C a - Rigshospitalet

Transcription

Basic perfusion theory
January 24th 2012
by
Henrik BW Larsson
Functional Imaging Unit, Diagnostic Department
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Outline
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What is perfusion
Why measure perfusion
Measures
The easy part: What to do and why
The complicated part: Formalism and
models
•  The really complicated part:
Deconvolution
•  Conclusion
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What is perfusion?
Large vessels : flow
½ mm
Perfusion: related to the
microvascular system ~ the
capillaries
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The vascular system of the brain
and perfusion
Venules: capacity
vessels
20% Artery:conductance
vessels
50%
Veins
30% Capillaries: exchange
vessels ~
transport~diffusion
Arteriole:resistance
vessels
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Perfusion : ml/100g/min
½ mm
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Perfusion : ml/100g/min
½ mm
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Perfusion metrics in imaging: ml/min/
100g or ml/min/100ml
½ mm
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Number of transport (ml) vehicles entering
100 ml tissue pr. time unit::
20 - 80 ml/min/100 ml tissue volume
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Important metrics
•  Perfusion: – f [ml/min/100g] or [ ml/min/100ml ]
•  Brain Perfusion (‘flow’) : Cerebral blood flow CBF [ml/100g/min]
•  Cerebral blood volume: CBV [ml/100g]
½ mm
•  Volume of Distibution: Vd [ml/100g] or [ml/100ml]
•  Mean transit time: MTT [s]
•  Blood brain permeability: PS product [ml/100g/min]
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Important metrics
•  Perfusion: – f [ml/min/100g] or [ ml/min/100ml ]
•  Brain Perfusion (‘flow’) : Cerebral blood flow CBF [ml/100g/min]
•  Cerebral blood volume: CBV [ml/100g]
½ mm
•  Mean transit time: MTT [s]
•  Blood brain permeability: PS product [ml/100g/min]
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Blood flow changes and energy metabolism in
brain and skeletal muscle
Brain
Muscle
5 – 30 %
Activation
Increases up
to 30 x
Rest
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Why measure brain perfusion?
•  It intimately related to brain
activation
•  Govern oxygen delivery and CMRO2:
CMRO2=CBF x (Ca – Cv) = CBF x Ca x OEF
•  Is profoundly changed in nearly all
brain diseases either primarily or
secondary or in a more subtle way
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Non-invasive perfusion:
What to do
and
the easy part
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Measuring perfusion by an external
registration: CT,SPECT,PET,MRI
detector
artery
vein
f
f: perfusion in [ml/min /100g]
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How can it be measured ?
Add a contrast agent carried by the blood to the tissue
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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Bolus of
tracer or
contrast
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How can it be measured ?
Add a contrast agent carried by the blood to the tissue
Contrast agent
exogent
endogent
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The complicated part:
Single bolus injection
and
external registration
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The complicated part:
Single bolus injection
and
external registration
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time
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Signal ≈ Ctis(0) : f Ca(0)
Perfusion (f) = vehicles/min
ml/min
x
Conc (Ca) = the cargo they
carry
mmol/ml
time
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Ctis(t) = f Ca(0) Δt RF(t)
RF(t) =1 for t < MTT
Ctis(0) =: f Ca(0) Δt
RF(t) =0 for t > MTT
flux
MTT
time
dose
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Ctis(0) = f Ca(0) Δt
time
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Summing up: direct short bolus
Measure the
tissue conc
Measure the input conc i.e.
input function
Scanner signal : Ctis(t) = f Ca(0) Δt RF(t)
Estimate f and RF(t)
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Summing up
Measure the
tissue conc
input function
Scanner signal : Ctis(t) = f Ca(0) Δt RF(t)
RF(t) by ’model free’ methods, or assume a model
e.g. RF(t) =e-k2t
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Different perfusion tracers
behaves differently
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Ctis(t) = f Ca(0) RF(t)
time (s)
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RF(t) = e-k2t
1
2
time (s)
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RF(t) = e-k2t
100
200
time (s)
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Ctis(t) = f Ca(0) RF(t)
RF(t) = e-k2t
100
200
time (s)
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RF(t) = e-k2t + e-k3t
100
200
time (s)
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The residue impulse response function RF(t)
RF(t) : the fraction of the injected dose
remaining in the tissue (voxel) as a function of
time
Mean transit time : MTT
MTT = ∫RF(t)
0
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Mean transit time : MTT
MTT = ∫RF(t)dt
RF(t)
0
MTT=
RF(t)
1
t
∑
n
t
N
RF(t)
1
t
MTT
MTT
1
t
n
N
MTT
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Generally
Perfusion: f
Distribution vol: Vd
f=
Mean transit time: MTT
Vd
MTT
For an intravascular contrast agent, the case in brain
MRI we have:
Brain perfusion: CBF
Brain blood volume: CBV
CBF =
CBV
MTT
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Generally
For an intravascular contrast agent, the case in brain
perfusion MRI we have:
Brain perfusion: CBF
Brain blood volume: CBV
CBF =
CBV
MTT
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The really complicated part:
Deconvolution
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We cannot apply a bolus directly in the tissue !
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Input :
Tissue enhancement :
∞
Ca(t)
Ctis(t) = ∫f Ca(τ) RF(t- τ) dτ
0
tissue
Deconvolution :
find f RF(t)
f
time
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Input : Ca(t)
Ctis(t) = ?
tissue
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Input : Ca(t)
Ctis(t) = f Ca(0) RF(t) Δt
tissue
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Input : Ca(t)
Ctis(t) = ?
tissue
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Input : Ca(t)
composed of many
small input
Ctis(t) = ?
tissue
If the linearity of the system exist
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Input : Ca(t)
composed of many
small input
Ctis(t) = f Ca(0) RF(t - 0) Δτ
tissue
0
0
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Input : Ca(t)
composed of many
small input
tissue
1
1
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Input : Ca(t)
composed of many
small input
tissue
2
2
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Input : Ca(t)
composed of many
small input
tissue
3
3
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Input : Ca(t)
composed of many
small input
tissue
4
4
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Input : Ca(t)
composed of many
small input
tissue
5
5
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Input : Ca(t)
composed of many
small input
tissue
6
6
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Input : Ca(t)
composed of many
small input
tissue
7
7
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Input : Ca(t)
composed of many
small input
tissue
8
8
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Input : Ca(t)
composed of many
small input
tissue
9
9
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Input : Ca(t)
composed of many
small input
tissue
10
10
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Input : Ca(t)
composed of many
small input
tissue
11
11
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Input : Ca(t)
composed of many
small input
tissue
12
12
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Input : Ca(t)
composed of many
small input
tissue
13
13
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Input : Ca(t)
composed of many
small input
tissue
14
14
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Input : Ca(t)
composed of many
small input
tissue
15
15
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Input : Ca(t)
composed of many
small input
tissue
16
16
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Input : Ca(t)
composed of many
small input
tissue
17
17
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Input : Ca(t)
composed of many
small input
tissue
18
18
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Input : Ca(t)
composed of many
small input
tissue
19
19
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Input : Ca(t)
composed of many
small input
tissue
20
20
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Input : Ca(t)
composed of many
small input
tissue
21
21
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Input : Ca(t)
composed of many
small input
tissue
22
22
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Input : Ca(t)
composed of many
small input
tissue
23
23
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Input : Ca(t)
composed of many
small input
tissue
24
24
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Input : Ca(t)
composed of many
small input
tissue
25
25
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Input : Ca(t)
composed of many
small input
tissue
26
26
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Input : Ca(t)
composed of many
small input
tissue
27
27
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Input : Ca(t)
composed of many
small input
tissue
28
28
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Input : Ca(t)
composed of many
small input
tissue
29
29
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Input : Ca(t)
composed of many
small input
tissue
30
30
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Input : Ca(t)
composed of many
small input
tissue
31
31
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Input : Ca(t)
composed of many
small input
tissue
32
32
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Input : Ca(t)
composed of many
small input
tissue
32
32
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Input : Ca(t)
composed of many
small input
tissue
33
33
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f Ca(τ) RF(t - τ ) Δτ ; τ = 0:33
τ: 0
20
33
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Total tissue enhancement :
Ctis(t)= ∑f Ca(τ) RF(t - τ ) Δτ ; τ = 0:33
τ: 0
20
33
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Total tissue concentration:
t
Ctis(t)= ∫f Ca(τ) RF(t - τ ) dτ
0
The convolution integral
τ: 0
20
33
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Input :
Ca(t)
Ctis(t) = f ∫ Ca(τ) RF(t- τ) dτ
tissue
Deconvolution :
find f and RF(t)
f
time
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Conclusion
Measure the
tissue conc
input function
Bolus input : Ctis(t) = f Ca(0) Δt RF(t)
Veneous injection : Ctis(t) = f ∫ Ca(τ) RF(t- τ) dτ
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Deconvolution ~ Modelbased
•  Use a model e.g.: Monoexponentiel, biexponentiel,
•  Optimise the free parameters by least square fit to
tissue enhancement curve
•  It is robust
•  Relative insensitive to noise
•  Incorrect if the model is inappropriately chosen
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Deconvolution ~ Modelfree
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No model a priory
Very flexible: many of free parameters
A projection
Very sensitive to noise
Incorrect if not regularized rigoriously
Fourier transform, SVD, GSVD, Tikhonov, GPD
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The story can begin
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DCE T1 perfusion and blood brain barrier:
Methodological considerations and applications
January 24. 2012
by
Henrik BW Larsson
Functional Imaging Unit, Diagnostic Department
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Acute MS lesions
T1
T1-Gd
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Paramagnetic Contrast, Gd-DTPA
• Decreases homogeneity
in molecular environment
• Increases relaxation
speed!
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Acute MS lesions
T1
T1-Gd
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BBB permeability : PS / Ktrans / Ki
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Dynamic Contrast Enhanced
Heart Perfusion, normal
MR signal
blood
tissue
time
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Dynamic Contrast Enhanced
Heart Perfusion, normal
MR signal
blood
tissue
time
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Rest scan : healthy subject
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Stress scan: healthy subject
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Gadolinium-DTPA
as perfusion CA
T1w MR-signal
T2*w MR-signal
extravascular
intravascular
Time to peak
time
bolus
time
bolus
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Gadolinium-DTPA
as perfusion CA
T1w MR-signal
T2*w MR-signal
extravascular
intravascular
Time to peak
time
bolus
time
bolus
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Dynamic T1 weighted contrast enhanced
perfusion MRI in brain at 1.5 tesla
F = 83 ml/100/min
Larsson at al MRM 2001, p272
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Dynamic T1 weighted contrast
enhanced perfusion MRI in brain at
3 tesla
Time resolution:
5 slices pr. 1.24s
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3 tesla
Time resolution:
5 slices pr. 1.24s
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Gd gives shorter T1 = faster recovery
•  Short range – works only in
same compartment
•  Increased signal in blood and
tissue on T1W images
•  Normally BBB - Ktrans
•  Now perfusion - CBF
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MRI Perfusion Measurement
Procedure, Gd:
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Intravenous injection of Gd-DTPA
Rapid imaging using T1W FFE (SR TurboFLASH)
Conversion of signal units to concentration
via relaxation rate units
Data analysis: deconvolution approach
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From MR signal to concentration of
contrast agent
R1 = 1/T1
Concentration
MR signal
Ctis Ca
callibration by
external phantoms
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R1Gd+ - R1Gd- = relaxivity • C
ΔR1 (t) = relaxivity • C(t)
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Conversion of MR signal to tracer concentration
Measured
MR signal
Saturation
recovery delay
Equilibrium
magnetization
Tissue R1
before bolus
Flip angle
Change of tissue R1
due to Gd bolus
s(t) = M0sin(α)[1-exp(-TD(R1+ΔR1(t)))] , ΔR1(t) = r1c(t)
Saturation recovery equation
M0sin(α)
Relaxivity of
contrast agent
Tracer
concentration
s(TD)
1/R1
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TD
T1 measurement
s(t) = M0sin(α)[1-exp(-TD· R1)]
T1 = 1.23 s
(frontal
gray matter)
R1
M0
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Favorite brain arteries for AIF
Middle Cerebral Artery (MCA)
ICA
Internal Carotid Artery (ICA)
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Slice position in DCE
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3 tesla
Sat-Recovey:
TI = 120ms
TR= 4 ms
TE= 2 ms
Angle = 30o
Voxel = 3x3x6 mm
Time resolution:
5 slices pr. 1.24s
Dose:
Magnevist/
Dotarem
0.05mmol/kg
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3 tesla
Sat-Recovey:
TI = 120ms
TR= 4 ms
TE= 2 ms
Angle = 30o
Voxel = 3x3x6 mm
Time resolution:
5 slices pr. 1.24s
Dose:
Magnevist/
Dotarem
0.05mmol/kg
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Deconvolution approach to quantitative
perfusion measurement
arterial input
tissue response
⊗
t (s)
RF(t)
=F
ca(t) (mM)
ct(t) (mM)
tissue curve
t (s)
t (s)
t
Ct(t) = F· Ca(t) ⊗ RF(t) = F · ∫ Ca(t’) RF(t-t’) dt’
0
MTT = ∫ RF(t)dt
CBV = F· MTT
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Dynamic T1w contrast enhanced MRIperfusion
CBF map
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Deconvolution methods
gray matter ROI
arterial input
ct(t) = F· ca(t) ⊗ RF(t)
RF(t):
monoexp
tissue curve
RF(t): deconvolution
with SVD
RF(t):
deconvolution with
Tikhonov
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The residue impulse response function
gray matter ROI
arterial input
tissue curve
with SVD
with Tikhonov
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Tikhonov’s deconvolution
or
Generalized SVD
large
λ
small
Larsson at al JMRI 2008, p754
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Examples of CBF maps
ml/100g/min
120
100
80
60
40
20
We found perfusion value for ROI’s to be
62 ml/100g/min in gray matter and
21 ml/100g/min in white matter
in 7 patients with acute optic neuritis.
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Combined Anatomical and Functional
MRI: Anatomy & perfusion of the brain
ml/100g/min
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Two patients with stroke (one week old)
T2- w image
DWI
CBF
ml/100g/min
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CBV
ml/100g
MTT
s
10
40
8
32
6
24
4
16
2
8
0
0
10
40
8
32
6
24
4
16
2
8
0
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Perfusion in clinical desicision
making
•  Assesment of cerebral ischemia
•  Assesment of reversible versus
irreversible tissue damage before
treatement
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Comparison of MR perfusion
methods:
Carotic flow measurement (PCM)
DCE
ASL
PET (15H2O)
Otto Henriksen at al JMRI 2012, in press
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17 healthy subjects, 20-30 years
Performed twice - Variation: Within persons – method variation
Between persons variation
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Table 1. Cerebral blood flow measurements by different modalities
Bias *
Mean
Global CBF
Gray matter CBF
White matter
CBF
pvalue
sbetw
swith
CVbetw
CVwith
**
PCM
65.19†
0.43
0.813
11.32
4.80
17.4%
7.4%
ASL
37.01
-0.30
0.762
6.00
1.76
16.2%
4.8%
DCE
42.99
-3.77
0.100
8.60
6.47
20.0%
15.1%
PET
41.88
0.69
0.757
6.69
4.99
16.5%
11.9%
ASL
50.15
-0.00
0.998
9.42
3.05
18.8%
6.1%
DCE
65.55‡
-5.90
0.095
12.83
10.01
19.6%
15.3%
PET
58.55
0.55
0.859
10.12
6.91
17.3%
11.8%
ASL
21.72
-0.40
0.290
3.53
1.07
16.3%
4.9%
DCE
16.75‡
-1.23
0.186
5.61
2.64
33.5%
15.8%
PET
22.57
0.87
0.487
3.41
2.80
15.1%
12.4%
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Table 1. Cerebral blood flow measurements by different modalities
Bias *
Mean
Global CBF
Gray matter
CBF
White matter CBF
pvalue
sbetw
swith
CVbetw
CVwith
**
PCM
65.19†
0.43
0.813
11.32
4.80
17.4%
7.4%
ASL
37.01
-0.30
0.762
6.00
1.76
16.2%
4.8%
DCE
42.99
-3.77
0.100
8.60
6.47
20.0%
15.1%
PET
41.88
0.69
0.757
6.69
4.99
16.5%
11.9%
ASL
50.15
-0.00 0.998 9.42
3.05
18.8%
6.1%
DCE
PET
65.55‡
58.55
-5.90 0.095 12.83
0.55 0.859 10.12
10.01
6.91
19.6%
17.3%
15.3%
11.8%
ASL
21.72
-0.40
0.290
3.53
1.07
16.3%
4.9%
DCE
16.75‡
-1.23
0.186
5.61
2.64
33.5%
15.8%
PET
22.57
0.87
0.487
3.41
2.80
15.1%
12.4%
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Comparison of MR perfusion
methods:
Otto Henriksen at al JMRI 2012, in press
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Conclusion
• 
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• 
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• 
Large inter-individual variability – all methods
Same mean global CBF across ASL, DCE, PET
PCM global flow > global ASL, DCE, PET
No correlation between methods, except
A (weak) correlation between PCM and DCE
Existence of significant subject-method interaction
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Does it works if BBB is leaky?
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• 
Can we still estimate CBF?
Can we estimate PS (Ki or Ktrans)?
Can we estimate CBV ?
Can we differentiate between Vd and CBV?
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Blood brain barrier defect in brain tumors
After CA
Before CA
Tikonov: CBF = 53ml/100g/min
90
Gray matter
80
Tikonov: CBF = 157 ml/100g/min
350
Tumor lesion
300
70
250
Concentration a.u.
Concentration a.u.
60
50
40
30
20
200
150
100
50
10
0
0
-10
0
20
40
60
80
100
time (sec)
120
140
160
180
-50
0
20
40
60
80
time (sec)
100
120
160
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140
180
Blood brain barrier defect in brain tumors
After CA
Before CA
Tikonov: CBF = 53ml/100g/min
90
Gray matter
80
Tikonov: CBF = 157 ml/100g/min
350
Tumor lesion
300
70
250
Concentration a.u.
Concentration a.u.
60
50
40
30
20
200
150
100
50
10
0
0
-10
0
20
40
60
80
100
time (sec)
120
140
160
180
-50
0
20
40
60
80
time (sec)
100
120
160
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140
180
Permeability - surface area map
ml/100g/min
50
25
0
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Measurement of Brain Perfusion, Blood
Brain Barrier Permeability using
Dynamic Contrast Enhanced T1Weighted MRI at 3 T
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Compartment model
BBB
arteries
Ca(t)
veins
F
F
blood
Cb(t)
Vb
Ki
Ki(1-Hct)
tissue
Ce(t)
Ve
Intracellular
space
Vtis
Vd
HBWL
BBB
arteries
Ca(t)
veins
F
F
blood
Cb(t)
Vb
Ki
Ki(1-Hct)
tissue
Ce(t)
Ve
Intracellula
r
space
Vtis, Ctis
Vd
Tissue
voxel
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Patlak & Gjedde method
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Calculation of BBB permeability
Patlak & Gjedde method
or
two-compartment model & Tikhonov
CBF estimation
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Gray matter
Tumor
Tumor
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Does it works if BBB is leaky?
• 
• 
• 
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Can we still estimate CBF?
Can we estimate PS (Ki or Ktrans)?
Can we estimate CBV ?
Can we differentiate between Vd and CBV?
yes
yes
yes
yes
In the relevant range !
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F (ml/100g/min)
120
Ki (ml/100g/min)
5
100
4
80
3
60
3
40
2
20
1
0
0
Anatomy, T2w
Vd (ml/100g)
20
CBVVb (ml/100g)
20
17
17
13
13
10
10
7
7
3
3
0
0
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F (ml/100g/min)
100
Ki (ml/100g/min)
5
83
4
67
3
50
3
33
2
17
1
0
0
Anatomy,
T2w
T2 w TSE
Vd (ml/100g)
20
CBVVb (ml/100g)
20
17
17
13
13
10
10
7
7
3
3
0
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0
DCE in evaluation of tumor
recurrence versus radiation
necrosis
FDG-PET as referene
Vibeke A Larsen et al Submitted
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Tumor
recurrence
Tumor
recurrence
Radiation
necrosis
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Recurence versus necrosis
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Recurence versus necrosis
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DCE in evaluation of tumor
recurrence versus radiation
necrosis
FDG-PET as referene:
CBV from DCE seems a sensible parameter
Larsen VA at al Submitted
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Pivotal for all measurement
The input function
Partial volume effect on the arterial input
function in T1-weighted perfusion imaging and
limitations of the multiplicative rescaling
approach
Adam E Hansen et al. MRM 2009, p1055
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Effect of partial volume on the arterial input function
high in-plane
resolution:
(1.15mm)2
voxel
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Point spread function of input function
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Future directions
•  The feasibility at 7 T ?
•  Incorporation of water exchange,
i.e. water permeability
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T1 versus T2 Gd based perfusion
Advantage T1
• 
• 
• 
• 
No image distortion (no susceptibility)
Input function clearly defined
No bias due to defect BBB
Half of normal clinical dose
Disadvantage T1
• 
• 
• 
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Fewer slices
Lower S/N for tissue conc time function
Necessitate high field strength 3 tesla
Injection of contrast agent
Can only be repeated a few times
Advantage T2
•  Many slices
•  High S/N for the tissue conc time function
Disadvantage T2
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Input function cannot be defined clearly
Perfusion is estimated to high
MR signal to conc is problematic
Perfusion is bias when BBB is defect
Injection of contrast agent
Repeatable ?
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Conclusion
•  It is possible to generate CBF maps using DCE T1 weighted MRI at 3 T
•  Perfusion values are consistent with literature
•  Tikhonov’s method is best suited for deconvolution
•  DCE T1 weighted MRI appears promising for distinguishing tumor
recurrence and radiation necrosis employing CBV
•  Easy identification of vasculature with DCE T1 weighted MRI allows to
study details of input function
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Thanks to
Egill Rostrup, Adam E Hansen, Otto Henriksen, Glostrup Hospital
Bente Sonne Møller, Helle Juhl Simonsen, Marjut Lindhart, Glostrup Hospital
Olav Haraldseth, Trondheim
Vibeke Andrée Larsen, Ian Law, Julie M Grüner, RH
Frederic Courivaud, Philips Clinical Scientist
Lundbeck Centre for Neurovascular Signaling
Thank you for your attention !
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C a - Rigshospitalet

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