Analysis of a two-scale system for gas-liquid reactions with non-linear Henry-type transfer

In this paper, we consider a coupled two-scale nonlinear reaction-diffusion system modelling gas-liquid reactions. The novel feature of the model is the nonlinear transmission condition between the microscopic and macroscopic concentrations, given by a nonlinear Henry-type transfer function. The solution is approximated by using a Galerkin method adapted to the multiscale form of the system. This approach leads to existence and uniqueness of the solution, and can also be used for numerical computations for a larger class of nonlinear multiscale problems

Homogenization of a pore scale model for precipitation and dissolution in porous media

In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a coupled system of evolution equations, involving a parabolic equation and an ordinary differential equation. The former models ion transport and is defined in a periodically perforated medium. It is further coupled through the boundary conditions to the latter, defined on the boundaries of the perforations and modelling the dissolution and precipitation of the precipitate. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but multi-valued mapping. Due to this, the micro-scale solution lacks regularity. With e being the scale parameter (the ratio between the micro scale and the macro scale length), we adopt the 2-scale framework to achieve the convergence of the homogenization procedure as e approaches zero

Reconstructing the intrinsic statistical properties of intermittent locomotion through corrections for boundary effects

Locomotion characteristics are often recorded within bounded spaces, a constraint which introduces geometry-specific biases and potentially complicates the inference of behavioural features from empirical observations. We describe how statistical properties of an uncorrelated random walk, namely the steady-state stopping location probability density and the empirical step probability density, are affected by enclosure in a bounded space. The random walk here is considered as a null model for an organism moving intermittently in such a space, that is, the points represent stopping locations and the step is the displacement between them. Closed-form expressions are derived for motion in one dimension and simple two-dimensional geometries, in addition to an implicit expression for arbitrary (convex) geometries. For the particular choice of no-go boundary conditions, we demonstrate that the empirical step distribution is related to the intrinsic step distribution, i.e. the one we would observe in unbounded space, via a multiplicative transformation dependent solely on the boundary geometry. This conclusion allows in practice for the compensation of boundary effects and the reconstruction of the intrinsic step distribution from empirical observations

Model-Based Design of Biochemical Microreactors

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.Comment: 22 pages, 1 figure, submitted to Japan Journal of Industrial and Applied Mathematic

Performance Measures Based on How Adults With Cancer Feel and Function: Stakeholder Recommendations and Feasibility Testing in Six Cancer Centers

PURPOSE Patient-reported outcome measures (PROMs) that assess how patients feel and function have potential for evaluating quality of care. Stakeholder recommendations for PRO-based performance measures (PMs) were elicited, and feasibility testing was conducted at six cancer centers. METHODS Interviews were conducted with 124 stakeholders to determine priority symptoms and risk adjustment variables for PRO-PMs and perceived acceptability. Stakeholders included patients and advocates, caregivers, clinicians, administrators, and thought leaders. Feasibility testing was conducted in six cancer centers. Patients completed PROMs at home 5-15 days into a chemotherapy cycle. Feasibility was operationalized as $75$ 75% patient acceptability. RESULTS Stakeholder priority PRO-PMs for systemic therapy were GI symptoms (diarrhea, constipation, nausea, vomiting), depression/anxiety, pain, insomnia, fatigue, dyspnea, physical function, and neuropathy. Recommended risk adjusters included demographics, insurance type, cancer type, comorbidities, emetic risk, and difficulty paying bills. In feasibility testing, 653 patients enrolled (approximately 110 per site), and 607 (93%) completed PROMs, which indicated high feasibility for home collection. The majority of patients (470 of 607; 77%) completed PROMs without a reminder call, and 137 (23%) of 607 completed them after a reminder call. Most patients (72%) completed PROMs through web, 17% paper, or 2% interactive voice response (automated call that verbally asked patient questions). For acceptability, . 95% of patients found PROM items to be easy to understand and complete. CONCLUSION Clinicians, patients, and other stakeholders agree that PMs that are based on how patients feel and function would be an important addition to quality measurement. This study also shows that PRO-PMs can be feasibly captured at home during systemic therapy and are acceptable to patients. PRO-PMs may add value to the portfolio of PMs as oncology transitions from fee-for-service payment models to performance-based care that emphasizes outcome measures