Doppler optical coherence imaging of converging flow

The experimental methods of Doppler optical coherence tomography are applied for two-dimensional flow mapping of highly scattering fluid in flow with complex geometry. Converging flow (die entry) is used to demonstrate non-invasive methods to map varying velocity profiles before and after the entry. Complex geometry flow is scanned with approximately 10 x 10 x 10 microm3 spatial resolution. Structural images of the phantom and specific velocity images are demonstrated. A variety of velocity profiles have been obtained before and after the entry. Concave, blunted, parabolic and triangular profiles are obtained at different distances after the entry. Application of the technique to the study of blood circulation is discussed.     

Numerical and experimental study of blood flow through a patient-specific arteriovenous fistula used for hemodialysis

Arteriovenous fistula (AVF) pathologies related to blood flow necessitate valid calculation tools for local velocity and wall shear stress determination to overcome the clinical diagnostic limits. To illustrate this issue, a reconstructed patient-specific AVF was investigated, using computational fluid dynamics (CFDs) and particle image velocimetry (PIV). The aim of this study was to validate the methodology from medical images to numerical simulations of an AVF by comparing numerical and experimental data. Two numerical grids were presented with a refinement difference of a factor of four. A mold of the same volume was created and mounted on an experimental bench with similar boundary conditions. The patient's acquired echo D006Fppler flow waveform was injected at the arterial inlet. Experimental and numerical velocity vector cartography qualitatively produced similar flow fields. Quantification with a point-to-point approach thoroughly investigated the velocity profiles using the mean difference between both results. The finest mesh generated CFD results with a mean percentage of the difference in velocity magnitude, taking the PIV as reference, did not exceed 10%. At specific zones, the coarse mesh required adaptive meshing to improve fitting with experimental data. Meshing refinement was necessary to improve velocity accuracy at wide diameters and wall shear stress at narrow diameters. Provided that these criteria were properly respected, we show through this difficult example the validity of using CFD to properly describe flow patterns in image-based reconstructed blood vessels.     

Noninvasive Measurement of Steady and Pulsating Velocity Profiles and Shear Rates in Arteries Using Echo PIV: In Vitro Validation Studies

Although accurate measurement of velocity profiles, multiple velocity vectors, and shear stress in arteries is important, there is still no easy method to obtain such information in vivo. We report on the utility of combining ultrasound contrast imaging with particle image velocimetry (PIV) for noninvasive measurement of velocity vectors. This method (echo PIV) takes advantage of the strong backscatter characteristics of small gas-filled microbubbles (contrast) seeded into the flow. The method was tested in vitro. The steady flow analytical solution and optical PIV measurements (for pulsatile flow) were used for comparison. When compared to the analytical solution, both echo PIV and optical PIV resolved the steady velocity profile well. Error in shear rate as measured by echo PIV (8%) was comparable to the error of optical PIV (6.5%). In pulsatile flow, echo PIV velocity profiles agreed well with optical PIV profiles. Echo PIV followed the general profile of pulsatile shear stress across the artery but underestimated wall shear at certain time points. However, error in shear from echo PIV was an order of magnitude less than error from current shear measurement methods. These studies indicate that echo PIV is a promising technique for noninvasive measurement of velocity profiles and shear stress.     

Investigations into the relationship between hemodynamics and vascular alterations in an established arteriovenous fistula

Arteriovenous fistula are specific vessels created by a vascular operation in order to provide sufficient blood access for extracorporeal circulation in hemodialysis. They are subject to numerous pathologies that may be caused by hemodynamic effects. To better understand these effects, a specific patient's arteriovenous fistula was reconstructed from computed tomography angiography. Computational fluid dynamics software made it possible to solve fluid mechanics equations under physiological conditions. An accurate map of unsteady velocity profiles and wall shear stress was drawn up. The computed velocity profiles were successfully confronted with Echo Doppler investigation. Selected regions with or without calcification, the end stage of wall alteration, were examined in terms of the mechanical constraints generated by blood flow. In contrast with other authors, we did not observe any association between calcification and areas of oscillating shear stress. Nevertheless, a statistical analysis of the whole vessel envelop and specific sites of calcification suggested a potential association between calcification and high temporal wall shear stress gradients.     

Accuracy of Computational Cerebral Aneurysm Hemodynamics Using Patient-Specific Endovascular Measurements

Computational hemodynamic simulations of cerebral aneurysms have traditionally relied on stereotypical boundary conditions (such as blood flow velocity and blood pressure) derived from published values as patient-specific measurements are unavailable or difficult to collect. However, controversy persists over the necessity of incorporating such patient-specific conditions into computational analyses. We perform simulations using both endovascularly-derived patient-specific and typical literature-derived inflow and outflow boundary conditions. Detailed three-dimensional anatomical models of the cerebral vasculature are developed from rotational angiography data, and blood flow velocity and pressure are measured in situ by a dual-sensor pressure and velocity endovascular guidewire at multiple peri-aneurysmal locations in 10 unruptured cerebral aneurysms. These measurements are used to define inflow and outflow boundary conditions for computational hemodynamic models of the aneurysms. The additional in situ measurements which are not prescribed in the simulation are then used to assess the accuracy of the simulated flow velocity and pressure drop. Simulated velocities using patient-specific boundary conditions show good agreement with the guidewire measurements at measurement locations inside the domain, with no bias in the agreement and a random scatter of ≈25%. Simulated velocities using the simplified, literature-derived values show a systematic bias and over-predicted velocity by ≈30% with a random scatter of ≈40%. Computational hemodynamics using endovascularly measured patient-specific boundary conditions have the potential to improve treatment predictions as they provide more accurate and precise results of the aneurysmal hemodynamics than those based on commonly accepted reference values for boundary conditions.     

In vivo validation of a fluid dynamics model of mitral valve M-mode echocardiogram

A fluid dynamics model of mitral valve motion during diastolic filling of the left heart is described. Given a pulsed Doppler velocity pattern in the mitral annulus, the radius of circular mitral orifice, the length of leaflets and the end-systolic left ventricular volume, the numerical model predicts the time course of the mitral leaflets during diastole: the mitral valve M-mode echocardiogram. Results obtained by computer simulation have been validated with in vivo data. It is shown that mitral valve flow is essentially a fluid dynamics process of floating mitral valve leaflets with blood flow due to the atrioventricular pressure gradient. In addition, a partial opening of the mitral valve as the initial boundary condition is required to simulate the overshooting of the leaflets during early peak filling. Some back flow is a condition for perfect closing of the native mitral valve. The higher the unsteady character of mitral flow, the less efficient is the opening and closing processes of the mitral valve.     

Imaging of non-parabolic velocity profiles in converging flow with optical coherence tomography

The optical coherence tomography method was explored for two-dimensional flow mapping of a highly scattering fluid in flow with complex geometry. Converging flow (capillary entry) with 4:1 constriction was used for demonstration of non-invasive and remote methods of mapping varying velocity profiles. Downstream of the geometry was scanned with approximately 10 x 10 x 10 microm3 spatial resolution and structural imaging of the lumen and images of one particular velocity were acquired. Stable concave, blunted and parabolic profiles are obtained at different distances of the inlet length. Application of the technique for the blood circulation is also discussed.     

Response to pulsatile flow of a miniaturised electromagnetic blood flow sensor studied by means of a laser-Doppler method

Electromagnetic (e.m.) flowmeter systems are commonly used in physiological experiments. Little information, however, is available about their accuracy in a time-dependent flow field. In miniaturised sensors especially the magnetic flux density cannot be made uniform, which may result in a non-ideal response to axisymmetric flows. The measured flow rate may therefore differ from the actual flow rate owing to the varying shape of the velocity profile. To study this effect unsteady flow experiments were performed to relate the e.m. flowmeter reading to the flow rate deduced from laser-Doppler anemometry. The experiments were performed in a straight circular tube with an internal diameter of 4 mm. The fluid (saline) flow was fully developed, laminar and pulsatile with flow reversal occurring near the wall in certain phases of the cycle. The frequency of the pulsations varied from 0·2 to 2 Hz. The fluid velocity was measured with a single component laser-Doppler system. The velocity profiles obtained were integrated to obtain the instantaneous flow rates and compared with those measured electromagnetically (Transflow 601). The results show no significant differences in the mean volume flow rates (averaged during one cycle). For momentary flow rates the differences are hardly significant. Small but briefly significant differences were found in the instantaneous flow rates, the largest deviation (7·8%) being found at flow reversal. Variation of the pulsation frequency (by a factor 10) or the mean flow rate (by a factor 4) has no significant effect on these differences.     

Numerical Experiment of Transient and Steady Characteristics of Ultrasonic-Measurement-Integrated Simulation in Three-Dimensional Blood Flow Analysis

In ultrasonic-measurement-integrated (UMI) simulation of blood flows, feedback signals proportional to the difference of velocity vector optimally estimated from Doppler velocities are applied in the feedback domain to reproduce the flow field. In this paper, we investigated the transient and steady characteristics of UMI simulation by numerical experiment. A steady standard numerical solution of a three-dimensional blood flow in an aneurysmal aorta was first defined with realistic boundary conditions. The UMI simulation was performed assuming that the realistic velocity profiles in the upstream and downstream boundaries were unknown but that the Doppler velocities of the standard solution were available in the aneurysmal domain or the feedback domain by virtual color Doppler imaging. The application of feedback in UMI simulation resulted in a computational result approach to the standard solution. As feedback gain increased, the error decreased faster and the steady error became smaller, implying the traceability to the standard solution improves. The positioning of ultrasound probes influenced the result. The height less than or equal to the aneurysm seemed better choice for UMI simulation using one probe. Increasing the velocity information by using multiple probes enhanced the UMI simulation by achieving ten times faster convergence and more reduction of error.     

Intensity modulated arc therapy (IMAT) with centrally blocked rotational fields

A new technique for intensity-modulated beam (IMB) delivery that combines the features of intensity modulated arc therapy (IMAT) with the use of 'classical blocks' is proposed. The role of the blocks is to realize the high-gradient modulation of the intensity profile corresponding to the region to be protected within the body contour, while the MLC leaves or the secondary collimator defines the rest of the field and delivers intensity-modulated multiple rotational segments. The centrally blocked radiation fields are applied sequentially, in several rotations. Each rotation of the gantry is responsible for delivering one segment of the optimal intensity profile. The new IMAT technique is applied for a treatment geometry represented by an annular target volume centrally located within a circular body contour. The annulus encompasses a circular critical structure, which is to be protected. The beam opening and corresponding weight of each segment are determined in two ways. The first method applies a linear optimization algorithm to precalculated centrally blocked radial dose profiles. These radial profiles are calculated for a set of beam openings, ranging from the largest field that covers the whole planning target volume (PTV) to the smallest, which is 1 cm larger than the width of the central block. The optimization is subjected to dose homogeneity constraints imposed on a linear combination of these profiles and finally delivers the dimensions and weights of the rotational beams to be used in combination. The second method decomposes into several subfields the fluence profile of a rotational beam known to deliver a constant dose level to PTV. This fluence profile is determined by using the analytical method proposed by Brahme for the case of the annular PTV and the concentric organ at risk (OAR). The proper segmentation of this intensity profile provides the field sizes and corresponding weights of the subfields to be used in combination. Both methods show that for this particular treatment geometry, three to seven segments are sufficient to cover the PTV with the 95% dose level and to keep the dose level to the central critical structure under 30% of the maximum dose. These results were verified by experimentally delivering the calculated segments to radiotherapy verification films sandwiched between two cylindrical pieces of a pressed-wood phantom. The total beam time for a three-field irradiation was 77 s. The predicted and experimental dose profiles along the radius of the phantom agreed to within 5%. Generalization of this technique to real-patient treatment geometry and advantages over other conformal radiotherapy techniques are also discussed.     

Error Checking and Graphical Representation of Multiple–Complete–Digest (MCD) Restriction-Fragment Maps

Genetic and physical maps display the relative positions of objects or markers occurring within a target DNA molecule. In constructing maps, the primary objective is to determine the ordering of these objects. A further objective is to assign a coordinate to each object, indicating its distance from a reference end of the target molecule. This paper describes a computational method and a body of software for assigning coordinates to map objects, given a solution or partial solution to the ordering problem. We describe our method in the context of multiple–complete–digest (MCD) mapping, but it should be applicable to a variety of other mapping problems. Because of errors in the data or insufficient clone coverage to uniquely identify the true ordering of the map objects, a partial ordering is typically the best one can hope for. Once a partial ordering has been established, one often seeks to overlay a metric along the map to assess the distances between the map objects. This problem often proves intractable because of data errors such as erroneous local length measurements (e.g., large clone lengths on low-resolution physical maps). We present a solution to the coordinate assignment problem for MCD restriction-fragment mapping, in which a coordinated set of single-enzyme restriction maps are simultaneously constructed. We show that the coordinate assignment problem can be expressed as the solution of a system of linear constraints. If the linear system is free of inconsistencies, it can be solved using the standard Bellman–Ford algorithm. In the more typical case where the system is inconsistent, our program perturbs it to find a new consistent system of linear constraints, close to those of the given inconsistent system, using a modified Bellman–Ford algorithm. Examples are provided of simple map inconsistencies and the methods by which our program detects candidate data errors and directs the user to potential suspect regions of the map.     

Micro-scale Dynamic Simulation of Erythrocyte–Platelet Interaction in Blood Flow

Platelet activation, adhesion, and aggregation on the blood vessel and implants result in the formation of mural thrombi. Platelet dynamics in blood flow is influenced by the far more numerous erythrocytes (RBCs). This is particularly the case in the smaller blood vessels (arterioles) and in constricted regions of blood flow (such as in valve leakage and hinge regions) where the dimensions of formed elements of blood become comparable with that of the flow geometry. In such regions, models to predict platelet motion, activation, aggregation and adhesion must account for platelet–RBC interactions. This paper studies platelet–RBC interactions in shear flows by performing simulations of micro-scale dynamics using a computational fluid dynamics (CFD) model. A level-set sharp-interface immersed boundary method is employed in the computations in which RBC and platelet boundaries are tracked on a two-dimensional Cartesian grid. The RBCs are assumed to have an elliptical shape and to deform elastically under fluid forces while the platelets are assumed to behave as rigid particles of circular shape. Forces and torques between colliding blood cells are modeled using an extension of the soft-sphere model for elliptical particles. RBCs and platelets are transported under the forces and torques induced by fluid flow and cell–cell and cell–platelet collisions. The simulations show that platelet migration toward the wall is enhanced with increasing hematocrit, in agreement with past experimental observations. This margination is seen to occur due to hydrodynamic forces rather than collisional forces or volumetric exclusion effects. The effect of fluid shear forces on the platelets increases exponentially as a function of hematocrit for the range of parameters covered in this study. The micro-scale analysis can be potentially employed to obtain a deterministic relationship between fluid forces and platelet activation and aggregation in blood flow past cardiovascular implants.     

锥形血管内血液脉动流的数值模拟

将锥形血管与人体血液的脉动流动联系起来研究发展中的血液流动问题 ,给出了锥形血管的几何模型、血液流动的理论模型、生理边界条件以及计算条件 ;根据人体生理脉动流条件 ,建立了血流平均速度函数 ,并就此对三维锥形血管内的血液脉动流动进行了数值模拟 ,获得心动周期不同时刻的轴向速度、径向速度、断面压力和轴向压力分布曲线。将数值模拟计算结果与实验和分析计算结果进行对照 ,讨论了锥形血管内血液脉动流的特点。     

A Computational Fluid Dynamic Model of Antigen–Antibody Surface Adsorption on a Piezoelectric Immunosensor

A novel computational fluid dynamic model describing the antigen–antibody binding on an electrode surface is presented. It was assumed that the adsorption rate of the antibody sample is dependent upon the flow field in the vicinity of the electrode. Numerical solution of the steady flow in a two-dimensional triangular cell using the Navier–Stokes equations was carried out for predicting mass adsorption on the surface of the crystal. The relationships between the mass adsorbed over the area surface of the electrode, the kinetics of the binding process, and the flow field were determined. The effect of the inlet conditions (location, velocity magnitude, and direction) on the time constant of the mass adsorption process was investigated. It was found that the time constant was decreased by moving the inlet near the edge of the crystal or increasing the normal to the boundary component of the velocity. These changes may significantly reduce the time needed to conduct the test. © 2000 Biomedical Engineering Society. PAC00: 8780-y, 8550+k, 8710+e     

Experimental investigation and computational modeling of hydrodynamics in bifurcating microchannels

Methods involving microfluidics have been used in several chemical, biological and medical applications. In particular, a network of bifurcating microchannels can be used to distribute flow in a large space. In this work, we carried out experiments to determine hydrodynamic characteristics of bifurcating microfluidic networks. We measured pressure drop across bifurcating networks of various complexities for various flow rates. We also measured planar velocity fields in these networks by using particle image velocimetry. We further analyzed hydrodynamics in these networks using mathematical and computational modeling. Our results show that the experimental frictional resistances of complex bifurcating microchannels are 25–30% greater than that predicted by Navier–Stokes equations. Experimentally measured velocity profiles indicate that flow distributes equally at a bifurcation regardless of the complexity of the network. Flow division other than bifurcation such as trifurcation or quadruplication can lead to heterogeneities. These findings were verified by the results from the numerical simulations.     

一种避免多道脉冲多普勒的血管中流速（横向）剖面的估计方法

血流速度剖面是研究血管特性的重要信息，它的得到通常用多道脉冲多普勒系统才能完成，由于脉冲多普勒系统存在着测速精度和测距精度的相互制约，且系统比较复杂，不太实用。文中提出一种新的估计方法，从超声多普勒血流音频信号出发，先得出其最大频率值和平均频率值，然后根据假设条件估计血流的速度剖面，从而使在一定精度上对血流速度剖面的估计成为可能。本文还给出了利用这种方法对血流速度剖面进行估计的一些结果。     

Pulsatile blood flow in a stenosed artery—a theoretical model

To understand the special flow conditions which may be produced by the presence of stenosis in arteries, an analytical solution is obtained for pulsatile laminar flow in an elliptic tube. Blood is approximated by a Newtonian model and the geometry of the stenosis is introduced by specifying the change in area of cross-section of the stenosed artery with axial distance. The results for velocity, pressure, shear stress and impedance are presented. These are compared with the steady flow results as well as with those of the flow in a stenosed tube of circular cross-section. The study indicates that the fluid dynamic characteristics of the flow are affected by the percentage of stenosis as well as the geometry of the stenosis. The frequency of oscillation is also found to influence shearing stress and the impedance.     

Endothelial Nitric Oxide Production and Transport in Flow Chambers: The Importance of Convection

A computational model of Nitric Oxide (NO) production and transport within a parallel-plate flow chamber coated with endothelial cells is presented. The relationship between NO concentration and Wall Shear Stress (WSS) at the endothelium is investigated in detail. An increase in WSS is associated with two phenomena: enhanced NO production by the endothelial cells, and an increase in the velocity at which NO is convected out of the chamber. These two phenomena have opposite effects on endothelial NO concentration. In physiologically realistic cases, the balance between them is found to vary as WSS is raised, resulting in a complex non-monotonic dependence of endothelial NO concentration on WSS. Also, it is found that a NO concentration boundary layer develops within the chamber, leading to substantial spatial variations in NO concentration along the length of the device. Finally, the implications of a negative feedback mechanism (that affects NO production) are presented. The results emphasize the role of convection on NO transport within flow chambers, which has been overlooked or misinterpreted in most previous theoretical studies. It is hoped that the conclusions of this study can be used to aid accurate interpretation of related experimental data.     

Comparison of CFD and MRI Flow and Velocities in an <Emphasis Type="Italic">In Vitro</Emphasis> Large Artery Bypass Graft Model

Bypass graft failures have been attributed to various hemodynamic factors, including flow stasis and low shear stress. Ideally, surgeries would minimize the occurrence of these detrimental flow conditions, but surgeons cannot currently assess this. Numerical simulation techniques have been proposed as one method for predicting changes in flow distributions and patterns from surgical bypass procedures, but comparisons against experimental results are needed to assess their usefulness. Previous in vitro studies compared simulated results against experimentally obtained measurements, but they focused on peripheral arteries, which have lower Reynolds numbers than those found in the larger arteries. In this study, we compared simulation results against measurements obtained using magnetic resonance imaging (MRI) techniques for a phantom model of a stenotic vessel with a bypass graft under conditions suitable for surgical planning purposes and with inlet Reynolds numbers closer to those found in the larger arteries. Comparisons of flow rate and velocity profiles were performed at maximum and minimum flows at four locations and used simulation results that were temporally and spatially averaged, key postprocessing when comparing against phase contrast MRI measurements. The maximum error in the computed volumetric flow rates was 6% of the measured values, and excellent qualitative agreement was obtained for the through-plane velocity profiles in both magnitude and shape. The in-plane velocities also agreed reasonably well at most locations.     

Quantitative Measurement of Blood Flow Dynamics in Embryonic Vasculature Using Spectral Doppler Velocimetry

The biophysical effects of blood flow are known to influence the structure and function of adult cardiovascular systems. Similar effects on the maturation of the cardiovascular system have been difficult to directly and non‐invasively measure due to the small size of the embryo. Optical coherence tomography (OCT) has been shown to provide high spatial and temporal structural imaging of the early embryonic chicken heart. We have developed an extension of Doppler OCT, called spectral Doppler velocimetry (SDV), that will enable direct, non‐invasive quantification of blood flow and shear rate from the early embryonic cardiovascular system. Using this technique, we calculated volumetric flow rate and shear rate from chicken embryo vitelline vessels. We present blood flow dynamics and spatial velocity profiles from three different vessels in the embryo as well as measurements from the outflow tract of the embryonic heart tube. This technology can potentially provide spatial mapping of blood flowand shear rate in embryonic cardiovascular structures, producing quantitative measurements that can be correlated with gene expression and normal and abnormal morphology. Anat Rec, 2009. © 2008 Wiley‐Liss, Inc.