Three-dimensional velocity field reconstruction

The problem of inter-slice magnetic resonance (MR) image reconstruction is encountered often in medical imaging applications, in such scenarios, there is a need to approximate information not captured in contiguously acquired MR images due to hardware sampling limitations. In the context of velocity field reconstruction, these data are required for visualization and computational analyses of flow fields to be effective. To provide more complete velocity information, a method has been developed for the reconstruction of flow fields based on adaptive control grid interpolation (ACGI). In this study, data for reconstruction were acquired via MRJ from in vitro models of surgically corrected pediatric cardiac vasculatures. Reconstructed velocity fields showed strong qualitative agreement with those obtained via other acquisition techniques. Quantitatively reconstruction was shown to produce data of comparable quality to accepted velocity data acquisition methods. Results indicate that ACGI-based velocity field reconstruction is capable of producing information suitable for a variety of applications demanding three-dimensional in vivo velocity data.     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

Model studies of nonsteady flow using magnetic resonance imaging

A bolus-tracking magnetic resonance imaging (MRI) method has been employed to measure velocity profiles for oscillatory flow with and without a steady flow component as well as pulsatile flow in an axisymmetric tube model. A range of flow conditions within normal physiological limits was tested. The imaged velocity profiles were observed to be generally in accord with theoretical predictions. Instantaneous flow rates calculated from the MR images agreed well with those assessed using an ultrasonic flowmeter. Because MRI is noninvasive and poses few risks to subjects, this technique is potentially useful for studying vascular hemodynamics in vivo.     

Visualization and quantification of the human blood flow by magnetic resonance imaging.

Magnetic Resonance Imaging (MRI) offers new possibilities for the visualization and the noninvasive quantification of the blood flow in human vessels. By the application of conventional gradient echo sequences with electrocardiographic gating on a 1.5 Tesla whole body MRI system the flow induced phase shifts in the ascending and the abdominal aorta are analyzed. The instantaneous two-dimensional velocity profiles and the instantaneous flow rates are determined in a series of subsequent images with high temporal resolution throughout the cardiac cycle. For the flow analysis in further vessels and for the analysis of more complex flow patterns, as they occur in bifurcations or stenoses, a new MR flow imaging technique called FAcE with extremely short echo times is introduced and the first results of flow examinations in a bifurcation phantom and in the carotid artery are presented.     

Evaluation of magnetic resonance velocimetry for steady flow

Whole body magnetic resonance (MR) imaging has recently become an important diagnostic tool for cardiovascular diseases. The technique of magnetic resonance phase velocity encoding allows the quantitative measurement of velocity for an arbitrary component direction. A study was initiated to determine the ability and accuracy of MR velocimetry to measure a wide range of flow conditions including flow separation, three-dimensional secondary flow, high velocity gradients, and turbulence. A steady flow system pumped water doped with manganese chloride through a variety of test sections. Images were produced using gradient echo sequences on test sections including a straight tube, a curved tube, a smoothly converging-diverging nozzle, and an orifice. Magnetic resonance measurements of laminar and turbulent flows were depicted as cross-sectional velocity profiles. MR velocity measurements revealed such flow behavior as spatially varying velocity, recirculation and secondary flows over a wide range of conditions. Comparisons made with published experimental laser Doppler anemometry measurements and theoretical calculations for similar flow conditions revealed excellent accuracy and precision levels. The successful measurement of velocity profiles for a variety of flow conditions and geometries indicate that magnetic resonance imaging is an accurate, non-contacting velocimeter.     

Echo Particle Image Velocimetry

The transport of mass, momentum, and energy in fluid flows is ultimately determined by spatiotemporal distributions of the fluid velocity field.¹ Consequently, a prerequisite for understanding, predicting, and controlling fluid flows is the capability to measure the velocity field with adequate spatial and temporal resolution.² For velocity measurements in optically opaque fluids or through optically opaque geometries, echo particle image velocimetry (EPIV) is an attractive diagnostic technique to generate "instantaneous" two-dimensional fields of velocity.^3,4,5,6 In this paper, the operating protocol for an EPIV system built by integrating a commercial medical ultrasound machine⁷ with a PC running commercial particle image velocimetry (PIV) software⁸ is described, and validation measurements in Hagen-Poiseuille (i.e., laminar pipe) flow are reported.For the EPIV measurements, a phased array probe connected to the medical ultrasound machine is used to generate a two-dimensional ultrasound image by pulsing the piezoelectric probe elements at different times. Each probe element transmits an ultrasound pulse into the fluid, and tracer particles in the fluid (either naturally occurring or seeded) reflect ultrasound echoes back to the probe where they are recorded. The amplitude of the reflected ultrasound waves and their time delay relative to transmission are used to create what is known as B-mode (brightness mode) two-dimensional ultrasound images. Specifically, the time delay is used to determine the position of the scatterer in the fluid and the amplitude is used to assign intensity to the scatterer. The time required to obtain a single B-mode image, t, is determined by the time it take to pulse all the elements of the phased array probe. For acquiring multiple B-mode images, the frame rate of the system in frames per second (fps) = 1/δt. (See 9 for a review of ultrasound imaging.)For a typical EPIV experiment, the frame rate is between 20-60 fps, depending on flow conditions, and 100-1000 B-mode images of the spatial distribution of the tracer particles in the flow are acquired. Once acquired, the B-mode ultrasound images are transmitted via an ethernet connection to the PC running the PIV commercial software. Using the PIV software, tracer particle displacement fields, D(x,y)[pixels], (where x and y denote horizontal and vertical spatial position in the ultrasound image, respectively) are acquired by applying cross correlation algorithms to successive ultrasound B-mode images.¹⁰ The velocity fields, u(x,y)[m/s], are determined from the displacements fields, knowing the time step between image pairs, ΔT[s], and the image magnification, M[meter/pixel], i.e., u(x,y) = MD(x,y)/ΔT. The time step between images ΔT = 1/fps + D(x,y)/B, where B[pixels/s] is the time it takes for the ultrasound probe to sweep across the image width. In the present study, M = 77[μm/pixel], fps = 49.5[1/s], and B = 25,047[pixels/s]. Once acquired, the velocity fields can be analyzed to compute flow quantities of interest.     

Pressure flow patterns in a cylinder with reabsorbing walls

The problem of fluid motion in renal tubules, in contrast to ordinary flow through cylinders with impermeable walls, is complicated by the existence of radial velocities generated by reabsorption processes. As a first approach to this problem, the Navier Stokes equations for axially symmetric, slow flow in an infinite cylinder whose walls reabsorb fluid are integrated. If the rate of reabsorption is constant, the solutions resemble the conventional Poiseuille flow, i.e., the longitudinal velocity profile is parabolic. In addition the drop in mean pressure is proportional to the mean axial flow, the length of tube between reference points, and inversely proportional to the fourth power of the radius. If the rate of reabsorption is a linear function of the distance from the origin, the presence of an additive term alters these relations. If, for example, the gradient in reabsorption is positive, the axial velocity profile tends to flatten and when the gradient is sufficiently large, the maximum velocity moves from the center of the stream toward the periphery, leaving a relative minimum at the center. In passing from the center of the tube to the walls, the radial velocity passes through a miximum, regardless of the reabsorption properties of the wall.     

Formation of a boundary layer in steady-state blood flow

This paper is devoted to a study of boundary layer formation in the steady flow of blood through the human aorta. Blood is treated as an incompressible fluid. Consideration is given to a flat-top velocity profile which combines the potential flow with the boundary layer; expressions for the displacement thickness, skin-friction and pressure in the entry region are derived.     

Computer Simulation of Magnetic Resonance Angiography Imaging: Model Description and Validation

With the development of medical imaging modalities and image processing algorithms, there arises a need for methods of their comprehensive quantitative evaluation. In particular, this concerns the algorithms for vessel tracking and segmentation in magnetic resonance angiography images. The problem can be approached by using synthetic images, where true geometry of vessels is known. This paper presents a framework for computer modeling of MRA imaging and the results of its validation. A new model incorporates blood flow simulation within MR signal computation kernel. The proposed solution is unique, especially with respect to the interface between flow and image formation processes. Furthermore it utilizes the concept of particle tracing. The particles reflect the flow of fluid they are immersed in and they are assigned magnetization vectors with temporal evolution controlled by MR physics. Such an approach ensures flexibility as the designed simulator is able to reconstruct flow profiles of any type. The proposed model is validated in a series of experiments with physical and digital flow phantoms. The synthesized 3D images contain various features (including artifacts) characteristic for the time-of-flight protocol and exhibit remarkable correlation with the data acquired in a real MR scanner. The obtained results support the primary goal of the conducted research, i.e. establishing a reference technique for a quantified validation of MR angiography image processing algorithms.     

Computational and experimental investigation of flow and fluid mixing in the roller bottle bioreactor

The fully three-dimensional velocity field in a roller bottle bioreactor is simulated for two systems (creeping flow and inertial flow conditions) using a control volume-finite element method, and validated experimentally using particle imaging velocimetry. The velocity fields and flow patterns are described in detail using velocity contour plots and tracer particle pathline computations. Bulk fluid mixing in the roller bottle is then examined using a computational fluid tracer program and flow visualization experiments. It is shown that the velocity fields and flow patterns are substantially different for each of these flow cases. For creeping flow conditions the flow streamlines consist of symmetric, closed three-dimensional loops; and for inertial flow conditions, streamlines consist of asymmetric toroidal surfaces. Fluid tracers remain trapped on these streamlines and are unable to contact other regions of the flow domain. As a result, fluid mixing is greatly hindered, especially in the axial direction. The lack of efficient axial mixing is verified computationally and experimentally. Such mixing limitations, however, are readily overcome by introducing a small-amplitude vertical rocking motion that disrupts both symmetry and recirculation, leading to much faster and complete axial mixing. The frequency of such motion is shown to have a significant effect on mixing rate, which is a critical parameter in the overall performance of roller bottles.     

齐口裂腹鱼上溯过程中“冲刺-滑行”行为对水动力的响应

研究以西南山区特有鱼种齐口裂腹鱼(Schizothorax prenanti)为研究对象, 对其游泳行为模式进行量化解译, 寻找其偏好的水动力学条件, 构建水流条件与生态行为的纽带。运用具有流速梯度的水槽创造非均匀流场条件, 得到齐口裂腹鱼在室内试验水槽内上溯的视频图像。运用图像识别技术, 计算上溯全过程的游泳动力学指标摆尾角度与摆尾频率, 在此基础上实现生态学与水动力学的耦合研究。研究表明, 齐口裂腹鱼在上溯过程中喜好在具有流速梯度处通过改变摆尾角度和摆尾频率等来适应非均匀流场, 其喜好摆尾角度为25°—35°, 喜好摆尾频率为2.5—3.5次/s, 偏好流速为0.20—0.40 m/s。随着水流速度的增大, 摆尾角度呈现逐渐减小的趋势, 且齐口裂腹鱼偏好选择在流速由大变小的区域, 进行摆尾冲刺加速, 且更趋向于摆尾角度变化为“弱强弱”的摆尾模式。滑行阶段引入滑行流速系数, 量化表示摆尾角度、滑行距离和流速三者间的耦合关系, 通过计算滑行距离对水流负方向上位移的贡献率, 得到滑行方向与水流负方向夹角。研究表明, 滑行流速系数为1.0—3.0时具有代表性, 齐口裂腹鱼对滑行方向与水流负方向夹角的偏好为40°—60°。研究利用多指标量化评价的方法, 以复杂流场为背景条件, 进一步满足过鱼设施建设需求。     

In vivo micro particle image velocimetry measurements of blood-plasma in the embryonic avian heart

The measurement of blood-plasma velocity distributions with spatial and temporal resolution in vivo is inevitable for the determination of shear stress distributions in complex geometries at unsteady flow conditions like in the beating heart. A non-intrusive, whole-field velocity measurement technique is required that is capable of measuring instantaneous flow fields at sub-millimeter scales in highly unsteady flows. Micro particle image velocimetry (muPIV) meets these demands, but requires special consideration and methodologies in order to be utilized for in vivo studies in medical and biological research. We adapt muPIV to measure the blood-plasma velocity in the beating heart of a chicken embryo. In the current work, bio-inert, fluorescent liposomes with a nominal diameter of 400 nm are added to the flow as a tracer. Because of their small dimension and neutral buoyancy the liposomes closely follow the movement of the blood-plasma and allow the determination of the velocity gradient close to the wall. The measurements quantitatively resolve the velocity distribution in the developing ventricle and atrium of the embryo at nine different stages within the cardiac cycle. Up to 400 velocity vectors per measurement give detailed insight into the fluid dynamics of the primitive beating heart. A rapid peristaltic contraction accelerates the flow to peak velocities of 26 mm/s, with the velocity distribution showing a distinct asymmetrical profile in the highly curved section of the outflow tract. In relation to earlier published gene-expression experiments, the results underline the significance of fluid forces for embryonic cardiogenesis. In general, the measurements demonstrate that muPIV has the potential to develop into a general tool for instationary flow conditions in complex flow geometries encountered in cardiovascular research.     

A human cell model for dynamic testing of MR contrast agents

To determine the initial feasibility of using magnetic resonance (MR) imaging to detect early atherosclerosis, we investigated inflammatory cells labeled with a positive contrast agent in an endothelial cell-based testing system. The human monocytic cell line THP-1 was labeled by overnight incubation with a gadolinium colloid (Gado CELLTrack) prior to determination of the in vitro release profile from T1-weighted MR images. Next, MR signals arising from both a synthetic model of THP-1/human umbilical vein endothelial cell (HUVEC) accumulation and the dynamic adhesion of THP-1 cells to activated HUVECs under flow were obtained. THP-1 cells were found to be successfully--but not optimally--labeled with gadolinium colloid, and MR images demonstrated increased signal from labeled cells in both the synthetic and dynamic THP-1/HUVEC models. The observed THP-1 contrast release profile was rapid, suggesting the need for an agent that is optimized for retention in the target cells for use in further studies. Detection of labeled THP-1 cells was accomplished with no signal enhancement from unlabeled cells. These achievements demonstrate the feasibility of targeting early atherosclerosis with MR imaging, and suggest that using an in vitro system like the one described provides a rapid, efficient, and cost-effective way to support the development and evaluation of novel MR contrast agents.     

The Influence of Drag on Nonlinear Oscillatory Flow through Concentric Annulus

A mathematical model has been developed to study the effect of particle drag parameter and frequency parameter on velocity and pressure gradient in nonlinear oscillatory two phase flow. The main purpose is to apply the model to study the combined effect of introduction of the catheter and elastic properties of the arterial wall on the pulsatile nature of the blood flow. We model the artery as an isotropic thin walled elastic tube and the catheter as a coaxial flexible tube. Blood is modeled as an incompressible particulate viscous Newtonian fluid. Perturbation technique has been applied to find the approximations for velocity and pressure gradient up to second order. Numerical solutions are investigated with graphical presentations to understand the effects of drag parameter, frequency parameter and phase angle on velocity along radial direction and pressure gradient along axial directions. As the drag parameter increases, mean pressure gradient and mean velocity will be decreased. As frequency parameter increases mean velocity profile bends near the outer wall. Due to elastic nature of artery wall, a thin catheter experience small oscillations and a thick catheter remains stationary inside the artery. Finally, the effect of catheterization on various physiologically important flow rate characteristics—mean velocity, mean pressure gradient are studied for a range of different catheter sizes, particle drag parameter and frequency parameters.     

Optimisation of a Stirred Bioreactor through the Use of a Novel Holographic Correlation Velocimetry Flow Measurement Technique

We describe a method for measuring three dimensional (3D) velocity fields of a fluid at high speed, by combining a correlation-based approach with in-line holography. While this method utilizes tracer particles contained within the flow, our method does not require the holographic reconstruction of 3D images. The direct flow reconstruction approach developed here allows for measurements at seeding densities in excess of the allowable levels for techniques based on image or particle reconstruction, thus making it suited for biological flow measurement, such as the flow in bioreactor. We outline the theory behind our method, which we term Holographic Correlation Velocimetry (HCV), and subsequently apply it to both synthetic and laboratory data. Moreover, because the system is based on in-line holography, it is very efficient with regard to the use of light, as it does not rely on side scattering. This efficiency could be utilized to create a very high quality system at a modest cost. Alternatively, this efficiency makes the system appropriate for high-speed flows and low exposure times, which is essential for imaging dynamic systems.     

Colorization and automated segmentation of human T2 MR brain images for characterization of soft tissues

Characterization of tissues like brain by using magnetic resonance (MR) images and colorization of the gray scale image has been reported in the literature, along with the advantages and drawbacks. Here, we present two independent methods; (i) a novel colorization method to underscore the variability in brain MR images, indicative of the underlying physical density of bio tissue, (ii) a segmentation method (both hard and soft segmentation) to characterize gray brain MR images. The segmented images are then transformed into color using the above-mentioned colorization method, yielding promising results for manual tracing. Our color transformation incorporates the voxel classification by matching the luminance of voxels of the source MR image and provided color image by measuring the distance between them. The segmentation method is based on single-phase clustering for 2D and 3D image segmentation with a new auto centroid selection method, which divides the image into three distinct regions (gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) using prior anatomical knowledge). Results have been successfully validated on human T2-weighted (T2) brain MR images. The proposed method can be potentially applied to gray-scale images from other imaging modalities, in bringing out additional diagnostic tissue information contained in the colorized image processing approach as described.     

Deformation of the human brain induced by mild angular head acceleration

Deformation of the human brain was measured in tagged magnetic resonance images (MRI) obtained dynamically during angular acceleration of the head. This study was undertaken to provide quantitative experimental data to illuminate the mechanics of traumatic brain injury (TBI). Mild angular acceleration was imparted to the skull of a human volunteer inside an MR scanner, using a custom MR-compatible device to constrain motion. A grid of MR "tag" lines was applied to the MR images via spatial modulation of magnetization (SPAMM) in a fast gradient echo imaging sequence. Images of the moving brain were obtained dynamically by synchronizing the imaging process with the motion of the head. Deformation of the brain was characterized quantitatively via Lagrangian strain. Consistent patterns of radial-circumferential shear strain occur in the brain, similar to those observed in models of a viscoelastic gel cylinder subjected to angular acceleration. Strain fields in the brain, however, are clearly mediated by the effects of heterogeneity, divisions between regions of the brain (such as the central fissure and central sulcus) and the brain's tethering and suspension system, including the dura mater, falx cerebri, and tentorium membranes.     

Optimization of Tagged MRI for Quantification of Liver Stiffness Using Computer Simulated Data

The heartbeat has been proposed as an intrinsic source of motion that can be used in combination with tagged Magnetic Resonance Imaging (MRI) to measure displacements induced in the liver as an index of liver stiffness. Optimizing a tagged MRI acquisition protocol in terms of sensitivity to these displacements, which are in the order of pixel size, is necessary to develop the method as a quantification tool for staging fibrosis. We reproduced a study of cardiac-induced strain in the liver at 3T and simulated tagged MR images with different grid tag patterns to evaluate the performance of the Harmonic Phase (HARP) image analysis method and its dependence on the parameters of tag spacing and grid angle. The Partial Volume Effect (PVE), T1 relaxation, and different levels of noise were taken into account. Four displacement fields of increasing intensity were created and applied to the tagged MR images of the liver. These fields simulated the deformation at different liver stiffnesses. An Error Index (EI) was calculated to evaluate the estimation accuracy for various parameter values. In the absence of noise, the estimation accuracy of the displacement fields increased as tag spacings decreased. EIs for each of the four displacement fields were lower at 0° and the local minima of the EI were found to correspond to multiples of pixel size. The accuracy of the estimation decreased for increasing levels of added noise; as the level increased, the improved estimation caused by decreasing the tag spacing tended to zero. The optimal tag spacing turned out to be a compromise between the smallest tag period that is a multiple of the pixel size and is achievable in a real acquisition and the tag spacing that guarantees an accurate liver displacement measure in the presence of realistic levels of noise.