Modeling of a foamed emulsion bioreactor: II. model parametric sensitivity

The sensitivity of a conceptual model of a foam emulsion bioreactor (FEBR) used for the control of toluene vapors in air was examined. Model parametric sensitivity studies showed which parameters affect the removal of toluene (as model pollutant) in the FEBR the most significantly, and enabled definition of the limits of the process. Detailed examination of the results indicated that the process is highly complex and that both mass transfer and kinetic limitations can coexist in the bioreactor system. These results will help with the optimization of the design and operation of FEBRs.     

Spectral methods for parametric sensitivity in stochastic dynamical systems

Stochastic dynamical systems governed by the chemical master equation find use in the modeling of biological phenomena in cells, where they provide more accurate representations than their deterministic counterparts, particularly when the levels of molecular population are small. The analysis of parametric sensitivity in such systems requires appropriate methods to capture the sensitivity of the system dynamics with respect to variations of the parameters amid the noise from inherent internal stochastic effects. We use spectral polynomial chaos expansions to represent statistics of the system dynamics as polynomial functions of the model parameters. These expansions capture the nonlinear behavior of the system statistics as a result of finite-sized parametric perturbations. We obtain the normalized sensitivity coefficients by taking the derivative of this functional representation with respect to the parameters. We apply this method in two stochastic dynamical systems exhibiting bimodal behavior, including a biologically relevant viral infection model.     

Lumped parametric model of the human ear for sound transmission

A lumped parametric model of the human auditoria peripherals consisting of six masses suspended with six springs and ten dashpots was proposed. This model will provide the quantitative basis for the construction of a physical model of the human middle ear. The lumped model parameters were first identified using published anatomical data, and then determined through a parameter optimization process. The transfer function of the middle ear obtained from human temporal bone experiments with laser Doppler interferometers was used for creating the target function during the optimization process. It was found that, among 14 spring and dashpot parameters, there were five parameters which had pronounced effects on the dynamic behaviors of the model. The detailed discussion on the sensitivity of those parameters was provided with appropriate applications for sound transmission in the ear. We expect that the methods for characterizing the lumped model of the human ear and the model parameters will be useful for theoretical modeling of the ear function and construction of the ear physical model.Supported by Oklahoma Center for the Advancement of Science and Technology.     

A Dynamical Model of Lipoprotein Metabolism

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.     

Sensitivity analysis for causal inference using inverse probability weighting

Evaluation of impact of potential uncontrolled confounding is an important component for causal inference based on observational studies. In this article, we introduce a general framework of sensitivity analysis that is based on inverse probability weighting. We propose a general methodology that allows both non‐parametric and parametric analyses, which are driven by two parameters that govern the magnitude of the variation of the multiplicative errors of the propensity score and their correlations with the potential outcomes. We also introduce a specific parametric model that offers a mechanistic view on how the uncontrolled confounding may bias the inference through these parameters. Our method can be readily applied to both binary and continuous outcomes and depends on the covariates only through the propensity score that can be estimated by any parametric or non‐parametric method. We illustrate our method with two medical data sets.     

Parametric stability evaluation in computer experiments on the mathematical model of Drosophila control gene subnetwork

Using the method of generalized threshold models, the problem is formulated and solved to evaluate the parametric stability of the model of a gene subnetwork controlling the early ontogenesis of the fruit fly Drosophila melanogaster. Computer experiments have been performed to test the parametric stability of the model. Quantitative evaluations have been obtained for parametric stability of the Drosophila gene subnetwork in nuclei along the embryo's anterior-posterior axis. The results of computer experiments have been compared with the previous research data on "sensitivity" of functioning regimes to random changes of the parameters in the models of prokaryotic and eukaryotic systems, namely the system controlling the lambda-phage development and the subsystem controlling the flower morphogenesis of Arabidopsis thaliana. The obtained results confirm high parametric stability of gene networks that control the development of organisms.     

Bayesian semiparametric analysis of developmental toxicology data

Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.     

A novel population balance model to investigate the kinetics of in vitro cell proliferation: part II. Numerical solution, parameters' determination, and model outcomes

Based on the general theoretical model developed in Part I of this work, a series of numerical simulations related to the in vitro proliferation kinetics of adherent cells is here presented. First the complex task of assigning a specific value to all the parameters of the proposed population balance (PB) model is addressed, by also highlighting the difficulties arising when performing proper comparisons with experimental data. Then, a parametric sensitivity analysis is performed, thus identifying the more relevant parameters from a kinetics perspective. The proposed PB model can be adapted to describe cell growth under various conditions, by properly changing the value of the adjustable parameters. For this reason, model parameters able to mimic cell culture behavior under microgravity conditions are identified by means of a suitable parametric sensitivity analysis. Specifically, it is found that, as the volume growth parameter is reduced, proliferation slows down while cells arrest in G0/G1 or G2/M depending on the initial distribution of cell population. On the basis of this result, model capabilities have been tested by means of a proper comparison with literature experimental data related to the behavior of synchronized and not-synchronized cells under micro- and standard gravity levels.     

The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions

Although variability in connective tissue parameters is widely reported and recognized, systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking. As such, a sensitivity analysis was performed to consider the behavior of a three-dimensional, non-linear, finite element knee model with connective tissue material parameters that varied within a given interval. The model included the coupled mechanics of the tibio-femoral and patello-femoral degrees of freedom. Seven primary connective tissues modeled as non-linear continua, articular cartilages described by a linear elastic model, and menisci modeled as transverse isotropic elastic materials were included. In this study, a multi-factorial global sensitivity analysis is proposed, which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions. To illustrate the effect of material uncertainties on model predictions, exemplar loading conditions reported in a number of isolated experimental paradigms were used. Our findings illustrated that the inclusion of material uncertainties in a coupled tibio-femoral and patello-femoral model reveals biomechanical interactions that otherwise would remain unknown. For example, our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello-femoral kinematic and kinetic response sensitivities was significantly larger, over a range of flexion angles, when compared to variations associated with material parameters of tissues intrinsic to the patello-femoral joint. We argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response.     

Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection

Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.     

On parametric stability of gene networks controlling ontogenetic processes

The problem of evaluating the parametric stability of three models of pro- and eukaryotic gene networks controlling ontogenetic processes has been defined and solved. Experimental plans of testing gene networks for parametric stability based on the method of generalized threshold models were developed and realized as a software application. We examined the "sensitivity" of the functioning modes to random variations of the parameters in the three model systems: the system of developmental control of phage lambda, the subsystem of morphogenetic control of Arabidopsis thaliana flower, and the gene subnetwork controlling early ontogeny in Drosophila melanogaster. The parametric stability was quantitatively assessed for these models.     

An unbiased sensitivity analysis reveals important parameters controlling periodicity of circadian clock

To assess the importance of model parameters in kinetic models, sensitivity analysis is generally employed to provide key measures. However, it is quite often that no information is available for a significant number of parameters in biochemical models. Therefore, the results of sensitivity analysis that heavily rely on the accuracy of parameters are largely ambiguous. In this study, we propose a computational approach to determine the relative importance of parameters controlling the performance of the circadian clock in Drosophila. While previous attempts to sensitivity analysis largely depend on the knowledge of model parameters which are generally unknown, our study depicts a consistent picture of sensitivity assessment for a large number of parameters, even when the values of these parameters are not available in vivo. The resulting parametric sensitivity analysis suggests that PER/TIM negative loop is critical to maintain the stable periodicity of the circadian clock, which is consistent to the previously experimental and computational findings. Furthermore, our analysis generates a rich hypothesis of important parameters in the circadian clock that can be further tested experimentally. This approach can also be extended to assess the sensitivity of parameters in any biochemical system where a large number of parameters have unknown values. Biotechnol. Bioeng. 2010; 105: 250–259. © 2009 Wiley Periodicals, Inc.     

A hyperelastic fibre-reinforced continuum model of healing tendons with distributed collagen fibre orientations

The healing process of ruptured tendons is problematic due to scar tissue formation and deteriorated material properties, and in some cases, it may take nearly a year to complete. Mechanical loading has been shown to positively influence tendon healing; however, the mechanisms remain unclear. Computational mechanobiology methods employed extensively to model bone healing have achieved high fidelity. This study aimed to investigate whether an established hyperelastic fibre-reinforced continuum model introduced by Gasser, Ogden and Holzapfel (GOH) can be used to capture the mechanical behaviour of the Achilles tendon under loading during discrete timepoints of the healing process and to assess the model’s sensitivity to its microstructural parameters. Curve fitting of the GOH model against experimental tensile testing data of rat Achilles tendons at four timepoints during the tendon repair was used and achieved excellent fits (\(0.9903 < R^{2 }<0.9986\)). A parametric sensitivity study using a three-level central composite design, which is a fractional factorial design method, showed that the collagen-fibre-related parameters in the GOH model—\(\kappa , {k_{{1}}}^{{\prime }}\) and \({k_{{2}}}^{{\prime }}\)—had almost equal influence on the fitting. This study demonstrates that the GOH hyperelastic fibre-reinforced model is capable of describing the mechanical behaviour of healing tendons and that further experiments should focus on establishing the structural and material parameters of collagen fibres in the healing tissue.     

Modeling of a foamed emulsion bioreactor: I. Model development and experimental validation

Recently, a new type of bioreactor for air pollution control referred to as the foamed emulsion bioreactor (FEBR) has been developed. The process relies on the emulsion of an organic phase with a suspension of an actively growing culture of pollutant-degrading microorganisms, made into a foam with the air undergoing treatment. In the current paper, a diffusion and reaction model of the FEBR is presented and discussed. The model considers the fate of the volatile pollutant in the emulsion that constitutes the liquid films of the FEBR. Oxygen limitation as well as substrate inhibition were included in the biokinetic relationships. The removal of toluene vapors served for the validation of the model. All the model parameters were determined by independent experiments or taken from the literature. The model predictions were found to be in good agreement with the experimental data and the model provided useful insights on the phenomena occurring in the FEBR. Model parametric sensitivity studies and further discussion of the factors that limit the performance of the FEBR are presented in Part 2 of this paper.     

How can a life cycle inventory parametric model streamline life cycle assessment in the wooden pallet sector?

Purpose

This study discusses the use of parameterization within the life cycle inventory (LCI) in the wooden pallet sector, in order to test the effectiveness of LCI parametric models to calculate the environmental impacts of similar products. Starting from a single case study, the objectives of this paper are (1) to develop a LCI parametric model adaptable to a range of wooden pallets, (2) to test this model with a reference product (non-reversible pallet with four-way blocks) and (3) to determine numerical correlations between the environmental impacts and the most significant LCI parameters; these correlations can be used to improve the design of new wooden pallets.

Methods

The conceptual scheme for defining the model is based on ISO14040-44 standards. First of all, the product system was defined identifying the life cycle of a generic wood pallet, as well as its life cycle stages. A list of independent and dependent parameters was used to describe the LCI flows of a generic wooden pallet. The LCI parametric model was applied to calculate the environmental impacts of the reference product, with regard to a selection of impact categories at midpoint level (climate change, human toxicity, particulate matter formation, agricultural land occupation, fossil depletion). The model was then applied to further 11 wooden pallets belonging to the same category.

Results and discussion

The definition of a LCI parametric model based on 31 independent parameters and 21 dependent parameters streamlined the data collection process, as the information required for fulfilling the LCI are standard information about the features of the wooden pallet and its manufacturing process. The contribution analysis on the reference product revealed that the most contributing life cycle stages are wood and nails extraction and manufacturing (positive value of environmental impact) and end-of-life (avoided impact). This result is driven by two parameters: mass of wood and average distance for transport of wood. Based on the results of the application of the LCI parametric model to the identified products, one parameter-based regression and one multiple non-linear regression allowed to define a correlation between the life cycle impact assessment (LCIA) category indicators considered and the most influencing parameters.

Conclusions

The definition of LCI parametric model in the wooden pallet sector can effectively be used for calculating the environmental impacts of products with different designs, as well as for obtaining a preliminary estimation of the life cycle environmental impacts of new products.     

Systematic Modeling Approach to Selective Plugging Using In Situ Bacterial Biopolymer Production and Its Potential for Microbial-enhanced Oil Recovery

This study presents a systematic modeling approach for examining the efficiency of the MEOR process based on in situ selective plugging by bacterial biopolymer production and optimization of the nutrient injection strategy to yield the maximum oil recovery. This study focuses on modeling in situ selective plugging by the bacterial biopolymer dextran that is generated by Leuconostoc mesenteroides. Bacterial growth and dextran generation were described by a stoichiometric equation and kinetic reactions using batch model simulation. Based on the parameters for permeability reduction obtained from the sandpack model, the MEOR process was implemented in a pilot-scale system that included a highly permeable thief zone in a low-permeability reservoir. The base MEOR design yielded a 61.5% improvement of the recovery factor compared to that obtained with waterflooding. The parametric simulations revealed that the recovery efficiency was influenced by the amount of dextran, as well as the distribution of dextran, and thus, the injection strategy is critical for controlling the dextran distribution. By incorporating the results from the sensitivity analysis and optimization to determine the optimal design parameters, a 36.7% improvement of the oil recovery was achieved with the optimized MEOR process in comparison with the base case.     

Quantitative performance metrics for robustness in circadian rhythms

MOTIVATION: Sensitivity analysis provides key measures that aid in unraveling the design principles responsible for the robust performance of biological networks. Such metrics allow researchers to investigate comprehensively model performance, to develop more realistic models, and to design informative experiments. However, sensitivity analysis of oscillatory systems focuses on period and amplitude characteristics, while biologically relevant effects on phase are neglected. RESULTS: Here, we introduce a novel set of phase-based sensitivity metrics for performance: period, phase, corrected phase and relative phase. Both state- and phase-based tools are applied to free-running Drosophila melanogaster and Mus musculus circadian models. Each metric produces unique sensitivity values used to rank parameters from least to most sensitive. Similarities among the resulting rank distributions strongly suggest a conservation of sensitivity with respect to parameter function and type. A consistent result, for instance, is that model performance of biological oscillators is more sensitive to global parameters than local (i.e. circadian specific) parameters. Discrepancies among these distributions highlight the individual metrics' definition of performance as specific parametric sensitivity values depend on the defined metric, or output. AVAILABILITY: An implementation of the algorithm in MATLAB (Mathworks, Inc.) is available from the authors. SUPPLEMENTARY INFORMATION: Supplementary Data are available at Bioinformatics online.     

Flexible parametric measurement error models

Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect, the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference, we propose using flexible parametric models that can accommodate departures from standard parametric models. We use mixtures of normals for this purpose. We study two cases in detail: a linear errors-in-variables model and a change-point Berkson model.     

Batch cultivation ofSaccharomyces cerevisiae with increased content of Δ5’7 — Sterols

Changes of the physiological state were studied in a batch cultivation ofSaccharomyces cerevisiae, concentration of proteins and Δ5,7-sterols in yeast dry matter being taken as markers of these changes. Time variations of the markers were studied in relation to changing concentrations of carbon, nitrogen and phosphorus sources. A mathematical model of the batch cultivation was set up and identified. The method of parametric sensitivity was used to evaluate the effect of different technological parameters on the content of Δ5’7-sterols in yeast dry matter.     

Developmental Models for Estimating Ecological Responses to Environmental Variability: Structural,Parametric, and Experimental Issues

Developmental models that account for the metabolic effect of temperature variability on poikilotherms, such as degree-day models, have been widely used to study organism emergence, range and development, particularly in agricultural and vector-borne disease contexts. Though simple and easy to use, structural and parametric issues can influence the outputs of such models, often substantially. Because the underlying assumptions and limitations of these models have rarely been considered, this paper reviews the structural, parametric, and experimental issues that arise when using degree-day models, including the implications of particular structural or parametric choices, as well as assumptions that underlie commonly used models. Linear and non-linear developmental functions are compared, as are common methods used to incorporate temperature thresholds and calculate daily degree-days. Substantial differences in predicted emergence time arose when using linear versus non-linear developmental functions to model the emergence time in a model organism. The optimal method for calculating degree-days depends upon where key temperature threshold parameters fall relative to the daily minimum and maximum temperatures, as well as the shape of the daily temperature curve. No method is shown to be universally superior, though one commonly used method, the daily average method, consistently provides accurate results. The sensitivity of model projections to these methodological issues highlights the need to make structural and parametric selections based on a careful consideration of the specific biological response of the organism under study, and the specific temperature conditions of the geographic regions of interest. When degree-day model limitations are considered and model assumptions met, the models can be a powerful tool for studying temperature-dependent development.