Discrete breathers in Klein-Gordon lattices: A deflation-based approach.

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices. We compare different approaches to using deflation for periodic orbits, including ones based on Fourier decomposition of the solution, as well as ones based on the solution's energy density profile. We demonstrate the ability of the method to obtain a wide variety of multibreather solutions without prior knowledge about their spatial profile.

Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation.

We perform a bifurcation analysis of the steady states of Rayleigh-Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialization strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this nonlinear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the disconnected branches we find contains an S-shaped curve with hysteresis, which is the origin of a flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyze the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.

Anisotropic mesh adaptivity for multi-scale ocean modelling.

Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.

Outcome and assessment after the modified Fontan procedure for hypoplastic left heart syndrome.

BACKGROUND: We reviewed the outcome of 76 consecutive patients (age range, 5 months to 6 years; median age, 19 months) who underwent a modified Fontan procedure after initial palliative surgery for hypoplastic left heart syndrome (HLHS) between January 1984 and December 1989. METHODS AND RESULTS: Modifications of the Fontan procedure included transatrial baffle of pulmonary venous return to the tricuspid valve (n = 10) or inferior vena cava baffle within the right atrium to the superior vena caval-pulmonary artery anastomosis, with pulmonary artery augmentation (n = 66). Actuarial survival rates were 74% (1 month), 58% (12 months), 56% (2 years), and 52% (4 years). Of the 43 survivors, 25 patients have returned for postoperative cardiac catheterization at a medium of 13 months after the Fontan procedure. Mean +/- SD hemodynamic values were cardiac index, 2.8 +/- 0.6 l/min/m2; right arterial pressure, 11 +/- 2 mm Hg; pulmonary artery wedge pressure, 6 +/- 3 mm Hg; and arterial oxygen saturation, 94 +/- 3%. No patient had significant tricuspid or native pulmonary valve insufficiency. CONCLUSIONS: Survival after the Fontan procedure in patients with HLHS is comparable to survival after a Fontan procedure in patients with other complex congenital heart lesions. In the subgroup of patients with HLHS who survived both reconstructive surgery and a Fontan procedure and have been evaluated by cardiac catheterization after a Fontan procedure, the use of the right ventricle as the systemic ventricle yielded excellent intermediate results for Fontan physiology.

Hypoplastic left heart syndrome: hemodynamic and angiographic assessment after initial reconstructive surgery and relevance to modified Fontan procedure.

After undergoing initial reconstructive surgery for hypoplastic left heart syndrome performed between August 1985 and March 1989, 59 patients (age range 3 to 27 months, mean 13.8 +/- 4.5) underwent elective cardiac catheterization in anticipation of a modified Fontan procedure. Five important hemodynamic and anatomic features considered to be components of successful reconstructive surgery were specifically addressed. 1) Interatrial communication: Only two patients had a measured pressure difference of greater than 4 mm Hg across the atrial septum. 2) Tricuspid valve function: Angiography demonstrated significant tricuspid valve regurgitation in only five patients (moderate in two and severe in three). 3) Aortic arch: Pressure tracings from the right ventricle to the descending aorta revealed a gradient greater than 25 mm Hg in only two patients. 4) Pulmonary vasculature: Ten patients had a calculated pulmonary vascular resistance greater than 4 U.m2; 51 (86%) of the 59 patients had no evidence of distortion (stenosis or hypoplasia) of either the left or the right pulmonary artery. 5) Right ventricular function: Five patients had an end-diastolic pressure in the right ventricle greater than 12 mm Hg and two patients had qualitative assessment of decreased ventricular function. Comparison of catheterization data between survivors and nonsurvivors of the subsequent modified Fontan procedure showed that only significant tricuspid regurgitation is a possible predictor of poor outcome. After first stage reconstructive surgery for hypoplastic left heart syndrome, most survivors have favorable anatomy and hemodynamics at follow-up cardiac catheterization for a subsequent Fontan procedure.

Hypoplastic left heart syndrome. Outcome after initial reconstruction and before modified Fontan procedure.

The outcome and clinical course before modified Fontan procedure were reviewed for 200 patients with hypoplastic left heart syndrome who underwent initial reconstructive surgery between August 1985 and March 1989. The median age at the time of initial reconstruction was 6 days (range, 1 day to 7.2 months). In 28 patients, a right modified Blalock-Taussig shunt was used; in 172 patients, a central shunt was placed. Additional procedures (n = 41) performed in 38 patients (median age, 5 months; range, 6 days to 17.5 months) were revision of systemic-to-pulmonary shunt (n = 15), arch reconstruction (n = 8), balloon angioplasty of arch obstruction (n = 7), atrial septectomy (n = 4), pulmonary artery angioplasty (n = 2), tricuspid valve annuloplasty or replacement (n = 4), and modified Glenn shunt (n = 1). There was no significant difference in the frequency of additional procedures performed more than 30 postoperative days in the survivors compared with the nonsurvivors. Actuarial survival rates were 0.66 (1 month), 0.48 (12 months), and 0.44 (18 months). Seventy percent of all deaths occurred during the initial admission, with 32% resulting from acute cardiovascular collapse during the first postoperative day. There was no statistical difference in actuarial survival when assessed by the type of shunt used or by anatomical subtype or when the influence of additional interventions was considered. Substantial improvement in outcome may be possible if immediate perioperative mortality can be reduced. We speculate that some of the intermediate mortality (30 days to 1 year) may be related to the effects of chronic exposure of the right ventricle to volume overload at systemic pressure.(ABSTRACT TRUNCATED AT 250 WORDS)

Pulmonary artery index. A nonpredictor of operative survival in patients undergoing modified Fontan repair.

The importance of pulmonary artery size and the value of a standardized pulmonary artery index (PAI) in predicting outcome after Fontan's repair have previously been reported and questioned. We retrospectively reviewed 29 patients undergoing modified Fontan repair at The Children's Hospital of Philadelphia to examine the relation between preoperative PAI (determined echocardiographically) and operative mortality. Twenty-four of these 29 patients underwent pulmonary artery augmentation at the time of Fontan repair. PAIs ranged from 48 to 541 mm2/m2. Operative mortality was 21%. PAI ranged from 68 to 233 mm2/m2 in nonsurvivors and from 48 to 541 mm2/m2 in survivors. There was no statistically significant difference in PAI between survivors and nonsurvivors; the lowest PAI associated with survival (48 mm2/m2) was one fourth of the lowest PAI value previously reported. There was a trend, not statistically significant, toward increased survival in those with larger PAIs. We conclude that patients should not be excluded from consideration for Fontan's repair solely on the basis of pulmonary artery size.

Effects of the calcium channel activator BAY-K-8644 on in vitro secretion of calcitonin and parathyroid hormone.

The recently discovered calcium (Ca) channel activator BAY-K-8644 [methyl-1,4-dihydro-2,6-dimethyl-3-nitro-4-(2-trifluoromethylphenyl) pyridine-5-carboxylate], an analog of the calcium channel blockers nifedipine and nitrendipine, was tested to determine its potential for altering hormone secretion in an in vitro system designed to study concurrent secretion of calcitonin (CT) and PTH. Addition of BAY-K-8644 (10(-4)-10(-5) M) to medium (1 mM Ca) bathing baby rat thyroparathyroids enhanced secretion of CT at least 2- to 4-fold and suppressed PTH release by as much as 75-85%. Addition of BAY-K-8644 alone to medium containing high (2.5 mM) Ca did not further enhance the already high rate of CT release, nor did it cause any further suppression of PTH secretion. BAY-K-8644 did not stimulate CT release or suppress PTH release in the absence of medium Ca. Addition of the Ca channel blocker nitrendipine (10(-5) M) inhibited CT release at either 1 or 2.5 mM Ca, and at 1 mM Ca, nitrendipine negated the simulatory effect of 10(-5) M BAY-K-8644 on CT release. However, at 2.5 mM Ca, 10(-5) M BAY-K-8644 reversed the marked inhibitory effect of 10(-5) M nitrendipine on CT release. At 1 mM Ca, PTH secretion was inhibited equally well by BAY-K-8644 and nitrendipine, and both agents together caused a further suppression of PTH release. The results indicate that Ca entry into the thyroid C-cell and parathyroid chief cell may occur via classical voltage-sensitive Ca channels and that the newly described Ca channel activator BAY-K-8644 should prove useful as a probe for studying hormone secretion in Ca-dependent secretory systems.