Accuracy of carotid strain estimates from ultrasonic wall tracking: a study based on multiphysics simulations and in vivo data

We used a multiphysics model to assess the accuracy of carotid strain estimates derived from a 1-D ultrasonic wall tracking algorithm. The presented tool integrates fluid-structure interaction (FSI) simulations with an ultrasound simulator (Field II), which allows comparison of the ultrasound (US) images with a ground truth. Field II represents tissue as random points on which US waves reflect and whose position can be updated based on the flow field and vessel wall deformation from FSI. We simulated the RF-signal of a patient-specific carotid bifurcation, including the blood pool as well as the vessel wall and surrounding tissue. Distension estimates were obtained from a wall tracking algorithm using tracking points at various depths within the wall, and further processed to assess radial and circumferential strain. The simulated data demonstrated that circumferential strain can be estimated with reasonable accuracy (especially for the common carotid artery and at the lumen-intima and media-adventitia interface), but the technique does not allow to reliably assess intra-arterial radial strain. These findings were supported by in vivo data of 10 healthy adults, showing similar circumferential and radial strain profiles throughout the arterial wall. We concluded that these deviations are present due to the complex 3-D vessel wall deformation, the presence of specular reflections and, to a lesser extent, the spatially varying beam profile, with the error depending on the phase in the cardiac cycle and the scanning location.     

血管壁动态信息的频谱分析

将功率谱分析的理论运用于血管壁动态信息的分析中,得出了正常人组和病人组压力位移波信号及其速度波信号的典型波形图.其分析结果表明:A信号和D信号的G参数和H参数不但具有统计学意义,而且与人体血管壁的弹性程度成正比,因此该两信号可以作为血管壁弹性程度疾病定量诊断的主要特征量,对早期定量诊断血管性疾病具有一定的临床意义.     

Design, fabrication, and in vitro evaluation of an in vivoultrasonic Doppler wall shear rate measuring device

In vivo wall shear rates have been obtained based on estimates from either volume flow rate or single-point velocity measurements along with the wall no slip assumption and a simple linear regression. Recent results (R.S. Fatemi and S.E. Rittgers, 1994) have shown that, under pulsatile flow conditions, wall shear rates are more accurately predicted by using up to four velocity points and a second- or third-order polynomial curve fit. The authors evaluate the accuracy of a new, in vivo transducer capable of determining wall shear rates nonintrusively from velocities at three points along a line perpendicular to the vessel wall. Three 20-MHz ultrasound crystals were embedded in an elastomer at distances of 1.5 and 2.1 mm with beam angles of 30°, 15°, and 60° to the horizontal plane. Microscopic examination showed that intercrystal spacings were within 1.5% of the design and the crystal angles were placed within 2.0%. In vitro calibration was performed under steady and pulsatile flow conditions with average shear rates being within 4.3±17.3% and 0.2±0.6.0% respectively, of the theoretically predicted values. Furthermore, peak and oscillatory shear rates were within -5.6±2.2% and -2.4±5.7% accuracy, respectively. Results from this study show this device to be capable of providing accurate wall shear rates in vivo     

In vivo hemodynamic evaluation based on transverse Dopplermeasurements of blood velocities and vessel diameter

We have developed a method for simultaneously measuring the blood flow velocity distributions along a line perpendicular to the vessel wall and the instantaneous diameter of the common carotid artery. Thus, the wall shear rates and shear rate distribution across the arterial lumen could be computed accurately. In this method, transverse Doppler technique is combined with ultrasonic A echo-mode, using only one single crystal transducer. In order to satisfy the requirements of high spatial and velocity resolutions, especially extending to a very low velocity range in the case of low signal-to-noise ratio, a combination scheme of 10-MHz operating frequency, sample volume tracking, 12-bit A/D, 512-point fast Fourier transform with 5-kHz sample rate, spectrum average, variable threshold for bandwidth estimation, smoothing of velocity curves, and hardware was carefully designed. The velocity distribution measurements based on transverse Doppler spectrums were also validated under the steady flow conditions using a flow loop system. Results from this study show this ultrasonic system to be capable of measuring the shear rates at wall accurately and shear rate distributions across the common carotid arterial lumen.     

Patient-Specific Prediction of Coronary Plaque Growth From CTA Angiography: A Multiscale Model for Plaque Formation and Progression

Computational fluid dynamics methods based on in vivo 3-D vessel reconstructions have recently been identified the influence of wall shear stress on endothelial cells as well as on vascular smooth muscle cells, resulting in different events such as flow mediated vasodilatation, atherosclerosis, and vascular remodeling. Development of image-based modeling technologies for simulating patient-specific local blood flows is introducing a novel approach to risk prediction for coronary plaque growth and progression. In this study, we developed 3-D model of plaque formation and progression that was tested in a set of patients who underwent coronary computed tomography angiography (CTA) for anginal symptoms. The 3-D blood flow is described by the Navier-Stokes equations, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The low density lipoprotein (LDL) transports in lumen of the vessel and through the vessel tissue (which has a mass consumption term) are coupled by Kedem-Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. A full 3-D model was created. It includes blood flow and LDL concentration, as well as plaque formation and progression. Furthermore, features potentially affecting plaque growth, such as patient risk score, circulating biomarkers, localization and composition of the initial plaque, and coronary vasodilating capability were also investigated. The proof of concept of the model effectiveness was assessed by repetition of CTA, six months after.     

The removal of wall components in Doppler ultrasound signals by using the empirical mode decomposition algorithm

Doppler ultrasound systems, used for the noninvasive detection of the vascular diseases, normally employ a high-pass filter (HPF) to remove the large, low-frequency components from the vessel wall from the blood flow signal. Unfortunately, the filter also removes the low-frequency Doppler signals arising from slow-moving blood. In this paper, we propose to use a novel technique, called the empirical mode decomposition (EMD), to remove the wall components from the mixed signals. The EMD is firstly to decompose a signal into a finite and usually small number of individual components named intrinsic mode functions (IMFs). Then a strategy based on the ratios between two adjacent values of the wall-to-blood signal ratio (WBSR) has been developed to automatically identify and remove the relevant IMFs that contribute to the wall components. This method is applied to process the simulated and clinical Doppler ultrasound signals. Compared with the results based on the traditional high-pass filter, the new approach obtains improved performance for wall components removal from the mixed signals effectively and objectively, and provides us with more accurate low blood flow.     

Ultrasound measurement of brachial flow-mediated vasodilator response

Brachial artery flow-mediated vasodilation is increasingly used as a measure of endothelial function. High resolution ultrasound provides a noninvasive method to observe this flow-mediated vasodilation by monitoring the diameter of the artery over time following a transient flow stimulus. Since hundreds of ultrasound images are required to continuously monitor brachial diameter for the 2-3 min during which the vasodilator response occurs, an automated diameter estimation is desirable. However, vascular ultrasound images suffer from structural noise caused by the constructive and destructive interference of the backscattered signals, and the true boundaries of interest that define the diameter are frequently obscured by the multiple-layer structure of the vessel wall. These problems make automated diameter estimation strategies based on the detection of the vessel wall boundary difficult. We obtain a robust automated measurement of the vasodilator response by automatically locating the artery using a variable window method, which gives both the lumen center and width. The vessel wall boundary is detected by a global constraint deformable model, which is insensitive to the structural noise in the boundary area. The ambiguity between the desired boundary and other undesired boundaries is resolved by a spatiotemporal strategy. Our method provides excellent reproducibility both for interreader and intrareader analyzes of percent change in diameter, and has been successfully used in analyzing over 4000 brachial flow-mediated vasodilation scans from several medical centers in the United States.     

血管壁小应变数学模型研究

分析血管壁的弹性形变,对心血管疾病的临床诊治和手术方案选择有重要意义.在进行合理假设的前提下,首先建立微元线段的小应变分析模型,再利用有限元分析方法将血管壁区域划分为若干三角形面微元,用三角形的三个顶点和三条边的位移函数导出三角形微元域的形变模型,通过模型计算结果分析及有效性验证表明:血管壁小应变力学模型具有较好的适用性和实用性.与文献方法相比,最后呈现的结果不仅能计算出应变大小,还能显示应变方向,而且分别给出三个方向的应变值.     

A reconstruction method for gappy and noisy arterial flow data

Proper orthogonal decomposition (POD), Kriging interpolation, and smoothing are applied to reconstruct gappy and noisy data of blood flow in a carotid artery. While we have applied these techniques to clinical data, in this paper in order to rigorously evaluate their effectiveness we rely on data obtained by computational fluid dynamics (CFD). Specifically, gappy data sets are generated by removing nodal values from high-resolution 3-D CFD data (at random or in a fixed area) while noisy data sets are formed by superimposing speckle noise on the CFD results. A combined POD-Kriging procedure is applied to planar data sets mimicking coarse resolution "ultrasound-like" blood flow images. A method for locating the vessel wall boundary and for calculating the wall shear stress (WSS) is also proposed. The results show good agreement with the original CFD data. The combined POD-Kriging method, enhanced by proper smoothing if needed, holds great potential in dealing effectively with gappy and noisy data reconstruction of in vivo velocity measurements based on color Doppler ultrasound (CDUS) imaging or magnetic resonance angiography (MRA).     

ARTreat Project: three-dimensional numerical simulation of plaque formation and development in the arteries

Atherosclerosis is a progressive disease characterized by the accumulation of lipids and fibrous elements in arteries. It is characterized by dysfunction of endothelium and vasculitis, and accumulation of lipid, cholesterol, and cell elements inside blood vessel wall. In this study, a continuum-based approach for plaque formation and development in 3-D is presented. The blood flow is simulated by the 3-D Navier-Stokes equations, together with the continuity equation while low-density lipoprotein (LDL) transport in lumen of the vessel is coupled with Kedem-Katchalsky equations. The inflammatory process was solved using three additional reaction-diffusion partial differential equations. Transport of labeled LDL was fitted with our experiment on the rabbit animal model. Matching with histological data for LDL localization was achieved. Also, 3-D model of the straight artery with initial mild constriction of 30% plaque for formation and development is presented.     

Vessel boundary tracking for intravital microscopy via multiscale gradient vector flow snakes

Due to movement of the specimen, vasodilation, and intense clutter, the intravital location of a vessel boundary from video microscopy is a difficult but necessary task in analyzing the mechanics of inflammation and the structure of the microvasculature. This paper details an active contour model for vessel boundary detection and tracking. In developing the method, two innovations are introduced. First, the B-spline model is combined with the gradient vector flow (GVF) external force. Second, a multiscale gradient vector flow (MSGVF) is employed to elude clutter and to reliably localize the vessel boundaries. Using synthetic experiments and video microscopy obtained via transillumination of the mouse cremaster muscle, we demonstrate that the MSGVF approach is superior to the fixed-scale GVF approach in terms of boundary localization. In each experiment, the fixed scale approach yielded at least a 50% increase in root mean squared error over the multiscale approach. In addition to delineating the vessel boundary so that cells can be detected and tracked, we demonstrate the boundary location technique enables automatic blood flow velocity computation in vivo.     

Model-based quantitation of 3-D magnetic resonance angiographic images

Quantification of the degree of stenosis or vessel dimensions are important for diagnosis of vascular diseases and planning vascular interventions. Although diagnosis from three-dimensional (3-D) magnetic resonance angiograms (MRA's) is mainly performed on two-dimensional (2-D) maximum intensity projections, automated quantification of vascular segments directly from the 3-D dataset is desirable to provide accurate and objective measurements of the 3-D anatomy. A model-based method for quantitative 3-D MRA is proposed. Linear vessel segments are modeled with a central vessel axis curve coupled to a vessel wall surface. A novel image feature to guide the deformation of the central vessel axis is introduced. Subsequently, concepts of deformable models are combined with knowledge of the physics of the acquisition technique to accurately segment the vessel wall and compute the vessel diameter and other geometrical properties. The method is illustrated and validated on a carotid bifurcation phantom, with ground truth and medical experts as comparisons. Also, results on 3-D time-of-flight (TOF) MRA images of the carotids are shown. The approach is a promising technique to assess several geometrical vascular parameters directly on the source 3-D images, providing an objective mechanism for stenosis grading.     

Noninvasive vascular elastography: theoretical framework

Changes in vessel wall elasticity may be indicative of vessel pathologies. It is known, for example, that the presence of plaque stiffens the vascular wall, and that the heterogeneity of its composition may lead to plaque rupture and thrombosis. Another domain of application where ultrasound elastography may be of interest is the study of vascular wall elasticity to predict the risk of aneurysmal tissue rupture. In this paper, this technology is introduced as an approach to noninvasively characterize superficial arteries. In such a case, a linear array ultrasound transducer is applied on the skin over the region of interest, and the arterial tissue is dilated by the normal cardiac pulsation. The elastograms, the equivalent elasticity images, are computed from the assessment of the vascular tissue motion. Investigating the forward problem, it is shown that motion parameters might be difficult to interpret; that is because tissue motion occurs radially within the vessel wall while the ultrasound beam propagates axially. As a consequence of that, the elastograms are subjected to hardening and softening artefacts, which are to be counteracted. In this paper, the Von Mises (VM) coefficient is proposed as a new parameter to circumvent such mechanical artefacts and to appropriately characterize the vessel wall. Regarding the motion assessment, the Lagrangian estimator was used; that is because it provides the full two-dimensional strain tensor necessary to compute the VM coefficient. The theoretical model was validated with biomechanical simulations of the vascular wall properties. The results allow believing in the potential of the method to differentiate hard plaques and lipid pools from normal vascular tissue. Potential in vivo implementation of noninvasive vascular elastography to characterize abdominal aneurysms and superficial arteries such as the femoral and the carotid is discussed.     

Development and application of three-dimensional light distribution model for laser irradiated tissue

A three-dimensional model for estimating light distribution in laser irradiated tissue is presented. Multiple scattering and absorption of the laser beam are modeled using seven fluxes. One-, two-, and three-dimensional solutions are discussed and light distributions computed from the seven flux model are compared to those computed with the diffusion approximation. Methods for obtaining the phase function, absorption coefficient, and scattering coefficient for tissue are discussed and illustrated with measurements for human aortic vessel wall at the wavelength of 632.8 nm. Measured values are used in the seven flux model to estimate the rate of heat generation in the vessel wall.     

Accuracy in Prediction of Catheter Rotation in IVUS With Feature-Based Optical Flow—A Phantom Study

The quantitative assessment of and compensation for catheter rotation in intravascular ultrasound images presents a fundamental problem for noninvasive characterization of the mechanical properties of the coronary arteries. A method based on the scale-space optical flow algorithm with a feature-based weighting scheme is proposed to account for the aforementioned artifact. The computed vector field, describing the misalignment between two consecutive frames, allows the quantitative assessment of the amount of vessel wall tissue motion, which is directly related to the catheter rotation. Algorithm accuracy and robustness were demonstrated on two tissue-mimicking phantoms, subjected to controlled amount of angular deviation. The proposed method shows a great reliability in the prediction of catheter rotational motion up to 4deg.     

Identification of hemodynamically optimal coronary stent designs based on vessel caliber

Coronary stent design influences local patterns of wall shear stress (WSS) that are associated with neointimal growth, restenosis, and the endothelialization of stent struts. The number of circumferentially repeating crowns N(C) for a given stent design is often modified depending on the target vessel caliber, but the hemodynamic implications of altering N(C) have not previously been studied. In this investigation, we analyzed the relationship between vessel diameter and the hemodynamically optimal N(C) using a derivative-free optimization algorithm coupled with computational fluid dynamics. The algorithm computed the optimal vessel diameter, defined as minimizing the area of stent-induced low WSS, for various configurations (i.e., N(C)) of a generic slotted-tube design and designs that resemble commercially available stents. Stents were modeled in idealized coronary arteries with a vessel diameter that was allowed to vary between 2 and 5 mm. The results indicate that the optimal vessel diameter increases for stent configurations with greater N(C), and the designs of current commercial stents incorporate a greater N(C) than hemodynamically optimal stent designs. This finding suggests that reducing the N(C) of current stents may improve the hemodynamic environment within stented arteries and reduce the likelihood of excessive neointimal growth and thrombus formation.     

Endovascular magnetically guided robots: navigation modeling and optimization

This paper deals with the benefits of using a nonlinear model-based approach for controlling magnetically guided therapeutic microrobots in the cardiovascular system. Such robots used for minimally invasive interventions consist of a polymer binded aggregate of nanosized ferromagnetic particles functionalized by drug-conjugated micelles. The proposed modeling addresses wall effects (blood velocity in minor and major vessels' bifurcations, pulsatile blood flow and vessel walls, and effect of robot-to-vessel diameter ratio), wall interactions (contact, van der Waals, electrostatic, and steric forces), non-Newtonian behavior of blood, and different driving designs as well. Despite nonlinear and thorough, the resulting model can both be exploited to improve the targeting ability and be controlled in closed-loop using nonlinear control theory tools. In particular, we infer from the model an optimization of both the designs and the reference trajectory to minimize the control efforts. Efficiency and robustness to noise and model parameter's uncertainties are then illustrated through simulations results for a bead pulled robot of radius 250 μm in a small artery.     

狭窄血管多普勒血流信号的频谱仿真分析

通过数值仿真的方法分析狭窄血管内定常流多普勒血流信号的频谱特性,可为利用超声多普勒技术临床诊断血管狭窄提供依据.利用涡度－流函数方法计算狭窄管内的流场分布,估计出血管内不同位置的多普勒信号的功率谱密度函数,从中计算最大频率、平均频率和频谱宽度等参数,并分析它们在不同流速和狭窄程度下所表现出来的特征.     

Intravascular ultrasound image segmentation: a three-dimensional fast-marching method based on gray level distributions

Intravascular ultrasound (IVUS) is a catheter based medical imaging technique particularly useful for studying atherosclerotic disease. It produces cross-sectional images of blood vessels that provide quantitative assessment of the vascular wall, information about the nature of atherosclerotic lesions as well as plaque shape and size. Automatic processing of large IVUS data sets represents an important challenge due to ultrasound speckle, catheter artifacts or calcification shadows. A new three-dimensional (3-D) IVUS segmentation model, that is based on the fast-marching method and uses gray level probability density functions (PDFs) of the vessel wall structures, was developed. The gray level distribution of the whole IVUS pullback was modeled with a mixture of Rayleigh PDFs. With multiple interface fast-marching segmentation, the lumen, intima plus plaque structure, and media layers of the vessel wall were computed simultaneously. The PDF-based fast-marching was applied to 9 in vivo IVUS pullbacks of superficial femoral arteries and to a simulated IVUS pullback. Accurate results were obtained on simulated data with average point to point distances between detected vessel wall borders and ground truth <0.072 mm. On in vivo IVUS, a good overall performance was obtained with average distance between segmentation results and manually traced contours <0.16 mm. Moreover, the worst point to point variation between detected and manually traced contours stayed low with Hausdorff distances <0.40 mm, indicating a good performance in regions lacking information or containing artifacts. In conclusion, segmentation results demonstrated the potential of gray level PDF and fast-marching methods in 3-D IVUS image processing.     

Multiscale FEM modeling of vascular tone: from membrane currents to vessel mechanics

Regulation of vascular tone is a complex process that remains poorly understood. Here, we present our recent efforts for the development of physiologically realistic models of arterial segments for the analysis of vasoreactivity in health and disease. Multiscale modeling integrates intracellular and cell membrane components into whole-cell models of calcium and membrane potential dynamics. Single-cell models of vascular cells are combined into a multicellular model of the vascular wall, and vessel wall biomechanics are integrated with calcium dynamics in the smooth muscle layer. At each scale, continuum models using finite element method can account for spatial heterogeneity in calcium signaling and for nonuniform deformations of a vessel segment. The outlined approach can be used to investigate cellular mechanisms underlying altered vasoreactivity in hypertension.