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  • computed from the surface area was The

    2018-11-02

    computed from the surface area, was 75 %. The shape of the stenosis was non-axisymmetric and was described by the formulae for the upper (x) and the lower (x) borders of the stenosis in the mean longitudinal cross-section: where .where R is the radius of the tube; φ are the mean flow, the axial and the peripheral velocities, respectively. The swirl parameter for the insert used in the experiments (computed for the cross-section before the stenosis) is equal to 0.10 and weakly depends on the Reynolds number. The ratio of the maximum peripheral velocity to the maximum axial velocity of the swirling flow in the cross-section before the stenosis is 0.21, which is close to the physiological swirl parameter of the blood flow measured in clinic by the ultrasonic Doppler method [3]. An ultrasound LogicScan 64 scanner equipped with a linear transducer with an operational frequency of 5MHz was used to obtain the experimental data on the velocity field in the stenosed vessel model. When working with the device, the Doppler velocity spectrum was displayed on the computer screen in real time through the EchoWave II program interface processing the scanner signals. The length of the reverse-flow zone was measured through Doppler color flow mapping by the following procedure. The transducer was fixed on a holder above the vessel model so that the angle θ between the scanning plane and the vessel axis was equal to 60°, and the axes of the vessel and the transducer lay in a plane perpendicular to the symmetry plane of the stenosis (Fig. 3). Initially, the scanning plane was located in such a cross-section behind the stenosis for which a blue-colored area with velocities directed away from the transducer was clearly visible in the graphical interface window of EchoWave II (see the gray-colored area in Fig. 3). The transducer was then moved downstream until it kras-pdeδ inhibitor reached a cross-section where the blue zone vanished. The distance between this cross-section and the minimum cross-section of the stenosis was interpreted as the length of the reverse-flow zone (assuming that the flow separates from the wall in the center of the stenosis). We should note that the actual length L of the reverse-flow zone exceeded the LUS measured by the described procedure (see Fig. 3). The reason for this is that the ultrasound scanner is incapable of measuring flow velocities slower than a certain limit (by its absolute value); consequently, osteoclasts becomes impossible to visualize the zone of low negative velocities in the vicinity of the point (line) of the flow attaching to the wall. One of the below-described results of the present study is in determining a refining computed correction Δ L for the measured length of the reverse-flow zone. The maximum axial velocity was measured in the pulsed wave Doppler mode in the following way. A Doppler angle equal to 60° and a maximum measuring volume with a characteristic size of 5mm were set in EchoWave II. The center of this volume was matched with the vessel axis; the maximum value of the axial velocity in the measuring volume was read from the screen. From now on, the quantity shall be called the maximum axial Doppler velocity. We should emphasize that its value adequately reflects the value of the real maximum axial velocity in the current cross-section only if the transverse velocities are relatively slow (Fig. 4). In the general case, the connection between the maximum axial Doppler velocity , measured by the ultrasound scanner, and the actual maximum axial velocity in this cross-section is determined by the relation, where θ is the angle between the ultrasound transducer and the vessel axis. It should be noted here that the chosen arrangement of the transducer relative to the symmetry plane of the stenosis (see Fig. 4) allowed to virtually eliminate the influence of the velocity component on the results of measuring the maximum axial velocity. Indeed, without swirling, the flow is symmetrical relative to the middle plane of the stenosis, and the maximum axial velocity lies in this plane or close to it, while the transverse velocity is neglectably slow there. The numerical simulation data (obtained by the below-described procedure) was used to estimate the discrepancy between the actual axial velocity and the one measured by the ultrasound scanner for the case of the swirling flow, when the value is largely, if not mainly, determined by the circular velocity component. According to the above-mentioned data, this discrepancy did not exceed 15% in the zone past the stenosis.