3.1. Obtaining vortex regions through echo photovoltaic tracking of calcite particles
As shown in Figure 2 (see Section 2.1), calcite particles are clearly visible with medical ultrasound. The brightness of grayscale particles is 7-8 times (30-40 arbitrary units) the brightness of the surrounding water. In addition, the motion of particles in fluids is also well determined. Figure 6 shows an example of visualization of the vortex zone under the same experimental conditions. One can see that the upper part of the area behind the stenosis is free of particles, so the shape and size of the area are clearly visible.
In general, calcite particles are a very suitable material for the evaluation of vortex zones in narrow arteries using Echo-PV technology. High echogenicity of the particles is ensured due to the optimal density and size of the material. Furthermore, the particle size is at least an order of magnitude larger than that of blood cells (∼10 µm). This means that particle-cell interactions have no significant impact on particle trajectories.
Recently, Echo-PV introduced modern ultrasonic localization microscopy (ULM) technology with higher spatiotemporal resolution. ULM operates on scattered ultrasound vibrations reflected from microbubbles and serves as an echo contrast agent [54]. The size of individual microbubbles ranges from 3-10 microns. ULM uses high-speed recording of reflected echo signals (up to 20,000 frames/second). A specially developed visualization algorithm is applied to obtain the position of each microbubble and its movement from frame to frame. Therefore, ULM provides a spatial resolution of 5–20 µm.
The ULM method is a promising tool for in vivo measurements, especially for microvascular mapping [55,56,57]. However, the movement of microvesicles depends on their mechanical interactions with blood cells. The entry of bubbles into areas with eddies and high shear stress may lead to coalescence, fission, or dissolution of microbubbles, which may affect the accuracy of streamline detection in eddy areas. Therefore, it is necessary to verify the accuracy of ULM to determine local hemodynamic properties. For this purpose, it may be necessary to develop more complex models than solid particles.
It is worth noting that the limitations of medical ultrasound used in this work, related to the advantages of the ULM method for vascular ex vivo Echo-PV, can be overcome by enlarging the vessel size of the model, maintaining the size of the post-narrow vortex zone. Further in vitro studies are planned to confirm the feasibility of this large-scale transformation.
3.2. Computer Simulation and Accuracy Investigation
The results of the comparison between simulation and experiment are summarized below.
Figure 7 shows the field simulation results for 20 µm aluminum particles (used in the experiments) and 200 µm calcite particles.Modeling results superimposed on photos of particle motion during the Azuma experiment [1]. We note that the volume fraction distribution of the model particles has a good qualitative correspondence with the density and trajectory of the real particles.
However, analysis of model particle velocities (Fig. 8) shows that the slow vortices behind the stenosis do not capture larger particles well. As the particle size increases, the drag force increases more slowly than the inertia. Therefore, the inertia of the larger calcite particles begins to dominate and straightens the particle trajectories in the vortex zone. At the same time, the motion of small aluminum particles is largely determined by drag force, which carries the particles along the streamlines in the rear narrow vortex region. This causes the circulation trajectories of calcite particles in the area to become obscured. We can see this effect in Figure 6. At the same time, the small aluminum particles in the model gave clear circulation streamlines, which is consistent with the Azuma experiment.
A comparison of the absolute values of particle velocities (Figure 9) shows that particles are captured by the flow equally well regardless of size (the difference is no more than 0.1% of the fluid velocity). However, in the post-stenotic region (highlighted and enlarged by the red box), the circulating vortex profiles determined by the gradient method are significantly different.
To evaluate quantitative differences between methods using calcite and aluminum particles, we prepared templates for measured parameters in the poststenotic zone. Figure 10 schematically shows the profile of the circulating vortex, which was determined by the gradient method (Figure 9).
Using this template, process the simulation results and summarize the results.
Table 4 quantifies the poststenotic circulation area. The largest deviations observed were for the parameters “length” and “”. This is because larger calcite particles have greater inertia and are not well captured by eddies. It can be seen that using large calcite particles for detection does not result in a severe increase in eddy area size (up to 5%), which is important for The validation process is of great significance. Note that the largest errors are observed when determining the length of the vortex zone. This is explained by the influence of the greater inertia of large calcite particles, which, as mentioned earlier, rarely enter the vortex zone and Surround it. Therefore, the area closes later than when using small aluminum particles.
Experiments and modeling allowed us to develop some constraints for the Echo-PV technology under consideration.
This method has significant dependence on the characteristics of the ultrasonic equipment (low resolution, high noise, difficulty in restoring particle trajectories and smearing vortex zone boundaries), the liquid environment must be pre-cleaned and degassed to reduce noise, and fluid pumps must be provided in the occluded area Uniform fluid flow. For phantom vessels, this condition is not a big problem, but in the case of the body, it is much more difficult to provide them.
The particle (marker) size should significantly exceed the size of blood cells and aggregates. If the size of the marker is comparable to that of a red blood cell, the trajectory of the marker will be determined largely not by fluid flow but by interaction with the blood cells. Therefore, PV technology using large particles (>100 µm) is more suitable for detecting flow in containers. On the other hand, the use of large particles results in a nonlinear dependence of hydrodynamic and rheological forces on velocity. Therefore, the accuracy of in vivo detection will depend heavily on the shape of the container, the properties of the liquid, and the characteristics of the ultrasound machine.
For asymmetric vessels, the choice of acoustic focus projection and depth will play a key role. Multiple measurements in different projections may be required. Finally, it should be considered that, especially in low-speed fluid flows, the effect of gravity increases.
For in vitro experiments in model blood vessels, any available particulate material with sufficient echogenicity can be used. However, in vivo experiments are needed to confirm the safety of the material and its concentration. Selecting large solid particles with such properties is very difficult.In in vivo practice, bubbles are often used as tracers [58,59]. However, bubbles have several disadvantages. Solid particles have stronger acoustic backscatter and higher echo intensity than bubbles. This enhanced acoustic response allows for more reliable and accurate detection of solids, even in difficult flow conditions or in the presence of background noise. On the other hand, the acoustic signal of bubbles is weak, resulting in lower detection sensitivity and possible measurement errors. Particulate matter allows greater control over particle characteristics such as size, shape, and density that directly impact velocity measurement accuracy. Bubbles can introduce uncertainties and errors in velocity measurements due to their inherent variability in size and shape. Therefore, additional theoretical and clinical studies are needed to select granular materials that have a sufficiently strong acoustic response, have stable controllable properties, and are capable of providing high-precision local eddy current measurements.