An introduction to heat transfer

Solar Engineering Of Thermal Processes

Frank’s Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload.

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The arterial Windkessel

Infusion Nursing Standards of Practice

Discoveries leading to an improved understanding of immune surveillance of the central nervous system (CNS) have repeatedly provoked dismissal of the existence of immune privilege of the CNS. Recent rediscoveries of lymphatic vessels within the dura mater surrounding the brain, made possible by modern live-cell imaging technologies, have revived this discussion. This review emphasizes the fact that understanding immune privilege of the CNS requires intimate knowledge of its unique anatomy. Endothelial, epithelial and glial brain barriers establish compartments in the CNS that differ strikingly with regard to their accessibility to immune-cell subsets. There is a unique system of lymphatic drainage from the CNS to the peripheral lymph nodes. We summarize current knowledge on the cellular and molecular mechanisms involved in immune-cell trafficking and lymphatic drainage from the CNS, and we take into account differences in rodent and human CNS anatomy.

The movers and shapers in immune privilege of the CNS

Transport of solutes has been observed in the spaces surrounding cerebral arteries and veins. Indeed, transport has been found in opposite directions in two different spaces around arteries. These findings have motivated hypotheses of bulk flow within these spaces. The glymphatic circulation hypothesis involves flow of cerebrospinal fluid from the cortical subarachnoid space to the parenchyma along the paraarterial (extramural, Virchow–Robin) space around arteries, and return flow to the cerebrospinal fluid (CSF) space via paravenous channels. The second hypothesis involves flow of interstitial fluid from the parenchyma to lymphatic vessels along basement membranes between arterial smooth muscle cells. This article evaluates the plausibility of steady, pressure-driven flow in these channels with one-dimensional branching models. According to the models, the hydraulic resistance of arterial basement membranes is too large to accommodate estimated interstitial perfusion of the brain, unless the flow empties to lymphatic ducts after only several generations (still within the parenchyma). The estimated pressure drops required to drive paraarterial and paravenous flows of the same magnitude are not large, but paravenous flow back to the CSF space means that the total pressure difference driving both flows is limited to local pressure differences among the different CSF compartments, which are estimated to be small. Periarterial flow and glymphatic circulation driven by steady pressure are both found to be implausible, given current estimates of anatomical and fluid dynamic parameters.

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Is bulk flow plausible in perivascular, paravascular and paravenous channels?

Wall shear stress (WSS) on anchored cells affects their responses, including cell proliferation and morphology. In this study, the effects of the directionality of pulsatile WSS on endothelial cell proliferation and morphology were investigated for cells grown in a Petri dish orbiting on a shaker platform. Time and location dependent WSS was determined by computational fluid dynamics (CFD). At low orbital speed (50 rpm), WSS was shown to be uniform (0-1 dyne/cm(2)) across the bottom of the dish, while at higher orbital speed (100 and 150 rpm), WSS remained fairly uniform near the center and fluctuated significantly (0-9 dyne/cm(2)) near the side walls of the dish. Since WSS on the bottom of the dish is two-dimensional, a new directional oscillatory shear index (DOSI) was developed to quantify the directionality of oscillating shear. DOSI approached zero for biaxial oscillatory shear of equal magnitudes near the center and approached one for uniaxial pulsatile shear near the wall, where large tangential WSS dominated a much smaller radial component. Near the center (low DOSI), more, smaller and less elongated cells grew, whereas larger cells with greater elongation were observed in the more uniaxial oscillatory shear (high DOSI) near the periphery of the dish. Further, cells aligned with the direction of the largest component of shear but were randomly oriented in low magnitude biaxial shear. Statistical analyses of the individual and interacting effects of multiple factors (DOSI, shear magnitudes and orbital speeds) showed that DOSI significantly affected all the responses, indicating that directionality is an important determinant of cellular responses.

Effects of biaxial oscillatory shear stress on endothelial cell proliferation and morphology.

Despite decades of research related to hemolysis, the accuracy of prediction algorithms for complex flows leaves much to be desired. Fundamental questions remain about how different types of fluid stresses translate to red cell membrane failure. While cellular- and molecular-level simulations hold promise, spatial resolution to such small scales is computationally intensive. This review summarizes approaches to continuum-level modeling of hemolysis, a method that is likely to be useful well into the future for design of typical cardiovascular devices. Weaknesses are revealed for the Eulerian method of hemolysis prediction and for the linearized damage function. Wide variations in scaling of red cell membrane tension are demonstrated with different types of fluid stresses when the scalar fluid stress is the same, as well as when the energy dissipation rate is the same. New experimental data are needed for red cell damage in simple flows with controlled levels of different types of stresses, including laminar shear, laminar extension (normal), turbulent shear, and turbulent extension. Such data can be curve-fit to create more universal continuum-level models and can serve to validate numerical simulations.

Modeling and prediction of flow-induced hemolysis: a review

As an alternative to advection, solute transport by shear-augmented dispersion within oscillatory cerebrospinal fluid flow was investigated in small channels representing the basement membranes located between cerebral arterial smooth muscle cells, the paraarterial space surrounding the vessel wall and in large channels modeling the spinal subarachnoid space (SSS). Geometries were modeled as two-dimensional. Fully developed flows in the channels were modeled by the Darcy–Brinkman momentum equation and dispersion by the passive transport equation. Scaling of the enhancement of axial dispersion relative to molecular diffusion was developed for regimes of flow including quasi-steady, porous and unsteady, and for regimes of dispersion including diffusive and unsteady. Maximum enhancement occurs when the characteristic time for lateral dispersion is matched to the cycle period. The Darcy–Brinkman model represents the porous media as a continuous flow resistance, and also imposes no-slip boundary conditions at the walls of the channel. Consequently, predicted dispersion is always reduced relative to that of a channel without porous media, except when the flow and dispersion are both unsteady. In the basement membranes, flow and dispersion are both quasi-steady and enhancement of dispersion is small even if lateral dispersion is reduced by the porous media to achieve maximum enhancement. In the paraarterial space, maximum enhancement Rmax = 73,200 has the potential to be significant. In the SSS, the dispersion is unsteady and the flow is in the transition zone between porous and unsteady. Enhancement is 5.8 times that of molecular diffusion, and grows to a maximum of 1.6E+6 when lateral dispersion is increased. The maximum enhancement produces rostral transport time in agreement with experiments.

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Dispersion in porous media in oscillatory flow between flat plates: applications to intrathecal, periarterial and paraarterial solute transport in the central nervous system

M. Keith Sharp

Papers

Is bulk flow plausible in perivascular, paravascular and paravenous channels?

Effects of biaxial oscillatory shear stress on endothelial cell proliferation and morphology.

Modeling and prediction of flow-induced hemolysis: a review

Dispersion in porous media in oscillatory flow between flat plates: applications to intrathecal, periarterial and paraarterial solute transport in the central nervous system

Simulated and experimental performance of a heat pipe assisted solar wall