Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation. These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.

Identification of vascular endothelial genes differentially responsive to fluid mechanical stimuli: cyclooxygenase-2, manganese superoxide dismutase, and endothelial cell nitric oxide synthase are selectively up-regulated by steady laminar shear stress.

Early atherosclerotic lesions develop in a topographical pattern that strongly suggests involvement of hemodynamic forces in their pathogenesis. We hypothesized that certain endothelial genes, which exhibit differential responsiveness to distinct fluid mechanical stimuli, may participate in the atherogenic process by modulating, on a local level within the arterial wall, the effects of systemic risk factors. A differential display strategy using cultured human endothelial cells has identified two genes, manganese superoxide dismutase and cyclooxygenase-2, that exhibit selective and sustained up-regulation by steady laminar shear stress (LSS). Turbulent shear stress, a nonlaminar fluid mechanical stimulus, does not induce these genes. The endothelial form of nitric oxide synthase also demonstrates a similar LSS-selective pattern of induction. Thus, three genes with potential atheroprotective (antioxidant, antithrombotic, and antiadhesive) activities manifest a differential response to distinct fluid mechanical stimuli, providing a possible mechanistic link between endothelial gene expression and early events in atherogenesis. The activities of these and other LSS-responsive genes may have important implications for the pathogenesis and prevention of atherosclerosis.

Biomechanical activation of vascular endothelium as a determinant of its functional phenotype

One of the striking features of vascular endothelium, the single-cell-thick lining of the cardiovascular system, is its phenotypic plasticity. Various pathophysiologic factors, such as cytokines, growth factors, hormones, and metabolic products, can modulate its functional phenotype in health and disease. In addition to these humoral stimuli, endothelial cells respond to their biomechanical environment, although the functional implications of this biomechanical paradigm of activation have not been fully explored. Here we describe a high-throughput genomic analysis of modulation of gene expression observed in cultured human endothelial cells exposed to two well defined biomechanical stimuli—a steady laminar shear stress and a turbulent shear stress of equivalent spatial and temporal average intensity. Comparison of the transcriptional activity of 11,397 unique genes revealed distinctive patterns of up- and down-regulation associated with each type of stimulus. Cluster analyses of transcriptional profiling data were coupled with other molecular and cell biological techniques to examine whether these global patterns of biomechanical activation are translated into distinct functional phenotypes. Confocal immunofluorescence microscopy of structural and contractile proteins revealed the formation of a complex apical cytoskeleton in response to laminar shear stress. Cell cycle analysis documented different effects of laminar and turbulent shear stresses on cell proliferation. Thus, endothelial cells have the capacity to discriminate among specific biomechanical forces and to translate these input stimuli into distinctive phenotypes. The demonstration that hemodynamically derived stimuli can be strong modulators of endothelial gene expression has important implications for our understanding of the mechanisms of vascular homeostasis and atherogenesis.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Fluid shear stress inhibits TNF-α activation of JNK but not ERK1/2 or p38 in human umbilical vein endothelial cells: Inhibitory crosstalk among MAPK family members

Atherosclerosis preferentially occurs in areas of turbulent flow and low fluid shear stress, whereas laminar flow and high shear stress are atheroprotective. Inflammatory cytokines, such as tumor necrosis factor-α (TNF-α) and IL-1 stimulate expression of endothelial cell (EC) genes that may promote atherosclerosis. TNF-α and IL-1 regulate gene expression in ECs, in part, by stimulating mitogen-activated protein kinases (MAPK), which phosphorylate transcription factors. We hypothesized that steady laminar flow inhibits cytokine-mediated activation of MAPK in EC. To test this hypothesis, we determined the effects of flow (shear stress = 12 dynes/cm2) on TNF-α and IL-1-stimulated activity of three MAPK in human umbilical vein ECs (HUVEC): extracellular signal-regulated kinase (ERK1/2), p38, and c-Jun N-terminal kinase (JNK). Flow alone stimulated ERK1/2 and p38 activity but decreased JNK activity compared with static controls. TNF-α or IL-1 alone activated ERK1/2, p38, and JNK maximally at 15 min in HUVEC. Preexposing HUVEC for 10 min to flow inhibited TNF-α and IL-1 activation of JNK by 46% and 49%, respectively, but had no significant effect on ERK1/2 or p38 activation. Incubation of HUVEC with PD98059, which inhibits flow-mediated ERK1/2 activation, prevented flow from inhibiting cytokine activation of JNK. Phorbol 12-myristate 13-acetate, which strongly activates ERK1/2, also inhibited TNF-α activation of JNK. These findings indicate that fluid shear stress inhibits TNF-α-mediated signaling events in HUVEC via the activation of the ERK1/2 signaling pathway. Inhibition of TNF-α signal transduction represents a mechanism by which steady laminar flow may exert atheroprotective effects on the endothelium.