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 584

determination of the shape of CBF · R(t) can allow an assessment and correc-
tion of this error. In such cases, the conventional SVD method is not suitable.
In order to overcome SVD limitations, several deconvolution methods have
been proposed during the last 10 yr. Thus, for instance, one of the disadvan-
tages of SVD applied to DSC-MRI data is a tendency to underestimate the
flow when the tissue tracer arrival is delayed relative to the AIF. This problem
has been circumvented by the so-called block-circulant SVD proposed by Wu
et al. [36]. This technique is made time-shift insensitive by the use of a block-
circulant matrix W c for deconvolution. Block-circulant SVD looks promising
in providing tracer-arrival time-insensitive flow estimates and a more specific
indicator of ischemic injury, but more work is necessary to better define its
domain of validity. Andersen et al. [38] proposed the use of a Gaussian process
to approximate the convolution kernel, i.e., the residue function. The method
is termed Gaussian process deconvolution (GPD) and allows accounting for
the smoothness (but not for nonnegativity) of the residue function by incor-
porating this constrain as a priori information. More recently, Calamante
et al. [22] improved upon SVD by implementing the Tikhonov regularization
method in order to overcome the presence of unwanted oscillations in the
residue function. However, even if this new method was shown to provide an
improved characterization (as compared to SVD) of the shape of R(t), it does
not account for nonnegativity of R(t). Along this line, Zanderigo et al. [39]
proposed the application of a nonlinear stochastic regularization (NSR)
method, which is able to account for the smoothness of the residue function
and handle possible violations of the nonnegativity constraint of CBF · R(t).
NSR is a deconvolution method that exploits a model of the unknown residue
function, only allowing nonnegative values. NSR considers CBF · R(t) com-
posed by the exponential of a Brownian motion. This approach shows advan-
tages over SVD in detecting only positive and smoothed (i.e., physiological)
CBF · R(t) without fixing any threshold value and requiring only the knowledge
of AIF and tissue data.

19.3.4 A BSOLUTE Q UANTIFICATION I SSUES

The fundamental steps for CBF, CBV, and MTT quantification are summarized
in Figure 19.3 . The accuracy of CBF measures is strongly dependent on the values
of the density of brain tissue, and of the hematocrit in capillaries and large

vessels, H SV and H LV , respectively. In particular, the frequently used values

ρ

ρ =

1.04 g/ml, H LV 0.25 [11] have been shown to generate in

normal subjects CBF values that are in agreement with the flow values obtained
with other techniques such as PET [11,40], but, on the contrary, for instance, in
healthy smoker subjects, the same values of

= 0.45, and H SV =

, H LV , and H SV have been unable to
provide reliable quantitative perfusion measurements [41]. In addition, nobody has
tested the validity of the use of these values in pathologic conditions. To overcome
these limitations, several other approaches have been proposed. In Reference 16,
the authors obtained absolute CBF values assuming the microvascular hematocrit

ρ