Image Processing Reference
In-Depth Information
(where AIF stands for arterial input function), respectively [3,4,6,7]. Normalizing
CBV to the density
ρ
of brain tissue:
∞
∫
∫
Cd
()
ττ
k
VOI
CBV
=
H
0
(19.6)
ρ
∞
Cd
()
ττ
AIF
0
where k
accounts for the difference in hematocrit (H) between large vessels
(LV) and small vessels (SV) because only the plasma volume is accessible to the
tracer, i.e., k
H
). In fact, the CBV may be split into a cerebral
plasma volume (CPV) and cerebral red cell volume (CRCV) [8], i.e.,
=
(1
−
H
)/(1
−
H
H
LV
SV
CBV
=
CPV
+
CRCV
(19.7)
However, because hematocrit is defined by the ratio
CRCV
CBV
H
=
100
(19.8)
we have:
CBV
=
CPV
+
H
⋅
CBV
(19.9)
(
1
−
HCBV
)
=
CPV
(19.10)
and, consequently,
1
ρ
amount
area
of blood in a VOI
under the blood input curve
CBV
=
1
−
H
1
ρ
amount
of plasma in
aVOI
=
LV
1
−
H
area under the plasma input
curve
SV
(19.11)
×
(
because the tracer is in the pla
sma only)
∞
∞
∫
∫
∫
Cd
()
ττ
Cd
()
ττ
1
1
−
H
1 1
1
−
−
H
H
VOI
VOI
=
0
LV
=
LV
0
∞
∞
ρ
1
−
H
ρ
∫
SV
Cd
()
τ
τ
SV
Cd
()
ττ
AIF
AIF
0
0
Search WWH ::
Custom Search