Thermal convection in rotating spherical geometry: A numerical overview of the transitions from periodic axisymmetric to temporally complex three-dimensional flows.

The aim of this work is to elucidate the type of transitions that take place when the periodic axisymmetric flows, which can set up at the onset of thermal convection in rotating fluid spheres, lose stability and to study the behavior of the new stable velocity fields until the flows become temporally chaotic. The computations for Prandtl numbers Pr=0.715, 0.1, and 0.01 show that when it decreases, the range of stability of these flows becomes narrower because the kinetic energy of the axisymmetric periodic solutions increases very fast, favoring their instability. From the stability analysis and direct three-dimensional simulations it is found that the transition to stable quasiperiodic flows through Neimark-Sacker bifurcations is supercritical when Pr≥0.01. For Pr=0.1 two branches of stable periodic flows emerging from the conduction state have been found due to the proximity to a double Hopf bifurcation. However, only the branches bifurcating from the azimuthal rotating waves are stable at large Rayleigh numbers. Far from this bifurcation the stable flows keep the influence of the axisymmetric dynamics up to large Rayleigh numbers. For small Pr they behave as repeated transients of mixed dynamics, controlled by the azimuthal wave numbers m=0, m=1, and m=2.

Continuation and stability of convective modulated rotating waves in spherical shells.

Modulated rotating waves (MRW), bifurcated from the thermal-Rossby waves that arise at the onset of convection of a fluid contained in a rotating spherical shell, and their stability, are studied. For this purpose, Newton-Krylov continuation techniques are applied. Nonslip boundary conditions, an Ekman number E=10^{-4}, and a low Prandtl number fluid Pr=0.1 in a moderately thick shell of radius ratio η=0.35, differentially heated, are considered. The MRW are obtained as periodic orbits by rewriting the equations of motion in the rotating frame of reference where the rotating waves become steady states. Newton-Krylov continuation allows us to obtain unstable MRW that cannot be found by using only time integrations, and identify regions of multistability. For instance, unstable MRW without any azimuthal symmetry have been computed. It is shown how they become stable in a small Rayleigh-number interval, in which two branches of traveling waves are also stable. The study of the stability of the MRW helps to locate and classify the large sequence of bifurcations, which takes place in the range analyzed. In particular, tertiary Hopf bifurcations giving rise to three-frequency stable solutions are accurately determined.

Cold chain monitoring during cold transportation of human corneas for transplantation.

BACKGROUND: As recommended by international standards the cornea should be maintained in a specific temperature range (2 degrees -8 degrees C) to guarantee its viability. However, there is no standard packaging method to maintain these conditions during transport. Our packaging system is similar to those used by the main eye banks in Spain and elsewhere in Europe. The objective is to monitor the cold chain in the current packaging method to validate the maintenance of temperature within the adequate range for a minimum 24-hour period. METHODS: The effects of the following variables were studied: number and freezing temperature of the cold packs; air volume in the packaging system; position of the cornea in the packaging system; and the wall section of the container. Exterior temperature was maintained constant at 20 degrees to 24 degrees C. The cold chain was monitored using a device that measures temperature continuously and for which a histogram of temperature variation can be downloaded to a computer for further analysis. RESULTS: When the cold packs were frozen to -40 degrees C or the number of cold packs increased to four, the temperature decreased quickly to 0 degrees C and the transport period was not prolonged. The main objective was to improve isolation by reducing inner air volume, and maintaining the position of the cornea in the container. CONCLUSIONS: The currently used cold packaging systems (not frozen, 4 degrees C) do not maintain the temperature within the accepted range for the required distribution period. The improved system maintains the cornea at between 2 degrees C and 6 degrees C for a minimum of 24 hours.

Hepatic xanthine levels as viability predictor of livers procured from non-heart-beating donor pigs.

BACKGROUND: The aim of the present study was to evaluate hepatic content of adenine nucleotides and their degradation products in non-heart-beating donor (NHBD) pigs and its relationship with recipient survival. METHODS: Thirty animals were transplanted with an allograft from NHBDs. After warm ischemia (WI) time (20, 30, or 40 min), cardiopulmonary bypass and normothermic recirculation (NR) were run for 30 min. Afterward, the animals were cooled to 15 degrees C and liver procurement was performed. RESULTS: Survival rate was 100% in the 20WI, 70% in the 30WI, and 50% in the 40WI. Livers from non-surviving animals had higher levels of xanthine after NR than livers from surviving animals. Logistic regression analysis revealed that xanthine at the end of NR was the only variable able to predict survival with a calculated sensitivity of 80% and a specificity of 60%. Prolongation of warm ischemic period leaded to a greater xanthine accumulation as well as increased plasma alpha-glutathione S-transferase levels at reperfusion. Xanthine at NR and alpha-glutathione S-transferase at reperfusion significantly correlated, indicating that donor xanthine contributes to some extent to the severity of the lesion by ischemia-reperfusion. CONCLUSIONS: It is suggested that xanthine content in the donor is able to predict survival after transplantation. Xanthine is significantly involved in the hepatic lesion elicited by warm ischemia and subsequent ischemia-reperfusion associated to liver transplantation from a NHBD.

Thermal Rossby waves in a rotating annulus. Their stability.

Nonlinear thermal convection in a fast rotating annulus about its axis, with slightly inclined ends, radial gravity and heating, is studied numerically for a fluid of Prandtl number sigma=0.7 and different values of the radius ratio and rotation rate. The properties of the rotating waves that appear after the Hopf bifurcation of the conductive state are analyzed. Near the critical Rayleigh number, different types of solutions with the same wave number coexist, and they are classified as a function of their connection with the two types of modes identified in the linear analysis for this Prandtl number. For different rotation rates, the stability of the primary solutions as a function of the radius ratio is also studied. The shape of the stability regions and the type of dominant disturbances that limit these regions are very sensitive to the proximity to the value of the radius ratio for which the type of dominant mode changes.

Oscillatory binary fluid convection in large aspect-ratio containers.

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.

Thermal and inertial modes of convection in a rapidly rotating annulus

The nature of the primary instabilities that arise in a fluid contained in a fast rotating cylindrical annulus with slightly inclined plane top and bottom boundaries, radial gravity, and internal heating is numerically analyzed. It is shown that for moderate and high Prandtl numbers, the onset of convection is described by a competition of azimuthal thermal modes with different radial structure, which dominate in different regions of the parameter space. By the combined effect of the inclined ends and rotation, there are modes that are attached to the heated wall and slanted to the prograde direction of rotation, and others which are straight and fill the convective layer. Nevertheless, for very small Prandtl numbers the velocity field of the dominant modes corresponds essentially to the inertial solution of the Poincare equation, and the temperature perturbation is forced by this velocity field. In addition, a detailed exploration of the critical Rayleigh numbers and precession frequencies of the convective modes versus the radius ratio and the Coriolis parameter, for different Prandtl numbers, is presented.

L-arginine reduces liver and biliary tract damage after liver transplantation from non-heart-beating donor pigs.

BACKGROUND: To evaluate whether L-arginine reduces liver and biliary tract damage after transplantation from non heart-beating donor pigs. METHODS: Twenty-five animals received an allograft from non-heart-beating donors. After 40 min of cardiac arrest, normothermic recirculation was run for 30 min. The animals were randomly treated with L-arginine (400 mg x kg(-1) during normothermic recirculation) or saline (control group). Then, the animals were cooled and their livers were transplanted after 6 hr of cold ischemia. The animals were killed on the 5th day, liver damage was assessed on wedged liver biopsies by a semiquantitative analysis and by morphometric analysis of the necrotic areas, and biliary tract damage by histological examination of the explanted liver. RESULTS: Seventeen animals survived the study period. The histological parameters assessed (sinusoidal congestion and dilatation, sinusoidal infiltration by polymorphonuclear cells and lymphocytes, endothelitis, dissociation of liver cell plates, and centrilobular necrosis) were significantly worse in the control group. The necrotic area affected 15.9 +/- 14.5% of the liver biopsies in the control group and 3.7 +/- 3.1% in the L-arginine group (P<0.05). Six of eight animal in the control group and only one of eight survivors in the L-arginine group developed ischemic cholangitis (P<0.01). L-Arginine administration was associated with higher portal blood flow (676.9 +/- 149.46 vs. 475.2 +/- 205.6 ml x min x m(-2); P<0.05), higher hepatic hialuronic acid extraction at normothermic recirculation (38.8 +/- 53.7% vs. -4.2 +/- 18.2%; P<0.05) and after reperfusion (28.6 +/- 55.5% vs. -10.9 +/- 15.5%; P<0.05) and lower levels of alpha-glutation-S-transferase at reperfusion (1325 +/- 1098% respect to baseline vs. 6488 +/- 5612%; P<0.02). CONCLUSIONS: L-Arginine administration during liver procurement from non heart beating donors prevents liver and biliary tract damage.

Onset of oscillatory binary fluid convection in finite containers.

The onset of oscillatory convection in binary fluid mixtures in a two-dimensional domain with realistic boundary conditions on all boundaries is determined as a function of the fluid parameters and the aspect ratio Gamma of the container. The first unstable mode has either odd or even parity under left-right reflection. Depending on Gamma and the separation ratio S, this mode has the form of a standing wave, or a "chevron," consisting of a pair of waves propagating outwards from the cell center (or, in some cases, inwards towards it). Codimension--two points at which odd and even parity modes are simultaneously marginally stable are determined, as are various Takens-Bogdanov points. For fixed Sinfinity, and to the gap (in Rayleigh number and oscillation frequency) between successively unstable modes. The results quantify the parameter regime in which the weakly nonlinear dynamics of the system can be described in terms of the interaction of the first odd and even parity oscillatory modes.

Subharmonic instabilities of Tollmien-Schlichting waves in two-dimensional Poiseuille flow.

The stability of the upper branch of shear traveling waves in two-dimensional Poiseuille flow, when the total flux through the channel is held constant, is considered. Taking into account the length of the periodic channel, perturbations of the same wave number (superharmonic), and different wave number (subharmonic) of the uniform wave trains are imposed. We mainly consider channels long enough to contain M=4 and M=8 basic wavelengths. In these cases, subharmonic bifurcations are found to be dominant except in a small region of parameters. From this type of bifurcation, we show that if the wave number is decreased, the periodic train of finite amplitude waves evolves continuously towards the stable localized wave packets obtained in long channels by other authors and whose existence has been associated to the vicinity of an inverted Hopf bifurcation. Depending on the basic wave number of the periodic train destabilized, different types of solutions for a given length of the channel can be obtained. Furthermore, for moderate Reynolds numbers, configurations of linearly stable wave trains exist, provided that their basic wave number is alpha approximately 1.5.

Evaluation of ischemic injury during liver procurement from non-heart-beating donors.

UNLABELLED: The aim of this study was to assess liver viability after different periods of cardiac arrest and the predictive value of two markers of ischemia-reperfusion injury. METHODS: A pig liver transplantation model of non-heart-beating donors was studied. Four donor groups were designed; three groups were submitted to different periods of cardiac arrest (20, 30 and 40 min), and the fourth group served as the control group (without cardiac arrest). In the non-heart-beating donor groups, normothermic recirculation was established 30 min prior to total body cooling. Aminotransferase, alpha-glutathione-S-transferase, and hyaluronic acid determinations as well as liver biopsies, were serially performed. RESULTS: Although hepatocellular function could be preserved after 40 min of cardiac arrest, histological lesions at 5 days were considered irreversible due to the presence of a necrotic biliary tract. An overall significant relationship was found between the time period of cardiac arrest (20, 30 or 40 min) and the levels of hyaluronic acid (p = 0.004) or alpha-glutathione-S-transferase (p = 0.01) obtained during liver procurement and transplantation. CONCLUSIONS: The period of cardiac arrest is the determinant factor of liver viability after liver transplantation from non-heart-beating donors. As early markers of endothelial or hepatocellular damage, hyaluronic acid or alpha-glutathione-S-transferase levels may help to evaluate the ischemic injury of a potential donor.