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Elucidating dispersion effects in perfusion MRI by means of dispersion-compliant bases

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Elucidating Dispersion Eects in Perfusion MRI by
Means of Dispersion-Compliant Bases
Marco Pizzolato, Timothé Boutelier, Rutger Fick, Rachid Deriche
To cite this version:
Marco Pizzolato, Timothé Boutelier, Rutger Fick, Rachid Deriche. Elucidating Dispersion Eects
in Perfusion MRI by Means of Dispersion-Compliant Bases. International Symposium on Biomed-
ical Imaging (ISBI), Apr 2016, Prague, Czech Republic. IEEE 13th International Symposium on
Biomedical Imaging. <10.1109/I978-1-4799-2349-6/16>. <hal-01309243>
Marco Pizzolato?Timoth´
e BoutelierRutger Fick ?Rachid Deriche?
?Athena Project-Team, Inria Sophia Antipolis - M´
ee, France
Olea Medical, La Ciotat, France
Dispersion effects in perfusion MRI data have a relevant influ-
ence on the residue function computed from deconvolution of
the measured arterial and tissular concentration time-curves.
Their characterization allows reliable estimation of hemody-
namic parameters and can reveal pathological tissue condi-
tions. However, the time-delay between the measured con-
centration time-curves is a confounding factor. We perform
deconvolution by means of dispersion-compliant bases, sep-
arating the effects of dispersion and delay. In order to char-
acterize dispersion, we introduce shape parameters, such as
the dispersion time and index. We propose a new formulation
for the dispersed residue function and perform in silico ex-
periments that validate the reliability of our approach against
the block-circulant Singular Value Decomposition. We suc-
cessfully apply the approach to stroke MRI data and show
that the calculated parameters are coherent with physiologi-
cal considerations, highlighting the importance of dispersion
as an effect to be measured rather than discarded.
Index Termsperfusion, dispersion, delay, deconvolu-
tion, bases
The perfusion in the brain can be characterized with Dynamic
Susceptibility Contrast Magnetic Resonance Imaging (DSC-
MRI). A bolus of paramagnetic agent (PA) is injected into
the subject’s vascular system and the corresponding concen-
tration time-curve is measured for each voxel. In standard
practice, the concentration curve Cts(t)of a tissular voxel is
deconvolved with that measured in an arterial area Ca(t)to
obtain the residue function R(t)that characterizes the local
perfusion. From this, the hemodynamic parameters such as
the blood flow (BF) and mean transit time (MTT) are com-
puted. However, the bolus of PA may undergo dispersion after
injection, causing the calculated residue function to change
according to macro-vascular properties [1]. Dispersion can
be present in healthy subjects [2] but it can also be caused
by specific pathological conditions, such as the presence of
The author expresses his thanks to Olea Medical and to the Provence-
ote d’Azur Regional Council for providing grant and support.
a steno-occlusive disease in the artery [3]. Moreover, disper-
sion leads to an erroneous quantification of the true perfusion
deficit [1]. Indeed, the dispersion of the injected PA bolus
causes a modification in the shape of the actual arterial in-
put, which induces a non-monotonic shape in the computed
R(t)[1]. This effect is described by an additional unknown
convolution kernel - a dispersion kernel - called the vascular
transport function (VTF). Another issue in perfusion data pro-
cessing is the possible presence of a time delay between the
tissular concentration time-curve and the measured arterial in-
put. This is a confounding factor for dispersion characteriza-
tion [4, 5]. Assessment of dispersion is a challenging task but
is crucial for decoupling perfusion and macro-vascular influ-
ences on the residue function estimated via deconvolution.
Dispersion effects have been tackled by few techniques.
One allows to classify voxels where either dispersion or delay
is present [4]. The VM+VTF and CPI+VTF [5] aim at quanti-
fying perfusion and dispersion separately, but assume a model
for the VTF together with the prior information required for
the optimization procedure. The CPI0[5] retains a ”model-
free” nature but fixes the initial value of the residue function
to 0, thus preventing an optimal solution in the absence of dis-
persion. The block-circulant Singular Value Decomposition
(oSVD) [6], despite not explicitly aiming at dispersion char-
acterization, allows the reconstruction of dispersed residue
functions with no assumptions, and performs comparably to
other methods for relative cerebral blood flow estimation in
the presence of dispersion [5].
We propose to characterize bolus dispersion in DSC-MRI
data without any a priori assumption on the residue function
and vascular transport function. We perform deconvolution
with dispersion-compliant bases [7] obtaining a representa-
tion of the residue function which allows the decoupling of
time-delay and dispersion effects. We derive an analytic rep-
resentation of the dispersed residue function, to be used for in
silico experiments that validate the reliability of the adopted
approach against oSVD [6] at different levels of dispersion.
We introduce the use of shape parameters, the dispersion time
and index, to detect presence and amount of dispersion in the
shape of the residue function. We show the effectiveness of
the approach with synthetic experiments and on stroke MRI
According to the indicator-dilution theory [8], the tissular
concentration time-curve Cts(t)in a voxel is expressed as
the convolution between the arterial input Ca(t)and the un-
known residue function R(t), which expresses at each time t
the residual amount of PA in the voxel
Cts(t) = BF ·CaR(t)(1)
where BF is the unknown cerebral blood flow parameter.
In presence of dispersion, the true arterial input is the re-
sult of the convolution of Ca(t)with the vascular transport
function V T F (t), which represents the probability density of
the transit times tfrom the arterial measurement location to
the voxel where Cts(t)is measured [1]. Therefore eq. (1)
Cts(t) = BF ·[CaV T F (t)] R(t)
=BF ·Ca[V T F R(t)] (t)
=BF ·CaRd(t)
where Rd(t)is the dispersed residue function resulting from
the use of the associative property.
In order to perform in silico experiments, we derive a for-
mulation of Rd(t) = V T F R(t). Among the several ana-
lytic formulations of R(t), the bi-exponential shows the best
in vivo fitting performance in normal and Diffusion Positive
tissue [9]. It includes a fast and a slow flowing capillary com-
Rbiexp(t) = f·eτFt+ (1 f)·eτSt(3)
where τFand τSare the fast and slow time-rates respectively,
and fis the relative weight of the fast component. We special-
ize Rd(t)for the bi-exponential model of eq. (3) in the case
of a mono-exponential dispersion kernel V T F (t) = βeβt
[1, 3, 4] obtaining
Rd(t) = β
(βτF)(βτS)[(f(τFτS) + βτF)eβt
+f(τSβ)eτFt+ (f(βτF)β+τF)eτSt]
which holds for β > 0and, similarly to what observed for the
case of the mono-exponential residue function [1], depends
on the original mean transit time M T T =f F+(1f)S.
The dispersion amount induced by V T F (t)on the calcu-
lated residue function can be expressed by the vascular mean
transit time, which in the case of eq. (4) is M T Tv=β1[1].
Its influence is illustrated in Fig. 1, where the top image shows
that dispersion effects increase with M T Tv, being a pure bi-
exponential decay for M T Tv= 0, whereas the bottom image
shows that for a specific value of MT Tv>0dispersion ef-
fects increase also with M T T .
0t (s)
0t (s)
Fig. 1. Influence of dispersion on the calculated residue func-
tion and time-delay τbetween Cts(t)and Ca(t). Top: the
maximum decreases, and the time of the maximum tmax and
dispersion time τδincrease with the vascular mean transit
time M T Tv. Bottom: tmax, τδincrease with M T T (curves
are normalized).
We propose to quantify the deviation of the residue func-
tion from a purely decaying shape as the difference between
the integrals of the decreasing and increasing parts of the
curve, normalized by the total area
R(t)dt Ztmax
R(t)dt (5)
where tmax is the time of maximum and τthe time-delay as
shown in Fig. 1. The dispersion index indicates the absence
of dispersion when δ= 1 or its presence when δ < 1. In addi-
tion we note that Fig. 1 illustrates that the difference between
tmax and τ, henceforth called dispersion time τδ=tmax τ,
increases with M T T and M T Tv. We then propose to cal-
culate dispersion time τδand index δas shape descriptors of
the residue function sensitive to the presence and amount of
The next section describes the deconvolution strategy to
calculate these parameters and the experimental setup to test
dispersion characterization reliability in silico and in vivo.
The detection of dispersion is carried out by deconvolving
the measured Ca(t)and Cts(t)while representing the residue
function by means of dispersion-compliant bases [7]
R(t) = Θ(tτ)
where Nis the maximum basis order and Θ(t)is the Heav-
iside step function assuming Θ(0) = 1. The deconvolution
problem is solved linearly for an,bnsubject to an, bn0
to avoid negative solutions, with αnestimated a priori and τ
determined via grid search [7].
We perform in silico experiments to test the reliability of
the adopted deconvolution strategy against oSVD [6]. The
measured arterial input Ca(t)is simulated in range [0,90]s
with time step t= 1sas a gamma-variate function [1]. The
tissular concentration Cts(t)is obtained via eq. (2) using the
derived dispersed kernel in eq. (4) when β > 0. Gaussian
noise with zero mean is added to obtain concentration time-
curves as previously reported [7] with SN R = 50 [5]. De-
convolution is performed with the dispersion-compliant bases
(N= 20) searching for τin range [5,15]s[7] and with
oSVD [6]. The effective blood flow B F is obtained as the
maximum value of the estimated residue function R(t), the
blood volume BV as the ratio between the time integrals
of Cts(t)and Ca(t), and the mean transit time as the ra-
tio M T T =BV /BF . Results are studied as dispersion
effects increase for increasing values of MT Tv, assuming
no dispersion for M T Tv= 0, i.e., data is generated with
eq. (3). We simulate the concentration curves 100 times for
each combination of dispersion, M T Tv[0 : 1 : 10]s, de-
lay τ[5:1:5]s, original value of blood flow, BF
[20 : 10 : 60]ml/100g/min with blood volume BV 2%
and original mean transit time M T T 4s(τF= 0.34, τS=
0.025, f = 0.97). Results for τ= 2sand original BF =
30ml/100g/min are shown in the left column of Fig. 2 and
mean relative or absolute errors among all the tested combi-
nations are shown in the right column. We note that decon-
volution via dispersion-compliant bases results in more accu-
rate estimates than oSVD. The mean relative errors on BF
estimates are lower than 20% and uncorrelated with the un-
derlying amount of dispersion (M T Tv). As in the case of
oSVD, the performance in estimating M T T ameliorates as
dispersion increases with an improved accuracy. The mean
absolute precision on tmax always falls below the sampling
time t= 1sand below 2sfor τδ, as depicted from the green
bars in Fig. 2, allowing for dispersion time estimation.
We then applied the compared techniques on 256 ×256 ×
15 stroke MRI data, t= 1.5s. The techniques’ setups are
identical to those of in silico experiments. We compute the
hemodynamic parameters BF ,BV and M T T and remove
large vessels and cerebrospinal fluid (CSF) from the results
by setting voxels with BV > 3% to zero. The data reveals
an infarcted region in the right hemisphere and iso-perfused
tissue. We report the maps of tmax in Fig. 3 where oSVD
results confirm the overestimation tendency shown in the last
row of Fig. 2, particularly in the infarcted region. Moreover,
our approach accounts for both the contribution of the time-
delay τand dispersion time τδwhich are shown in the top row
of Fig. 4. Indeed, the dispersion-compliant bases encompass
delayed and dispersed shapes allowing to distinguish between
the two different contributions. Although the infarcted region
is distinguishable in both the tmax and τmaps, the proposed
0 2 4 6 8 10
bases: τ
0 2 4 6 8 10
0 2 4 6 8 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
BF* (ml/100g/min)
MTT* (s)
error (%)
tmax (s)
error (%)error (s)
MTTv (s) MTTv (s)
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Fig. 2. Estimated (effective) hemodynamic parameters for
τ= 2s, BF = 30 ml/100g/min (left column), and overall
errors (right column) as dispersion increases according to the
vascular mean transit time M T Tv(SNR = 50).
dispersion time τδmap improves the contrast between the in-
side and the outside of the infarcted region itself. The map of
the dispersion index proposed in eq. (5) is shown in the bot-
tom left corner of Fig. 4. Non-dispersed regions are colored
in red (δ= 1), whereas green and blue regions denote moder-
ate and high dispersion respectively. We distinguish two areas
within the infarcted region: an upper area mainly character-
ized by the absence of dispersion, and a lower one dominated
by high dispersion (blue color). Moderately dispersed shapes
dominate the iso-perfused region which may be caused by
natural dispersion effects in the data [2] and noise effects. The
dispersion index δis a relative shape parameter since it char-
acterizes the residue function regardless of its actual size. In
order to understand the actual spread of the dispersed residue
function, it is interesting to relate its δvalue with its measure
of the aperture given by the MT T . We show the correlation
term ρ1δ,MT T = (1 δ)M T T /M T T
max in the bottom
right corner of Fig. 4. As expected this map highly correlates
with the above dispersion time map τδ,[r0.95, p < 0.001].
Indeed, as previously described and illustrated in Fig. 1, the
dispersion time depends on both dispersion effects - M T Tv
and its influence on δ- and the mean transit time. We further
note how both the τδand ρ1δ,MT T maps are insensitive to
regions where no dispersion is detected - the red areas in the
δmap - being non-zero only in complementary regions.
Overall our approach allows low relative error of B F ,
M T T estimates, sub-second precision for tmax, and reli-
able estimation of delay τand dispersion time τδregardless
oSVD bases
Fig. 3. The time of the maximum tmax (s) of the residue
function R(t)calculated via oSVD, and dispersion-compliant
bases: these reduce overestimation as shown in Fig. 2.
τ τδ
Fig. 4. Maps obtained with dispersion-compliant bases.
Time-delay τ(s) and the proposed dispersion time τδ(s), dis-
persion index δand its correlation with M T T ,ρ1δ,MT T .
the amount of dispersion. Furthermore, the proposed index δ
provides new insights on dispersion, and its correlation with
M T T is consistent with τδ.
Dispersion is a phenomenon that can be present in perfusion-
weighted data and its characterization is fundamental to as-
sess the reliability of perfusion-related estimates while po-
tentially revealing pathological conditions [4]. In this work
we propose a way of characterizing dispersion effects in vivo
without making any assumption on the dispersion kernel.
This is achieved by introducing shape parameters, such as the
dispersion time and index, that are calculated on the residue
function estimated via deconvolution by means of dispersion-
compliant bases. The approach outperforms oSVD and yields
reliable estimates specially when the underlying residue func-
tion has a dispersed shape, such as in the case of the derived
formulation. Results on stroke MRI data confirm in vivo the
influence of the mean transit time on the dispersed shape,
showing consistency with the estimated dispersion time and
index. The dispersion time is useful in the delimitation of the
infarcted area whereas the dispersion index gives new insights
on the shape of the residue function. The proposed strategy
allows to decouple dispersion effects from the confounding
effect of the delay. This opens for dispersion characterization,
thus providing a better understanding of the tissue perfusion
and vascular dynamic.
[1] Calamante et al., “Delay and dispersion effects in dy-
namic susceptibility contrast MRI: simulations using sin-
gular value decomposition, Magn Reson Med, vol.
44(3), pp. 466–473, 2000.
[2] Østergaard et al., “Cerebral blood flow measurements by
magnetic resonance imaging bolus tracking: comparison
with [15o]h2opositron emission tomography in humans,”
J Cerebr Blood F Met, vol. 18(9), pp. 935–940, 1998.
[3] Calamante et al., “Estimation of bolus dispersion effects
in perfusion MRI using image-based computational fluid
dynamics,” NeuroImage, vol. 19, pp. 341–353, 2003.
[4] Willats et al., “Improved deconvolution of perfusion MRI
data in the presence of bolus delay and dispersion,” Magn
Reson Med, vol. 56, pp. 146–156, 2006.
[5] Mehndiratta et al., “Modeling and correction of bolus
dispersion effects in dynamic susceptibility contrast MRI:
Dispersion correction with cpi in DSC–MRI,” Magn Re-
son Med, vol. 72, pp. 1762–1774, 2014.
[6] Wu et al., “Tracer arrival timinginsensitive technique for
estimating flow in MR perfusionweighted imaging using
singular value decomposition with a blockcirculant de-
convolution matrix, Magn Reson Med, vol. 50(1), pp.
164–174, 2003.
[7] Pizzolato et al., “Perfusion MRI deconvolution with de-
lay estimation and non-negativity constraints, in 12th
International Symposium on Biomedical Imaging (ISBI).
IEEE, 2015, pp. 1073–1076.
[8] Meier et al., “On the theory of the indicator-dilution
method for measurement of blood flow and volume, J
Appl Physiol, vol. 6(12), pp. 731–744, 1954.
[9] Mehndiratta et al., “Modeling the residue function in
DSC-MRI simulations: Analytical approximation to in
vivo data, Magn Reson Med, vol. 72, pp. 1486–1491,
Full-text available
This thesis is dedicated to furthering neuroscientific understanding of the human brain using diffusion-sensitized Magnetic Resonance Imaging (dMRI). Within dMRI, we focus on the estimation and interpretation of microstructure-related markers, often referred to as ``Microstructure Imaging''. This thesis is organized in three parts. Part I focuses on understanding the state-of-the-art in Microstructure Imaging. We start with the basic of diffusion MRI and a brief overview of diffusion anisotropy. We then review and compare most state-of-the-art microstructure models in PGSE-based Microstructure Imaging, emphasizing model assumptions and limitations, as well as validating them using spinal cord data with registered ground truth histology. In Part II we present our contributions to 3D q-space imaging and microstructure recovery. We propose closed-form Laplacian regularization for the recent MAP functional basis, allowing robust estimation of tissue-related q-space indices. We also apply this approach to Human Connectome Project data, where we use it as a preprocessing for other microstructure models. Finally, we compare tissue biomarkers in a ex-vivo study of Alzheimer rats at different ages. In Part III, we present our contributions to representing the qt-space - varying over 3D q-space and diffusion time. We present an initial approach that focuses on 3D axon diameter estimation from the qt-space. We end with our final approach, where we propose a novel, regularized functional basis to represent the qt-signal, which we call qt-dMRI. Our approach allows for the estimation of time-dependent q-space indices, which quantify the time-dependence of the diffusion signal.
Conference Paper
Full-text available
Perfusion MRI deconvolution aims to recover the time-dependent residual amount of indicator (residue function) from the measured arterial and tissue concentration time-curves. The deconvolution is complicated by the presence of a time lag between the measured concentrations. Moreover the residue function must be non-negative and its shape may become non-monotonic due to dispersion phenomena. We introduce Modified Exponential Bases (MEB) to perform deconvolution. The MEB generalize the previously proposed exponential approximation (EA) by taking into account the time lag and introducing non-negativity constraints for the recovered residue function also in the case of non-monotonic dispersed shapes, thus overcoming the limitation due to the non-increasing assumtion of the EA. The deconvolution problem is solved linearly. Quantitative comparisons with the widespread block-circulant Singular Value Decomposition show favorable results in recovering the residue function.
Bolus dispersion in DSC-MRI can lead to errors in cerebral blood flow (CBF) estimation by up to 70% when using singular value decomposition analysis. However, it might be possible to correct for dispersion using two alternative methods: the vascular model (VM) and control point interpolation (CPI). Additionally, these approaches potentially provide a means to quantify the microvascular residue function. VM and CPI were extended to correct for dispersion by means of a vascular transport function. Simulations were performed at multiple dispersion levels and an in vivo analysis was performed on a healthy subject and two patients with carotid atherosclerotic disease. Simulations showed that methods that could not address dispersion tended to underestimate CBF (ratio in CBF estimation, CBFratio = 0.57-0.77) in the presence of dispersion; whereas modified CPI showed the best performance at low-to-medium dispersion; CBFratio = 0.99 and 0.81, respectively. The in vivo data showed trends in CBF estimation and residue function that were consistent with the predictions from simulations. In patients with atherosclerotic disease the estimated residue function showed considerable differences in the ipsilateral hemisphere. These differences could partly be attributed to dispersive effects arising from the stenosis when dispersion corrected CPI was used. It is thus beneficial to correct for dispersion in perfusion analysis using this method. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.
PurposeAn exponential residue function is commonly used in numerical simulations to assess the accuracy of perfusion quantification using dynamic susceptibility contrast (DSC) MRI. Although this might be a reasonable assumption for normal tissue, microvascular hemodynamics are likely to be significantly altered in pathology. Thus the exponential function may no longer be appropriate and the estimated accuracy of DSC-MRI quantification might be inappropriate. The purpose of this study was to characterize in vivo residue function variations in normal and infarcted tissue in a chronic atherosclerotic disease cohort, and to find the most appropriate model for use in DSC simulations. Methods Residue functions were measured in vivo in patients with atherosclerotic disease using a nonparametric Control Point Interpolation method, which has been shown to provide a robust characterization of the shape of the residue function. The observed residue functions were approximated with five commonly used analytical expressions: exponential, bi-exponential, Lorentzian, and Fermi functions, and a previously proposed Vascular Model. ResultsThe lowest error was found with the bi-exponential function approximations to the in vivo residue functions from both normal and infarcted tissue. ConclusionA bi-exponential model should therefore be used in future numerical simulations of DSC-MRI instead of the exponential function. Magn Reson Med 000:000–000, 2013. © 2013 Wiley Periodicals, Inc.
In six young, healthy volunteers, a novel method to determine cerebral blood flow (CBF) using magnetic resonance (MR) bolus tracking was compared with [(15)O]H2O positron emission tomography (PET). The method yielded parametric CBF images with tissue contrast in good agreement with parametric PET CBF images. Introducing a common conversion factor, MR CBF values could be converted into absolute flow rates, allowing comparison of CBF values among normal subjects.
Dynamic susceptibility contrast (DSC) MRI is now increasingly used for measuring perfusion in many different applications. The quantification of DSC data requires the measurement of the arterial input function (AIF) and the deconvolution of the tissue concentration time curve. One of the most accepted deconvolution methods is the use of singular value decomposition (SVD). Simulations were performed to evaluate the effects on DSC quantification of the presence of delay and dispersion in the estimated AIF. Both delay and dispersion were found to introduce significant underestimation of cerebral blood flow (CBF) and overestimation of mean transit time (MTT). While the error introduced by the delay can be corrected by using the information of the arrival time of the bolus, the correction for the dispersion is less straightforward and requires a model for the vasculature.
Bolus tracking magnetic resonance imaging (MRI) is a powerful technique for measuring perfusion, and is playing an increasing role in the investigation of acute stroke. However, limitations have been reported when assessing patients with steno-occlusive disease. The presence of a steno-occlusive disease in the artery may cause bolus dispersion, which has been shown to introduce significant errors in cerebral blood flow (CBF) quantification. Bolus dispersion is commonly described by a vascular transport function, but the function that properly characterizes the dispersion is unknown. A novel method to quantify bolus dispersion errors on perfusion measurements is presented. A realistic patient-specific model is constructed from anatomical and physiologic MR data, and the arterial blood flow pattern and the transport of the bolus of contrast agent are computed using finite element analysis. The methodology presented was used also to evaluate the accuracy of three simple vascular models. The methodology was tested on MR data from two normal subjects and two subjects with mild carotid artery stenosis. The estimated CBF errors were of the order of 15% to 20%. However, the presence of stenosis did not necessarily introduce larger dispersion (not only the geometrical model but also the particular physiologic conditions influence the degree of bolus dispersion). The method described will contribute to a better understanding of errors introduced by dispersion effects, to the assessment and validation of vascular models, and to the development of new methods for the correction of dispersion errors in CBF quantification.
Relative cerebral blood flow (CBF) and tissue mean transit time (MTT) estimates from bolus-tracking MR perfusion-weighted imaging (PWI) have been shown to be sensitive to delay and dispersion when using singular value decomposition (SVD) with a single measured arterial input function. This study proposes a technique that is made time-shift insensitive by the use of a block-circulant matrix for deconvolution with (oSVD) and without (cSVD) minimization of oscillation of the derived residue function. The performances of these methods are compared with standard SVD (sSVD) in both numerical simulations and in clinically acquired data. An additional index of disturbed hemodynamics (oDelay) is proposed that represents the tracer arrival time difference between the AIF and tissue signal. Results show that PWI estimates from sSVD are weighted by tracer arrival time differences, while those from oSVD and cSVD are not. oSVD also provides estimates that are less sensitive to blood volume compared to cSVD. Using PWI data that can be routinely collected clinically, oSVD shows promise in providing tracer arrival timing-insensitive flow estimates and hence a more specific indicator of ischemic injury. Shift maps can continue to provide a sensitive reflection of disturbed hemodynamics.
Cerebral blood flow (CBF) is commonly estimated from the maximum of the residue function deconvolved from bolus-tracking data. The bolus may become delayed and/or dispersed in the vessels feeding the tissue, resulting in the calculation of an effective residue function, Reff(t), whose shape reflects the distortion of the bolus as well as the hemodynamic tissue status. Consequently the CBF is often underestimated. Since regularizing the deconvolution introduces additional distortions to Reff(t), it is impossible to distinguish a true decrease in the CBF from bias introduced by abnormal vasculature. This may result in misidentification of tissue regions at risk of infarction, which could have serious clinical consequences. We propose a modified maximum-likelihood expectation-maximization (mML-EM) method, which is shown by way of simulations to improve the characterization of Reff(t) across a wide range of shapes. A pointwise termination approach for the iteration minimizes the effects of noise, and appropriate integral approximations minimize discretization errors. mML-EM was applied to data from a patient with left internal carotid artery (ICA) occlusion. The shape of each calculated Reff(t) was used to create a map indicating voxels affected by bolus delay and/or dispersion, where CBF estimates are inherently unreliable. Such maps would be a useful adjunct for interpreting bolus-tracking data.