A sensitivity analysis on 3D velocity reconstruction from multiple registered echo Doppler views

Full-volume three-component intraventricular vector flow mapping by triplane color Doppler

Objective. Intraventricular vector flow mapping (iVFM) is a velocimetric technique for retrieving two-dimensional velocity vector fields of blood flow in the left ventricular cavity. This method is based on conventional color Doppler imaging, which makes iVFM compatible with the clinical setting. We have generalized the iVFM for a three-dimensional reconstruction (3D-iVFM). Approach. 3D-iVFM is able to recover three-component velocity vector fields in a full intraventricular volume by using a clinical echocardiographic triplane mode. The 3D-iVFM problem was written in the spherical (radial, polar, azimuthal) coordinate system associated to the six half-planes produced by the triplane mode. As with the 2D version, the method is based on the mass conservation, and free-slip boundary conditions on the endocardial wall. These mechanical constraints were imposed in a least-squares minimization problem that was solved through the method of Lagrange multipliers. We validated 3D-iVFM in silico in a patient-specific CFD (computational fluid dynamics) model of cardiac flow and tested its clinical feasibility in vivo in patients and in one volunteer. Main results. The radial and polar components of the velocity were recovered satisfactorily in the CFD setup (correlation coefficients, r  = 0.99 and 0.78). The azimuthal components were estimated with larger errors ( r  = 0.57) as only six samples were available in this direction. In both in silico and in vivo investigations, the dynamics of the intraventricular vortex that forms during diastole was deciphered by 3D-iVFM. In particular, the CFD results showed that the mean vorticity can be estimated accurately by 3D-iVFM. Significance. Our results tend to indicate that 3D-iVFM could provide full-volume echocardiographic information on left intraventricular hemodynamics from the clinical modality of triplane color Doppler.

Colour-Doppler echocardiography flow field velocity reconstruction using a streamfunction-vorticity formulation

We introduce a new method (Doppler Velocity Reconstruction or DoVeR), for reconstructing two-component velocity fields from colour Doppler scans. DoVeR employs the streamfunction-vorticity equation, which satisfies mass conservation while accurately approximating the flow rate of rotation. We validated DoVeR using artificial colour Doppler images generated from computational fluid dynamics models of left ventricle (LV) flow. We compare DoVeR against the conventional intraventricular vector flow mapping (iVFM_1D) and reformulated iVFM (iVFM_2D). LV model error analysis showed that DoVeR is more robust to noise and probe placement, with noise RMS errors (nRMSE) between 3.81% and 6.67%, while the iVFM methods delivered 4.16-24.17% for iVFM_1D and 4.06-400.21% for iVFM_2D. We test the DoVeR and iVFM methods using in vivo mouse LV ultrasound scans. DoVeR yielded more haemodynamically accurate reconstructions, suggesting that it can provide a more reliable approach for robust quantification of cardiac flow.

Parameterized Strain Estimation for Vascular Ultrasound Elastography With Sparse Representation

Ultrasound vascular strain imaging has shown its potential to interrogate the motion of the vessel wall induced by the cardiac pulsation for predicting plaque instability. In this study, a sparse model strain estimator (SMSE) is proposed to reconstruct a dense strain field at a high resolution, with no spatial derivatives, and a high computation efficiency. This sparse model utilizes the highly-compacted property of discrete cosine transform (DCT) coefficients, thereby allowing to parameterize displacement and strain fields with truncated DCT coefficients. The derivation of affine strain components (axial and lateral strains and shears) was reformulated into solving truncated DCT coefficients and then reconstructed with them. Moreover, an analytical solution was derived to reduce estimation time. With simulations, the SMSE reduced estimation errors by up to 50% compared with the state-of-the-art window-based Lagrangian speckle model estimator (LSME). The SMSE was also proven to be more robust than the LSME against global and local noise. For in vitro and in vivo tests, residual strains assessing cumulated errors with the SMSE were 2 to 3 times lower than with the LSME. Regarding computation efficiency, the processing time of the SMSE was reduced by 4 to 25 times compared with the LSME, according to simulations, in vitro and in vivo results. Finally, phantom studies demonstrated the enhanced spatial resolution of the proposed SMSE algorithm against LSME.

Blood Speckle-Tracking Based on High-Frame Rate Ultrasound Imaging in Pediatric Cardiology

BACKGROUND

Flow properties play an important role in cardiac function, remodeling, and morphogenesis but cannot be displayed in detail with today's echocardiographic techniques. The authors hypothesized that blood speckle-tracking (BST) could visualize and quantify flow patterns. The aim of this study was to determine the feasibility, accuracy, and potential clinical applications of BST in pediatric cardiology.

METHODS

BST is based on high-frame rate ultrasound, using a combination of plane-wave imaging and parallel receive beamforming. Pattern-matching techniques are used to quantify blood speckle motion. Accuracy of BST velocity measurements was validated using a rotating phantom and by comparing BST-derived inflow velocities with pulsed-wave Doppler obtained in the left ventricles of healthy control subjects. To test clinical feasibility, 102 subjects (21 weeks to 11.5 years of age) were prospectively enrolled, including healthy fetuses (n = 4), healthy control subjects (n = 51), and patients with different cardiac diseases (n = 47).

RESULTS

The phantom data showed a good correlation (r = 0.95, with a tracking quality threshold of 0.4) between estimated BST velocities and reference velocities down to a depth of 8 cm. There was a good correlation (r = 0.76) between left ventricular inflow velocity measured using BST and pulsed-wave Doppler. BST displayed lower velocities (mean ± SD, 0.59 ± 0.14 vs 0.82 ± 0.21 m/sec for pulsed-wave Doppler). However, the velocity amplitude in BST increases with reduced smoothing. The clinical feasibility of BST was high, as flow patterns in the area of interest could be visualized in all but one case (>99%).

CONCLUSIONS

BST is highly feasible in fetal and pediatric echocardiography and provides a novel approach for visualizing blood flow patterns. BST provides accurate velocity measurements down to 8 cm, but compared with pulsed-wave Doppler, BST displays lower velocities. Studying blood flow properties may provide novel insights into the pathophysiology of pediatric heart disease and could become an important diagnostic tool.

Assessing the Performance of Ultrafast Vector Flow Imaging in the Neonatal Heart via Multiphysics Modeling and In Vitro Experiments

Ultrafast vector flow imaging would benefit newborn patients with congenital heart disorders, but still requires thorough validation before translation to clinical practice. This paper investigates 2-D speckle tracking (ST) of intraventricular blood flow in neonates when transmitting diverging waves at ultrafast frame rate. Computational and in vitro studies enabled us to quantify the performance and identify artifacts related to the flow and the imaging sequence. First, synthetic ultrasound images of a neonate's left ventricular flow pattern were obtained with the ultrasound simulator Field II by propagating point scatterers according to 3-D intraventricular flow fields obtained with computational fluid dynamics (CFD). Noncompounded diverging waves (opening angle of 60°) were transmitted at a pulse repetition frequency of 9 kHz. ST of the B-mode data provided 2-D flow estimates at 180 Hz, which were compared with the CFD flow field. We demonstrated that the diastolic inflow jet showed a strong bias in the lateral velocity estimates at the edges of the jet, as confirmed by additional in vitro tests on a jet flow phantom. Furthermore, ST performance was highly dependent on the cardiac phase with low flows (<5 cm/s), high spatial flow gradients, and out-of-plane flow as deteriorating factors. Despite the observed artifacts, a good overall performance of 2-D ST was obtained with a median magnitude underestimation and angular deviation of, respectively, 28% and 13.5° during systole and 16% and 10.5° during diastole.

Ultrasound Vector Flow Imaging-Part I: Sequential Systems

This paper gives a review of the most important methods for blood velocity vector flow imaging (VFI) for conventional sequential data acquisition. This includes multibeam methods, speckle tracking, transverse oscillation, color flow mapping derived VFI, directional beamforming, and variants of these. The review covers both 2-D and 3-D velocity estimation and gives a historical perspective on the development along with a summary of various vector flow visualization algorithms. The current state of the art is explained along with an overview of clinical studies conducted and methods for presenting and using VFI. A number of examples of VFI images are presented, and the current limitations and potential solutions are discussed.

Inverse Problem for Color Doppler Ultrasound-Assisted Intracardiac Blood Flow Imaging

For the assessment of the left ventricle (LV), echocardiography has been widely used to visualize and quantify geometrical variations of LV. However, echocardiographic image itself is not sufficient to describe a swirling pattern which is a characteristic blood flow pattern inside LV without any treatment on the image. We propose a mathematical framework based on an inverse problem for three-dimensional (3D) LV blood flow reconstruction. The reconstruction model combines the incompressible Navier-Stokes equations with one-direction velocity component of the synthetic flow data (or color Doppler data) from the forward simulation (or measurement). Moreover, time-varying LV boundaries are extracted from the intensity data to determine boundary conditions of the reconstruction model. Forward simulations of intracardiac blood flow are performed using a fluid-structure interaction model in order to obtain synthetic flow data. The proposed model significantly reduces the local and global errors of the reconstructed flow fields. We demonstrate the feasibility and potential usefulness of the proposed reconstruction model in predicting dynamic swirling patterns inside the LV over a cardiac cycle.

A novel methodology for personalized simulations of ventricular hemodynamics from noninvasive imaging data

Current state-of-the-art imaging techniques can provide quantitative information to characterize ventricular function within the limits of the spatiotemporal resolution achievable in a realistic acquisition time. These imaging data can be used to personalize computer models, which in turn can help treatment planning by quantifying biomarkers that cannot be directly imaged, such as flow energy, shear stress and pressure gradients. To date, computer models have typically relied on invasive pressure measurements to be made patient-specific. When these data are not available, the scope and validity of the models are limited. To address this problem, we propose a new methodology for modeling patient-specific hemodynamics based exclusively on noninvasive velocity and anatomical data from 3D+t echocardiography or Magnetic Resonance Imaging (MRI). Numerical simulations of the cardiac cycle are driven by the image-derived velocities prescribed at the model boundaries using a penalty method that recovers a physical solution by minimizing the energy imparted to the system. This numerical approach circumvents the mathematical challenges due to the poor conditioning that arises from the imposition of boundary conditions on velocity only. We demonstrate that through this technique we are able to reconstruct given flow fields using Dirichlet only conditions. We also perform a sensitivity analysis to investigate the accuracy of this approach for different images with varying spatiotemporal resolution. Finally, we examine the influence of noise on the computed result, showing robustness to unbiased noise with an average error in the simulated velocity approximately 7% for a typical voxel size of 2mm(3) and temporal resolution of 30ms. The methodology is eventually applied to a patient case to highlight the potential for a direct clinical translation.

4D Blood Flow Reconstruction Over the Entire Ventricle From Wall Motion and Blood Velocity Derived From Ultrasound Data

We demonstrate a new method to recover 4D blood flow over the entire ventricle from partial blood velocity measurements using multiple 3D+t colour Doppler images and ventricular wall motion estimated using 3D+t BMode images. We apply our approach to realistic simulated data to ascertain the ability of the method to deal with incomplete data, as typically happens in clinical practice. Experiments using synthetic data show that the use of wall motion improves velocity reconstruction, shows more accurate flow patterns and improves mean accuracy particularly when coverage of the ventricle is poor. The method was applied to patient data from 6 congenital cases, producing results consistent with the simulations. The use of wall motion produced more plausible flow patterns and reduced the reconstruction error in all patients.

A Reconstruction Method of Blood Flow Velocity in Left Ventricle Using Color Flow Ultrasound

Vortex flow imaging is a relatively new medical imaging method for the dynamic visualization of intracardiac blood flow, a potentially useful index of cardiac dysfunction. A reconstruction method is proposed here to quantify the distribution of blood flow velocity fields inside the left ventricle from color flow images compiled from ultrasound measurements. In this paper, a 2D incompressible Navier-Stokes equation with a mass source term is proposed to utilize the measurable color flow ultrasound data in a plane along with the moving boundary condition. The proposed model reflects out-of-plane blood flows on the imaging plane through the mass source term. The boundary conditions to solve the system of equations are derived from the dimensions of the ventricle extracted from 2D echocardiography data. The performance of the proposed method is evaluated numerically using synthetic flow data acquired from simulating left ventricle flows. The numerical simulations show the feasibility and potential usefulness of the proposed method of reconstructing the intracardiac flow fields. Of particular note is the finding that the mass source term in the proposed model improves the reconstruction performance.

3D velocity field and flow profile reconstruction from arbitrarily sampled Doppler ultrasound data

With the need for adequate analysis of blood flow dynamics, different maging modalities have been developed to measure varying blood velocities over time. Due to its numerous advantages, Doppler ultrasound sonography remains one of the most widely used techniques in clinical routine, but requires additional preprocessing to recover 3D velocity information. Despite great progress in the last years, recent approaches do not jointly consider spatial and temporal variation in blood flow. In this work, we present a novel gating- and compounding-free method to simultaneously reconstruct a 3D velocity field and a temporal flow profile from arbitrarily sampled Doppler ultrasound measurements obtained from multiple directions. Based on a laminar flow assumption, a patch-wise B-spline formulation of blood velocity is coupled for the first time with a global waveform model acting as temporal regularization. We evaluated our method on three virtual phantom datasets, demonstrating robustness in terms of noise, angle between measurements and data sparsity, and applied it successfully to five real case datasets of carotid artery examination.

3D echocardiography in congenital heart disease: a valuable tool for the surgeon

Real-time 3D echocardiography has been used increasingly in the assessment of patients with congenital heart disease. A number of studies have confirmed that this modality can be used as a complementary method to delineate morphology and spatial relationships of simple and more complex congenital heart lesions during surgical planning. Communication between the echocardiographer and surgeon can be simplified as simulation of surgical views can be achieved, thus minimizing the potential for error related to mental reconstruction. This review summarizes the available evidence for the role of real-time 3D echocardiography in congenital heart disease as an imaging modality to assist surgeons.

Towards a fast and efficient approach for modelling the patient-specific ventricular haemodynamics

Computer modelling of the heart has emerged over the past decade as a powerful technique to explore the cardiovascular pathophysiology and inform clinical diagnosis. The current state-of-the-art in biophysical modelling requires a wealth of, potentially invasive, clinical data for the parametrisation and validation of the models, a process that is still too long and complex to be compatible with the clinical decision-making time. Therefore, there remains a need for models that can be quickly customised to reconstruct physical processes difficult to measure directly in patients. In this paper, we propose a less resource-intensive approach to modelling, whereby computational fluid-dynamics (CFD) models are constrained exclusively by boundary motion derived from imaging data through a validated wall tracking algorithm. These models are generated and parametrised based solely on ultrasound data, whose acquisition is fast, inexpensive and routine in all patients. To maximise the time and computational efficiency, a semi-automated pipeline is embedded in an image processing workflow to personalise the models. Applying this approach to two patient cases, we demonstrate this tool can be directly used in the clinic to interpret and complement the available clinical data by providing a quantitative indication of clinical markers that cannot be easily derived from imaging, such as pressure gradients and the flow energy.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

3D intraventricular flow mapping from colour Doppler images and wall motion

We propose a new method to recover 3D time-resolved velocity vectors within the left ventricle (LV) using a combination of multiple registered 3D colour Doppler images and LV wall motion. Incorporation of wall motion, calculated from 3D B-Mode images, and the use of a multi-scale reconstruction framework allow recovery of 3D velocity over the entire ventricle, even in regions where there is little or no Doppler data. Our method is tested on the LV of a paediatric patient and is compared to 2D and 3D flow Magnetic Resonance Imaging (MRI). Use of wall motion information increased stroke volume accuracy by 14%, and enabled full 3D velocity mapping within the ventricle. Velocity distribution showed good agreement with respect to MRI, and vortex formation during diastole was successfully reconstructed.