A mixed finite element method for nearly incompressible multiple-network poroelasticity

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium that is permeated by multiple fluid networks of differing characteristics. As such, the MPET equations represent a generalization of Biot's equations, and numerical discretizations of the MPET equations face similar challenges. Here, we focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, we propose a new mixed finite element formulation based on introducing an additional total pressure variable. By presenting energy estimates for the continuous solutions and a priori error estimates for a family of compatible semi-discretizations, we show that this formulation is robust in the limits of incompressibility, vanishing storage coefficients, and vanishing transfer between networks. These theoretical results are corroborated by numerical experiments. Our primary interest in the MPET equations stems from the use of these equations in modelling interactions between biological fluids and tissues in physiological settings. So, we additionally present physiologically realistic numerical results for blood and tissue fluid flow interactions in the human brain

Forensic drug screening by liquid chromatography hyphenated with high-resolution mass spectrometry (LC-HRMS)

Liquid chromatography-high resolution mass spectrometry (LC-HRMS) has been widely used for screening small organic molecules in complex samples. Its selectivity and sensitivity allow for broad-scope screening of thousands of analytes. However, the complexity of the acquired data has complicated its implementation in high-throughput laboratories that analyze hundreds of samples per week and require that multiple users be able to analyze the data. Forensic laboratories have managed to harvest the merits of LC-HRMS technology using robust and often leveled data analysis(/acquisition) workflows, without spending a disproportionate amount of time evaluating inconclusive or false positive identifications. This critical review describes the full analytical process of LC-HRMS-based forensic drug screening, from sample preparation to data analysis and beyond. Interesting solutions are highlighted, and two emerging trends will be discussed: i) the use of free online tools to improve forensic drug screening, and ii) re-use of data to improve forensic services

Accurate Discretization Of Poroelasticity Without Darcy Stability -- Stokes-Biot Stability Revisited

In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability? Stokes-Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot's equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage coefficient and a vanishing hydraulic conductivity. The basic premise of a Stokes-Biot stable discretization is: one part Stokes stability and one part mixed Darcy stability. In this manuscript we remark on the observation that the latter condition can be generalized to a wider class of discrete spaces. In particular: a parameter-uniform inf-sup condition for a mixed Darcy sub-problem is not strictly necessary to retain the practical advantages currently enjoyed by the class of Stokes-Biot stable Euler-Galerkin discretization schemes.Comment: 25 page

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Parameter robust preconditioning by congruence for multiple-network poroelasticity

The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or multi-porosity/multi-permeability systems. These equations generalize Biot's equations, which describe the mechanics of the one-network case. The efficient numerical solution of the MPET equations is challenging, in part due to the complexity of the system and in part due to the presence of interacting parameter regimes. In this paper, we present a new strategy for efficiently and robustly solving the MPET equations numerically. In particular, we introduce a new approach to formulating finite element methods and associated preconditioners for the MPET equations. The approach is based on designing transformations of variables that simultaneously diagonalize (by congruence) the equations' key operators and subsequently constructing parameter-robust block-diagonal preconditioners for the transformed system. Our methodology is supported by theoretical considerations as well as by numerical results

Scalable Analysis of Untargeted LC-HRMS Data by Means of SQL Database Archiving

Liquid chromatography-high-resolution mass spectrometry (LC-HRMS) is widely used to detect chemicals with a broad range of physiochemical properties in complex biological samples. However, the current data analysis strategies are not sufficiently scalable because of data complexity and amplitude. In this article, we report a novel data analysis strategy for HRMS data founded on structured query language database archiving. A database called ScreenDB was populated with parsed untargeted LC-HRMS data after peak deconvolution from forensic drug screening data. The data were acquired using the same analytical method over 8 years. ScreenDB currently holds data from around 40,000 data files, including forensic cases and quality control samples that can be readily sliced and diced across data layers. Long-term monitoring of system performance, retrospective data analysis for new targets, and identification of alternative analytical targets for poorly ionized analytes are examples of ScreenDB applications. These examples demonstrate that ScreenDB makes a significant improvement to forensic services and that the concept has potential for broad applications for all large-scale biomonitoring projects that rely on untargeted LC-HRMS data

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Metabolic profiling of four synthetic stimulants, including the novel indanyl-cathinone 5-PPDi, after human hepatocyte incubation

Synthetic cathinones are new psychoactive substances that represent a health risk worldwide. For most of the 130 reported compounds, information about toxicology and/or metabolism is not available, which hampers their detection (and subsequent medical treatment) in intoxication cases. The principles of forensic analytical chemistry and the use of powerful analytical techniques are indispensable for stablishing the most appropriate biomarkers for these substances. Human metabolic fate of synthetic cathinones can be assessed by the analysis of urine and blood obtained from authentic consumers; however, this type of samples is limited and difficult to access. In this work, the metabolic behaviour of three synthetic cathinones (4-CEC, 4-CPrC and 5-PPDi) and one amphetamine (3-FEA) has been evaluated by incubation with pooled human hepatocytes and metabolite identification has been performed by high-resolution mass spectrometry. This in vitro approach has previously shown its feasibility for obtaining excretory human metabolites. 4-CEC and 3-FEA were not metabolised, and for 4-CPrC only two minor metabolites were obtained. On the contrary, for the recently reported 5-PPDi, twelve phase I metabolites were elucidated. Up to our knowledge, this is the first metabolic study of an indanyl-cathinone. Data reported in this paper will allow the detection of these synthetic stimulants in intoxication cases, and will facilitate future research on the metabolic behaviour of other indanyl-based cathinones