Figure 1.
Blood flow and measurement volume.
Schematic representation of blood flow measurement using either red blood cells or artificial tracers. The depth of the measurement volume is shown as the shaded region and is bounded by and
.
Table 1.
Overview of imaging characteristics.
Figure 2.
Overview of experimental method.
Schematic representation of optical paths for in the vivo flow measurement: (left) using fluorescent tracers illuminated by a pulsed laser and (middle) using red blood cells illuminated by a pulsed LED. (right) A typical result of the measurements: a composite image of the PIV results for the fluorescent tracer particles (top) and red blood cells (bottom).
Figure 3.
(Left): Superposition of the vector fields using fluorescent tracers (bold, blue vectors) and red blood cells (red vectors) at systole; a small off-set is used between the vector fields for clarity. (Top right): velocity magnitude for both methods along profile A for 7 subsequent cardiac phases, ; artificial tracer (
) and RBCs (
). (Bottom right): Centerline velocity at profile A during the cardiac cycle for both methods.
Figure 4.
A scatterplot of the displacement measured using red blood cells versus the results using artificial tracers. Three time steps are shown, with an offset for clarity (0, 3 and 6 pixels). Horizontal and vertical components are shown separately ( and +, respectively). The dashed lines indicate perfect agreement.
Figure 5.
(Left): Superposition of the vector fields using fluorescent tracers (bold, blue vectors) and red blood cells (red vectors) at systole; a small off-set is used between the vector fields for clarity. (Top right): velocity magnitude for both methods along profile A for two time steps ( and
). (Bottom right): Centerline velocity at profile A for during the cardiac cycle for both methods.
Figure 6.
A scatterplot of the displacement measured using red blood cells versus the results using tracers. Data of the first three time steps are shown in one figure; horizontal and vertical components are shown separately ( and +, respectively). The dashed line indicates perfect agreement, the solid line is a quadratic fit. The inset shows the relative underestimation
based on the polynomial fit.
Figure 7.
Bland-Altman plots of the angle () and magnitude (
) of the measurements using laser
tracers and led
red blood cells.
. The error in angle is relatively small compared to the error in magnitude.
Figure 8.
Model prediction for underestimation.
Predicted underestimation of the measured velocity (compared to the true centerline velocity) as a function of blood vessel diameter, based on the ‘in silico’ PIV model.
Figure 9.
Example of predicted underestimation for various diameters.
Schematic representation of depth-of-correlation and resulting flow rate underestimation for red blood cells (RBC) and artificial tracers for measurements in geometries of 300, 200 and 100
. Model predictions for
= 25
.
Figure 10.
Effect of tracer choice on 3D reconstructions.
(A): Three-dimensional reconstruction using tracers. Left: single measurement result of the velocity magnitude. Top right: cross-section taken along the white line in the left-hand figure. Bottom right: in-plane and out-of-plane velocity profile. (B): Three-dimensional reconstruction using RBCs. Left: single measurement result of the velocity magnitude. Top right: cross-section taken along the white line in the left-hand figure; is the axis in the coordinate system aligned with the profile. Bottom right: in-plane and out-of-plane velocity profile.
. Note the apparent stretching along the
-axis, which is discussed in the section ‘Implications for 3D reconstructions’.