Hi Frederico,

I'm not sure I have really understood the question, if so I apologize.

I can only ask about TCD because I don't know about umbilical arteries, so, in emergerncy condition (brain injury) we focuse on diastolic velocity and PI, because we want to know about the arteries resistance and flow. High velocity reflex only the cardiac output and is not really interesting to evaluate how is the circulation in the brain (after brain injury)

Hope that will help and sorry if it's not the subject

Philippe

Hello Philippe, 

First of all thanks for your answer, it's interesting that you focus on the diastolic flow and the PI. To my knowledge they are correlated with intracranial pressure (ICP) which could explain the pessimistic outcome when PI is elevated. 

What I meant in my question is the following though: 

When using Doppler ultrasonography (pulsed Doppler) we insonate a specific sample volume, e.g. a segment of an artery (let's say the M1 segment of the MCA in TCD) and 'measure' blood flow velocity. What is measured is the backscattered acoustic pulse which is the sum of all backscattered pulses (scatterers are mainly red blood cells). Each red blood cell introduces a frequency shift which is proportional to its velocity. To the best of my knowledge in larger arteries, such as the middle cerebral artery (MCA) or the internal carotid artery (ICA) the flow is more or less laminar.

Thereby we get a velocity DISTRIBUTION (and not a single velocity). We can see this in the spectrogram from the fact that not only one frequency (i.e. one velocity is present). Now we take the maximal velocity envelope of the spectrogram and call this blood flow velocity (and use this signal (the envelope of the spectrogram) to compute the diastolic velocity or the PI in your case). How come we focus only on the maximal velocity present in the spectrogram and not the mean velocity or any other quantity?

Thanks again! 

What I mean by envelope is the yellow line in the attached figure in my question (envelope of the spectrogram)

Dear Federico,

We pick the maximum velocity because, in laminar flow, the mean velocity is half the maximum velocity (derivable from the parabolic velocity distribution characteristic of laminar flow). Laminar blood flow is the condition, aside from just above the aortic valve of the heart, in all  healthy vessels (according to "McDonald's Blood Flow in Arteries" -- the "Bible" for study of blood flow). With the mean velocity and the diameter of vessel, the flow is calculated....

If you are interested in the Doppler spectrum and determining the peak velocity in a flow, may I suggest (suspending modesty) some of the recent publications by me and Stefano Ricci in Florence.

Regards,

David

Thanks a lot for your great answer David!

I will definitely look into your papers.

Two follow-up questions,

You wrote, that with the mean velocity and the diameter of the vessel, flow is calculated. Aren't vessels elastic, such that during systole (maximal pressure) there is a passive distention (I'm not talking about active mygenoic or neurologic autoregulation) and during diastole vessels contrast. Do you also take the mean diameter then or is this change in diameter negligible (let's say in cerebral arteries such as the MCA)?

I am primarily interested in transcranial Doppler, I suppose there is no way to measure the lumen of cerebral vessels such as the MCA via ultrasound, right?

Kind Regards,

Federico

Federico,

If you are interested in flow volume, yes, the systolic diameter is the significant one, as most of flow occurs during the systolic phase. Accurate absolute flow volume, however, is rarely of clinical interest: person-to-person variation, as well as the impedance of the vasculature, varies so much that there is no "correct" volume flow like 37C for temperature. What is generally clinically significant are  gross changes, e.g. no flow indicating a blockage, or high flow indicating a hemorrhage, or relative changes, e.g. change in cerebral flow while holding your breath.

Various methods have been proposed for determining the lumen. One method that is appealing to engineers, is to use a narrow beam, and then a beam wide enough to ensure full insonation of the vessel, and look at the difference in backscattered energy at the same distance (so the attenuation is the same); if you know the diameter of the narrow beam, the ratio of the wide to narrow backscatter energy times the diameter of the narrow beam gives the lumen cross-section. (To do this right you must take into account the non-uniformities of the beams, so its not so simple -- or often used.)

See David Evans's publications for real expertise in this and other areas of transcranial Doppler measurements.

Regards,

David

I agree with David: Poiseuille’s law states that shear rate equals 8 * measured mean blood flow velocity / internal artery diameter. Alternatively, if only center line (or peak) flow velocity is determined, in conjunction with the assumption of a parabolic velocity profile, the numerator in the equation becomes 4 * measured peak blood flow velocity.

Relating to systolic/diastolic diameter, it is important to differentiate peripheral arteries (high RI) from low RI arteries. In femoral artery, diastolic flow at rest is negligible. In carotid, cerebral, renal and splenic arteries there are significant diastolic flows.

I found a rather old (Stroke, 1989) paper:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.602.3486&rep=rep1&type=pdf

There it is stated on the first page:

"The substitution of maximum velocity for average velocity was justified by Aaslid et al on the grounds that these two variables correlate in the femoral artery and that the blood flow velocity profile in the carotid artery would be expected to be relatively flat."

Now I am a bit confused what they mean by flat velocity profile. I suppose the velocity profile in the MCA is indeed laminar (parabolic and not flat), however the insonated sample volume might be so small to measure flow only in a fraction (e.g. 1/3) of the cross-sectional area. Thus inside that sample volume the velocity is more or less constant, resulting in a flat velocity profile (v = const).

The figure I attached in my question (screenshot) does not seem to have a very flat velocity profile though. A flat velocity profile would, to my understanding result in a "thin" line.

Does that reasoning make sense?

Dear Federico,

Aaslid was a terrific researcher -- really got TCD going -- but not an expert on blood flow. Yes, the peak and mean velocity are correlated (factor of 2 as discussed) in the femorals; the velocity distribution is NOT flat in the carotids.

Mario is indeed quite correct to say the RI is important to considerfor relative contribution of systolic flow to total flow. In theory, if you wanted to measure absolute flow volumes accurately, the diameter would be included as a function of the cardiac cycle, with the diameter changing from peak pressure to diastole (and keeping in mind that the diameter is not a linear function of pressure for arterial vessels). As mentioned, in general good approximations provide all the information that is useful clinically.....

You are quite right that the "width" of the line in the spectrogram is  related to the size of the beam; if it insonifies only the very center of flow, only the peak velocity will be measured. If  the beam is wide, you will see a wide spectrographic line representing the spread of velocities across the lumen -- but not the very lowest (next to the wall) velocities that are filtered out by the thump filter (sometimes called the wall filter).

Ideally, you can measure your beam width at the distance you're measuring  and compare it to the size of the MCA to see how "wide" the line should be. However, be warned:  the beam size you see in water will be much affected by the non-uniform transmission of the skull and tissue....so you will see a wider spectrographic line than such a measurement would suggest.  

It's a challenging area.

Regards,

David

agreed with David Vilkomerson's answers. thanx