Mesoscopic Simulation of Slip Motion for Gas Flow in Nanochannels

In this paper the Lattice Boltzmann method (LBM) was used to investigate gas flow in nano-channels, the critical region beyond which indefinite slip motion occurs in this channel and its effect on the deduced permeability. We defined a parallel-bounded planar two-dimensional domain for our simulation and calculated the system velocity profile. Numerical conformity was achieved when compared with the Hagen-Poiseuille’s equation. Good agreement was also established between the simulation and existing models reported in literature. A closer look at the region of full slip motion was also done and we observed that above a critical slip coefficient, a sudden significant increase in slip motion sets-in indefinitely with respect to the system time scale. The results indicate that when the LBM is used in gas flow simulation in nano-channels, if the slip effect is increased there is an effective increase in the fluid velocity and this affects the deduced permeability.

Computation of blood flow through collateral circulation of the superficial femoral artery

Objective Obliteration of collaterals during (endo)vascular treatment of peripheral arterial occlusive disease is considered detrimental. We use a model to calculate maximum collateral bed flow of the superficial femoral artery in order to provide insight in their hemodynamic relevance. Method A computational model was developed using digital subtraction angiographies in combination with Poiseuille's equation and Ohm's law. Lesions were divided into short and long (<15 cm and ≥15 cm, respectively) and into stenosis and occlusions. Data are presented in relation to the calculated maximum healthy superficial femoral artery flow. Results Stenotic lesions are longer than occlusive lesions ( P < 0.05) and occlusions had more and larger collaterals ( P < 0.05). In all four study groups the collateral flow significantly increased the total flow ( P < 0.05). The maximum collateral system flow in the stenosis and occlusion groups was 5.1% and 20.8% of healthy superficial femoral artery flow, respectively ( P < 0.05), and there were no significant differences between short and long lesions (11.2% and 6.7% of healthy superficial femoral artery flow, respectively). Conclusion The maximum collateral system flow of the superficial femoral artery is only a fraction, with a maximum of one fifth, of healthy superficial femoral artery flow. Effects of collateral vessel occlusion during (endo)vascular treatment may therefore be without detrimental consequences.

An educational device for a hands-on activity to visualize the effect of atherosclerosis on blood flow

An educational device was created to develop a hands-on activity to illustrate how atherosclerosis can dramatically reduce blood flow in human vessels. The device was conceived, designed, and built at the University of Coimbra, in response to a request from the Exploratório Infante D. Henrique Science Centre Museum, where it is presently installed. The device was designed to allow lay audience to operate it, including school-age youngsters. The two blood flow reduction mechanisms that can be visualized are 1) thickening of the artery wall and 2) hardening of the artery wall. The main objective is to promote the understanding of atherosclerotic cardiovascular physiology by simple and direct experiments. This original educational interactive device was constructed using, in the conceptual and design stages of the project, a Newtonian theoretical flow model based on Poiseuille's equation. This device is driven by human force and provides a visualization of the effect of atherosclerosis on flow. The main aspects relating to its design and construction are described here to explain and disseminate this approach. Throughout more than 4 yr of real operation, this educational device proved to be a simple and attractive way of understanding atherosclerosis, especially among young people.

Beyond Poiseuille: Preservation Fluid Flow in an Experimental Model

Poiseuille’s equation describes the relationship between fluid viscosity, pressure, tubing diameter, and flow, yet it is not known if cold organ perfusion systems follow this equation. We investigated these relationships in anex vivomodel and aimed to offer some rationale for equipment selection. Increasing the cannula size from 14 to 20 Fr increased flow rate by a mean (SD) of 13 (12)%. Marshall’s hyperosmolar citrate was three times less viscous than UW solution, but flows were only 45% faster. Doubling the bag pressure led to a mean (SD) flow rate increase of only 19 (13)%, not twice the rate. When external pressure devices were used, 100 mmHg of continuous pressure increased flow by a mean (SD) of 43 (17)% when compared to the same pressure applied initially only. Poiseuille’s equation was not followed; this is most likely due to “slipping” of preservation fluid within the plastic tubing. Cannula size made little difference over the ranges examined; flows are primarily determined by bag pressure and fluid viscosity. External infusor devices require continuous pressurisation to deliver high flow. Future studies examining the impact of perfusion variables on graft outcomes should include detailed equipment descriptions.

A First-Order Mechanical Device to Model Traumatized Craniovascular Biodynamics

Mathematical models currently exist that explore the physiology of normal and traumatized intracranial function. Mechanical models are used to assess harsh environments that may potentially cause head injuries. However, few mechanical models are designed to study the adaptive physiologic response to traumatic brain injury. We describe a first-order physical model designed and fabricated to elucidate the complex biomechanical factors associated with dynamic intracranial physiology. The uni-directional flow device can be used to study interactions between the cranium, brain tissue, cerebrospinal fluid, vasculature, blood, and the heart. Solid and fluid materials were selected to simulate key properties of the cranial system. Total constituent volumes (solid and fluid) and volumetric flow (650ml∕min) represent adult human physiology, and the lengths of the individual segments along the flow-path are in accord with Poiseuille’s equation. The physical model includes a mechanism to simulate autoregulatory vessel dynamics. Intracranial pressures were measured at multiple locations throughout the model during simulations with and without post-injury brain tissue swelling. Two scenarios were modeled for both cases: Applications of vasodilation/constriction and changes in the head of bed position. Statistical results indicate that all independent variables had significant influence over fluid pressures measured throughout the model (p<0.0001) including the vasoconstriction mechanism (p=0.0255). The physical model represents a first-order design realization that helps to establish a link between mathematical and mechanical models. Future designs will provide further insight into traumatic head injury and provide a framework for unifying the knowledge gained from mathematical models, injury mechanics, clinical observations, and the response to therapies.

Measurements of Hemodialysis Catheter Blood Flow in Vivo

The relationship between the blood flow and inflow and outflow pressures was determined in PermCath, dual lumen catheters during regular hemodialyses in vivo in eight patients with average hematocrit of 38%. From the luer lock connector the catheters had an average length of 32 cm to the outflow tip and 30 cm to the inflow tip. The catheters had an internal diameter of 0.2 cm and were straight before implantation. Dialyses were performed on Fresenius 2008 D or E machines with ReadySet™ blood lines with an 8 mm ID pump segment and a noncollapsible arterial chamber. Pressures and blood flows were measured at pump speeds from 50 to 500 ml/min in increments of 50 ml/min with lines in normal configuration. Blood flow was measured continuously using ultrasound. The correlations between pressures and flows are not linear. The best correlations are according to the Stirling model of exponential growth category equation. Inflow pressure = -9.07–0.4865*(exp(0.0020*blood flow)-1)/0.0020 Outflow pressure = -28.14+0.5002*(exp(0.0015*blood flow)-1/0.0015 Based on these results and Poiseuille's equation a table was developed for the optimal relationship between catheter length and diameter to achieve standardized (average, low and high) blood flows regardless of the lengths of the catheters. The diameter/length relationships are based on theoretical considerations. Because resistances depend on the material and shape of the tubing, the actual measurements of flow/pressure relationships should be done once tubings of different diameters are manufactured, and final catheter design has to be based on these measurements.