The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Assessing the extent of colon lengthening due to splenic flexure mobilization techniques: a cadaver study

CONTEXT: Failure of a colorectal anastomosis represents a life-threatening complication of colorectal surgery. Splenic flexure mobilization may contribute to reduce the occurrence of anastomotic complications due to technical flaws. There are no published reports measuring the impact of splenic flexure mobilization on the length of mobilized colon viable to construct a safe colorectal anastomosis. OBJECTIVE: The aim of the present study was to determine the effect of two techniques for splenic flexure mobilization on colon lengthening during open left-sided colon surgery using a cadaver model. DESIGN: Anatomical dissections for left colectomy and colorectal anastomosis at the sacral promontory level were conducted in 20 fresh cadavers by the same team of four surgeons. The effect of partial and full splenic flexure mobilization on the extent of mobilized left colon segment was determined. SETTING: University of Sao Paulo Medical School, Sao Paulo, SP, Brazil. Tertiary medical institution and university hospital. PARTICIPANTS: A team of four surgeons operated on 20 fresh cadavers. RESULTS: The length of resected left colon enabling a tension-free colorectal anastomosis at the level of sacral promontory achieved without mobilizing the splenic flexure was 46.3 (35-81) cm. After partial mobilization of the splenic flexure, an additionally mobilized colon segment measuring 10.7 (2-30) cm was obtained. After full mobilization of the distal transverse colon, a mean 28.3 (10-65) cm segment was achieved. CONCLUSION: Splenic flexure mobilization techniques are associated to effective left colon lengthening for colorectal anastomosis. This result may contribute to decision-making during rectal surgery and low colorectal and coloanal anastomosis.

Biphasic positive airway pressure minimizes biological impact on lung tissue in mild acute lung injury independent of etiology

Abstract Introduction Biphasic positive airway pressure (BIVENT) is a partial support mode that employs pressure-controlled, time-cycled ventilation set at two levels of continuous positive airway pressure with unrestricted spontaneous breathing. BIVENT can modulate inspiratory effort by modifying the frequency of controlled breaths. Nevertheless, the optimal amount of inspiratory effort to improve respiratory function while minimizing ventilator-associated lung injury during partial ventilatory assistance has not been determined. Furthermore, it is unclear whether the effects of partial ventilatory support depend on acute lung injury (ALI) etiology. This study aimed to investigate the impact of spontaneous and time-cycled control breaths during BIVENT on the lung and diaphragm in experimental pulmonary (p) and extrapulmonary (exp) ALI. Methods This was a prospective, randomized, controlled experimental study of 60 adult male Wistar rats. Mild ALI was induced by Escherichia coli lipopolysaccharide either intratracheally (ALIp) or intraperitoneally (ALIexp). After 24 hours, animals were anesthetized and further randomized as follows: (1) pressure-controlled ventilation (PCV) with tidal volume (Vt) = 6 ml/kg, respiratory rate = 100 breaths/min, PEEP = 5 cmH2O, and inspiratory-to-expiratory ratio (I:E) = 1:2; or (2) BIVENT with three spontaneous and time-cycled control breath modes (100, 75, and 50 breaths/min). BIVENT was set with two levels of CPAP (Phigh = 10 cmH2O and Plow = 5 cmH2O). Inspiratory time was kept constant (Thigh = 0.3 s). Results BIVENT was associated with reduced markers of inflammation, apoptosis, fibrogenesis, and epithelial and endothelial cell damage in lung tissue in both ALI models when compared to PCV. The inspiratory effort during spontaneous breaths increased during BIVENT-50 in both ALI models. In ALIp, alveolar collapse was higher in BIVENT-100 than PCV, but decreased during BIVENT-50, and diaphragmatic injury was lower during BIVENT-50 compared to PCV and BIVENT-100. In ALIexp, alveolar collapse during BIVENT-100 and BIVENT-75 was comparable to PCV, while decreasing with BIVENT-50, and diaphragmatic injury increased during BIVENT-50. Conclusions In mild ALI, BIVENT had a lower biological impact on lung tissue compared to PCV. In contrast, the response of atelectasis and diaphragmatic injury to BIVENT differed according to the rate of spontaneous/controlled breaths and ALI etiology.