SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.

Hypothesis: Computed tomography (CT) and ultrasonography (US) do not improve the overall diagnostic accuracy for acute appendicitis.

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Perforated appendicitis, as defined by a visible hole in the appendix or an appendicolith free within the abdomen, carries significant morbidity in the pediatric population. Accurate diagnosis is challenging as there is no single symptom or sign that accurately predicts perforated appendicitis. Younger patients and those with increased duration of symptoms are at higher risk of perforated appendicitis. Elevated leukocytosis, bandemia, high C-reactive protein, hyponatremia, ultrasound, and CT are all useful tools in diagnosis. Distinguishing patients with perforation from those without is important given the influence of a perforation diagnosis on the management of the patient. Treatment for perforated appendicitis remains controversial as several options exist, each with its indications and merits, illustrating the complexity of this disease process. Patients may be managed non-operatively with antibiotics, with or without interval appendectomy. Patients may also undergo appendectomy early in the course of their index hospitalization. Factors known to predict failure of non-operative management include appendicolith, leukocytosis greater than 15,000 white blood cells per microliter, increased bands, and CT evidence of disease beyond the right lower quadrant. In this review, the indications and benefits of each treatment strategy will be discussed and an algorithm to guide treatment decisions will be proposed.

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