what can we learn with intravascular tracers?
Post on 29-Jan-2016
29 Views
Preview:
DESCRIPTION
TRANSCRIPT
Perfusion Imaging
What can we learn with
intravascular tracers?
Perfusion Imaging
Good Modeling References
Axel, L. Methods using Blood Pool Tracers in “Diffusion and Perfusion Magnetic Resonance Imaging”, D. Le Bihan (ed.),
Raven, 1995.
Thomas DL et al. Measuring diffusion and perfusion using MRI. Phys Med Biol (2000) R97–R138. (see sect. 3.2) (on website)
Weisskoff RM, et al., Pitfalls in MR Measurement of Tissue Blood Flow with Intravenous Tracers: Which Mean Transit Time? MRM 29:553-559, 1993.
Jacquez, J. “Compartmental Modeling in Biology and Medicine”, pages 193-203. U Michigan Press, 1984.
Perfusion Imaging
MTT
CBV
CBF
Today’s Parametric ImagesWhat is the mapping from
data to parameter?
Perfusion Imaging
Lets consider the data in time.
See plots
Perfusion Imaging
Today’s deep thoughts:MTT = CBV /
CBFMTT = proability-weighted
average transit time
Perfusion Imaging
What do we mean by ‘blood flow’?
Is that the same as CBF?
What do we mean by ‘Perfusion’?
Perfusion Imaging
“Arterial” Inflow“Arterial” Inflow “Venous” Outflow“Venous” Outflow
Lets examine the ‘Perfusion’ of this system. The is the U.S. Brain
Trust. What’s the ‘model’?
Map of NIH
Perfusion Imaging
“Arterial” Inflow“Arterial” Inflow “Venous” Outflow“Venous” Outflow
Q. What is the ‘perfusion’ of people within a single region
(i.e., building)?
Perfusion Imaging
Lets examine this single region in detail.
Perfusion Imaging
Each building (pixel) has an inflow and an outflow. But there are
multiple paths through the building.
inflow outflow
Analogies
p i x
e l
• A building (e.g., CC) is a ... pixel• Rate of people entering CC at inflow: F• Average time spent in CC building: MTT• Fraction of people passing through CC: V (compared to other buildings)
Perfusion Imaging
How to understand the major parameters?
• F is a measure of the (fractional) rate of flow supplying (i.e., ‘external’ to) a particular area.
• V is a measure of (steady state) capacity of the given area.
• MTT is a measure of the time spent inside a given area - perhaps due to internal ‘tortuosity’.
Perfusion Imaging
In
Out
Method: Inject an “impulse” of runners into the system, then monitor
their arrival(s) downstream.
Perfusion Imaging
Lets further idealize the picture
In the ideal case, we would examine the inflow to, and the outflow from every region (i.e., pixel).
Thus, we would expect the outflow signal to be equal to the inflow signal convolved with the impulse response:
outflowinflow
p i x e l
hSS inout
Perfusion Imaging
What is the impulse response, h(t)?
The response to an impulse input is the distribution of all possible transit times through the system. (Think p.d.f.)
h(t)dt is the fraction of “particles” that leave the system between t and t+t
The Mean transit time is at the center of mass of the distribution, h(t). I.e., 1st moment.
0
50
100
150
200
250
300
350
400
0 5 10 15 20 25t t + t time
0
)( dtthtt
Perfusion Imaging
Where to make our observations?
In this idealization, we would need to image every inflow and outflow (i.e., impulse response)
of every building (aka., pixel).
Inflow to CCOutflow from CC
Perfusion Imaging
But, consider our actual observation points...
Rather than measure at inflow and outflow, we make observations of something equivalent to
• signal at ~inflow (the arterial function) and,
• signal from the entire pixel.
outflowinflow
p i x e l
Perfusion Imaging
Q. How do our observations relate to the
histogram of transit times, h(t)?
0
50
100
150
200
250
300
350
400
0 5 10 15 20 25t t + t time
h(t)
The integral H(t), of the histogram is all the tracer that has LEFT the system. (Think c.d.f)
The residue function, R(t), describes all tracer still remaining, at time t and NOT yet drained from the system.
R(t) = 1 - H(t)
dtthtH )()(
0
50
100
150
200
250
0 5 10 15 20 25
Our observations are related to R(t).
Perfusion Imaging
How to understand R(t)?
Thus, R(t) is - in effect - the impulse response as viewed from within the pixel. Recall:
In the case of an ideal input, the view from within the pixel would look like:
View at input
View of ‘runners’ remaining within the pixel
100%
0%
Perfusion Imaging
Practically, we image a convo-lution of the Residue function.
S
S
SS
S
t
at dTTtRTCScaletC0
)()()(
CaCt
Ct
Ct
CtCt
Perfusion Imaging
What’s in a shape? What does the shape of R(t) mean?
S
S
SS
S
t
at dTTtRTCScaletC0
)()()(
CaCt
Ct
Ct
CtCt
Long Transit time
Short Transit time
Dispersed (non-ideal) bolus.
Perfusion Imaging
What do the Residue Functions that we get from deconvolution look like?
See plots
Perfusion Imaging
What is MTT in terms of the residue function, R(t)? - 1.
0
00
)(
)()(
dttht
dtthdtthtt
The Mean transit time is at the center of mass of the distribution, h(t). I.e., 1st/0th moments.
h(t)
Recall that the Residue function is related to the integral of the histogram.
dtthdR
dhtRt
)(
)(1)(0
Perfusion Imaging
What is MTT in terms of the residue function, R(t)? - 2.
0
00
)(
)(|
dttR
dttRRtt
Substituting dR into the expression for MTT,
Integrating by parts we see that,
0
dRtt
Recall that we measure the one entity which is the Scaled Residue Function, F*R(t), so we must divide accordingly.
ScaledttRScalet
0
)(
Where by convention Scale is the maximum point on the scaled residue curve.
Perfusion Imaging
What is MTT in terms of the residue function, R(t)? - 3.
Is equivalent to area / height = 1/2 base.
)]([)(0
tRScaleMaxdttRScalet
If we approximate the Residue function as a triangle, we can see that the MTT lies at mid-point of the base.
Scale*R(t)
Perfusion Imaging
Why is the Output Equation Scaled by the Flow Arriving at
the Pixel?
t
at dTTtRTCScaletC0
)()()(
‘Scale’ is the relative inflow, F, to the pixel because the fraction of tracer arriving at a given pixel is proportional to the fractional flow to that pixel.
Perfusion Imaging
Q. What assumptions do we make in applying our simple
input-output model?
1. Every pixel is supplied directly by the input.
2. All dispersion of a bolus input is due to multiple path-lengths inside a ‘pixel’
3. Feeding and draining vessels are ‘outside’ the pixel
4. No recirculation.
Test your modeling IQ!
Test your modeling IQ!
Test your modeling IQ!
Test your modeling IQ!
Perfusion Imaging
1. An impulse input at the artery would arrive at the ‘pixel’ as an impulse.
2. Measured CBF is an upper bound. So, MTT = CBV/CBF may be biased.
3. Model is only valid for regions on the order of the size of the capillary bed. I.e., with its own supplying arteriole and draining venule.
3a. Different tissue types may require different minimum pixels sizes
4. Recirculation must be removed before applying model.
What implications are there to our assumptions?
FI
FA ?
Ideal Actual
invalid
valid
Perfusion Imaging
What about recirculation?
HW #1
Perfusion Imaging
What is Volume Fraction, V?
CBV is a measure of relative blood carrying capacity of a region.
We measure it as the ratio of all the tracer that passes through a voxel over time
to
all the tracer that passes through a point in the vasuclature over all time.
0
0
)(
)(
dttCk
dttCCBV
a
t
Perfusion Imaging
Why measure CBV?
1. Vasodilation (increased CBV ) may occur distal to narrowed
carotid arteries.
2. Decreased CBV/CBF may reflect slowed cerebral
circulation.
3. CBV necessary to measure CMRO2
Perfusion Imaging
An analogy to understand CBV as relative capacity.
• Consider a multiplex movie theatre
• But, all theatres in the multiplex play the same movie.
• People spread themselves across all theatres at constant concentration of people per seats.
• The fraction of patrons that enter a given theatre over all time is a measure of the relative size of that theatre.
Perfusion Imaging
V: Total # people to enter is proportional to capacity
dtPeople
0
dtPeople
0
0
dtPeople
Exit
Exit
Exit
Perfusion Imaging
CBV - Assumptions
• All people entering leave after ‘residing’ (i.e., no staying for a second show).
• Implication: Leakage of Blood Brain Barrier violates the model.
Perfusion Imaging
Consequence of BBB Leakage to Contrast Agent
If contrast agent does NOT stay wholly intravascular (as in case of damage to BBB),
and CBV is overestimated.
Ideal
With Leakage
larger is )(0
dttCt
Perfusion Imaging
Consequence of BBB Leakage to Contrast Agent
If CBV is overestimated, then MTT = CBV/CBF is also overestimated.
This makes sense: leakage makes the effective mean path-length longer
outflowinflow
p i x e l
Perfusion Imaging
A Contrast Agent that leaks across the BBB is also called a
“freely diffusable tracer”.
Freely diffusable tracers are the domain of PET…
outflowinflow
p i x e l
Perfusion Imaging
How’s it done? - Data Flow1. Inject
2. Scan over time
3. Convert signal to concentration
4. Find AIF
5. Fit First Pass
6. Calculate CBV, CBF,
MTT
7. Post-process, tabulate stats
Gd-DTPA
CBFGMC
BFWM
= 2
CBV = CBF =
or
Perfusion Imaging
top related