First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic

Changes in the gastric enteric nervous system and muscle: A case report on two patients with diabetic gastroparesis

<p>Abstract</p> <p>Background</p> <p>The pathophysiological basis of diabetic gastroparesis is poorly understood, in large part due to the almost complete lack of data on neuropathological and molecular changes in the stomachs of patients. Experimental models indicate various lesions affecting the vagus, muscle, enteric neurons, interstitial cells of Cajal (ICC) or other cellular components. The aim of this study was to use modern analytical methods to determine morphological and molecular changes in the gastric wall in patients with diabetic gastroparesis.</p> <p>Methods</p> <p>Full thickness gastric biopsies were obtained laparoscopically from two gastroparetic patients undergoing surgical intervention and from disease-free areas of control subjects undergoing other forms of gastric surgery. Samples were processed for histological and immunohistochemical examination.</p> <p>Results</p> <p>Although both patients had severe refractory symptoms with malnutrition, requiring the placement of a gastric stimulator, one of them had no significant abnormalities as compared with controls. This patient had an abrupt onset of symptoms with a relatively short duration of diabetes that was well controlled. By contrast, the other patient had long standing brittle and poorly controlled diabetes with numerous episodes of diabetic ketoacidosis and frequent hypoglycemic episodes. Histological examination in this patient revealed increased fibrosis in the muscle layers as well as significantly fewer nerve fibers and myenteric neurons as assessed by PGP9.5 staining. Further, significant reduction was seen in staining for neuronal nitric oxide synthase, heme oxygenase-2, tyrosine hydroxylase as well as for c-KIT.</p> <p>Conclusion</p> <p>We conclude that poor metabolic control is associated with significant pathological changes in the gastric wall that affect all major components including muscle, neurons and ICC. Severe symptoms can occur in the absence of these changes, however and may reflect vagal, central or hormonal influences. Gastroparesis is therefore likely to be a heterogeneous disorder. Careful molecular and pathological analysis may allow more precise phenotypic differentiation and shed insight into the underlying mechanisms as well as identify novel therapeutic targets.</p