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

A posteriori error estimation and adaptivity for multiple-network poroelasticity

The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled elliptic–parabolic problems, (ii) use this context to derive residual-based a posteriori error estimates and indicators for fully discrete MPET solutions and (iii) evaluate the performance of these error estimators in adaptive algorithms for a set of test cases: ranging from synthetic scenarios to physiologically realistic simulations of brain mechanics.publishedVersio

Brain chains as topological signatures for Alzheimer’s disease

Topology is providing new insights for neuroscience. For instance, graphs, simplicial complexes, directed graphs, flag complexes, persistent homology and convex covers have been used to study functional brain networks, synaptic connectivity, and hippocampal place cell codes. We propose a topological framework to study the evolution of Alzheimer’s disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic protein in a specific region represented by a vertex. Over time, the accumulation of toxic proteins at vertices and their propagation along edges are modeled by a dynamical system on this graph. These dynamics provide an order on the edges of the graph according to the damage created by high concentrations of proteins. This sequence of edges defines a filtration of the graph. We consider different filtrations given by different disease seeding locations. To study these filtrations we propose a new combinatorial and topological method. A filtration defines a maximal chain in the partially ordered set of spanning subgraphs ordered by inclusion. To identify similar graphs, and define a topological signature, we quotient this poset by graph homotopy equivalence, which gives maximal chains in a smaller poset. We provide an algorithm to compute this direct quotient without computing all subgraphs and then propose bounds on the total number of graphs up to homotopy equivalence. To compare the maximal chains generated by this method, we extend Kendall’s dK metric for permutations to more general graded posets and establish bounds for this metric. We then demonstrate the utility of this framework on actual brain graphs by studying the dynamics of tau proteins on the structural connectome. We show that the proposed topological brain chain equivalence classes distinguish different simulated subtypes of Alzheimer’s disease

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

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

Mesocorticolimbic monoamine correlates of methamphetamine sensitization and motivation.

Methamphetamine (MA) is a highly addictive psychomotor stimulant, with life-time prevalence rates of abuse ranging from 5-10% world-wide. Yet, a paucity of research exists regarding MA addiction vulnerability/resiliency and neurobiological mediators of the transition to addiction that might occur upon repeated low-dose MA exposure, more characteristic of early drug use. As stimulant-elicited neuroplasticity within dopamine neurons innervating the nucleus accumbens (NAC) and prefrontal cortex (PFC) is theorized as central for addiction-related behavioral anomalies, we used a multi-disciplinary research approach in mice to examine the interactions between sub-toxic MA dosing, motivation for MA and mesocorticolimbic monoamines. Biochemical studies of C57BL/6J (B6) mice revealed short- (1 day), as well as longer-term (21 days), changes in extracellular dopamine, DAT and/or D2 receptors during withdrawal from 10, once daily, 2 mg/kg MA injections. Follow-up biochemical studies conducted in mice selectively bred for high vs. low MA drinking (respectively, MAHDR vs. MALDR mice), provided novel support for anomalies in mesocorticolimbic dopamine as a correlate of genetic vulnerability to high MA intake. Finally, neuropharmacological targeting of NAC dopamine in MA-treated B6 mice demonstrated a bi-directional regulation of MA-induced place-conditioning. These results extend extant literature for MA neurotoxicity by demonstrating that even subchronic exposure to relatively low MA doses are sufficient to elicit relatively long-lasting changes in mesocorticolimbic dopamine and that drug-induced or idiopathic anomalies in mesocorticolimbic dopamine may underpin vulnerability/resiliency to MA addiction

Physician decision making in selection of second-line treatments in immune thrombocytopenia in children.

Immune thrombocytopenia (ITP) is an acquired autoimmune bleeding disorder which presents with isolated thrombocytopenia and risk of hemorrhage. While most children with ITP promptly recover with or without drug therapy, ITP is persistent or chronic in others. When needed, how to select second-line therapies is not clear. ICON1, conducted within the Pediatric ITP Consortium of North America (ICON), is a prospective, observational, longitudinal cohort study of 120 children from 21 centers starting second-line treatments for ITP which examined treatment decisions. Treating physicians reported reasons for selecting therapies, ranking the top three. In a propensity weighted model, the most important factors were patient/parental preference (53%) and treatment-related factors: side effect profile (58%), long-term toxicity (54%), ease of administration (46%), possibility of remission (45%), and perceived efficacy (30%). Physician, health system, and clinical factors rarely influenced decision-making. Patient/parent preferences were selected as reasons more often in chronic ITP (85.7%) than in newly diagnosed (0%) or persistent ITP (14.3%, P = .003). Splenectomy and rituximab were chosen for the possibility of inducing long-term remission (P < .001). Oral agents, such as eltrombopag and immunosuppressants, were chosen for ease of administration and expected adherence (P < .001). Physicians chose rituximab in patients with lower expected adherence (P = .017). Treatment choice showed some physician and treatment center bias. This study illustrates the complexity and many factors involved in decision-making in selecting second-line ITP treatments, given the absence of comparative trials. It highlights shared decision-making and the need for well-conducted, comparative effectiveness studies to allow for informed discussion between patients and clinicians

Sociological and Human Developmental Explanations of Crime: Conflict or Consensus

This paper examines multidisciplinary correlates of delinquency in an attempt to integrate sociological and environmental theories of crime with human developmental and biological explanations of crime. Structural equation models are applied to assess links among biological, psychological, and environmental variables collected prospectively from birth through age 17 on a sample of 800 black children at high risk for learning and behavioral disorders. Results show that for both males and females, aggression and disciplinary problems in school during adolescence are the strongest predictors of repeat offense behavior. Whereas school achievement and family income and stability are also significant predictors of delinquency for males, early physical development is the next strongest predictor for females. Results indicate that some effects on delinquency also vary during different ages. It is suggested that behavioral and learning disorders have both sociological and developmental correlates and that adequate educational resources are necessary to ensure channels of legitimate opportunities for high-risk youths