Description of true volumetric blood flow measurement in the internal jugular vein with PixelFlux 4D measurements

The measurement of the flow volume in the internal jugular vein cannot be performed accurately with 2D or 3D sonographic imaging techniques. This is the reason why we (my son, Prof. Dr. rer. nat. habil Jakob Scholbach, now Professor of Mathematics at the University of Padova in Italy, and I) developed the four-dimensional volume flow measurements with the PixelFlux technique. Four-dimensional means that we record a three-dimensional image of the blood vessel in real time for a few heart cycles. So time is the fourth dimension.

Why is this necessary?

Measuring volume flow in blood vessels with ultrasound has to overcome a number of technical difficulties.

1. The flow signal reflects only a partial flow vector due to the angle between the ultrasound wave and the direction of blood flow (the so-called Doppler angle). The recorded signal is the true flow velocity signal multiplied by the cosine of the Doppler angle. Therefore, all flow velocities within a blood vessel must be recalculated with the cosine of the Doppler angle when using conventional two-dimensional ultrasound.
2. However, two-dimensional ultrasound can only show blood flow in a single imaging plane, the central axis of the blood vessel. However, the colour signals in this plane show much faster velocities than would be seen in imaging planes at the periphery of the vessel. Simple two-dimensional measurements therefore overestimate blood flow volume by using the fastest flow signals to calculate a mean flow velocity that is applied to the entire blood vessel.
3. Vessel size changes during heartbeat and respiration. However, conventional flow volume measurements use a fixed vessel size to calculate the cross-sectional area of the vessel, assuming that the vessel has a strictly circular shape.
4. Correct flow volume measurements, however, must take into account the ever-changing size of the blood vessel, which is only possible if the time axis is included not only for the spectral analysis of the velocities, but also for the display of the blood vessel itself, which is the basis for the area calculation. This is necessary because the flow volume is calculated by multiplying the instantaneous area of the blood vessel by the actual mean flow velocity of all red blood cells.
5. Veins are much softer than arteries and are therefore easily deformed by external pressure. This makes them unsuitable for simple flow volume calculations assuming a circular vessel shape.
6. Venous flow often shows a reverse flow next to an antegrade flow, for example at the inner part of a curved vessel segment. This requires subtraction of the retrograde flow volume from the antegrade flow volume. However, the ratio of the two flow volumes changes with respiration or pulsation of the adjacent arteries. This again requires the time axis for the measurements.
7. Correct flow volume measurement requires pixel-by-pixel measurement of the flow velocity of each pixel and the area occupied by the pixel to calculate the flow volume of each pixel. The total flow volume of the blood vessel is then the sum of the flow volumes of all individual pixels within the vessel.
8. The simultaneous measurement of all pixels within the blood vessel requires a transverse section of the pelvis and the representation of all flowing blood cells.
9. In a horizontal imaging plane, the spatial angle of the blood vessel to a horizontal plane extends the area but reduces the partial vector representing the velocity by the same factor – the cosine of the Doppler angle. thus, measurements from the horizontal plane allow simultaneous calculation of the changing area of the vessel and the changing velocity over the entire blood vessel.
10. Only the PixelFlux technique is able to calculate the pixel corrected flow velocity and area from such pulsating blood vessels, which are sliced in a horizontal plane by a matrix transducer.

The video available here shows a practical example of this bilateral jugular vein 4D flow measurement using the PixelFlux technique. It describes a patient with recurrent right-sided headaches and concomitant right-sided neck pain.

With the PixelFlux measurement, a strong discrepancy of the transported volume in favour of the right jugular vein could be reliably determined with low variation in multiple measurements. As the patient had bilateral jugular vein compression and a collateral route draining the compressed left renal vein (nutcracker syndrome) towards the spinal canal, the flow volume of this collateral route significantly influences the pressure in the spinal canal.

As the skull is drained mainly by the jugular veins, but also by the vertebral veins and the epidural plexus, congestion of the epidural plexus is critical in this patient. When the congestion increases due to increased volume draining from the left kidney towards the spinal canal, for example after a meal. The expanding stomach and intestines then put additional pressure on the left renal vein. Subsequently, compression of the jugular vein becomes symptomatic because compensatory drainage via the epidural plexus is reduced as intra-abdominal pressure increases.

The right jugular vein, which has a much greater transport capacity – 5 times greater than the left in this patient – reacts more strongly. The result is a greater increase in pressure in the right jugular vein, which has to dispose of more volume via the epidural plexus than the left, because the right jugular vein has a greater primary transport volume to begin with. If the secondary drainage via the epidural plexus is then reduced, a more rapid increase in pressure on the right side of the skull can be expected, causing pain in the pressurised right internal jugular vein and the right hemisphere of the skull. A large volume flow in a blood vessel is more sensitive to sudden changes in pressure. Larger volumes become congested and higher pressures build up very quickly. Thus, transport through the large right jugular vein is more sensitive to sudden changes in abdominal pressure than the left, which explains the right-sided migraine and neck pain in this patient.