Frontonasal Dysplasia, Severe Neuropsychological Delay, and Midline Central Nervous System Anomalies: Report of 10 Brazilian Male Patients

Here we report on 10 male patients with frontonasal dysplasia, cleft lip/palate, mental retardation, lack of language acquisition, and severe central nervous system involvement. Imaging studies disclosed absence of the corpus callosum, midline cysts, and an abnormally modeled cerebellum. Neuronal heterotopias were present in five patients and parieto-occipital encephalocele in three patients. We suggest that this pattern found exclusively in males, most likely represents a newly recognized syndrome distilled from the group of disorders subsumed under frontonasal dysplasia. (C) 2009 Wiley-Liss, Inc.

Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Retinoic Acid and VEGF Delay Smooth Muscle Relative to Endothelial Differentiation to Coordinate Inner and Outer Coronary Vessel Wall Morphogenesis

Rationale: Major coronary vessels derive from the proepicardium, the cellular progenitor of the epicardium, coronary endothelium, and coronary smooth muscle cells (CoSMCs). CoSMCs are delayed in their differentiation relative to coronary endothelial cells (CoEs), such that CoSMCs mature only after CoEs have assembled into tubes. The mechanisms underlying this sequential CoE/CoSMC differentiation are unknown. Retinoic acid (RA) is crucial for vascular development and the main RA-synthesizing enzyme is progressively lost from epicardially derived cells as they differentiate into blood vessel types. In parallel, myocardial vascular endothelial growth factor (VEGF) expression also decreases along coronary vessel muscularization. Objective: We hypothesized that RA and VEGF act coordinately as physiological brakes to CoSMC differentiation. Methods and Results: In vitro assays (proepicardial cultures, cocultures, and RALDH2 [retinaldehyde dehydrogenase-2]/VEGF adenoviral overexpression) and in vivo inhibition of RA synthesis show that RA and VEGF act as repressors of CoSMC differentiation, whereas VEGF biases epicardially derived cell differentiation toward the endothelial phenotype. Conclusion: Experiments support a model in which early high levels of RA and VEGF prevent CoSMC differentiation from epicardially derived cells before RA and VEGF levels decline as an extensive endothelial network is established. We suggest this physiological delay guarantees the formation of a complex, hierarchical, tree of coronary vessels. (Circ Res. 2010;107:204-216.)

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.