Image Processing Reference
In-Depth Information
from which
∞
ττ
ρ
∞
∞
∫
∫
∫
Cd
()
=
CBF
C
()
ττ
d
R
()
ττ
d
VOI
AIF
k
0
0
0
H
ρ
∞
∫
=
CBF
C
()
τ
⊗
R
()
τ τ
d
AIF
k
0
H
(19.17)
where
⊗
denotes the convolution operator and, thus,
ρ
ρ
t
∫
Ct
()
=
CBF C
⋅
()
t
⊗
R t
()
=
CBF
C
( ) (
τ
R
t
−
ττ
)
d
(19.18)
VOI
AIF
AIF
k
k
0
H
H
To obtain CBF, one needs to deconvolve (see following text) Equation 19.18
in order to calculate R
′
(t)
=
CBF
⋅
R(t) and, subsequently, the CBF from R
′
(t)
value at time t
=
0:
CBF
= ′
R
()
0
(19.19)
The commonly used units for CBF are milliliters per 100 grams of tissue per
minute (ml/100 g/min) and microliters per gram per second (
ml/g/s).
In conclusion, the algorithmic steps to assess cerebral hemodynamics are sum-
marized in Table 19.1: first, CBF is obtained by deconvolution (Equation 19.18),
and CBV from Equation 19.11, then MTT from Equation 19.14. Sometimes C
µ
AIF
is not measured. In this case, one can only measure a relative CBV, rCBV, from
∞
∫
rCBF
=
C
()
ττ
d
(19.20)
VOI
0
but CBF and MTT cannot be estimated.
TABLE 19.1
CBF, CBV, and MTT from DSC-MRI Images
Parameter
Formula
CBF
Cerebral Blood Flow
t
ρ
∫
Ct
()
=
CRt
( )
τ
′ −
(
τ τ
)
d
⇒ = ′
FR
( )
0
VOI
AIF
k
0
H
CBV
Cerebral Blood Volume
∞
∫
∫
Cd
()
ττ
1
1
1
−
−
H
H
VOI
LV
SV
0
CBV
=
∞
ρ
Cd
()
ττ
AIF
0
MTT
Mean Transit Time
CBV
CBF
MTT
=
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