The accuracy of volume flow measurements derived from pulsed wave Doppler: a study in the complex setting of forearm vascular access for hemodialysis

Purpose: Maturation of an arterio-venous fistula (AVF) frequently fails, with low postoperative fistula flow as a prognostic marker for this event. As pulsed wave Doppler (PWD) is commonly used to assess volume flow, we studied the accuracy of this measurement in the setting of a radio-cephalic AVF. Methods: As in-vivo validation of fistula flow measurements is cumbersome, we performed simulations, integrating computational fluid dynamics with an ultrasound (US) simulator. Flow in the arm was calculated, based on a patient-specific model of the arm vasculature pre and post AVF creation. Next, raw ultrasound signals were simulated, from which the Doppler spectra were calculated in both a proximal (brachial) and a distal (radial) location. Results: The velocity component in the direction of the US beam, in a centred, small, sample volume, can be captured accurately using PWD spectrum mean-tracking. However, deriving flow rate from these measurements is prone to errors: (i) the angle-correction which is influenced by the radial velocity components in the complex flow field; (ii) the largest error is introduced due to a lack of knowledge on the spatial flow profile

Synthetic vascular ultrasound imaging through coupled fluid-structure interaction and ultrasound simulations

Although ultrasonic imaging is commonly applied in cardiovascular research and clinical practice, current blood flow and vessel wall imaging methods are still hampered by several limitations. We developed a simulation environment integrating ultrasound (US) and fluid-structure interaction (FSI) simulations, allowing construction of synthetic US-images based on physiologically realistic behavior of an artery. An in-house code was developed to strongly couple the flow solver Fluent and structural solver Abaqus using an Interface Quasi-Newton technique. A distensible tube, representing the common carotid artery (length 5cm, inner diameter 6 mm, thickness 1 mm), was simulated. A mass flow inlet boundary condition, based on flow measured in a healthy subject, was applied. A downstream pressure condition, based on a non-invasively measured pressure waveform, was used. US-simulations were performed with Field II, allowing to model realistic transducers and scan sequences as used in clinical vascular imaging. To this end, scatterers were "seeded" in the fluid and structural domain and propagated during the simulated scan procedure based on flow and structural displacement fields from FSI. Simulations yielded raw ultrasound (RF) data, which were processed for arterial wall distension and shear rate imaging. Our simulations demonstrated that (i) the wall distension application is sensitive to measurement location (highest distension found when tracking the intima-lumen transition); (ii) strong reflections between tissue transitions can potentially cloud a correct measurement; (iii) maximum shear rate was underestimated during the complete cardiac cycle, with largest discrepancy during peak systole; (iv) due to difficulties measuring near-wall velocities with US, shear rate reached its maximal value at a distance from the wall (0.812 mm for anterior and 0.689 mm for posterior side). We conclude that our FSI-US simulation environment provides realistic RF-signals which can be processed into ultrasound-derived medical images and measurements

Fluid-structure interaction simulation of pulse propagation in arteries : numerical pitfalls and hemodynamic impact of a local stiffening

When simulating the propagation of a pressure pulse in arteries, the discretization parameters (i.e. the time step size and the grid size) need to be chosen carefully in order to avoid a decrease in amplitude of the traveling wave due to numerical dissipation. In this paper the effect of numerical dissipation is examined using a numerical fluid-structure interaction (FSI) model of the pulse propagation in an artery. More insight in the influence of the temporal and spatial resolution of the wave on the results of these simulations is gained using an analytical study in which the scalar linear one-dimensional transport equation is considered. Although this model does not take into account the full complexity of the problem under consideration, the results can be used as a guidance for the selection of the numerical parameters. Furthermore, this analysis illustrates the difference in accuracy that can be obtained using a second-order implicit time integration scheme instead of a first-order scheme. The results from the analytical and numerical studies are subsequently used to determine the settings necessary to obtain a grid and time step converged simulation of the wave propagation and reflection in a simplified model of an aorta with repaired aortic coarctation. This FSI model allows to study the hemodynamic impact of a stiff segment and demonstrates that the presence of a stiff segment has an important impact on a short pressure pulse, but has almost no influence on a physiological pressure pulse. This phenomenon is explained by analyzing the reflections induced by the stiff segment

Multiphysics modeling to support the development of vascular ultrasound imaging

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Developing Better Instructors Using the Principles to Actions Professional Learning Toolkit

This research report documents how a group of mathematics teacher educators collaborated to use the Principles to Actions (NCTM, 2014) (PtA) Professional Learning Toolkit in their classes, the tools they used to measure development in the future teachers, and the findings from the study. In keeping with other studies, using “effective mathematics teaching practices” as defined by Principles to Actions brought about changes in the beliefs of preservice elementary mathematics teachers toward best practices for teaching mathematics. There is hope that the benefits of seeing those instructional practices used by elementary classroom teachers through the PtA Toolkit videos help develop new commitments toward effective mathematics teaching practices in future educators

A multi-angle plane wave imaging approach for high frequency 2D flow visualization in small animals: simulation study in the murine arterial system

To preclinically investigate the role of hemodynamics in atherogenesis, mouse models are particularly useful due to the rapid disease development. As such, murine blood flow visualization has become an important tool, with current US systems equipped with traditional 1D flow imaging techniques, lacking spatial and/or temporal resolution to accurately resolve in-vivo flow fields. Hence, we investigated multi-angle plane wave imaging for ultrafast, 2D vector flow visualization and compared this approach with conventional pulsed Doppler in the setting of a mouse aorta with abdominal aortic aneurysm. For this purpose, we used a multiphysics model which allowed direct comparison of synthetic US images with the true flow field behind the image. In case of the abdominal aorta, we showed the mean flow estimation improved 9 % when using 2D vector Doppler compared to conventional Doppler, but still underestimated the true flow because the full spatial velocity distribution remained unknown. We also evaluated a more challenging measurement location, the mesenteric artery (aortic side branch), often assessed in a short-axis view close to the origin of the branch to avoid the smaller dimensions downstream. Even so, complex out-ofplane flow dynamics hampered a reliable flow assessment for both techniques. Hence, both cases illustrated the need for 3D vascular imaging, allowing acquisition of the full 3D spatial velocity profile