HIGH-FRAME RATE VECTOR FLOW
Recently HiFR-VF,
which derives the 2D velocity vectors at any location from multi-directional transmission and reception of plane waves based on Doppler technique [10,
11],
has been introduced on a high-end ultrasound commercial system equipped with linear transducers (bandwidth 3-9 MHz and 3-11 MHz) set for the vascular application.
The current version of the commercial HiFR-VF analyzes the flow at a pulse repetition frequency (PRF) of 3-10 kHz for 1.5 seconds,
thereby allowing the examination of at least one cardiac cycle,
and generates a frame rate of 374-1240 Hz.
The frame rate of 1240 Hz can be obtained only when
the maximum scale,
with a depth of 1.5 cm,
is selected: usually this can be applied to the superficial vessels with very high flow velocity,
such as AVF.
Both the magnitude and direction of the velocity are directly calculated by the velocity components along different scanning angles,
as shown in Fig.
1 [12,13].
There is no need to do angle corrections with the assumption of laminar flow.
The flow is represented by several colored arrows showing the different velocity,
magnitude,
and direction at every point of the vessel.
The color and size of the arrows allow visual quantification of the flow behavior (Fig.
2).
The high acquisition frame rate results in a detailed depiction and quantification of the complex flows [12,
14-16].
The flow characteristics can be evaluated visually,
to assess the flow pattern (e.g.,
laminar and helical flow,
recirculation,
counter eddy,
vortex,
and turbulence) by considering the vectors’ directions and lengths (Fig.
3).
WALL SHEAR STRESS
Also,
WSS measurements at different locations,
in which the spatial gradients of velocity components parallel to the vessel wall,
derived from the vector velocities,
can be calculated,
according to the definition of 2D WSS [17,
18],
by the general equation
τ = μ ∂v |
∂r | r=R
where τ is the so-called WSS,
μ is blood viscosity,
and the spatial gradient of velocity at r=R (location of the vessel wall) is also called wall shear rate (WSR).
Therefore,
the WSS can be thought of as the multiplication of blood viscosity and WSR.
In principle,
blood flow is non-Newtonian fluid,
and thus μ is not a constant and will be varied with WSR.
However,
some researchers [5,
19] are also of the opinion that the variation of μ is not that much and can be used directly as a constant to estimate WSS.
HIGH-FRAME RATE VECTOR FLOW AND WALL SHEAR STRESS
Using the HiFR-VF,
the WSS near complex flow can easily be estimated as vector velocities are already known,
and the calculation is done by finding the corresponding velocity components with the reference of vascular shape,
as presented in Fig.
4.
It can be seen that the conventional way with pulsed wave Doppler (PW) can only be used to estimate WSS with long and straight vessels based on the assumption of laminar flow.
For complex flow,
such as carotid bifurcation as shown in Fig.
4,
angle correction cannot be made by PW since the velocity direction is unknown at that location.
This can only be solved by measured vector velocities.
With the HiFR-VF,
velocity components used in WSS estimation can be derived by the vector quantities,
which therefore makes it possible for the calculation of WSS around non-laminar flow.
The instantaneous WSS for each frame can be calculated in the system using the general equation based on the vector velocities at each frame.
The max and mean WSS for a certain of a period (e.g.
one cardiac cycle including 300-600 frames approximately) can be obtained with the HiFR-VF for the further quantitative analysis (Fig.
5).
HiFR-VF supports a series of 6 WSS measurements along the vessel wall at the level of the inner layer in contact with the blood.
The WSS findings can be compared with the reference values already established in the literature: the normal max WSS in arteries is between 1 and 7 Pa; regions prone to plaque development experienced a WSS between -0.4 and +0.4 Pa [20].
CLINICAL APPLICATIONS OF WALL SHEAR STRESS MEASUREMENTS
Because local hemodynamic variations strongly influence the WSS,
the clinical applications of HiFR-VF relate to each change in vessel geometry variation and wall itself (e.g.
plaque),
which significantly affect the streamline profiles.
Consequently,
the consequence of flow behavior on the vessel wall can be analyzed by measuring the WSS values in case of laminar,
reverse,
and complex flows.
In the presence of mainly laminar flow,
shear stresses maintain their direction,
and their magnitude within a range of values and normal WSS values can be measured on the wall opposite to the flow divider in the internal carotid artery (ICA) (Fig.
6).
In the case of reverse flow,
abnormal WSS values can be detected on the wall opposite to the flow divider (Fig.
7).
When secondary complex flows develop at the level of the carotid sinus,
the HiFR-VF not only improves the understanding of streamlines separation and but highlights the area of flow instability and slow fluid movement where the WSS oscillates,
usually along the outer wall of the bifurcation (Fig.
8).
In the case of atherosclerosis,
the proper hemodynamic consistency of some plaques may be highlighted by HiFR-VF.
Different grades of stenosis generate different changes in shear stress (Fig.
9 and Fig.
10).
Higher shear stress values have been observed in regions where plaques promote turbulent flow or increase flow velocity (Fig.
11 and Fig 12).
Graphs obtained by measuring the WSS point-by-point along the anterior and posterior vessel walls can show the shear stress variations at the two edges of the plaque and on the plaque surface,
thus allowing a better understanding of the pathophysiological conditions.
HIGH-FRAME RATE VECTOR FLOW LIMITATIONS
HiFR-VF has some limitations which can affect WSS measurements.
At the moment HiFR-VF,
as a 2D technique,
doesn’t allow a precise comprehension of the actual 3D shape of the streamline.
Specifically,
WSS can currently be estimated in a 2D imaging plane only.
Nonetheless,
areas of oscillating WSS can be easily detected from the flow behaviour.
Despite the quantitative information on the flow,
the evaluation of complex flow with HiFR-VF is still visual,
thus subjected to inter-observer variability.