In vitro physical simulation and measurement of the vascular flow field
Generally, there are two key aspects of in vitro experimental studies targeting the intravascular flow field: production of the vessel structure model and measurement of the velocity field within the vessel model. First, the following two issues were included during modelling: the acquisition of vascular conformation data and the preparation of a solid blood vessel model. In terms of vessel configuration, early intravascular flow field studies mainly employed simple ideal models. For example, simulation studies of the carotid artery relied on a simple Y-shaped structure, which was convenient but significantly differed from the actual structure and inevitably led to insufficient flow field simulations [13-14]. For this reason, CT scanning techniques have been widely applied to obtain configuration information of real blood vessels and to accurately restore irregular vascular structures, such as intracranial aneurysms and carotid artery stenosis vessels [9, 15]. In regard to intracranial aneurysms, relatively systematic numerical and physical simulation studies have been carried out based on the actual structure, revealing the effect of stent placement on the haemodynamics occurring within the aneurysm . In terms of carotid stenotic vessels, haemodynamic analysis of the real vessel structure has only been performed via numerical simulation methods, but no physical simulation experiments have been conducted . To transform 3D structural data into solid models suitable for physical experiments, currently, only 3D printing technology can be relied upon to achieve high-precision recovery (a printing accuracy of 0.05 mm) , which has been applied to the fabrication of fine structures such as heart and aortic valves , but the preparation of vascular models for carotid stenosis research has not been reported. Two types of materials can be chosen to prepare solid models via 3D printing: rigid materials (photosensitive resin, with an elastic modulus of 2000 MPa) and flexible materials (hydrogel, with an elastic modulus of 80 kPa) [19-21]. Although the elasticity of the latter materials are close to that of carotid vessel walls (an elastic modulus of 47.7 kPa), the low transmittance (milky white colour) inhibits observation and measurement of the internal flow field of the model [21-22]. Thus, photosensitive resin is currently the only viable model material to achieve optical measurements of the stenotic flow field.
With regard to blood flow velocity field measurements, the spatial resolution of the measurement technique should be compatible with the physical model scale. To perform flow field analysis, at least 15 velocity data points are commonly measured in practice to yield a straight curve of the measured flow field [23-24]. Therefore, techniques with a resolution higher than 40 μm are required at carotid stenosis sites. The commonly applied clinical flow velocimetry methods, PC-MRI and ultrasound Doppler velocimetry, cannot realize intravascular velocity field measurements due to their low spatial resolution (0.5-1 mm) [6, 8-10, 25]. Echo-PIV with a higher spatial resolution (0.5 mm) relies on the microbubble contrast of tracer particles to measure the velocity field. Measurement of the velocity distribution characteristics in the radial section of the common carotid artery (10 mm in diameter) has been achieved [8-10, 26], but the spatial resolution remains insufficient for the study of the velocity field in stenosis vessels of the carotid artery (with an internal diameter of only approximately 1-3 mm). Currently, the micro-PIV technique with a maximum resolution of 1 μm can meet this requirement, which realizes the study of the velocity field of blood cells in smaller artificial microchannels (100 μm), yielding a parabolic distribution of the instantaneous velocity in the central plane [23, 27]. This technique has not yet been applied in the study of carotid stenosis vessels.
Based on the above discussion, it can be deduced that the combination of 3D printing technology and the micro-PIV technique represents the only feasible technical route to realize flow field measurement of carotid artery stenosis. In this study, this technical route was applied for the first time to achieve flow field measurement in stenotic vessels, and complete velocity field data of blood flowing across the stenosis location were measured within a flow field of 1.5 mm2 and 60 velocity points per unit length (1 mm) (in echo-PIV, only 2-3 data points are typically measured [8-9]), which notably improved the resolution and reliability of stenosis velocity measurement.
Radial cross-sectional velocity distribution characteristics of carotid artery stenosis.
The characteristics of the intravascular flow field distribution are fundamental elements of WSS calculations [9, 28]. Before this study, there were no reports on actual measurement of carotid artery stenosis or external flow field measurement, which left the divergence (parabolic and non-parabolic) between the different velocity distributions in numerical simulations unresolved. In this study, physical experiments and numerical calculations were performed to clarify the characteristics of the radial cross-sectional velocity distribution at the location of carotid stenosis: at normal human heart rates (heart rates ranging from 45-120 beats/min), the flow velocities in the central region of the stenosis location were similar and exhibited plateau-like distribution characteristics rather than an uncommon parabolic distribution.
From the available literature, as two common forms of the velocity distribution of blood flow, i.e., parabolic and plateau forms, the former form was mainly encountered in blood flow in healthy vessels and artificial microfluidic channels [6, 8-9, 29], while the latter was mainly found in the blood flow field of stenotic vessels with abrupt changes in vessel diameter . Studies have analysed blood flow in stenotic vessels of carotid arteries via computer simulations, and the characteristics of the blood velocity distribution in the vessel radial cross-section were considered the result of incomplete blood flow development in the vessel . Another numerical simulation study proposed that after blood flows across the location of blood vessel mutation, after a certain distance of a fixed tube diameter (5 times the tube diameter length), the blood velocity distribution completely developed into a parabolic distribution . Therefore, the sudden change in tube diameter caused by carotid plaques might be one of the important factors of the incomplete development of blood flow to form a plateau-like velocity distribution.
WSS estimation at the carotid artery stenosis location
Based on the characteristic plateau-like distribution of the velocity field at the carotid stenosis location, the WSS was calculated as 20.35 Pa considering the maximum velocity gradient near the vessel wall. However, under the premise of a lack of clinical flow field information, the WSS calculated based on the maximum velocity measured and the conventional parabolic distribution (the blue dotted line in Figure 8) [6-9] reached 7.25 Pa. Therefore, the current clinical estimation method of the WSS at the stenosis location could result in a difference up to 60%, which could notably affect the accuracy of mechanical analysis.
A full understanding of the distribution of the blood flow velocity field is very important for a more accurate calculation of the WSS of carotid artery stenosis. However, carotid vessels of different shapes and varying degrees of stenosis might exhibit notably different flow field characteristics [31-32], and clinical conditions do not facilitate comprehensive flow field measurement. To solve this problem, it is necessary to carry out more basic research to clarify the relationship between the plaque shape, flow field distribution and WSS, and amendments to the calculated WSS should be proposed for clinical stenosis research purposes to achieve accurate calculation.