Carola S. König

Study of the collateral capacity of the circle of Willis of patients with severe carotid artery stenosis by 3D computational modeling.

This numerical study aims to investigate the capacity of the circle of Wills (CoW) to provide collateral blood supply for patients with unilateral carotid arterial stenosis. The basic 3D geometry of the CoW was reconstructed based on a magnetic resonance angiogram of a normal human subject. A total of 52 computational fluid dynamics simulations were performed for four geometry configurations of the CoW with an artificially inserted axisymmetric stenosis of different luminal area reductions in an internal carotid artery (ICA) under a variety of boundary conditions. The CoW geometric configurations included (a) a normal CoW with all communicating arteries; (b) as model (a) but with enlarged communicating arterial diameters; (c) as (a) but with the ipsilateral posterior communicating artery missing, and (d) as (c) but with enlarged communicating arteries. It is found that the blood perfusion pressure drop between the ipsilateral ICA and the middle cerebral artery (MCA) only becomes significant when the degree of stenosis is greater than 86%. The cerebral autoregulation range varied significantly between the different CoW configurations for the severe stenosis cases. Without causing the flow rates to decrease at the efferent arterial ends, the mean perfusion pressure in the ipsilateral ICA can drop from 100 to 73, 67, 92 and 84 mmHg for the CoW models (a)-(d) with 96% luminal area reduction stenosis, respectively. The additional pathways are able to raise the ipsilateral MCA pressure significantly without reducing the total flow perfusion. Cerebral autoregulation effects were not directly included in the study. Therefore, the findings in the study should be interpreted with cautions when comes to the biological and clinical significance.

Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature

The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to the high vessel permeability, the low osmotic pressure gradient as well as the absence of functional lymphatic system inside tumors. In this paper, a coupled mathematical model of tumor microcirculation is developed, which provides the link between microvasculature and interstitial space perfusion through the matrices determining a neighbor point belonging to either connected vessel (matrix B) or interstitial space (matrix A), and combines the intravascular and interstitial flow by vascular leaky terms. In addition, the compliance of tumor vessels, blood rheology with hematocritic distribution at branches is also considered. The microvascular network, on which the microcirculation calculation is carried out, is generated from our two-dimensional 9-point (2D9P) model of tumor angiogenesis, improved from the previous 2D5P one. A specific coupling procedure is developed in the study to couple the intravascular and interstitial flow. It is based on the iteratively numerical simulation techniques, including local iterations at individual parameter level and one global loop to provide coupling and simulation convergence. The simulation results not only present the basic features and characteristics of tumor microcirculation, which agree with the corresponding experimental observations reported, but also predict an intimate relationship between the tumor intravascular and interstitial flow quantitatively. Among the parameters, the vascular leakiness is a key to govern the systemic flowing pattern, influence the tumor internal environment and contribute to the metastasis of tumor cells, which could not be presented by the previous uncoupled models.

Investigation of unsteady flow in a model of a ventricular assist device by numerical modelling and comparison with experiment

Prior to this study, a clinical prototype of a sac-type ventricular assist device (VAD) was investigated experimentally, using both flow visualisation and Laser Doppler anemometry (LDA), in order to optimise its geometry. As poor optical access precluded the experimental investigation of the flow in some areas of the prototype VAD, computational fluid dynamics (CFD) was used in the present work. Flow patterns during one full pumping cycle were investigated in a simplified model of the VAD. The numerical solutions were compared with experimental results from an identical physical model. The model consists of the hemispherical cylinder and two attached tubes for the inflow and outflow. Instead of a diaphragm in the clinical device, which deforms non-uniformly during pumping, a piston with a matching hemispherical crown was used. A finite volume method was employed to solve the governing equations for the three-dimensional, unsteady, laminar flow of an incompressible, Newtonian fluid. The general flow features were predicted very well by the simulation, with some differences in the details of the flow structures. This allows the conclusion that CFD can be used to facilitate improvement of the design of the clinical device. The comparison of one-component velocity time histories at selected points showed that the predicted velocities were approximately 20-50% lower than those measured by LDA. Such underprediction would lead to erroneous results for particle residence times and may result in an underestimation of wall shear stresses.

Flow mixing and fluid residence times in a model of a ventricular assist device

To provide a reliable tool for predicting the flow in a clinical sac-type ventricular assist device (VAD), a simplified model VAD was developed prior to this study for the purpose of experimental validation of computer simulations of the time-varying flow on a moving grid. At selected locations in the flow field, flow patterns, vortex core trajectories and velocities were compared between the numerical and physical models during one full pumping cycle. The computer simulations showed qualitatively very good agreement with the experiment. Quantitatively, the agreement was less favourable. In order to investigate flow mixing and to evaluate fluid residence times in the model VAD a new tool has been developed: the numerical simulations were extended by injecting a scalar into the flow domain. These simulations allow investigation of the flow mixing qualitatively by visualisation and quantification of fluid residence times. Experimental assessment of the numerical results using dye injection proved to be favourable. The numerical results have been extended to include some prediction of pressure which have been compared with experimental measurements.

Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile

In order to address the problem of blood flow over the endothelium in small arteries, the near-endothelial region is here studied in more detail. The method used is a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids, named unstructured Lattice Boltzmann equation (ULBE). It is a new scheme based on the idea of placing the unknown fields at the nodes of the mesh and evolving them based on the fluxes crossing the surfaces of the corresponding control volumes. The study shows a significant variation and a high sensitivity of wall shear stress to the height of the endothelium corrugation and the presence of erythrocytes. The latter were modelled as deformable, viscous particles within a fluid continuum.

Numerical study of buoyant plumes from a multi-flue chimney released into an atmospheric boundary layer

Abstract A numerical study has been carried out of three-dimensional, full-scale, turbulent, buoyant plumes from a four-flue chimney in an atmospheric boundary layer. The simulations were based on the k−e turbulence model and a finite-volume method. The investigation was aimed to verify the question of how closely the overall characteristics of merged plumes from a multi-flue chimney match those of an equivalent single plume. Therefore, the results for multi-flue plumes were compared with those for a single plume under the same release conditions for volume flow rate, momentum and temperature. The differences in the velocity, temperature and turbulence energy fields of a single plume and multiple plumes were mainly significant in the early stages of rise and spreading. The multiple plumes merged very quickly and by ten diameters downstream only small differences between the plumes’ cross-sections could be distinguished. Comparisons of the rise heights showed that the arrangement of the individual flues within the chimney, with respect to the cross-wind, affects the rise height of the merged plumes. One of the multi-flue cases, which allowed the cross-wind penetration between the adjacent plumes, resulted in a lower rise height of the merged plume, while one other case, which provided a greater shielding, led to a rise height which was in agreement with the plume from the single-flue chimney. The rise heights were compared with empirical data.

Multi-scale interaction of particulate flow and the artery wall

We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying the widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of particulate flow (blood is not a continuum fluid), and proceed to propose, then validate all the key components in a multiply-coupled, multi-scale modeling strategy (in qualitative terms only, note). Eventually, this strategy should lead to a quantitative, patient-specific understanding of the coupling between particulate flow and the endothelial state.

Comparison of flow in numerical and physical models of a ventricular assist device using low- and high-viscosity fluids

Abstract The flows in a model of a ventricular assist device (VAD) were investigated numerically and experimentally for two different Newtonian test fluids. These were a blood analogue fluid and a much higher viscosity fluid. A finite volume method was employed to solve the governing equations for a three-dimensional unsteady laminar flow on a transient grid. The numerical solutions were compared with experimental results from an identical physical model. The experimental flows were investigated by flow visualization and by laser Doppler velocity measurements at selected points in the flow field. The validation was based on comparisons of flow patterns and of one-component velocity-time histories. The maximum Reynolds numbers in the inflow tube of the model VAD were approximately 460 and 3300 using the high- and low-viscosity fluids respectively. The investigation showed that the flow patterns were better predicted for the high-viscosity fluid. However, the agreement between the velocity-time histories was found to be slightly better for the low-viscosity fluid. The discrepancies in the flow patterns may be due to intermittent turbulence with a further contribution from numerical diffusion.

An Investigation of the Influence of the Gravity Field on the Interface of Two Immiscible Liquids—A Computational Study Comparing Prediction with Experiment

Abstract The flow of two immiscible liquids in a tube was investigated using computational fluid dynamics (CFD). This work is a first step towards investigating the influence of a variable gravitational field on the interface between the upper and lower phase of immiscible solvents as used in counter‐current chromatography (CCC). Initially the tube was positioned horizontally with the heavier fluid (lower phase) at the bottom and the lighter fluid (upper phase) on the top. Then the tube was suddenly tilted to a fixed inclination angle α. The flow field was initially exposed to a standard 1g gravity field (case 1). Subsequently, runs for a 2g and 10g gravity vector were performed (cases 2 and 3, respectively). Predictions for case 1 compared favorably with experimental results, although it was noted that there was a slight time slippage. The numerical results for the cases 2 and 3 showed that the higher the gravitational force the sooner distinct waves occur at the interface and the more disturbed the interface becomes in time. The interface surface area becomes minimal more quickly in the high gravity case due to the fluids moving more quickly to their respective ends, hence reducing the time when mass transfer between the phases is possible. However, mass transfer is still likely to have been enhanced due to the better mixing as a result of the highly disturbed interface. These encouraging results indicate that CFD could become a powerful tool in understanding the complex nature of the fluid dynamics in coil planet centrifuges and countercurrent chromatography.

Association between triglyceride and high-density lipoprotein cholesterol change following fibrate therapy

BACKGROUND Debate surrounding the role of fibrates has followed mixed outcomes from several randomised controlled trials. Subgroup analysis of even the negative trials reveals significant reduction in cardiovascular risk amongst patients with low HDL-C and high TG. We previously described factors associated with HDL-C change following fibrates. As fibrates influence both HDL-C and TG levels via their action on PPAR-α, we now wished to study TG change following fibrate therapy and any associations with baseline and change in HDL-C and TC levels. METHODS Data was collected from case notes of patients started on fibrates (n=248) between 2002 and 2008 in the lipid clinics at Heart of England NHS Foundation Trust. Regression analyses were carried out to determine factors associated with changes in TG. RESULTS Multiple regression analysis revealed that TG change was associated with pre-treatment TG (p<0.001) and TC levels (p=0.029). The association between TG change and pre-treatment TG remained significant when all factors including gender, concurrent statin treatment, diabetes and baseline HDL-C were entered into the regression model. Our previous study demonstrated significant post-fibrate HDL-C change in the group with baseline HDL-C values <1.0mmol/l. In our present study significant TG reduction was observed regardless of the baseline patient characteristics including HDL-C levels. CONCLUSIONS The actions of fibrates are considered to be mediated via PPAR-α, but our data suggest that the effects on TG and HDL-C are different. Thus, the mechanisms mediating the changes of these lipids following fibrate treatment may vary.