Assessment of Cerebral Blood Flow, Volume, and Mean Transit Time from Bolus-Tracking MRI Images: Theory and Practice - Advance Image Processing in Magnetic Resonance Imaging - page 581

a local C AIF (t) instead of that coming from an LV such as the carotid artery can
reduce delay and dispersion, it can increase the presence of partial-volume effect.
Thus, particular care is required in selecting the best place for C AIF (t) measure-
ment, by evaluating all technical limitations and physiopathological conditions.
In fact, of note is that the use of a local C AIF (t) could be important not only to
minimize delay and dispersion but also in studying patients with cerebral ischemia
or stenosis.
C AIF (t) is also dependent on the sequence type used. Usually both spin-echo
and gradient-echo imaging are used to measure DSC-MRI signals because, at the
moment, there is no clear evidence on which is the best method to reach accurate
absolute CBF quantification. In Reference 12, the authors demonstrated that spin-
echo functional images have great microvascular sensitivity resulting in images
of good quality. But, as noted in Reference 13 and Reference 16, in this case
C AIF (t) obtained with these sequences reflects more the situation of the SVs and,
consequently, could be an underestimation of the “true” C AIF (t). On the other
hand, gradient-echo sequence arises from both LVs and SVs, but C AIF (t) results
are more affected by errors due to partial-volume effects [26].

19.3.3 D ECONVOLUTION

In order to derive CBF from Equation 19.18, the function CBF ·R(t) has to be
determined by deconvolution. In general, no analytical solution is available, but
several techniques allow one to compute an approximate numerical solution. These
deconvolution techniques can be classified into two main categories, model-dependent
and model-independent approaches.
In the model-dependent techniques, the function to be deconvolved is
described by a parametric function, so that deconvolution loses its ill-posedness
and ill-conditioning problems by having to solve a parameter estimation problem.
This approach implies formulating a priori assumptions on the shape of the
solution. Larson et al. [27] suggested an exponential residue model, which implies
that the microvasculature is like that of a single, well-mixed compartment. More
precisely, the following analytical expression was assumed for R(t) for t ≥ 0.

t
MTT

−

Rt () = e (19.25)

Note that R(t) given by Equation 19.25 satisfies the residue function proper-
ties, i.e., R ( t ) ≥ 0, R(0) = 1, and R ( t ) ∈ [0; 1]. Substituting Equation 19.25 in

Equation 19.18, one has

t t

MTT

− τ

ρ

∫

−

Ct () = CBF C ( ) τ e d τ (19.26)

VOI AIF

k

0

H