Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases

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

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

Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology

AbstractWe study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory

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

Mentalizing subtypes in eating disorders: A latent profile analysis

Background: Mentalizing, the mental capacity to understand oneself and others in terms of mental states, has been found to be reduced in several mental disorders. Some studies have suggested that eating disorders (EDs) may also be associated with impairments in mentalizing. The aim of this work is to investigate the possible presence of mentalizing subtypes in a sample of patients with EDs. Method: A sample of patients with eating disorders (N = 157) completed a battery of measures assessing mentalization and related variables, including the Reflective Functioning Questionnaire (RFQ), the Difficulties in Emotion Regulation Strategies (DERS), the Interpersonal Reactivity Index (IRI). Clinicians rated patients in relation to imbalances in different dimensions of mentalization to prementalizing modes and attachment style by using the Mentalization Imbalances Scale, the Modes of Mentalization Scale (MMS), and the Adult Attachment Questionnaire. A latent profile analysis was conducted to test the possible presence of different subgroups. MANOVA was used to test the possible differences between the four mentalizing profiles in relation to emotion dysregulation (DERS), empathy (IRI), and adequate and impairments in mentalizing (MMS and RFQ). Results: The latent profile analysis suggested the presence of four different profiles in relation to impairments in the dimensions of mentalization: (1) affective/self/automatic imbalances, (2) external imbalance, (3) cognitive/self/automatic imbalances, and (4) cognitive/other/automatic imbalances. Patients belonging to profile 1 are characterized by the prevalence of affective mentalization that overwhelms the capacity to reflect on mental states with an imbalance on the self-dimension; profile 2 patients are excessively focused on the external cues of mentalization; profile 3 patients are characterized by an over-involvement on the cognitive and self-facets of mentalization, with an impairment in adopting the other mind perspective; and profile 4 patients have similar impairments compared to profile 3 patients but with an excessive focus on others and deficits in self-reflection. These profiles were heterogeneous in terms of EDs represented in each group and presented significant differences on various variables such as attachment style, emotion dysregulation, empathy, interpersonal reactivity, and reflective function. This study represents, so far, the first work that confirms the presence of different mentalizing patterns in ED patients. Conclusions: ED patients can be classified in relation to impairments in different dimensions of mentalization above and beyond ED diagnosis