Biomedical Engineering Reference
In-Depth Information
value is consistent with the reported values in the literature, which
were measured by other independent techniques under similar
physiological condition
(98-100)
.
3.3. Establishing a
Robust and
Noninvasive
17
OMRS
Approach for Imaging
CMRO
2
The major technical limitation of the complete model for deter-
mining CMRO
2
using in vivo
17
O MRS is the requirement of
invasive measurements (e.g., CBF, C
a
(t)
,
n
). This could sig-
nificantly limit the potential of this in vivo approach for broad
biomedical applications, especially in humans. Thus, it is crucial
to examine the feasibility of developing a completely noninva-
sive
17
O approach for imaging CMRO
2
. Attempts have been
made to simplify the experimental procedures and the models
for determining CMRO
2
based on a number of approximations
(52, 53, 73, 79, 81, 87)
. We discuss one of these models, in which
the invasive measurements could be eliminated by using the sim-
plified model based on the Taylor's and Polynomial Theorems
(87)
.Briefly,theC
b
(t)
time course can be expressed by a polyno-
mial expansion
3.3.1. Noninvasive
Approach
a
2
t
2
a
3
t
3
C
b
(t)
=
a
1
t
+
+
+···
.
(15.10)
In this expansion, the first-order (or linear) coefficient of a
1
is directly proportional to CMRO
2
according to the following
equation
(87)
a
1
2
CMRO
2
=
(15.11)
α
f
1
where
and
f
1
are known constants (see above). Thus, using this
simplified model
, only the time course of C
b
(t)
measured nonin-
vasively by in vivo
17
O CSI approach is needed and it can be fit-
ted to the polynomial function given by
Eq. (15.10)
to calculate
the linear coefficient of a
1
, and ultimately determining CMRO
2
according to
Eq. (15.11)
. For practical applications, a quadratic
polynomial function provides a good approximation for fitting
the time course of
C
b
(t)
with moderate measurement fluctuation
(101)
. We have demonstrated that the CMRO
2
value obtained
based on the complete model with invasive procedures has no
statistical difference from that based on the simplified model and
quadratic function fitting where only a single noninvasive mea-
surement of
C
b
(t)
is required
(87)
. Moreover, our results also
validated that the linear fitting of
C
b
(t)
could provide a good
approximation for determining CMRO
2
in the rat brain when
the
17
O
2
inhalation time is relatively short (e.g., 2 minutes)
(87)
.
This is consistent with the prediction based on either
Eq. (15.8)
or
(15.10)
. During the initial
17
O
2
inhalation period, both
C
a
(t)
and
C
b
(t)
have not built up significantly resulting in near zero
value of the second term on the right side of
Eq. (15.8)
.There-
fore,
Eq. (15.8)
can be approximated as a linear differential equa-
α
