A parallel solver for reaction-diffusion systems in computational electrocardiology

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain %(AB) cardiac model, consisting of a system of two degenerate parabolic reaction-diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. %In case of equal anisotropy ratio, this system reduces to The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction-diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh-Nagumo (FHN) model to the more complex phase-I Luo-Rudy model (LR1). The solver employs structured isoparametric $Q_1$ finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to $O(10^7)$ unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains

Distributed optimal control of a nonstandard system of phase field equations

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field systems, first-order necessary optimality condition

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Towards a liquid Argon TPC without evacuation: filling of a 6 m^3 vessel with argon gas from air to ppm impurities concentration through flushing

In this paper we present a successful experimental test of filling a volume of 6 m$^3$ with argon gas, starting from normal ambient air and reducing the impurities content down to few parts per million (ppm) oxygen equivalent. This level of contamination was directly monitored measuring the slow component of the scintillation light of the Ar gas, which is sensitive to {\it all} sources of impurities affecting directly the argon scintillation.Comment: 9 pages, 6 figures, to appear in Proc. 1st International Workshop towards the Giant Liquid Argon Charge Imaging Experiment (GLA2010), Tsukuba, March 201

Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and [...].Comment: 20 pages, 12 figure

Comparison of Side Effects with Extended Release Epidural Morphine and Other Analgesic Modalities

Opioids are the mainstay of post-operative pain management and may produce side effects that impact patient recovery. Use of Extended Release Epidural Morphine (EREM) has been shown to result in significantly less average morphine usage and to have superior analgesic efficacy than other modes of postoperative pain management. The purpose of this retrospective review was to compare the incidence and onset of side effects of ERE and other post-operative Analgesic regiments

Cannabis consumption and the risk of psychosis

Summary Objectives: Cannabis is the most widely used illicit drug globally and its use has been linked to an increased risk for psychotic disorders. An association between cannabis consumption and psychotic symptoms was consistently reported by several studies. This case-control study aimed to widen the current findings about the impact of cannabis exposure on the risk of psychosis, by investigating the pattern of cannabis consumption in a sample of first-episode of psychosis (FEP) patients compared to healthy controls. Material and methods: 68 individuals who presented for the first time to mental health services of Palermo (Italy) with an ICD-10 diagnosis of psychotic disorders and 74 healthy were enrolled as part of the Sicilian Genetics and Psychosis study. Psychopathological assessment and diagnosis were carried out by the Schedule for Clinical Assessment in Neuropsychiatry (SCAN). Socio-demographic data were collected by the modified version of the Medical Research Council (MRC) socio-demographic scale. All participants were interviewed using the Cannabis Experience Questionnaire \u2013 Modified Version to obtain a detailed assessment of lifetime patterns of cannabis and other illicit drug consumption. Logistic regression was applied to investigate the relationships between various aspects of cannabis use (lifetime use, age at first use, duration, and frequency of use) and case-control status while controlling for potential confounders. Results: Patients started cannabis consumption about 3 years earlier than the control group (t = 3.1, p = 0.002) and were 8 times more likely to having started using cannabis before 15 years (adjusted OR = 8.0, 95% CI 2.4-27) than controls. Furthermore cases were more likely to smoke more frequently than controls (adjusted OR = 4.4, 95% CI 1.08-18). We did not find a difference in duration of cannabis use between cases and controls. Conclusions: The findings suggest that cannabis exposure, and especially daily cannabis consumption, is associated with the risk for psychosis; however, the retrospective study design does not allow drawing firm conclusions about causality