Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Copper and human health: biochemistry, genetics, and strategies for modeling dose-response relationships

Copper (Cu) and its alloys are used extensively in domestic and industrial applications. Cu is also an essential element in mammalian nutrition. Since both copper deficiency and copper excess produce adverse health effects, the dose-response curve is U-shaped, although the precise form has not yet been well characterized. Many animal and human studies were conducted on copper to provide a rich database from which data suitable for modeling the dose-response relationship for copper may be extracted. Possible dose-response modeling strategies are considered in this review, including those based on the benchmark dose and categorical regression. The usefulness of biologically based dose-response modeling techniques in understanding copper toxicity was difficult to assess at this time since the mechanisms underlying copper-induced toxicity have yet to be fully elucidated. A dose-response modeling strategy for copper toxicity was proposed associated with both deficiency and excess. This modeling strategy was applied to multiple studies of copper-induced toxicity, standardized with respect to severity of adverse health outcomes and selected on the basis of criteria reflecting the quality and relevance of individual studies. The use of a comprehensive database on copper-induced toxicity is essential for dose-response modeling since there is insufficient information in any single study to adequately characterize copper dose-response relationships. The dose-response modeling strategy envisioned here is designed to determine whether the existing toxicity data for copper excess or deficiency may be effectively utilized in defining the limits of the homeostatic range in humans and other species. By considering alternative techniques for determining a point of departure and low-dose extrapolation (including categorical regression, the benchmark dose, and identification of observed no-effect levels) this strategy will identify which techniques are most suitable for this purpose. This analysis also serves to identify areas in which additional data are needed to better define the characteristics of dose-response relationships for copper-induced toxicity in relation to excess or deficiency.

Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing

Our dynamic capillary electrophoresis model which uses material specific input data for estimation of electroosmosis was applied to investigate fundamental aspects of isoelectric focusing (IEF) in capillaries or microchannels made from bare fused-silica (FS), FS coated with a sulfonated polymer, polymethylmethacrylate (PMMA) and poly(dimethylsiloxane) (PDMS). Input data were generated via determination of the electroosmotic flow (EOF) using buffers with varying pH and ionic strength. Two models are distinguished, one that neglects changes of ionic strength and one that includes the dependence between electroosmotic mobility and ionic strength. For each configuration, the models provide insight into the magnitude and dynamics of electroosmosis. The contribution of each electrophoretic zone to the net EOF is thereby visualized and the amount of EOF required for the detection of the zone structures at a particular location along the capillary, including at its end for MS detection, is predicted. For bare FS, PDMS and PMMA, simulations reveal that EOF is decreasing with time and that the entire IEF process is characterized by the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic transport and electroosmotic zone displacement are opposite and of equal magnitude. The location of immobilization of the boundary between anolyte and most acidic carrier ampholyte is dependent on EOF, i.e. capillary material and anolyte. Overall time intervals for reaching this state in microchannels produced by PDMS and PMMA are predicted to be similar and about twice as long compared to uncoated FS. Additional mobilization for the detection of the entire pH gradient at the capillary end is required. Using concomitant electrophoretic mobilization with an acid as coanion in the catholyte is shown to provide sufficient additional cathodic transport for that purpose. FS capillaries dynamically double coated with polybrene and poly(vinylsulfonate) are predicted to provide sufficient electroosmotic pumping for detection of the entire IEF gradient at the cathodic column end.

An integrated approach for reconstructing surface models of the proximal femur from sparse input data for surgical navigation

A patient-specific surface model of the proximal femur plays an important role in planning and supporting various computer-assisted surgical procedures including total hip replacement, hip resurfacing, and osteotomy of the proximal femur. The common approach to derive 3D models of the proximal femur is to use imaging techniques such as computed tomography (CT) or magnetic resonance imaging (MRI). However, the high logistic effort, the extra radiation (CT-imaging), and the large quantity of data to be acquired and processed make them less functional. In this paper, we present an integrated approach using a multi-level point distribution model (ML-PDM) to reconstruct a patient-specific model of the proximal femur from intra-operatively available sparse data. Results of experiments performed on dry cadaveric bones using dozens of 3D points are presented, as well as experiments using a limited number of 2D X-ray images, which demonstrate promising accuracy of the present approach.

Modeling of transfer kinetics at the serum-cerebrospinal fluid barrier in rabbits with experimental meningitis: application to grepafloxacin

The goals of the present study were to model the population kinetics of in vivo influx and efflux processes of grepafloxacin at the serum-cerebrospinal fluid (CSF) barrier and to propose a simulation-based approach to optimize the design of dose-finding trials in the meningitis rabbit model. Twenty-nine rabbits with pneumococcal meningitis receiving grepafloxacin at 15 mg/kg of body weight (intravenous administration at 0 h), 30 mg/kg (at 0 h), or 50 mg/kg twice (at 0 and 4 h) were studied. A three-compartment population pharmacokinetic model was fit to the data with the program NONMEM (Nonlinear Mixed Effects Modeling). Passive diffusion clearance (CL(diff)) and active efflux clearance (CL(active)) are transfer kinetic modeling parameters. Influx clearance is assumed to be equal to CL(diff), and efflux clearance is the sum of CL(diff), CL(active), and bulk flow clearance (CL(bulk)). The average influx clearance for the population was 0.0055 ml/min (interindividual variability, 17%). Passive diffusion clearance was greater in rabbits receiving grepafloxacin at 15 mg/kg than in those treated with higher doses (0.0088 versus 0.0034 ml/min). Assuming a CL(bulk) of 0.01 ml/min, CL(active) was estimated to be 0.017 ml/min (11%), and clearance by total efflux was estimated to be 0.032 ml/min. The population kinetic model allows not only to quantify in vivo efflux and influx mechanisms at the serum-CSF barrier but also to analyze the effects of different dose regimens on transfer kinetic parameters in the rabbit meningitis model. The modeling-based approach also provides a tool for the simulation and prediction of various outcomes in which researchers might be interested, which is of great potential in designing dose-finding trials.

In-plane thermal conductivity modeling of carbon filled liquid crystal polymer based resins

Adding conductive carbon fillers to insulating thermoplastic resins increases composite electrical and thermal conductivity. Often, as much of a single type of carbon filler is added to achieve the desired conductivity, while still allowing the material to be molded into a bipolar plate for a fuel cell. In this study, varying amounts of three different carbons (carbon black, synthetic graphite particles, and carbon fiber) were added to Vectra A950RX Liquid Crystal Polymer. The in-plane thermal conductivity of the resulting single filler composites were tested. The results showed that adding synthetic graphite particles caused the largest increase in the in-plane thermal conductivity of the composite. The composites were modeled using ellipsoidal inclusion problems to predict the effective in-plane thermal conductivities at varying volume fractions with only physical property data of constituents. The synthetic graphite and carbon black were modeled using the average field approximation with ellipsoidal inclusions and the model showed good agreement with the experimental data. The carbon fiber polymer composite was modeled using an assemblage of coated ellipsoids and the model showed good agreement with the experimental data.

On the modeling of drug induced respiratory depression in the non-steady-state

The ability of anesthetic agents to provide adequate analgesia and sedation is limited by the ventilatory depression associated with overdosing in spontaneously breathing patients. Therefore, quantitation of drug induced ventilatory depression is a pharmacokinetic-pharmacodynamic problem relevant to the practice of anesthesia. Although several studies describe the effect of respiratory depressant drugs on isolated endpoints, an integrated description of drug induced respiratory depression with parameters identifiable from clinically available data is not available. This study proposes a physiological model of CO2 disposition, ventilatory regulation, and the effects of anesthetic agents on the control of breathing. The predictive performance of the model is evaluated through simulations aimed at reproducing experimental observations of drug induced hypercarbia and hypoventilation associated with intravenous administration of a fast-onset, highly potent anesthetic mu agonist (including previously unpublished experimental data determined after administration of 1 mg alfentanil bolus). The proposed model structure has substantial descriptive capability and can provide clinically relevant predictions of respiratory inhibition in the non-steady-state to enhance safety of drug delivery in the anesthetic practice.

Experimental and modeling study of the filtration and oxidation characteristics of a diesel oxidation catalyst and a catalyzed particulate filter

A diesel oxidation catalyst (DOC) with a catalyzed diesel particulate filter (CPF) is an effective exhaust aftertreatment device that reduces particulate emissions from diesel engines, and properly designed DOC-CPF systems provide passive regeneration of the filter by the oxidation of PM via thermal and NO2/temperature-assisted means under various vehicle duty cycles. However, controlling the backpressure on engines caused by the addition of the CPF to the exhaust system requires a good understanding of the filtration and oxidation processes taking place inside the filter as the deposition and oxidation of solid particulate matter (PM) change as functions of loading time. In order to understand the solid PM loading characteristics in the CPF, an experimental and modeling study was conducted using emissions data measured from the exhaust of a John Deere 6.8 liter, turbocharged and after-cooled engine with a low-pressure loop EGR system and a DOC-CPF system (or a CCRT® - Catalyzed Continuously Regenerating Trap®, as named by Johnson Matthey) in the exhaust system. A series of experiments were conducted to evaluate the performance of the DOC-only, CPF-only and DOC-CPF configurations at two engine speeds (2200 and 1650 rpm) and various loads on the engine ranging from 5 to 100% of maximum torque at both speeds. Pressure drop across the DOC and CPF, mass deposited in the CPF at the end of loading, upstream and downstream gaseous and particulate emissions, and particle size distributions were measured at different times during the experiments to characterize the pressure drop and filtration efficiency of the DOCCPF system as functions of loading time. Pressure drop characteristics measured experimentally across the DOC-CPF system showed a distinct deep-bed filtration region characterized by a non-linear pressure drop rise, followed by a transition region, and then by a cake-filtration region with steadily increasing pressure drop with loading time at engine load cases with CPF inlet temperatures less than 325 °C. At the engine load cases with CPF inlet temperatures greater than 360 °C, the deep-bed filtration region had a steep rise in pressure drop followed by a decrease in pressure drop (due to wall PM oxidation) in the cake filtration region. Filtration efficiencies observed during PM cake filtration were greater than 90% in all engine load cases. Two computer models, i.e., the MTU 1-D DOC model and the MTU 1-D 2-layer CPF model were developed and/or improved from existing models as part of this research and calibrated using the data obtained from these experiments. The 1-D DOC model employs a three-way catalytic reaction scheme for CO, HC and NO oxidation, and is used to predict CO, HC, NO and NO2 concentrations downstream of the DOC. Calibration results from the 1-D DOC model to experimental data at 2200 and 1650 rpm are presented. The 1-D 2-layer CPF model uses a ‘2-filters in series approach’ for filtration, PM deposition and oxidation in the PM cake and substrate wall via thermal (O2) and NO2/temperature-assisted mechanisms, and production of NO2 as the exhaust gas mixture passes through the CPF catalyst washcoat. Calibration results from the 1-D 2-layer CPF model to experimental data at 2200 rpm are presented. Comparisons of filtration and oxidation behavior of the CPF at sample load-cases in both configurations are also presented. The input parameters and selected results are also compared with a similar research work with an earlier version of the CCRT®, to compare and explain differences in the fundamental behavior of the CCRT® used in these two research studies. An analysis of the results from the calibrated CPF model suggests that pressure drop across the CPF depends mainly on PM loading and oxidation in the substrate wall, and also that the substrate wall initiates PM filtration and helps in forming a PM cake layer on the wall. After formation of the PM cake layer of about 1-2 µm on the wall, the PM cake becomes the primary filter and performs 98-99% of PM filtration. In all load cases, most of PM mass deposited was in the PM cake layer, and PM oxidation in the PM cake layer accounted for 95-99% of total PM mass oxidized during loading. Overall PM oxidation efficiency of the DOC-CPF device increased with increasing CPF inlet temperatures and NO2 flow rates, and was higher in the CCRT® configuration compared to the CPF-only configuration due to higher CPF inlet NO2 concentrations. Filtration efficiencies greater than 90% were observed within 90-100 minutes of loading time (starting with a clean filter) in all load cases, due to the fact that the PM cake on the substrate wall forms a very efficient filter. A good strategy for maintaining high filtration efficiency and low pressure drop of the device while performing active regeneration would be to clean the PM cake filter partially (i.e., by retaining a cake layer of 1-2 µm thickness on the substrate wall) and to completely oxidize the PM deposited in the substrate wall. The data presented support this strategy.

Development and modeling of thermally conductive resins for fuel cell bipolar plate applications

Thermally conductive resins are a class of material that show promise in many different applications. One growing field for their use is in the area of bipolar plate technology for fuel cell applications. In this work, a LCP was mixed with different types of carbon fillers to determine the effects of the individual carbon fillers on the thermal conductivity of the composite resin. In addition, mathematical modeling was performed on the thermal conductivity data with the goal of developing predictive models for the thermal conductivity of highly filled composite resins.

Simulating dioxane transport in a heterogeneous glacial aquifer system (Washtenaw County, Michigan) using publicly available models and data

The primary challenge in groundwater and contaminant transport modeling is obtaining the data needed for constructing, calibrating and testing the models. Large amounts of data are necessary for describing the hydrostratigraphy in areas with complex geology. Increasingly states are making spatial data available that can be used for input to groundwater flow models. The appropriateness of this data for large-scale flow systems has not been tested. This study focuses on modeling a plume of 1,4-dioxane in a heterogeneous aquifer system in Scio Township, Washtenaw County, Michigan. The analysis consisted of: (1) characterization of hydrogeology of the area and construction of a conceptual model based on publicly available spatial data, (2) development and calibration of a regional flow model for the site, (3) conversion of the regional model to a more highly resolved local model, (4) simulation of the dioxane plume, and (5) evaluation of the model's ability to simulate field data and estimation of the possible dioxane sources and subsequent migration until maximum concentrations are at or below the Michigan Department of Environmental Quality's residential cleanup standard for groundwater (85 ppb). MODFLOW-2000 and MT3D programs were utilized to simulate the groundwater flow and the development and movement of the 1, 4-dioxane plume, respectively. MODFLOW simulates transient groundwater flow in a quasi-3-dimensional sense, subject to a variety of boundary conditions that can simulate recharge, pumping, and surface-/groundwater interactions. MT3D simulates solute advection with groundwater flow (using the flow solution from MODFLOW), dispersion, source/sink mixing, and chemical reaction of contaminants. This modeling approach was successful at simulating the groundwater flows by calibrating recharge and hydraulic conductivities. The plume transport was adequately simulated using literature dispersivity and sorption coefficients, although the plume geometries were not well constrained.

Multiscale constitutive modeling of polymer materials

Materials are inherently multi-scale in nature consisting of distinct characteristics at various length scales from atoms to bulk material. There are no widely accepted predictive multi-scale modeling techniques that span from atomic level to bulk relating the effects of the structure at the nanometer (10-9 meter) on macro-scale properties. Traditional engineering deals with treating matter as continuous with no internal structure. In contrast to engineers, physicists have dealt with matter in its discrete structure at small length scales to understand fundamental behavior of materials. Multiscale modeling is of great scientific and technical importance as it can aid in designing novel materials that will enable us to tailor properties specific to an application like multi-functional materials. Polymer nanocomposite materials have the potential to provide significant increases in mechanical properties relative to current polymers used for structural applications. The nanoscale reinforcements have the potential to increase the effective interface between the reinforcement and the matrix by orders of magnitude for a given reinforcement volume fraction as relative to traditional micro- or macro-scale reinforcements. To facilitate the development of polymer nanocomposite materials, constitutive relationships must be established that predict the bulk mechanical properties of the materials as a function of the molecular structure. A computational hierarchical multiscale modeling technique is developed to study the bulk-level constitutive behavior of polymeric materials as a function of its molecular chemistry. Various parameters and modeling techniques from computational chemistry to continuum mechanics are utilized for the current modeling method. The cause and effect relationship of the parameters are studied to establish an efficient modeling framework. The proposed methodology is applied to three different polymers and validated using experimental data available in literature.

Dynamic modeling of active regeneration in catalyzed and non-catalyzed diesel particulate filters

Particulate matter (PM) emissions standards set by the US Environmental Protection Agency (EPA) have become increasingly stringent over the years. The EPA regulation for PM in heavy duty diesel engines has been reduced to 0.01 g/bhp-hr for the year 2010. Heavy duty diesel engines make use of an aftertreatment filtration device, the Diesel Particulate Filter (DPF). DPFs are highly efficient in filtering PM (known as soot) and are an integral part of 2010 heavy duty diesel aftertreatment system. PM is accumulated in the DPF as the exhaust gas flows through it. This PM needs to be removed by oxidation periodically for the efficient functioning of the filter. This oxidation process is also known as regeneration. There are 2 types of regeneration processes, namely active regeneration (oxidation of PM by external means) and passive oxidation (oxidation of PM by internal means). Active regeneration occurs typically in high temperature regions, about 500 - 600 °C, which is much higher than normal diesel exhaust temperatures. Thus, the exhaust temperature has to be raised with the help of external devices like a Diesel Oxidation Catalyst (DOC) or a fuel burner. The O2 oxidizes PM producing CO2 as oxidation product. In passive oxidation, one way of regeneration is by the use of NO2. NO2 oxidizes the PM producing NO and CO2 as oxidation products. The passive oxidation process occurs at lower temperatures (200 - 400 °C) in comparison to the active regeneration temperatures. Generally, DPF substrate walls are washcoated with catalyst material to speed up the rate of PM oxidation. The catalyst washcoat is observed to increase the rate of PM oxidation. The goal of this research is to develop a simple mathematical model to simulate the PM depletion during the active regeneration process in a DPF (catalyzed and non-catalyzed). A simple, zero-dimensional kinetic model was developed in MATLAB. Experimental data required for calibration was obtained by active regeneration experiments performed on PM loaded mini DPFs in an automated flow reactor. The DPFs were loaded with PM from the exhaust of a commercial heavy duty diesel engine. The model was calibrated to the data obtained from active regeneration experiments. Numerical gradient based optimization techniques were used to estimate the kinetic parameters of the model.

Parameter estimation for transformer modeling

Large Power transformers, an aging and vulnerable part of our energy infrastructure, are at choke points in the grid and are key to reliability and security. Damage or destruction due to vandalism, misoperation, or other unexpected events is of great concern, given replacement costs upward of $2M and lead time of 12 months. Transient overvoltages can cause great damage and there is much interest in improving computer simulation models to correctly predict and avoid the consequences. EMTP (the Electromagnetic Transients Program) has been developed for computer simulation of power system transients. Component models for most equipment have been developed and benchmarked. Power transformers would appear to be simple. However, due to their nonlinear and frequency-dependent behaviors, they can be one of the most complex system components to model. It is imperative that the applied models be appropriate for the range of frequencies and excitation levels that the system experiences. Thus, transformer modeling is not a mature field and newer improved models must be made available. In this work, improved topologically-correct duality-based models are developed for three-phase autotransformers having five-legged, three-legged, and shell-form cores. The main problem in the implementation of detailed models is the lack of complete and reliable data, as no international standard suggests how to measure and calculate parameters. Therefore, parameter estimation methods are developed here to determine the parameters of a given model in cases where available information is incomplete. The transformer nameplate data is required and relative physical dimensions of the core are estimated. The models include a separate representation of each segment of the core, including hysteresis of the core, λ-i saturation characteristic, capacitive effects, and frequency dependency of winding resistance and core loss. Steady-state excitation, and de-energization and re-energization transients are simulated and compared with an earlier-developed BCTRAN-based model. Black start energization cases are also simulated as a means of model evaluation and compared with actual event records. The simulated results using the model developed here are reasonable and more correct than those of the BCTRAN-based model. Simulation accuracy is dependent on the accuracy of the equipment model and its parameters. This work is significant in that it advances existing parameter estimation methods in cases where the available data and measurements are incomplete. The accuracy of EMTP simulation for power systems including three-phase autotransformers is thus enhanced. Theoretical results obtained from this work provide a sound foundation for development of transformer parameter estimation methods using engineering optimization. In addition, it should be possible to refine which information and measurement data are necessary for complete duality-based transformer models. To further refine and develop the models and transformer parameter estimation methods developed here, iterative full-scale laboratory tests using high-voltage and high-power three-phase transformer would be helpful.

Parametric combustion modeling for ethanol-gasoline fuelled spark ignition engines

Ethanol-gasoline fuel blends are increasingly being used in spark ignition (SI) engines due to continued growth in renewable fuels as part of a growing renewable portfolio standard (RPS). This leads to the need for a simple and accurate ethanol-gasoline blends combustion model that is applicable to one-dimensional engine simulation. A parametric combustion model has been developed, integrated into an engine simulation tool, and validated using SI engine experimental data. The parametric combustion model was built inside a user compound in GT-Power. In this model, selected burn durations were computed using correlations as functions of physically based non-dimensional groups that have been developed using the experimental engine database over a wide range of ethanol-gasoline blends, engine geometries, and operating conditions. A coefficient of variance (COV) of gross indicated mean effective pressure (IMEP) correlation was also added to the parametric combustion model. This correlation enables the cycle combustion variation modeling as a function of engine geometry and operating conditions. The computed burn durations were then used to fit single and double Wiebe functions. The single-Wiebe parametric combustion compound used the least squares method to compute the single-Wiebe parameters, while the double-Wiebe parametric combustion compound used an analytical solution to compute the double-Wiebe parameters. These compounds were then integrated into the engine model in GT-Power through the multi-Wiebe combustion template in which the values of Wiebe parameters (single-Wiebe or double-Wiebe) were sensed via RLT-dependence. The parametric combustion models were validated by overlaying the simulated pressure trace from GT-Power on to experimentally measured pressure traces. A thermodynamic engine model was also developed to study the effect of fuel blends, engine geometries and operating conditions on both the burn durations and COV of gross IMEP simulation results.

STUDY OF HYBRID ELECTRIC VEHICLE BATTERY MODELING AND CONTROL USING AUTONOMIE

This report presents the research results of battery modeling and control for hybrid electric vehicles (HEV). The simulation study is conducted using plug-and-play powertrain and vehicle development software, Autonomie. The base vehicle model used for testing the performance of battery model and battery control strategy is the Prius MY04, a power-split hybrid electric vehicle model in Autonomie. To evaluate the battery performance for HEV applications, the Prius MY04 model and its powertrain energy flow in various vehicle operating modes are analyzed. The power outputs of the major powertrain components under different driving cycles are discussed with a focus on battery performance. The simulation results show that the vehicle fuel economy calculated by the Autonomie Prius MY04 model does not match very well with the official data provided by the department of energy (DOE). It is also found that the original battery model does not consider the impact of environmental temperature on battery cell capacities. To improve battery model, this study includes battery current loss on coulomb coefficient and the impact of environmental temperature on battery cell capacity in the model. In addition, voltage losses on both double layer effect and diffusion effect are included in the new battery model. The simulation results with new battery model show the reduced fuel economy error to the DOE data comparing with the original Autonomie Prius MY04 model.