Platelet deposition in non-parallel flow

This paper deals with flow- and surface-related aspects of primary hemostasis. It investigates the influence of both shear stress and changes in surface reactivity on platelet adhesion. For this purpose, a mathematical model based on the Navier-Stokes equations and on particle conservation is developed. Several vessel geometries of physiological relevance are considered, such as stagnation point flow, sudden expansion and t-junction. Model parameters have been optimized to fit corresponding experimental data. When platelet adhesion was assumed independent of shear, numerically predicted spatial platelet distribution did not match these data at all. However, when adhesion was assumed shear-dependent, better agreement was achieved. Further improvement was obtained when changes in surface reactivity due to platelet adhesion were taken into account. This was done by coupling platelet flux conditions to ordinary differential equations for the evolution of surface-bound platelets. Existence of weak solutions is shown for generalized parabolic systems having such boundary conditions. This, together with proofs for uniqueness and positivity of solutions, guarantees mathematical well posedness of the presented model. Limitations due to the complexity of the hemostatic system are discussed, as well as possible applications in practice. The findings of this paper contribute to understand the roles of flow and surface in primary hemostasis, which is of paramount interest in bioengineering and clinical practice.     

Comparison of blood rheological models for physiological flow simulation

The present study investigates the flow effects that different blood constitutive equations induce when employed in numerical simulations in the framework of computational hemodynamics. In accord with experimental studies on the rheological behavior of blood, three blood constitutive equations namely the Casson, Power-Law and Quemada models were used for simulating the shear flow behavior of blood. The case studied is the flow in a channel with a moving part of the boundary and was selected because it reproduces the flow phenomena occurring in realistic arterial conditions. Flow simulation for every model is carried out assuming the same flow rate at the inlet of the channel and different Strouhal numbers reflecting different intensities of the boundary movement. Results show that the modeling of blood as non-Newtonian fluid has marked qualitative and quantitative effects on both the flow field and the wall shear stress whereas comparison of the different models shows good agreement between the flow effects by the Casson and Quemada models.     

Effects of curved inlet tubes on air flow and particle deposition in bifurcating lung models

In vivo bifurcating airways are complex and the airway segments leading to the bifurcations are not always straight, but curved to various degrees. How do such curved inlet tubes influence the motion as well as local deposition and hence the biological responses of inhaled particulate matter in lung airways? In this paper steady laminar dilute suspension flows of micron-particles are simulated in realistic double bifurcations with curved inlet tubes, i.e., 0 degrees < or =theta< or =90 degrees, using a commercial finite-volume code with user-enhanced programs. The resulting air-flow patterns as well as particle transport and wall depositions were analyzed for different flow inlet conditions, i.e., uniform and parabolic velocity profiles, and geometric configurations. The curved inlet segments have quite pronounced effects on air-flow, particle motion and wall deposition in the downstream bifurcating airways. In contrast to straight double bifurcations, those with bent parent tubes also exhibit irregular variations in particle deposition efficiencies as a function of Stokes number and Reynolds number. There are fewer particles deposited at mildly curved inlet segments, but the particle deposition efficiencies at the downstream sequential bifurcations vary much when compared to those with straight inlets. Under certain flow conditions in sharply curved lung airways, relatively high, localized particle depositions may take place. The findings provide necessary information for toxicologic or therapeutic impact assessments and for global lung dosimetry models of inhaled particulate matter.     

Comparison of models for flow induced deformation of soft biological tissue

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.     

Computational fluid dynamics simulations of particle deposition in large-scale, multigenerational lung models

Computational fluid dynamics (CFD) has emerged as a useful tool for the prediction of airflow and particle transport within the human lung airway. Several published studies have demonstrated the use of Eulerian finite-volume CFD simulations coupled with Lagrangian particle tracking methods to determine local and regional particle deposition rates in small subsections of the bronchopulmonary tree. However, the simulation of particle transport and deposition in large-scale models encompassing more than a few generations is less common, due in part to the sheer size and complexity of the human lung airway. Highly resolved, fully coupled flowfield solution and particle tracking in the entire lung, for example, is currently an intractable problem and will remain so for the foreseeable future. This paper adopts a previously reported methodology for simulating large-scale regions of the lung airway (Walters, D. K., and Luke, W. H., 2010, "A Method for Three-Dimensional Navier-Stokes Simulations of Large-Scale Regions of the Human Lung Airway," ASME J. Fluids Eng., 132(5), p. 051101), which was shown to produce results similar to fully resolved geometries using approximate, reduced geometry models. The methodology is extended here to particle transport and deposition simulations. Lagrangian particle tracking simulations are performed in combination with Eulerian simulations of the airflow in an idealized representation of the human lung airway tree. Results using the reduced models are compared with those using the fully resolved models for an eight-generation region of the conducting zone. The agreement between fully resolved and reduced geometry simulations indicates that the new method can provide an accurate alternative for large-scale CFD simulations while potentially reducing the computational cost of these simulations by several orders of magnitude.     

Computational model of particle deposition in the nasal cavity under steady and dynamic flow

A computational model for flow and particle deposition in a three-dimensional representation of the human nasal cavity is developed. Simulations of steady state and dynamic airflow during inhalation are performed at flow rates of 9–60 l/min. Depositions for particles of size 0.5–20 μm are determined and compared with experimental and simulation results from the literature in terms of deposition efficiencies. The nasal model is validated by comparison with experimental and simulation results from the literature for particle deposition under steady-state flow. The distribution of deposited particles in the nasal cavity is presented in terms of an axial deposition distribution as well as a bivariate axial deposition and particle size distribution. Simulations of dynamic airflow and particle deposition during an inhalation cycle are performed for different nasal cavity outlet pressure variations and different particle injections. The total particle deposition efficiency under dynamic flow is found to depend strongly on the dynamics of airflow as well as the type of particle injection.     

Importance of airway blood flow on particle clearance from the lung

Wagner, Elizabeth M., and W. Michael Foster. Importanceof airway blood flow on particle clearance from the lung.J. Appl. Physiol. 81(5):1878-1883, 1996.The role of the airway circulation insupporting mucociliary function has been essentially unstudied. Weevaluated the airway clearance of inert, insoluble particles inanesthetized ventilated sheep (n = 8),in which bronchial perfusion was controlled, to determine whetherairway mucosal blood flow is essential for maintaining surfacetransport of particles through airways. The bronchial branch of thebronchoesophageal artery was cannulated and perfused with autologousblood at control flow (0.6 ml ^· min^{1 ·} kg¹)or perfusion was stopped. With the sheep in a supine position and aftera steady-state ¹³³Xe ventilationscan for designation of lung zones of interest, an inert^99mTc-labeled sulfur colloidaerosol (2.1-µm diameter) was deposited in the lung. The clearancekinetics of the radiolabeled particles were determined from theactivity-time data obtained for right and left lung zones. At 60 minpostdeposition of aerosol, average airway particle retention forcontrol bronchial blood flow conditions was 57 ± 7 (SE)% for theright and 53 ± 8% for the left lung zones. Clearance of particleswas significantly impaired when bronchial blood flow was stopped, e.g.,right and left lung zones averaged 77 ± 6 and 76 ± 7% at 60 min, respectively (P < 0.05). Thesedata demonstrate a significant influence of the bronchial circulation on mucociliary transport of insoluble particles. Potential mechanisms that may account for these results include the importance of the bronchial circulation for nutrient flow, maintenance of airway walltemperature and humidity, and release of mediators and sequelae associated with tissue ischemia.

     

Comparison of two methods of altering blood pressures for assessing neonatal cerebral blood flow autoregulation

The cerebral blood flow of newborn lambs at reduced and elevated arterial blood pressures, induced by intravenous infusion of sodium nitroprusside and phenylephrine hydrochloride as well as blood withdrawal and reinfusion, were compared. Both blood withdrawal and sodium nitroprusside infusion reduced mean arterial pressure from 83 to 60 mmHg (1 mmHg = 133 Pa). Reinfusion of blood increased arterial pressure to 94 mmHg. Phenylephrine hydrochloride infusion increased arterial pressure to 102 mmHg. The cerebral blood flows at corresponding arterial pressures were similar (coefficient of correlation = 0.88, P less than 0.01). Cerebral blood flow before and after infusion of phenylephrine hydrochloride and sodium nitroprusside into the brain via the carotid artery did not change. The results indicate that blood-borne phenylephrine hydrochloride and sodium nitroprusside, in concentrations that would alter arterial blood pressure significantly from its resting level, do not change cerebral blood flow directly.     

Computational models of blood flow in the circle of Willis

A two-dimensional, steady state model of the circle of Willis has been developed. To simulate the peripheral resistance of the cerebrovascular tree, blocks of porous media were used. Their effective resistance was kept constant, disregarding the effects of arterial auto-regulation. The model was then used to simulate different common abnormalities of the circle of Willis while a range of varying boundary conditions was imposed to the right internal carotid artery (ICA). The total flux was tabulated and compared favourably with both clinical measurements and other models of the circle of Willis. Relevant fluid dynamics effects were also observed and analysed. The present model demonstrates that the use of CFD can produce physiological results if the appropriate boundary conditions are used. We can provide clinicians with a priority list of the severity of the flux reduction for the considered abnormalities for different degrees of stenosis of the right ICA. From this study it is apparent that the redistribution of blood via the circle of Willis is mainly driven by changes in the vascular resistance of the brain rather than in the local arterial geometry. The use of valid peripheral resistances allows for a more realistic model of the circle of Willis but also highlights the need for more accurate means to estimate the vascular resistance of a patient.     

An investigation of particle flow through capillary models with the resistive pulse technique

The use of the resistive pulse technique for the measurement of microsphere and red cell transit times through single-pore "Nuclepore" membranes (with pore diameters of 3.5 to 7.0 microns and pore length of approximately 11 microns) is described. The investigation of the fluid mechanics and electrical characteristics of the experimental system provides methods for the determination of particle and cell size, and entrance and transit times. Experimental measurement of the position dependent velocity of spherical particles through the pore shows close agreement with theoretical models. Red cell size and transit time through different sized pores at physiological shear stresses is also measured.     

3D models of blood flow in the cerebral vasculature

The circle of Willis (CoW) is a ring-like arterial structure located in the base of the brain and is responsible for the distribution of oxygenated blood throughout the cerebral mass. To investigate the effects of the complex 3D geometry and anatomical variability of the CoW on the cerebral hemodynamics, a technique for generating physiologically accurate models of the CoW has been created using a combination of magnetic resonance data and computer-aided design software. A mathematical model of the body's cerebral autoregulation mechanism has been developed and numerous computational fluid dynamics simulations performed to model the hemodynamics in response to changes in afferent blood pressure. Three pathological conditions were explored, namely a complete CoW, a fetal P1 and a missing A1. The methodology of the cerebral hemodynamic modelling is proposed with the potential for future clinical application in mind, as a diagnostic tool.     

Fluid particle diffusion through high-hematocrit blood flow within a capillary tube

Fluid particle diffusion through blood flow within a capillary tube is an important phenomenon to understand, especially for studies in mass transport in the microcirculation as well as in solving technical issues involved in mixing in biomedical microdevices. In this paper, the spreading of tracer particles through up to 20% hematocrit blood, flowing in a capillary tube, was studied using a confocal micro-PTV system. We tracked hundreds of particles in high-hematocrit blood and measured the radial dispersion coefficient. Results yielded significant enhancement of the particle diffusion, due to a micron-scale flow-field generated by red blood cell motions. By increasing the flow rate, the particle dispersion increased almost linearly under constant hematocrit levels. The particle dispersion also showed near linear dependency on hematocrit up to 20%. A scaling analysis of the results, on the assumption that the tracer trajectories were unbiased random walks, was shown to capture the main features of the results. The dispersion of tracer particles was about 0.7 times that of RBCs. These findings provide good insight into transport phenomena in the microcirculation and in biomedical microdevices.     

Computational analysis of flow structure and particle deposition in a single asthmatic human airway bifurcation

This paper aims to improve current understanding of flow structure and particle deposition in asthmatic human airways. A single, symmetric airway bifurcation, corresponding to generations 10–11 of Weibel’s model, is investigated through validated numerical simulations. The parent airway segment is modelled as a smooth circular tube. The child segments are considered asthmatic and their cross-section is modelled as a constricted tube with sinusoidal folds uniformly distributed along the circumference. The flow structure and particle deposition pattern for normal (i.e., healthy) and asthmatic airway bifurcations are compared and discussed. The numerical results reveal that the secondary flow in the asthmatic airway bifurcation is much stronger than in the healthy one, resulting in higher particle deposition. The effects of size of the lumen area and number of folds on particle deposition and pressure drop are also investigated. It is found that particle deposition efficiency is significantly affected by lumen area of the asthmatic segment (the smaller the lumen area, the higher the particle deposition efficiency). The effect of number of folds is small. Particle deposition efficiency also increases with Reynolds number. The pressure drop in the asthmatic airway bifurcation depends mainly on size of the lumen area. The effect of number of folds becomes important for strongly collapsed airways.     

Numerical models of auto-regulation and blood flow in the cerebral circulation

A two-dimensional time-dependent computational fluid dynamics model of the Circle of Willis has been developed. To simulate, not only the peripheral resistance of the cerebrovascular tree but also its auto-regulation function, a new "active" boundary condition has been defined and developed using control theory to provide a model of the feedback mechanism. The model was then used to simulate different common abnormalities of the Circle of Willis while a pressure drop, simulating a rapid compression of the right internal carotid artery, was imposed. Test results using a simple tube compared excellently with experiment. The total time-dependent flux for each efferent artery was tabulated and showed the important relationship between geometrical variations in the Circle of Willis and the auto-regulation of blood flow by vascular vaso-dilation and contraction. From this study, it was found that the worst case seemed to be that of a missing or dysfunctional right A1 segment of the anterior cerebral artery. The use of valid physiological models of the peripheral resistance allows for more realistic models of the blood flow in the Circle whilst allowing an easy extension to 3D patient specific simulations.     

Comparison of physiological and post-endovascular aneurysm repair infrarenal blood flow

Endovascular aneurysm repair (EVAR) of abdominal aortic aneurysms results in redirection of blood through the deployed endograft (EG). Even though EVAR is clinically effective, the absolute flow restoration is not warranted. Our purpose was to compare the physiological with the post-EVAR infrarenal flow conditions. We developed patient-specific models based on computed tomography data of five healthy volunteers and ten patients treated with the Endurant^® stent-graft system. Wall shear stress (WSS), helicity, pressure and velocity fields were calculated using computational fluid dynamics. The results showed a decrease of peak WSS on the part of the EG that resides in the iliac arteries, compared to the physiological value (p = 0.01). At the abdominal part, the average helicity seems to increase after EVAR, while at the iliac arteries part, the intensity of helical flow seems physiological. Pressure drop and peak velocity in the iliac arteries part are lower than the physiological values (p = 0.04). The comparison revealed that most hemodynamic properties converge to normal levels at the abdominal part whereas statistically significant variations were observed in the iliac arteries part. The delineation of the differences between physiological and postoperative flow data could pave the way for the improvement of EG designs.     

A head-to-head comparison between CT- and IVUS-derived coronary blood flow models

The goal of this work is to compare coronary hemodynamics as predicted by computational blood flow models derived from two imaging modalities: coronary computed tomography angiography (CCTA) and intravascular ultrasound integrated with angiography (IVUS). Criteria to define boundary conditions are proposed to overcome the dissimilar anatomical definition delivered by both modalities. The strategy to define boundary conditions is novel in the present context, and naturally accounts for the flow redistribution induced by the resistance of coronary vessels. Hyperemic conditions are assumed to assess model predictions under stressed hemodynamic environments similar to those encountered in Fractional Flow Reserve (FFR) calculations. As results, it was found that CCTA models predict larger pressure drops, higher average blood velocity and smaller FFR. Concerning the flow rate at distal locations in the major vessels of interest, it was found that CCTA predicted smaller flow than IVUS, which is a consequence of a larger sensitivity of CCTA models to coronary steal phenomena. Comparisons to in-vivo measurements of FFR are shown.