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

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

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

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

In vitro assessment of pacing as therapy for aortic regurgitation

Background and objective Clinical evaluation of pacing therapy in mitigating the aortic insufficiency after transchateter aortic valve implantation often gives contradictory outcomes. This study presents an in vitro investigation aimed at clarifying the effect of pacing on paravalvular leakage. Methods A series of in vitro tests reproducing the heart operating changes clinically obtained by pacing was carried out in a 26 mm Edwards Sapien XT prosthesis with mild paravalvular leakage. The effect of pacing on the regurgitant volumes per cycle and per minute was quantified, and the energy and power consumed by the left ventricle were calculated. Results Results indicate that though pacing results in some reduction in the total regurgitation per cycle, the volume of fluid regurgitating per minute increases substantially, causing overload of left ventricle. Conclusions Our tests indicate no effective haemodynamic benefit from pacing, suggesting a prudential clinical use of this therapy for the treatment of postoperative aortic regurgitation

In Vitro and Ex Vivo Hemodynamic Testing of an Innovative Occluder for Paravalvular Leak After Transcather Aortic Valve Implantation

This study aims at achieving a proof-of-concept for a novel device designed to occlude the orifices that may form between transcatheter valves and host tissues after TAVI. The device effect on the performance of a SAPIEN XT with a paravalvular gap was assessed into an in vitro and ex vivo pulse duplicator. The in vitro tests were performed complying with the standard international regulations, measuring the trasvalvular pressure and regurgitant volumes with and without the paravalvular gap, and with the occluder correctly positioned into the gap. In the second series of tests, the leakage reduction due to the presence of the occluder was assessed for the same setup, into a beating swine heart. The occluder implantation decreased the regurgitant fraction of about 50% for the in vitro assessment and 75% for the ex vivo test, under rest operating conditions. These results suggest that suitably designed occluders can lead to important benefit in the PVL treatment

The frequency of endometriosis in the general and selected populations: A systematic review

Background: In this article, we have reviewed available data on the frequency of endometriosis considering separately the incidence and the prevalence of the disease using data from papers published from 2000 to June 2019. Study design: Systematic review and meta-analysis. PubMed and EMBASE were searched for observational studies reporting data on the incidence or prevalence rates or ratios for the following pre-speci\ufb01ed populations: general population, infertile women, women reporting pelvic pain, women who underwent pelvic surgical procedures unrelated with endometriosis. Results: A total of 42 papers were included in this review. Considering the 11 studies that have analysed the prevalence of endometriosis in the general population, the reported prevalence ranged from 0.8% to 28.6% with an overall estimated of 4.4% (95% CI 3.6\u20135.2). When we considered separately the estimates reported in each study according to geographic area, the pooled estimate was lower in the European studies (1.4%), increased to 5.7% in the US studies and was 15.4% in the Asian ones. The pooled estimated prevalence of endometriosis was 33.5% (95% CI 24.3\u201342.8, Figure 2(c)) in women who underwent surgery for benign gynaecological conditions, 23.8% (95% CI 16.1\u201331.5, Figure 2(d)) in infertile women, and 49.7 % (95% CI 14.4\u201385.0) in women with chronic pelvic pain. Conclusion: This review offers an overview of the available data on the frequency of endometriosis in the general population and in selected population, in particular among infertile women and women with chronic pelvic pain