the running time. The average COP of the horizontal-coupled GSHP was 2.5. The numerical prediction showed that there was no significant difference in the specific heat extraction of the slinky heat exchanger at different coil diameters. However, the larger the diameter of coil, the higher the heat extraction per meter length of soil. The specific heat extraction also increased, but the heat extraction per meter length of soil decreased with the increase of coil central interval distance.

Comparison of the open-closed separatrix in a global magnetospheric simulation with observations: the role of the ring current

The development of global magnetospheric models, such as Space Weather Modeling Framework (SWMF), which can accurately reproduce and track space weather processes has high practical utility. We present an interval on 5 June 1998, where the location of the polar cap boundary, or open-closed field line boundary (OCB), can be determined in the ionosphere using a combination of instruments during a period encompassing a sharp northward to southward interplanetary field turning. We present both point- and time-varying comparisons of the observed and simulated boundaries in the ionosphere and find that when using solely the coupled ideal magnetohydrodynamic magnetosphere-ionosphere model, the rate of change of the OCB to a southward turning of the interplanetary field is significantly faster than that computed from the observational data. However, when the inner magnetospheric module is incorporated, the modeling framework both qualitatively, and often quantitatively, reproduces many elements of the studied interval prior to an observed substorm onset. This result demonstrates that the physics of the inner magnetosphere is critical in shaping the boundary between open and closed field lines during periods of southward interplanetary magnetic field (IMF) and provides significant insight into the 3-D time-dependent behavior of the Earth's magnetosphere in response to a northward-southward IMF turning. We assert that during periods that do not include the tens of minutes surrounding substorm expansion phase onset, the coupled SWMF model may provide a valuable and reliable tool for estimating both the OCB and magnetic field topology over a wide range of latitudes and local times.

Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

Modeling and simulation of cephalosporin C production in a fed-batch tower-type bioreactor

Immobilized cell utilization in tower-type bioreactor is one of the main alternatives being studied to improve the industrial bioprocess. Other alternatives for the production of beta -lactam antibiotics, such as a cephalosporin C fed-batch p recess in an aerated stirred-tank bioreactor with free cells of Cepha-losporium acremonium or a tower-type bioreactor with immobilized cells of this fungus, have proven to be more efficient than the batch profess. In the fed-batch process, it is possible to minimize the catabolite repression exerted by the rapidly utilization of carbon sources (such as glucose) in the synthesis of antibiotics by utilizing a suitable flow rate of supplementary medium. In this study, several runs for cephalosporin C production, each lasting 200 h, were conducted in a fed-batch tower-type bioreactor using different hydrolyzed sucrose concentrations, For this study's model, modifications were introduced to take into account the influence of supplementary medium flow rate. The balance equations considered the effect of oxygen limitation inside the bioparticles. In the Monod-type rate equations, eel concentrations, substrate concentrations, and dissolved oxygen were included as reactants affecting the bioreaction rate. The set of differential equations was solved by the numerical method, and the values of the parameters were estimated by the classic nonlinear regression method following Marquardt's procedure with a 95% confidence interval. The simulation results showed that the proposed model fit well with the experimental data,and based on the experimental data and the mathematical model an optimal mass flow rate to maximize the bioprocess productivity could be proposed.