Local Identifiability Analysis, Parameter Subset Selection and Verification for a Minimal Brain PBPK Model.

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models.

A Numerical Study of Sensitivity Coefficients for a Model of Amyloid Precursor Protein and Tubulin-Associated Unit Protein Transport and Agglomeration in Neurons at the Onset of Alzheimer's Disease.

Modeling of intracellular processes occurring during the development of Alzheimer's disease (AD) can be instrumental in understanding the disease and can potentially contribute to finding treatments for the disease. The model of intracellular processes in AD, which we previously developed, contains a large number of parameters. To distinguish between more important and less important parameters, we performed a local sensitivity analysis of this model around the values of parameters that give the best fit with published experimental results. We show that the influence of model parameters on the total concentrations of amyloid precursor protein (APP) and tubulin-associated unit (tau) protein in the axon is reciprocal to the influence of the same parameters on the average velocities of the same proteins during their transport in the axon. The results of our analysis also suggest that in the beginning of AD the aggregation of amyloid-ß and misfolded tau protein have little effect on transport of APP and tau in the axon, which suggests that early damage in AD may be reversible.

A cooperative construction strategy for multi-parameter spatial variant random fields and its application in groundwater pollution risk assessment.

The spatial variability of hydrogeological parameters is a significant source of uncertainty in groundwater numerical modeling and has a certain risk impact on the prediction of pollutant migration and transformation. Current research has focused on the effects of single-parameter spatial variant random fields or utilizing random sampling methods to randomly combine multiple-parameter spatial variant random fields while ignoring the correlation between parameters. This paper proposes an innovative concept of associated random variables to construct multi-parameter synergistic spatial variant random fields, ensuring both the spatial variability and inherent correlation of the parameters. A hypothetical case was constructed, and the Monte Carlo sampling experiment based on computer simulation was used to assess groundwater pollution risks with multiple associated parameters. The results show that hydraulic conductivity and porosity are the main sensitive parameters. The associated random variable allows for the representation of positive correlation, negative correlation, and no correlation between the hydraulic conductivity and porosity. The pollutant mass concentrations in each observation well conform to the generalized extreme value distribution, and the pollution risks of each water well as well as the concentration distribution intervals of pollutants with different probabilities can be obtained. The influence of associated parameters on the cumulative risk of contaminants in observation wells and pollution degree range is only related to their mathematical distribution and is independent of correlations between parameters. This study addresses the issues of spatial variability and inherent correlation of hydrogeological parameters, which are of great significance for groundwater pollution risk assessment and the promotion of sustainable water quality management of groundwater resources.

Analysis and Bayesian estimation of a model for Chikungunya dynamics with relapse: An outbreak in Acapulco, Mexico.

Chikungunya is a vector-borne viral disease transmitted by Aedes aegypti and Aedes albopictus mosquitoes. It does not have any specific treatment, and there is no vaccine. Recent epidemiological data have indicated that a relapse of the infection can occur within three months of the initial infection; however, until now, mathematical models for the spread of the disease have not considered this factor. We propose a mathematical model for the transmission of the Chikungunya virus that considers relapse. We calculated the basic reproductive number $ (R_0) $ of the disease by using the next-generation operator method. We proved the existence of a forward bifurcation. We determined the existence and the global stability of the equilibrium points by using the Lyapunov function method. We fitted the model to data from an outbreak in 2015 in Acapulco, Mexico to estimate the model parameters and $ R_0 $ with the Bayesian approach via a Hamiltonian Monte Carlo method. In the local sensitivity analysis, we found that the fraction of infected individuals who become asymptomatic has a strong impact on the basic reproductive number and makes some control measures insufficient. The impact of the fraction of infected individuals who become asymptomatic should be considered in Chikungunya control strategies.

Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data.

Incomplete data is a prevalent complication in longitudinal studies due to individuals' drop-out before intended completion time. Currently available methods via commercial software for analyzing incomplete longitudinal data at best rely on the ignorability of the drop-outs. If the underlying missing mechanism was non-ignorable, potential bias arises in the statistical inferences. To remove the bias when the drop-out is non-ignorable, joint complete-data and drop-out models have been proposed which involve computational difficulties and untestable assumptions. Since the critical ignorability assumption is unverifiable based on the observed part of the sample, some local sensitivity indices have been proposed in the literature. Specifically, Eftekhari Mahabadi (Second-order local sensitivity to non-ignorability in Bayesian inferences. Stat Med 2018;59:55-95) proposed a second-order local sensitivity tool for Bayesian analysis of cross-sectional studies and show its better performance for handling bias compared with the first-order ones. In this paper, we aim to extend this index for the Bayesian sensitivity analysis of normal longitudinal studies with drop-outs. The index is driven based on a selection model for the drop-out mechanism and a Bayesian linear mixed-effect complete-data model. The presented formulas are calculated using the posterior estimation and draws from the simpler ignorable model. The method is illustrated via some simulation studies and sensitivity analysis of a real antidepressant clinical trial data. Overall, the numerical analysis showed that when repeated outcomes are subject to missingness, regression coefficient estimates are nearly approximated well by a linear function in the neighbourhood of MAR model, but there are a considerable amount of second-order sensitivity for the error term and random effect variances in Bayesian linear mixed-effect model framework.

Dynamics of a dengue disease transmission model with two-stage structure in the human population.

Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.

Optimal Design of Double-Walled Corrugated Board Packaging.

Designing corrugated board packaging is a real challenge, especially when the packaging material comes from multiple recycling. Recycling itself is a pro-ecological and absolutely necessary process, but the mechanical properties of materials that are processed many times deteriorate with the number of cycles. Manufacturers are trying to use unprecedented design methods to preserve the load-bearing capacity of packaging, even when the material itself is of deteriorating quality. An additional obstacle in the process of designing the structure of paper packaging is the progressive systematic reduction of the grammage (the so-called lightweight process) of corrugated cardboard. Therefore, this research presents a critical look at the process of optimal selection of corrugated cardboard for packaging structures, depending on the paper used. The study utilizes analytical, simplified formulas to estimate the strength of cardboard itself as well as the strength of packaging, which are then analyzed to determine their sensitivity to changes in cardboard components, such as the types of paper of individual layers. In the performed sensitivity analysis, numerical homogenization was used, and the influence of initial imperfections on the packaging mechanics was determined. The paper presents a simple algorithm for the optimal selection of the composition of corrugated cardboard depending on the material used and the geometry of the packaging, which allows for a more conscious production of corrugated cardboard from materials derived, e.g., from multiple recycling.

Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging.

The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question "in which layer the basis weight of the paper should be increased?" is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures presented in our previous studies were used here to determine (1) the edge crush resistance, (2) critical load, and (3) the load capacity of corrugated cardboard packaging. The method proposed here allows for obtaining a comprehensive and hierarchical list of the parameters that play the most important role in the process of optimal packaging design.

Antibiotic Stewardship for Canine and Feline Acute Urinary Tract Infection: An Observational Study in a Small Animal Hospital in Northwest Italy.

Antimicrobial stewardship programs (ASPs) have been suggested to reduce antimicrobial resistance phenomena in veterinary medicine, as antibiotics are commonly used without microbiological confirmation. The aim of the present study is to design a specific working flow for a tailored antimicrobial treatment in the case of canine and feline urinary tract infections (UTIs). Urine samples were collected by cystocentesis from 16 dogs and 12 cats presenting acute signs of UTI. The therapy was decided according to the minimal inhibitory concentration, and it was possible to monitor 14 dogs and 11 cats. Rescue therapy (amoxicillin and clavulanic acid) was included in emergency cases. Escherichia coli, Proteus mirabilis, and Streptococcus canis were isolated in dogs, and Escherichia coli, Staphylococcus pseudintermedius, and Staphylococcus aureus were isolated in cats. No multidrug-resistant strains were detected, but all Staphylococci were methicillin resistant. Only one cat received rescue therapy, and only one dog was recruited. Dogs were treated with tetracycline (1/14), fluoroquinolones (6/14), beta-lactams (6/14), and gentamicin (1/14), while cats received fluoroquinolones (3/11), nitrofurans (1/11), clindamycin (1/11), and beta-lactams (6/11). The success rate was very high. Our findings are interesting because this is the first ASP in Italy, and it may be used as a model to develop ASPs for other pathologies.

[Sensitivity Analysis of Boundary Load Reduction in a Large Shallow Lake Water Quality Model].

To explore the spatial and temporal response of water quality to external load reduction in Lake Taihu, Jiangsu Province, China, and clarify the exogenous load reduction under different water inflow and pollution conditions, a water quality model was constructed and the inflow boundaries were divided into seven groups based on the EFDC model. Taking COD and ammonia nitrogen as output targets, the sensitivities of Taihu Lake water quality boundaries were analyzed using a local sensitivity analysis. The results showed that COD and ammonia nitrogen concentrations of each lake area were more sensitive to the boundary load of the lake area than the rest of the lake area, and the sensitivity index was the highest in the Northwest Lake area. Furthermore, the improvement rates of mean COD concentrations in the whole lake decreased by 28.40%-34.71% in the dry season relative to the wet season, and the ranked sensitivity order of the boundaries was as follows:Northwest Lake boundary > Zhushan Lake boundary > Gonghu Lake boundary > Meiliang Bay boundary > Southwest Lake area boundary > Eastern Lake area boundary > East Lake Taihu boundary. The average improvement rates of ammonia nitrogen concentrations in the whole lake were 41.59%-42.34% higher in the dry season relative to the wet season, and the ranked boundary sensitivity order was as follows:Northwest Lake boundary > Meiliang Bay boundary > Zhushan Lake boundary > Gonghu Lake boundary > Southwest Lake boundary > East Lake Taihu boundary > Eastern Lake area boundary. This difference was affected by algal growth and metabolism, and artificial water diversion and drainage. Therefore, it is necessary to consider the reduction period and inflow location according to different water-quality indicators when planning external prevention and control measures in large lakes.