Image Processing Reference
In-Depth Information
The commonly used units for CBV are milliliters per 100 grams of tissue
(ml/100 g) and microliters per gram (
µ
ml/g).
19.2.4
M
T
T
EAN
RANSIT
IME
An additional parameter that characterizes the VOI is the mean transit time
(MTT). MTT is defined as the center of mass of the distribution h(t) or, in different
words, the average time required for any given particle of tracer to pass through
the VOI. The MTT is given by
∞
∫
∫
th
i
()
ττ
d
MTT
=
0
(19.12)
∞
hd
()
ττ
0
and from Equation 19.2 and Equation 19.4, one has:
∞
∞
∫
∫
MTT
=
t h
i
()
ττ
d
=
R
()
ττ
d
(19.13)
0
0
MTT can also be calculated by using the central volume theorem of the
indicator dilution theory [5-7]. According to this theory, MTT is the ratio of CBV
to CBF in the VOI:
CBV
CBF
MTT
=
(19.14)
MTT has dimension of time.
19.2.5
C
B
F
EREBRAL
LOOD
LOW
In case of an intact BBB, following the preceding definitions, CBF can be
obtained by the convolution of C
(t), R(t), and the AIF C
(t):
VOI
AIF
t
ρ
∫
Ct
()
=
CBF
C
( ) (
τ
R t
−
τ τ
)
d
(19.15)
VOI
AIF
k
0
H
Equation 19.15 can be derived by starting from Equation 19.14:
∞
∫
∫
Cd
()
ττ
k
∞
CBV
MTT
VOI
∫
CBF
=
=
H
0
Rd
()
τ
τ
(19.16)
ρ
∞
0
Cd
()
ττ
AIF
0
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