The distribution of fluid forces on model arterial endothelium using computational fluid dynamics,

Numerical calculations are used in conjunction with linear perturbation theory to analyze the problem of laminar flow of an incompressible fluid over a wavy surface which approximates a monolayer of vascular endothelial cells. These calculations model flow conditions in an artery very near the vessel wall at any instant in time, providing a description of the velocity field with detail that would be difficult to identify experimentally. The surface pressure and shear stress distributions are qualitatively similar for linear theory and numerical computations. However, the results diverge as the amplitude of surface undulation is increased. The shear stress gradient along the cell model surface is reduced for geometries which correspond to aligned endothelial cells (versus nonaligned geometries). I Introduction The vascular endothelium is the simple epithelium that lines the cardiovascular system. It consists of a cellular monolayer which rests on a complicated matrix of cells and intercellular material. Intact endothelium provides a selectively permeable barrier to the passage of macromolecules from the bloodspace to the extravascular space. Moreover, the vascular endothelium bears the shear stress imparted by blood flow. The structure and function of the monolayer is affected by these mechanical factors (see A detailed description of the flow is needed. An endothelial cell in vivo witnesses flow which passes in rhythmic waves. The cells are only 1-2 fim thick and 20-50 ]x,m in the circumferential and axial dimensions. They are primarily affected by detailed flow behavior very near the wall. In this region, the fluid velocity profile is nearly linear, although the magnitude of the average velocity may vary by a factor of four or more from systole to diastole, and from point to point on the microscopically rough surface. Because of the small size of endothelial cells, flow at any instant may be considered quasisteady near the wall, as described by the local linear shear flow. One of the most difficult problems in fluid mechanics is studying flow details near a rough surface. The disturbed wall region is typically buried inside a boundary layer or is difficult to access in experiments. Additional complications include: [Davics et al. PNAS X3:2114 tiny dimensions (typically microns), wall probe interference effects, and the intrinsic difficulty of accurately measuring wall shear stress. Previous studies demonstrate that numerical solutions of the Navier-Stokes equations yield accurate predictions of flow characteristics in such circumstances • there is increased ATP utilization in cells exposed to shear stress, presumably in part due to contracting stress fibers 9 the permeability of a monolayer with no previous exposure to shear stress is transiently and acutely increased in response to flow DNA synthesis is altered in cells by exposure to flow affecting gene expression, and apparently producing a different phenotype. Few (if any) other cells in the body experience shearing forces of similar magnitude on only one side. Thus, it is difficult to identify analogous cellular models for comparison. An unrelated phenotypic modulation has been observed in microvessel endothelial cells in response to chemical factors In order to understand how shear stress produces such profound effects in endothelial cells, the detailed distribution of forces on a cell and monolayer of cells must first be known. In early studies, investigators did not consider cell shape. The average shearing force imparted by bulk fluid flow was considered determinant: high shear stress caused direct desquamation, and low shear stress caused concentration polarization effects at the wall The wavy wall problem has been studied in two dimensions by others Recent studies include numerical treatments of low Re flows over objects in shear flows. In one study, finite elements are used to estimate forces acting on a thrombus II Computational Methods A model surface was chosen which represents the cell monolayer (see Re Vw = 0 (2) The unknowns are the vector velocity u and the pressure/?. The single parameter appearing is the Reynold's number, Re = vr\ 2 /v, where a is the shear rate in the linear shear flow far from the surface, and rj is the surface undulation amplitude (characteristic length scale of the problem). The kinematic viscosity of the fluid is v = /x/p, where p is the fluid density and ix is the fluid viscosity. The equations are parabolic so velocity boundary conditions must be provided on all sides of the computational domain. The complete theoretical solution is included in the Appendix Our calculations simulate conditions in large arteries (such as the aorta) very near the vessel wall at any instant in time. The upper boundary can be represented as a shear flow at infinite distance from the surface. However, the computational code did not explicitly provide for boundary conditions at infinity. Instead we specified the upper boundary to be a rigid surface which is moved far enough away (at least 4 times the cell surface modulation amplitude) so that wall effects are no longer important. The velocity at the upper surface is fixed at the value corresponding to a linear shear flow field. The cell surface is the lower boundary of the domain. It is rigid and extends infinitely in x and z. Thus, the solution is determined by solving for one full period of the cell model surface in the relevant directions {x and z). Boundary conditions are expressed below: \u\ y^a> = ay (shear flow at large distance) \u\y= y =0 (zero velocity at wall) where a is the undisturbed shear rate far away from the wall. A shear rate of a = 800 s~' was specified for all calculations. Unsteady motion dynamics for physiologic frequencies are such that a quasi-steady approximation can be made (a = hsfcJv = 0.1 to 0.001). The computational code NEKTON was used for numerical solution of the problem 310/Vol. 114, AUGUST 1992 Transactions of the ASME surface as the lower boundary of the computational domain. NEKTON has powerful pre-and post-processing packages for mesh generation and visualization of results. The code runs on a wide variety of computers (from workstations to supercomputers). Thus, computational experiments can be performed on smaller machines, while production runs can be directed to the most efficient computers available The spectral element method for partial differential equations is the basis for spatial discretization. The method is summarized briefly in what follows. For an extensive description, one should see references 29 and 31. Spectral elements combine high-order (spectral) accuracy with the geometrical flexibility of low order finite-element methods. The computational domain is divided into K nondegenerate macro-quadrangles (spectral elements). In our problem, three-dimensional domains were broken up into "bricks," in which the two horizontal parallel faces are nondegenerate quadrangles The data, geometry, and solution, are approximated by high order polynomial expansions within each macro-element. A local Cartesian mesh is constructed within each element which corresponds to N x N x N tensor-product Gauss-Lobatto Legendre collocation points. The Gauss-Lobatto points are clustered near elemental boundaries; an arrangement which gives accurate approximation, and favorable interpolation and quadrature properties. Dependent variables are expanded in terms of (N -l) th order polynomial Lagrangian interpolants (through the Gauss-Lobatto Legendre collocation points) Spatially discrete equations are generated by inserting assumed forms of dependent variables into the governing equations, and requiring that the residual vanish in some integral and weighted sense. The computed numerical variables correspond to values occurring at the collocation points of the mesh. Convergence is obtained by increasing the number of macro-elements (K) or the order of the interpolants (TV) in the elements. The error decreases algebraically (like K~N) as K is increased; and exponentially for smooth solutions (like e~a N ) as N is increased Ill Results An analytical solution for linearized flow over a wavy wall is given in the Appendix Ty X is the normalized surface shear stress in the x-direction; and r yz is the normalized surface shear stress in the z-direction. The term jxa is the mean wall shear stress imposed by flow far (i.e., many times the cell height) from the endothelial surface. The solution predicts: 1. The surface shear stress in the x-direction consists of the sum of the average shear stress imposed by flow and a spatially varying stress perturbation due to cell shape. The magnitude of the shear stress perturbation depends on q and TJ/X X . AS T)/\ X (dimensionless surface amplitude) increases, the perturbation increases linearly. For q » 1 it is proportional to q. T yx is in phase with surface variations in x and z-it is maximum at the highest point on the cell surface, and minimum at the lowest point on the surface. 2. The presence of surface waviness introduces a lateral shear stress perturbation which is linear with rj/\ x . It is caused by the transverse flow away from surface peaks and toward surface valleys. As q becomes large (» 1), there is no dependence on q. T yz is 7r/2 out of phase with the surface waviness in the streamwise and transverse directions. It is maximum or minimum at points of maximum surface slope. 3. The pressure perturbation is linear with ^A*, but does not depend on q. It is asymmetric along the cell longitudinal axis, tending to increase the pressure on the proximal side and reduce it on the distal side. The pressure is 7r/2 out of phase with the surface variations in the direction of flow. Pressure is maximum or minimum at points of maximum slope in the cos(ax)cos(/3z) (5) fi ow direction. Numerical and analytical computations were compared for For a limited range, numerical results and linear theory predictions agree (not illustrated). Both numerical and theoretical methods predict that the wall shear stress r yx is maximum at the highest points of the coordinate surface, and minimum at the lowest points. The pressure distribution is 7r/2 out of phase in the direction of flow, and the wall shear stress and pressure distributions are periodic. Numerical magnitudes no longer agree with linear theory after the onset of separated flow. Maximum (r yXimax ) and minimum (r yx , m i n ) shear stress magnitudes for both numerical and analytical solutions are plotted in Figs. 5(a) and 6(a) for a range of parameter values. Groups of points corresponding to a particular geometry (fixed length/ width value) fall along the same line when shear stress and pressure are plotted vs. surface amplitude We did not resolve the exact amplitude where recirculation begins; however, the range which contains the critical amplitude is recorded in the table in •Transverse ribs **Vortices do not appear: streamwise ribs The analytical solution for surface pressure predicts a linear dependence on ?)/X x , and no dependence on q. The numerical result exhibits dependence on q\ namely, the slope increases with q IV Discussion The flow fields predicted by the numerical and analytical solutions are qualitatively similar. The wall shear stress and pressure distributions vary periodically at the wavy wall surface. However, the results from the two methods diverge as the amplitude of the surface waviness increases. ear theory predictions can be observed by comparing surface pressure distributions • a departure from linear growth of peak-to-peak pressure. • variation in the phase of pressure distribution. • contributions from higher harmonics of the pressure distribution. 9 dependence on the length/width ratio (parameter q). Others have obtained similar predictions At the highest surface points, the wall shear stress grows almost linearly with increasing surface amplitude as predicted by linear theory. Flow acceleration occurs along streamlines toward the peaks due to the constraint provided by the continuity equation. These processes are different than those producing flow separation in the lower surface regions. Nonuniform shear stress gradients of significant magnitude across a cell surface could be of potential importance for explaining flow induced morphological changes. The forces which result from a cell-to-cell variation on the order of the perturbation shear stress are sufficient to disturb protein-protein interactions. Bell [1] has determined that a noncovalent interaction is disrupted by a critical force of 10~5 dyne. The difference in shear force on 2 adjacent cells in laminar flow can be of order 10~4dyne, which corresponds to 10 protein-protein interactions. Experimental studies of others indicate that a force of ~ 1 dyne (10 5 protein-protein interactions) can detach a cell from a monolayer The predicted forces acting on the aligned monolayer are reduced in comparison to nonaligned endothelium. For a surface approximating a nonaligned monolayer, the perturbation shear stress can be as large as 34 percent of the average shear stress imposed by the primary flow. This decreases to 20 percent for aligned monolayers since the height/length ratio is reduced (essentially, the surface is less "bumpy"). Perhaps the monolayer is able to achieve stability by reconfiguring the actin filament system so that stress fibers attach to the apical membrane. Nonaligned cells do not have stress fibers in the proper arrangement to experience this stabilizing effect. Modeling the distribution of forces on cells also aids in understanding the role of shear stress in the pathophysiology of atherosclerosis. Endothelium exposed to large shear stress gradients displays dramatic changes in cell shape, density, and rate of division Acknowledgments We thank Prof. A. T. Patera of M.I.T. and Dr. Einar Ronquist of Nektonics for assistance with the computational program

Precision Measurement of the 29Si, 33S, and 36Cl Binding Energies

The binding energies of 29Si, 33S, and 36Cl have been measured with a relative uncertainty $< 0.59 \times 10^{-6}$ using a flat-crystal spectrometer. The unique features of these measurements are 1) nearly perfect crystals whose lattice spacing is known in meters, 2) a highly precise angle scale that is derived from first principles, and 3) a gamma-ray measurement facility that is coupled to a high flux reactor with near-core source capability. The binding energy is obtained by measuring all gamma-rays in a cascade scheme connecting the capture and ground states. The measurements require the extension of precision flat-crystal diffraction techniques to the 5 to 6 MeV energy region, a significant precision measurement challenge. The binding energies determined from these gamma-ray measurements are consistent with recent highly accurate atomic mass measurements within a relative uncertainty of $4.3 \times 10^{-7}$. The gamma-ray measurement uncertainties are the dominant contributors to the uncertainty of this consistency test. The measured gamma-ray energies are in agreement with earlier precision gamma-ray measurements.Comment: 13 pages, 4 figure

Power laws in microrheology experiments on living cells: comparative analysis and modelling

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a micrometric bead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e(\omega)$ is retrieved. Both $J(t)$ and $G_e(\omega)$ exhibit power law behavior: $J(t)= A(t/t_0)^\alpha$ and $\bar G_e(\omega)\bar = G_0 (\omega/\omega_0)^\alpha$, with the same exponent $\alpha\approx 0.2$. This power law behavior is very robust ; $\alpha$ is distributed over a narrow range, and shows almost no dependance on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors $A_0$ and $G_0$appear very sensitive to these parameters. Whereas the exponents $\alpha$ are normally distributed over the cell population, the prefactors $A_0$ and $G_0$ follow a log-normal repartition. These results are compared with other data published in the litterature. We propose a global interpretation, based on a semi-phenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: $\tau_m \approx 1000$ s.Comment: 47 pages, 14 figures // v2: PDF file is now Acrobat Reader 4 (and up) compatible // v3: Minor typos corrected - The presentation of the model have been substantially rewritten (p. 17-18), in order to give more details - Enhanced description of protocols // v4: Minor corrections in the text : the immersion angles are estimated and not measured // v5: Minor typos corrected. Two references were clarifie

Effectiveness of physiotherapy exercise following hip arthroplasty for osteoarthritis: a systematic review of clinical trials

Background: Physiotherapy has long been a routine component of patient rehabilitation following hip joint replacement. The purpose of this systematic review was to evaluate the effectiveness of physiotherapy exercise after discharge from hospital on function, walking, range of motion, quality of life and muscle strength, for osteoarthritic patients following elective primary total hip arthroplasty. Methods: Design: Systematic review, using the Cochrane Collaboration Handbook for Systematic Reviews of Interventions and the Quorom Statement. Database searches: AMED, CINAHL, EMBASE, KingsFund, MEDLINE, Cochrane library (Cochrane reviews, Cochrane Central Register of Controlled Trials, DARE), PEDro, The Department of Health National Research Register. Handsearches: Physiotherapy, Physical Therapy, Journal of Bone and Joint Surgery (Britain) Conference Proceedings. No language restrictions were applied. Selection: Trials comparing physiotherapy exercise versus usual/standard care, or comparing two types of relevant exercise physiotherapy, following discharge from hospital after elective primary total hip replacement for osteoarthritis were reviewed. Outcomes: Functional activities of daily living, walking, quality of life, muscle strength and range of hip joint motion. Trial quality was extensively evaluated. Narrative synthesis plus meta-analytic summaries were performed to summarise the data. Results: 8 trials were identified. Trial quality was mixed. Generally poor trial quality, quantity and diversity prevented explanatory meta-analyses. The results were synthesised and meta-analytic summaries were used where possible to provide a formal summary of results. Results indicate that physiotherapy exercise after discharge following total hip replacement has the potential to benefit patients. Conclusion: Insufficient evidence exists to establish the effectiveness of physiotherapy exercise following primary hip replacement for osteoarthritis. Further well designed trials are required to determine the value of post discharge exercise following this increasingly common surgical procedure

Production of Medical Radioisotopes with High Specific Activity in Photonuclear Reactions with γ\gamma Beams of High Intensity and Large Brilliance

We study the production of radioisotopes for nuclear medicine in $(\gamma,x{\rm n}+y{\rm p})$ photonuclear reactions or ($\gamma,\gamma'$) photoexcitation reactions with high flux [($10^{13}-10^{15}$)$\gamma$/s], small diameter $\sim (100 \, \mu$m$)^2$ and small band width ($\Delta E/E \approx 10^{-3}-10^{-4}$) $\gamma$ beams produced by Compton back-scattering of laser light from relativistic brilliant electron beams. We compare them to (ion,$x$n$+ y$p) reactions with (ion=p,d,$\alpha$) from particle accelerators like cyclotrons and (n,$\gamma$) or (n,f) reactions from nuclear reactors. For photonuclear reactions with a narrow $\gamma$ beam the energy deposition in the target can be managed by using a stack of thin target foils or wires, hence avoiding direct stopping of the Compton and pair electrons (positrons). $(\gamma,\gamma')$ isomer production via specially selected $\gamma$ cascades allows to produce high specific activity in multiple excitations, where no back-pumping of the isomer to the ground state occurs. We discuss in detail many specific radioisotopes for diagnostics and therapy applications. Photonuclear reactions with $\gamma$ beams allow to produce certain radioisotopes, e.g. $^{47}$Sc, $^{44}$Ti, $^{67}$Cu, $^{103}$Pd, $^{117m}$Sn, $^{169}$Er, $^{195m}$Pt or $^{225}$Ac, with higher specific activity and/or more economically than with classical methods. This will open the way for completely new clinical applications of radioisotopes. For example $^{195m}$Pt could be used to verify the patient's response to chemotherapy with platinum compounds before a complete treatment is performed. Also innovative isotopes like $^{47}$Sc, $^{67}$Cu and $^{225}$Ac could be produced for the first time in sufficient quantities for large-scale application in targeted radionuclide therapy.Comment: submitted to Appl. Phys.

Atomic structures of TDP-43 LCD segments and insights into reversible or pathogenic aggregation.

The normally soluble TAR DNA-binding protein 43 (TDP-43) is found aggregated both in reversible stress granules and in irreversible pathogenic amyloid. In TDP-43, the low-complexity domain (LCD) is believed to be involved in both types of aggregation. To uncover the structural origins of these two modes of β-sheet-rich aggregation, we have determined ten structures of segments of the LCD of human TDP-43. Six of these segments form steric zippers characteristic of the spines of pathogenic amyloid fibrils; four others form LARKS, the labile amyloid-like interactions characteristic of protein hydrogels and proteins found in membraneless organelles, including stress granules. Supporting a hypothetical pathway from reversible to irreversible amyloid aggregation, we found that familial ALS variants of TDP-43 convert LARKS to irreversible aggregates. Our structures suggest how TDP-43 adopts both reversible and irreversible β-sheet aggregates and the role of mutation in the possible transition of reversible to irreversible pathogenic aggregation

Prevalence of chronic fatigue syndrome in metropolitan, urban, and rural Georgia

© 2007 Reeves et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Massive stars as thermonuclear reactors and their explosions following core collapse

Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiescent conditions are discussed next. In the subsequent core-collapse phase, neutronization due to electron capture from the top of the Fermi sea in a degenerate core takes place. The expected signal of neutrinos from a nearby supernova is calculated. The supernova often explodes inside a dense circumstellar medium, which is established due to the progenitor star losing its outermost envelope in a stellar wind or mass transfer in a binary system. The nature of the circumstellar medium and the ejecta of the supernova and their dynamics are revealed by observations in the optical, IR, radio, and X-ray bands, and I discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry" Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure