3D Flow Imaging - SD

Introduction

I am Jonathan Rubin from the University of Michigan.
I'm a professor of radiology.
I'm the head of the section of ultrasound and,
and cross-sectional interventional radiology.
I'm gonna be talking today about 3D blood flow imaging,
whose time has come.
The application I think is robust
and will have a major impact on the way we perform
medical diagnoses in the future.
As you saw, I'm gonna be talking about 3D flow imaging.

Talk Outline

The outline of the talk is follows.
I'm gonna first talk about volume flow.
The major portion
of this talk is gonna be about volume flow.
To me this is one of the best applications
for 3D imaging and I think its time has come
and we should be doing this in very near future.
Then I'm gonna be talking about true flow,
true real 3D flow,
and that is mostly an intro to
pressure gradients measurements.

Volume Flow Imaging

Historical Background and Basis

First I'm gonna be talking about volume flow.
The volume flow technique I'm gonna be talking about was
initially described by Hot Ander Mindel in 1974.
However, really it was described by Gauss
at the end of the 18th
and 19th centuries when he lived.
The technique is based on
what's called Gauss's theorem, which says that
volume flow is a flux across any surface,
and I'm gonna be describing what
that means in just a minute.
The technique really was not viable until 3D
and four D imaging became available.
And now since both of them are available,
the method could be employed to actually measure volume,
flow volume, blood flow.

Current Limitations of Blood Flow Measurement

I'm sure you're all aware how
blood flow is measured.
Now there are many limitations to the actual acquisition
because of the way
that we acquire the data ourselves using ultrasound.
The properties that we would like to have,
which are not available now are we would like
the volume flow technique to be angle independent.
We'd like it not to assume any vessel geometry.
We'd like to not have to assume any flow profile,
and we'd like the measurement to be time independent.
None of those things exist presently.
This is a common carotid artery
and this is an example of
how volume flow might be detected presently.
First there's a Doppler sample line which you are all used to seeing.
The sample volume spans the vessel.
This first has to be angle corrected in order to compensate
for the change in the flow measurement based on the doppler shift.
Then you have to estimate the diameter
that estimation requires.
Assumes that the cross section is a circle.
The other thing is that the measurement is one dimensional.
As you can see, we are sampling along a line that implies
that the flow profile is cylindrically symmetric.
And since the diameter that we're measuring is fixed,
this doesn't compensate
for any of the pulsatility in the blood vessel, all
of these things are approximations,
which are almost invariably wrong.
And because of that, very few people use volume flow
as a standard portion of their imaging modality.
Once you actually make this measurement,
once you actually set this all up,
then you basically look for the mean velocity.
You'll notice that the envelope is what is being measured.
Here you measure the mean velocity.
Multiply that mean velocity times the cross-sectional area,
which you assume is a circle,
which we've already said is an assumption
that may not be correct
and that's the volume, that's volume flow.

The Volume Flow Technique

However, volume flow is really can be broken down into
a described in another way,
which is much more robust.
It turns out that if you have a whole bunch
of velocity vectors that are perpendicular
to a cross-sectional area
or a slice, if you can get every small unit of area,
which is what DA sub A means
and you can get the flow, the velocity
perpendicular to that slice, the mean velocity, all
that product and multiply it times the area, that product
is called flux.
If you then sum all of these fluxes up
and actually it's integrate, if it's a continuous process,
then sum is volume flow and that's all this says.
This is the velocity perpendicular to this area.
If you have a discreet sampling, which is what we have now,
then you take every local velocity,
multiply it times a small unit of area
and that's volume flow if you add them all up.
What's interesting about this is the velocity,
because this doppler is multiplied times the cosign
of theta, which is the doppler angle.
The area, however, increases by the cosign of theta.
For instance, if you have a circle
and then you rotate it at an angle, you get an ellipse.
The area of that ellipse increases by the angle
that you rotate it relative to the normal,
which is the doppler angle,
which would be equivalent to the Doppler angle.
And so that's divided by the cosign of theta.
If you can't, these two products cancel
and then all you end up
with again is local velocity times area.
And this now is angle independent
because the co-signs cancel.
I'll make that more clear in a few minutes.
So if you do all that stuff, you have volume flow.
What do you have to do to get this?
If this tube
or representation of a tube is a blood vessel,
the green arrow is the direction of the flow.
This plane, this black plane is
what a cross-sectional ultrasound slice would look
like in one dimension.
So we'd have a transducer up here producing this plane.
Actually the plane is two dimensions,
but we're cutting across this vessel.
Then the intersection of that plane with this
tube or the blood vessel is this yellow circle right here.
If you have a very small unit of area in that cross section when the blood flows through,
it displaces that area in a unit of time to produce this local volume.
That local volume divided
by the time in which it was displaced is the local
flux at that position.
If you take all of these guys, all of these small areas
and add 'em up, that like I said is volume flow.
The problem is that we sample across
this plane, this s represents a single cycle.
Sine wave shows where the ultrasound is going in
this particular rendition.
It turns out then that the doppler that you detect
is are doppler shifts in this plane.
That means that the flow that we see is totally
orthogonal or perpendicular to the flow we want to detect,
therefore every bit of flow
that's detected in this plane using a standard ultrasound,
if you've cut across the plane this way,
cut across the vessel this way would make,
would not be contributing anything to volume flow.
Because of that, we have to do what we do.
Now we have to do sagittal imaging
and estimate the cross section with a circle
and make all these symmetry assumptions.
However, if we have a 2D array
or can sample in which would allow us to sample in 3D, then
what you could do is propagate the sound
perpendicular to the surface.
So the sound beam now is going right at
that displaced volume.
That means that the normal
or the perpendicular flow to this plane
is now exactly what you measure with the dopp
with standard doppler at that position,
remember this flow is now perpendicular, is now
in the exact line of one
of these rays from the ultrasound scan head.
And that means that the doppler shift you measure
is actually perfectly corresponds to the velocity
of the blood at that point,
which remember is exactly what we want.
So now all we have to have is that area.
We now have the velocity independent of angle at
that point and that's volume flow.
So instead of having to correct all this stuff that we had
to do in 1D with a 1D array, we now using a 2D array,
producing a 3D image overcomes the major problems
that I talked about to show that it's angle independent,
we're now gonna rotate the scan head
and you can watch the cross-sectional area get larger
as you rotate the scan head
to make this more clear.

Angle Independence

If you use the normal component, that would be the component
of the blood that's going perpendicular to this plane,
which would be now right at the transducer.
You notice as you rotate the plane,
this component gets shorter,
but this area gets larger in exactly the same proportion
and since it's the product of that component times the area,
it's angle independent.
So volume flow is angle independent, which is a huge plus.
And this is just to show it again,
this is a cross-sectional area.
You're sampling the blood flow in this direction
perpendicular to that area.
That's the doppler angle, which you can see here the angle
to the blood flow, there's the blood flow
there, the angle's there.
The velocity that you measure, the correct velocity is that
where you measure times the cosign of theta,
but the area is divided by the cosine
of theta and they cancel.
So volume flow is angle independent.

Testing and Implementation

We've tested this technique.
Flow tubes using blood mimicking fluid.
We've tested it in dog carotid arteries
and femoral arteries.
We used a GE logic nine clinical 3D scanner.
This is a standard scanner.
We used linear array probes.
We also used the curve linear probe
and these are the linear arrays.
And then we had a research interface
where we actually took the Doppler data
and did this sum to calculate the flux.
However, like I said, this is,
this is conceptually quite simple
and could easily be done on the machine.
The integration calculates the flux as I said,
and that gives you volume flow.
There's some partial volume issues,
which I'm not gonna get into
and we use power doppler to correct those.
Here's what this looks like.
The curved array has two produces,
basically two curves.
There's one curve which corresponds to the face
of the transducer, and then there's another curve which
corresponds to the angle
that the transducer swings in space.
Now this is not a 2D array, this is a 1D array
with a mechanical motion that produces the third dimension.
This is very similar. This is exactly what's used in almost
all the 3D scanners today.
This still works for this technique and this is claimed.
There's volume flow, but you got two curves.
Now what's interesting about this is you don't need a
plane to integrate this flux.
All you need is a continuous curve sur a continuous surface.
It doesn't even, it can even be peace wise continuous,
it doesn't have to be smooth.
So this is very forgiving
and it turns out that the easiest surface to use is a curve,
a section of a Taurus or not a plane,
but that's a detail in the technique,
the technique works just fine with planes or curves.
What you end up with then is a cross section
of the vessel which corresponds to the ccan
and the ccan is where the money is.
That's why you need 3D.
If you now scan with this technique,
you can use multiple planes through the blood vessel.
All you have to do is cut the vessel with multiple surfaces.
Since this is volume flow,
if there's no branches coming off, blood is conserved.
So you can make multiple measurements.
So you can get very robust statistics
by scanning the flux across a whole bunch
of different surfaces going through the blood vessel.
This is a flow phantom, many
of you have seen this sort of thing.
This is a standard 2D image produced by A 1D array,
which one would see if scanning along the tube.
So this is flow along the tube
and this would be very similar to
what you would see if you were doing a standard color
doppler volume flow estimate.
However, when you swing the array across,
you get other planes.
So if you're swinging the array across the tube in the axial
elevational direction, you get this,
this would be equivalent to rotating the probe 90 degrees.
So this would be a very standard picture
and this doesn't provide the information you want.
What you want is this, which is the lateral elevational
slice, also known as a ccan where
you produce this image.
And every one of these images, every one of these pixels is
represents a doppler shift that's perpendicular
to the transducer face.
So all you have to do is add these up, you don't have
to angle correct them or anything.
And that's volume flow. So the ccan is where the money is.
This is a picture of this.
This is the ccan from,
transverse image.
And this would be what you would see
in the longitudinal image.
We want the plane that's corresponds
to this slice coming in and out of that section.
And this is what you get. You get this sort
of closed surface that's actually a Taurus but not a,
but it doesn't matter if you want to consider it a plane
where you just add up all of these velocity elements
and that's volume flow.

Consistency and Results

What kind of consistency can you get?
Here's a flow tube where we ran the pump at up
to 20 milliliters a second.
That's 1200 milliliters a minute, quite respectable.
The zeros correspond to the
transducer being parallel to the tube.
The X is correspond to the transducer
of the aperture being perpendicular to the tube.
Remember, it doesn't matter at all.
And you can see these estimates are really good up
to this highest estimate.
The problem with this one was that the flow was going
through so fast it was causing the pump to cavitate.
So we were getting gas bubbles, which skewed the
measurement estimate.
But up to that point, this gave very good
measurements in this setting.
It also works for pulsatile flow that was constant flow.
This, in this case, the pump is programmed like a carotid
artery and here the pump is programmed like a femoral artery
and you'll notice that there's forward
flow and reverse flow.
It's phasic just like a typical femoral arterial flow
that doesn't matter at all with this technique.
What you see here is something
I'm sure you're not used to seeing.
This is the original image, which is a transverse
by sweeping along the transverse plane, you get this image,
which is now a series of high velocity, low velocity
and no velocity positions throughout the tube.
The reason that that's happening is the pump is pulsatile,
but the sweep is slower than the pump rate.
So what we're seeing is the periodic flow in the tube
and the ccan, which is what we're interested in.
This has exactly the same property.
You can see there's high velocities and zeros
and lower velocities.
This doesn't matter if you wanna measure average flow.
And that's frankly what almost all the techniques
that exist today measure.
And what you do is you use something called the law
of large numbers to compensate for this variability
and you get a very good estimate of the mean.
I'll show you that in a minute.
Here's the flow in the simulated femoral artery.
You notice in this one particular cross section,
there's no flow because remember the flow is zero is
crossing zero several times
in the longitudinal scan you can see it's forward
and backwards blue represented by the red and blue
and zeros all the way down the blood vessel.
And in the ccan there's red and zero and blue.
None of this matters. It all works fine as long
as you can sample long enough.
That's the problem with pulsatile flow.
Here's the law of large numbers.
Here's a flow at 190 milliliters a minute.
And you can see as you take more
and more samples as the number
of volumes you can get arbitrarily
close to that measurement.
We all know that this works.
If this didn't work, casinos would be outta business.
So this frankly works perfectly fine.
The trouble is you have to sample a lot.
Now this is a characteristic of the fact
that we were using a mechanical scanner.
If we could have done this with a 2D array,
which is what's gonna happen in the future, this kind
of large number sampling will certainly be diminished.
And you can see what happens as you do more
and more samples, how the error falls off.
And this falls off as one over route N which is exactly
what you would expect in this kind of circumstance.
And you can get arbitrarily close estimates
to the correct value.
You can see that at 15 estimates where plus
or minus 5% standard error of the mean.
But like I said this, all of this is occurring
because we have a mechanical scan head.
If we had a real 2D array
and could do real time 3D, four D, this would not be as nearly as big an issue.
Here's a pulsatile phantom
and you can see there's femoral and there's a carotid.
And you can see they estimate the true values very closely
and you can do different heart rates
and you can use different tube sizes.
And remember it's angle independent.
So this measure is the correct match
and reason we did this this way is we have two different
flow rates on here, five millimeters a second
and 10 millimeters a second.
So the perfect match would be one,
and you can see that the distribution is well within 10%
or very close to 10, 10% in an upper limit of an error
for this, for the correct value
independent of the flow velocity.
What you'll notice however, is that there is a
wall filter range in which you can't detect doppler
and clearly that occurs.
This is a doppler technique,
so if you're absolutely perpendicular to the flow,
you can't see flow.
So this measurement will not alleviate that problem.
So there's a dead area in the middle just like
there is with any doppler technique,
but as long as you can measure doppler,
this thing works really well.
We've also done it, like I said, in dogs.
This is the femoral artery.
You can see there's reverse flow in diastole. It's phasic.
We then put a ligature around it
and you can see the classic pulses tarus parvis effect.
The diastolic flow is now above the baseline continuously.
However, if you knew the volume flow,
even though the waveform is different,
these are identical basically.
So there's no difference in the volume flow
even though the waveform has changed.
If you continue to tighten the ligature, you can see
that the volume flow, the waveform has gotten smaller
and the volume flow indeed does go down.
So we now plot these different flows as a function
of a flow meter measurement
where we had a flow meter on the artery of interest.
So we had gold standard measurements of all of these.
These lines are plus or minus 15%.
And you can see that these measurements are really tight
around the correct measurement.
The R squared was 0.95.
And if you force the line through zero,
the r squared is still a very respectable 0.93.
If you distribute the error, you get a mean error
of minus 7%.
However, this is still unbiased
because the standard deviation is plus or minus 9%.
The full width at half maximum is plus or minus 13%.
So this is a very good estimate.
The other thing that's important
to know is the flow meter itself,
which we had on the artery, has a plus or minus 5% error.
So this is a very respectable measurement of volume flow.

Conclusion on Volume Flow

In conclusion, this can be done with mechanical
or real time 2D arrays.
It eliminates the current limitations.
It does very well when compared to gold standards.
And I think this should be ready for prime time
and I would think
that in the very near future you're gonna be seeing volume
flow as one of the main applications for 3D scanners.

True 3D Flow Imaging

True Flow in 2D

The next thing I'm gonna talk about is true flow
the way, and I'm gonna talk about true flow in
two D I don't have any examples of true flow in 3D
but I'm gonna show you what the
ramifications of this will be.
I think in the future. So what you can do
to get true flow in 2D is to actually split the aperture of
an ultrasound array.
So you can scan from the right side steering from the right
to left, and then you can scan from the left side,
steering from left to right, and in the middle you end up
with two measurements of the velocity at every position.
That means you can orthogonally it into X and y
and produce a lateral
and axial velocity at every position.
You can either do this by sample receiving
from the same app, from the same apertures
that you're sending from, or you can always receive from the
center aperture as well.
But the ultimate result is the same.
And here's an example of this.
This is a rotating disc which contains scatterers
and as you'd expect, the beam is being steered from left
to right and the disc is rotating counterclockwise.
So the right side's gonna look red
and the left side is gonna look blue just
because of the rotation the set.
Now this is a 2D rotation as the
this phantom is rotating on a central axis.
So you can steer towards the left and you get this image
and then you can steer towards the right
and you get this image
and then you all you do is combine them
and then what you end up with
is the X component, which is transverse.
So these guys are all going that way and the
and these guys in the far field are going that way
and you can do the axial or the axial image.
So those guys going up there
and down there, you'll notice we're actually losing
some of the lateral components.
That's because we can't steer the beam enough to see from
points up here from two directions.
However, in the area that you can see it,
you can definitely get the true 2D velocity.
Remember the third component, there is no Z component
or out plane component here.
And this is what this looks like.
You can resolve the velocity components at every position
and this is very much what one would expect to see.
As you get further from the axis, the axis of rotation,
these vectors get longer
because the radial velocity gets longer
as you move away from the axis of rotation.
Some of this may be a surprise to you all
because no one does this, mostly
because the applications are very limited
and not particularly interesting.

Potential in 3D

However, if you could do it in 3D you could produce
pictures like this.
Now this is not a true velocity image.
These are images that I got off the web
and these are power doppler images.
So they have no directional information and that
because of that you can get 3D imaging and power doppler.
What you'd like to see in 3D is
that every position you would get the true
velocity measurement, the true 3D velocity,
that's gonna require 3D and four D sampling.
Once you do that, you can get the true 3D velocity.
And the consequence of that is you'll be able
to see the true velocity at every position in
and independent of the direction of sampling.
But you'll also be able
to measure pressure gradients potentially.
And that is the huge potential benefit for this.
This is a great application whose time
may be approaching in the future,
but what I'm talking to you about
to you now is not available, but the concepts are there.

Pressure Gradients and the Navier-Stokes Equation

What you'll be able to do with pressure gradients is solve
to generate a local solution
of what's called the Navier stokes equation.
The Navi stokes equation is a very complicated non-linear
differential equation, which is sort of the bread
and butter of fluid mechanics people.
It basically describes the equation of motion
of moving fluids.
It's a very tough problem because it's non-linear,
but if you can sample fast enough
and dense enough, it may be tractable locally.
And if it is tractable locally,
if you can solve it at a given position,
you could then theoretically measure pressure drops.
And by doing that you'd be able
to measure pressure drops without a catheter
or contrast agents and it would be a
totally benign measurement.
Whereas now to measure pressure drops, you have
to put a catheter or do a catheter procedure.
So it's an invasive technique.
So what we would be doing is removing a catheter procedure
and using a totally benign ultrasound technique
and 3D and four D will make, can make this happen.
I put this up here not to make people choke
because of the differential equation.
I just wanna show what we would have available
if we had real time 3D and four D measurements.
And this is the navier stokes equation in one direction
you, there's a similar solution
or a similar equation for Z, Y and X.
This is the X direction navi stokes equation.
RO is density. That's the density of blood.
VX is the velocity in the X direction.
Remember we have 3D velocities,
we have all that information.
We know the velocity in the X direction since it's real
time, we can sample in time so we can get the change,
the rate of change in velocity of the X direction.
That's acceleration.
So we've got that since we've got all the 3D parameters,
we know the velocity in the X direction
across the blood vessel.
So we have velocity and X locally,
then we have the local gradient in the velocity
of X in position.
So we've got that, we've got the velocity
and Y for the same reason.
We can look at the change in the velocity
of X in the Y direction.
We've got this, we've now, we can also get the velocity in Z
'cause we're sampling in 3D
and we also have the gradient of the velocity
of X in the Z direction.
We've got this. So we've got everything on the left side
of the equation by sampling dense enough
and fast enough in 3D.
Let's look at the right side of the equation.
FS of X is what's called a body force that corresponds
to gravity that has almost no effect on this.
We can ignore this. This is the pressure gradient.
This is what we want to calculate so we can, so
all we then need is this, which is mu, is viscosity.
And this is what's called the lelos of the velocity.
This is the second derivative of the local velocity.
This is an extremely noisy measurement.
This is a second derivative.
However, we could sample a very long time.
Remember we're in competition with a technique that
would be an invasive procedure.
So imagine how long it takes
to put a catheter into somebody.
You have to bring 'em into the x-ray room or
imaging suite.
You have to do a sterily, you have to clean the skin,
you have to put the catheter in, you have to feed it in,
you have to put it in the right position
and make a measurement.
So we have all that time at least
to do this in a non-invasive way.
So it's very possible we can get this measure,
this parameter as well.
We've got all the data, we just have to make sure
that we can overcome the noise.
We can then solve for the pressure grade in an X.
We have to do this for all the other equations.
However, remember this does
not have to be done in real time.
We're competing with a clearly non-real time technique.
And so this now becomes a potentially viable solution using
if we have true 3D four D.

Application to Stenosis

Here's a picture of the stenosis.
This is a smooth stenosis.
All we care about is right at the stenosis.
It might be prudent
to sample in three dimensions in from two directions.
That way if there's any components across the beam,
which we can't get doppler shifts across the field, then
we would have another way of sampling it.
Now it's clear that we can do this
because there are ways now to do correspondences
of images from different orientations.
They're very robust
and my guess is that they'll certainly work out
to be possible in the future.
What does this look like?
Here's a 2D image, which you're all used to seeing.
This is a carotid artery with this stenosis.
So what we wanna do is we wanna measure the pressure drop
across this stenosis.
Let's assume that we have 3D four D imaging.
So what we're gonna do is get the
velocities at every position.
So these arrows are representing the local velocities.
The colors don't mean anything.
I made them either black or white, just
for contrast purposes.
Their length sort of correspond to the how fast it's going.
But we'll have all that information.
So now we'll sample it there.
It's now getting wider in this
position, so it's slowing down.
We'll have samples there. Now it's narrowing again.
It's speeding up. It's still speeding up.
Now it's spreading out again, slowing down.
Now it's slowing down because we're going further
and there, now we're into the
we're into the normal blood vessel.
And so now we've got all the velocities
sampled across that stenosis.
So now what we do is measure the pressure drop
or the pressure gradient at every position.
We'll measure it there and then we'll measure it there.
Remember we've got all that information. We'll measure it
there, we'll measure it there, we'll measure it there.
And then all we'll do is integrate these pressure gradients.
So you take the basically the sum
of the gradients across here, multiply times delta X,
and we'll do it across here.
There's a standard integration procedure
across these planes.
Remember we have all of these planes as a function
of position that gives us the pressure drop.
So now we have the delta L is the length of the stenosis.
So we have now delta P across that stenosis,
we have the pressure drop.
This was done in a totally benign method.
Voila, pressure drops. Each time this is done.
It requires one fewer interventional procedure
and ultrasound, hopefully,
and possibly in the future will be able
to do this using 3D and four D imaging.

So thank you very much.