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366 15 Imaging Blood Circulation Using Nuclear Magnetic Resonance
including SE [23], echo-planar imaging (EPI) [24], and fast low-angle shot (FLASH)
[25]. Since the imaging plane contains magnetization from static tissue, a second
control image is acquired to subtract the tissue component (Figure 15.8).
The flow-driven AFP will not only invert flowing magnetization but also static
tissue due to MT [26]. To take this effect into account, a flow-driven AFP pulse
is also applied before the control image. The labeling plane is then positioned
mirrored to the imaging where no arteries can be expected. The flow-driven AFP
consists of an RF pulse and an accompanying magnetic field gradient, G, along
the direction of arterial flow [21]. RF pulse durations of several seconds are needed
to achieve CASL.
7)
The off-frequency f
lab
to provide a labeling location, r, a small
distance away from the imaging plane is for a given gradient strength, G, as follows
[27]:
f
lab
= γGr/2π (15.6)
The gradient strength also plays an important role for the flow-driven AFP. For
spins moving with a velocity, v, parallel to the gradient, G, the effective magnetic
field is changing in time according to B
eff
= γGvt.
When this dependency is combined with the AFP condition, we arrive at the
adiabatic condition for flow-driven adiabatic inversion [23, 28]
1
T
1
,
1
T
2
<<
G ·
v
B
1
<< γ
|
B
1
|
(15.7)
A more elegant way to find the degree of inversion is possible with a quantum
mechanical approach given by Zhernovoy [29]. He leads to the following expression
for
M
z
in terms of the
B
1
field
M
z
=
M
0
2exp(−
πγB
2
1
2
G ·
v
) −1
(15.8)
In practice, the degree of the inversion achieved by the flow-driven adiabatic
inversion scheme depends on the velocity of the blood, the orientation of the
vessels relative to the labeling plane, the RF power and gradient strength. It
is typically in the range of 80–95% [30 –33]. Following the long labeling pulse,
a spoiler gradient is often introduced to remove any transverse magnetization
formed by imperfections in the inversion pulse.
As we mentioned, AFP also produces another contrast in MRI, which is MT.
MT effects are problematic as they cause saturation at the imaging plane. These
effects cause signal loss in the perfusion-weighted images that leads to errors in
the subsequent quantification step.
The MT effects arise due to off-resonance excitation. Protons that are bound to
macromolecules in the tissue have extremely short T
2
relaxation times and are
therefore invisible to most imaging sequences. These protons are saturated over
the entire duration of the ASL pulse. Owing to their broad RF absorption spectrum,
7) Long RF pulsescaneasilyexceedregulatory
limits on specific absorption rate (SAR) and
the capability of the RF amplifiers.
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15.3 Perfusion Imaging 367
protons bound to macromolecules at the imaging plane are saturated, while free
water protons are largely unaffected at the imaging plane because of their narrow
RF absorption spectrum. Subsequent chemical exchange between protons from
macromolecules and free water results in MT. This culminates in a reduced signal
from the free water pool at the imaging plane.
MT is not a symmetric function of frequency. However, there have been
several schemes proposed in order to compensate for this source of error [34,
35]. The best way to reduce MT is the use of dedicated labeling coil, which is
actively decoupled from the imaging receive coil. The labeling coil is typically
small and placed far away from the imaging plane. Owing to the small sensitive
region of the labeling coil, no saturation of macromolecules at the imaging plane
occurs and this proves particularly useful when multislice perfusion imaging is
required.
15.3.1.2 Pulsed Arterial Spin Labeling (PASL)
In pulsed arterial spin labeling (PASL), short RF pulses inverting a defined volume
of blood perform the labeling of blood. From a mathematical view, one can say this
labeling method establishes an initial condition, which will then evolve in time. This
stands in contrast to CASL where we define a boundary condition at the labeling
plane. For effective saturation or inversion of flowing magnetization, the usage
of adiabatic RF pulses is of advantage. These can, in combination with gradients,
select any chosen defined volume. The labeled volume then flows into the imaging
plane for detection. Again, for separation of static and flowing magnetization, a
control imaging is required.
In the following, a short summary of different PASL techniques is given
1) Echo-planar imaging and signal targeting with alternating radio frequency
(EPISTAR) [36]. The labeling phase uses a slice-selective saturation pulse to
saturate magnetization at a defined ROI. Imaging occurs after a short period
of around 1 s to allow inflow of saturated magnetization. Afterward the control
image is acquired without any additional preparation.
2) Transfer insensitive labeling technique (TILT) [37]. The drawback with EPIS-
TAR is that it suffers from MT effects during the labeling phase. The TILT
labeling technique uses an inversion scheme. The inversion pulse consists of
two consecutive 90
◦
RF pulses of the same phase. The control phase also uses
two 90
◦
RF pulses but now with an opposite phase. The second 90
◦
pulse turns
the magnetization back to the nonexcited state. MT similarly influences both
images.
3) Flow-sensitive alternating inversion recovery (FAIR) [38]. This labeling
scheme consists of a slice-selective inversion pulse for the labeling
phase and a nonselective inversion for the control phase. Again, imaging
occurs after a short inflow period. FAIR is less sensitive to MT effects
than EPISTAR because it does not use off-resonance RF pulses with
respect to the imaging slice. This allows multislice perfusion-weighted
imaging.
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368 15 Imaging Blood Circulation Using Nuclear Magnetic Resonance
15.3.2
Quantification
Attempts to quantify microcirculation are as many as there are sequences. Here,
we offer a critical overview of the basic principles. They can be divided into three
principles, where two of those principles are adaptations of other medical tracer
methods.
15.3.2.1 Modified Fick’ Law
Detre and Williams [22, 23] modified the Bloch equation by adding in- and outflow
terms as introduced by Kety and Schmidt [39] in 1948. With this approach, a
monoexponential decay can be found to describe the tissue response function. In
the longitudinal direction, where the signal is altered by inflowing magnetization,
the modified Bloch equation then takes the following form [22, 23]:
dM(t)
dt
= fM
a
(t) −
f
λ
M(t) +
M
0
− M(t)
T
1
(15.9)
where f is defined as the blood flow (ml g
−1
s
−1
), λ is the blood/brain partition
coefficient for water (the ratio of the quantity of water per gram of blood to the
quantity of water per gram of brain), T
1
is the spin– lattice relaxation time of blood
water, M is the longitudinal magnetization per gram of brain tissue, M
0
is M under
fully relaxed conditions, and M
a
is the longitudinal magnetization per milliliter of
arterial blood. Using this equation, Detre et al. [22] found for a CASL experiment,
with a full saturation of the imaging plane, the following results
f =
λ
T
1app
M
ctrl
− M
lab
2M
ctrl
(15.9a)
where T
1app
is the relaxation time that describes the exponential decrease in
M
b
duetotheT
1
relaxation time of brain water and a flow and exchange term
(1/T
1app
= 1/T
1
+ f /λ), M
ctrl
is the image intensity in the control image, and M
lab
is the image intensity in the labeled image. However, a discussion of Eq. (15.9)
reveals the weakness of the model. The arterial magnetization does not have a T
1
relaxation dependency, although Calamante et al. [40] addressed this problem by
incorporating T
1
blood relaxation. Another problem related to T
1
relaxation is the
transit time from the labeling position to the imaging slice. Magnetization change
due to transit time was introduced by Kwong et al. [38].
15.3.2.2 Indicator-Dilution Model
Buxton [41] proposed a general kinetic model, where the magnetization difference
between the labeled and control images is described using a convolution integral.
This method was first proposed for tracer methods by Meier and Zierler [42]. The
convolution allows separation of the various physical processes involved. Buxton
described the following time-dependent functions: (i) the delivery function (or
fractional (arterial input function, AIF)) c(t), which is the normalized concentration
of labeled water arriving at the ROI at time t; (ii) the residue function r(t,t
), that
fraction of labeled water molecules, which arriving at the ROI at a time t
is still
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15.3 Perfusion Imaging 369
(a) (b)
Ctrl, data
Ctrl, fit
Act, fit
Act, data
0.00
012345
Time (s)
0.02
0.04
0.06
0.08
0.10
Signal change
Figure 15.9 (a) ASL perfusion map ac-
quired during electrical stimulation of a
rat’s forepaw. The corresponding increase
in cerebral perfusion in the right somatosen-
sory cortex can be clearly identified. (b) ASL
perfusion map acquired in resting state.
The graph shows a least-squares fit of the
bolus-tracking ASL data (yellow and red
asterisks for control and activation exper-
iments, respectively) to theoretical model
(blue and green solid lines for control and
activation experiments, respectively) for the
right somatosensory cortex.
present at time t; and (iii) the magnetization relaxation function m(t
), describing
the fraction of the original longitudinal magnetization associated with labeled water
molecules, which arrives at time t
and is still present at time t.
M ∝
t
c(t
) ·r(t −t
) ·m(t − t
)dt
(15.10)
Buxton based the model on a number of assumptions, which lead to a residue
function of the form, r(t) = exp[−ft/λ]. Parkes [43] showed that, with the choice of
this residue function, Buxton’s approach is the equivalent of the modified Bloch
equation (15.9). The fundamental assumption of the modified Bloch equation is
that water undergoes rapid exchange across the capillary walls. It is generally
accepted that this assumption is false and that labeled blood water actually remains
within the vessel for a time period relaxing with T
1a
before it exchanges across
the capillary wall into the extravascular (EV) water [43]. Therefore, some authors
introduced models with two compartments [43–46]. However, by addressing the
many physical processes involved while the labeled water is flowing from arteries
into capillaries and tissue, the models became so complex with many variables that
quantification with ASL is not possible at all.
In summary, we have seen that the Eq. (15.9) has been modified in many ways
to compensate for the inability to describe blood flow with ASL. The underlying
problem is simple. All ASL techniques are defined in space and time. The spatial
encoding through the labeling plane for CASL or the inflow volume in PASL cannot
be expressed with the Eq. (15.9) as there are no spatial variables present in this
equation. This problem has been identified using a different approach based on
the Fokker–Planck equation [28, 47].
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370 15 Imaging Blood Circulation Using Nuclear Magnetic Resonance
15.3.2.3 Fokker–Planck Approach
The Kety and Schmidt approach [39] was derived from 1. Fick’s law. They assumed
that inflow and outflow must be equal. In steady-state conditions, we know that
the same amount of blood that flows in must flow out again. But we also know a
concentration of tracer flowing in will be diluted when it flows out again. Therefore,
the description of Kety and Schmidt was well chosen for their experiment where
they observe in- and outflow. For ASL, this is not sufficient. We cannot observe
the outflow and the concentration of labeled blood gets lost due to T
1
relaxation.
But why is the concentration changing? The answer is simple: dilution. The blood
volume increases by a factor of around 100 when flowing from artery vessels
into capillary and brain tissue. Hereby, a tracer will be diluted by distortion and
diffusion processes, which can mathematically summarized and described with a
diffusion term. Fick’s law can then be expanded to a Fokker–Planck equation as
follows
∂c
∂t
=−F
∂c
∂V
+ P
∂
2
c
∂V
2
∂c
∂t
=−F
∂c
∂V
+ P
∂
2
c
∂V
2
(15.11)
where the first term describes the transport and the second the diffusion and
distortion processes.
When we consider the Fokker–Planck equation with constant parameters F and
P, this approach could be generalized. With F and P as function of space and time,
every thinkable hemodynamic process could well be approximated. The Eq. (15.11)
is a familiar equation in physics but not commonly used in medicine and biology.
The Fokker–Planck equation (Eq. 15.11) was used to expand the Bloch equation
(Eq. 15.1a) [28, 47].
∂c
∂t
=−F
∂c
∂V
+ P
∂
2
c
∂V
2
−
c
T
1
(15.12)
To show the advantages of this approach, we will consider a simple case. Let us
bear in mind the original CASL experiment again. The blood in the imaging voxel
gets saturated with labeled blood and reaches an equilibrium. The magnetization
change in time is then ∂c/∂/∂t = 0. Equation (15.12) can now easily be solved. We
find
c(V) = C
0
exp
1
2
F
P
1 −
1 +
4P
T
1
F
2
V
(15.13)
This results shows that the signal depends on blood volume and flow. It can
also be shown that the exponent only depends on the transit time (MTT, CTT)
defined below. One other important test is the case T
1
→∞. In this situation, the
magnetization found reaches the starting magnetization of the inversion C
0
(full
saturation). If we were to change the position of the labeling plane, the MTT would
change and with that the signal.
For the PASL solution, we take into account an initial value problem. The
concentration of excited magnetization at every point in the volume V is given by
c
0
(V
,0)fort = 0, where V
is some known function of the volume. Under this
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15.3 Perfusion Imaging 371
condition, the Fokker–Planck equation (Eq. (15.12)) can be solved using a Fourier
transformation as follows:
c(V, t) =
exp(−t/T
1
)
√
4πPt
∞
−∞
c
0
(V
,0)exp
−
(V − V
− Ft)
2
4Pt
dV
(15.14)
This formula determines the distribution of any contrast agent (T
1
→∞) in terms
of the given initial distribution. Considering the EPISTAR experiment, where only
arterial blood is tagged, we can assume that the initial distribution is approximated
by a delta function, δ(V) (arterial blood volume and capillary blood volume). The
integration of Eq. (15.14) leads to the solution for EPISTAR:
c(V, t) = C
0
exp(−t/T
1
)
√
4πPt
exp
−
(V − Ft)
2
4Pt
(15.15)
This condition would be related to the experimental condition of EPISTAR. Other
experimental conditions can be found by adjusting the integration limits to a
defined blood volume.
CASL, where the labeling is applied for a defined duration, is a boundary-value
problem. The magnetization labeled at the labeling plane, V = 0 (where V is being
used here as a coordinate to denote location in relation to the labeling plane),
enters the imaging plane as time progresses. However, at t = 0, the concentration
of excited spins in the brain is zero. This leads to the following result for all CASL
experiments
c(V, t) =
t
0
c
0
(τ )
exp
(
−t/T
1
)
√
4πP
(
t −τ
)
V
(
t −τ
)
exp
−
(
V − F
(
t −τ
))
2
4P
(
t −τ
)
dτ
(15.16)
where c
0
(t) is the input function.
What is interesting is that by defining the mean transit time, MTT = V/F, and
a capillary transit time, CTT = P/F
2
, the dependent variables of the solutions can
be reduced by one. The signal curve of a bolus-tracking ASL experiment will then
only depend on times, the only physical unit that is directly measurable in ASL
experiments. To quantify flow or volume, the signal intensity has to be related to
the actual blood volume in the imaging voxel.
For comparison with conventional bolus-tracking methods, we let T
1
=∞.
Then, we find that the MTT is equivalent to an MTT defined for indicator-dilution
approaches [22, 29]. Simplified for a delta function input, δ(t), the first moment is
given by
MTT
Zierler
=
∞
0
t ·r(V, t)dt
∞
0
r(V , t)dt
=
V
F
(15.17a)
where c(V,t) is the solutionof the Eq. (15.16) forthe initial conditions δ(V ), T
1
→∞,
which can be interpreted astissue response function. Similarly, the second moment
is given by
CTT =
1
2
∞
0
(t −t
1
)
2
·r(t)dt
∞
0
t ·r(t)dt
=
P
F
2
(15.17b)
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372 15 Imaging Blood Circulation Using Nuclear Magnetic Resonance
which has been interpreted as the time taken for the bolus to be distributed at an
ROI [48, 49]. These definitions are in agreement with the hypotheses that a bolus
is transported to the ROI due to bulk flow, F, and is then dispersed at the ROI due
to random effects within the microvasculature.
Further analysis of the solution (Eq. (15.16)), which describes the bolus-tracking
ASL solution, reveals the conventional structure of a residue detection experiment
with bolus dispersion [48]. Equation (15.16) can be rewritten as follows:
c(V, t) =
t
0
c
o
(t)
AIF
exp
−t
T
1
m(t)
V
4πP(t −τ)
3
exp
−
(
V − F
(
t −τ
))
2
4P
(
t −τ
)
r(t−τ )
dτ
(15.18)
From this equation, it can be seen that the solution is equivalent to a convolution
described by
c(V, t) = AIF ⊗r(t) ⊗m(t) (15.19)
where AIF is the arterial input function, m(t) is the relaxation function, and r(V,t)
is the residue function, as shown in the Eq. (15.18).
15.3.3
Perfusion Imaging Using Phase Shift
In the longitudinal direction, the signal is altered by inflowing magnetization. In
transverse directions, the inflow does not change the relaxation directly. How-
ever, motion can be influenced in this domain indirectly by local magnetic field
differences, which can be present in the imaging sample (for example in para-
magnetism) or which can be introduced by MRI sequence with magnetic field
gradients. The application of gradients allows the measurement of blood flow for
different purposes.
The IntraVoxel Incoherent Motion (IVIM) method developed by Le Bihan et al.
[50] is based on the use of diffusion-sensitizing gradients and used to detect
the movement of water within biological tissue containing flowing blood. It also
differentiates between diffusion and flow contributions. IVIM has its basis in the
assumption that an image voxel of tissues contains a large number of capillary
segments. Because of this large number, it is assumed that it is possible for
the water molecules in the capillary network to move in differing directions at
a distribution of speeds. At the voxel scale, microcirculation can be, therefore,
viewed as a collection of random movements modeled as a (distributed and
incoherent) pseudo-diffusion process. Such random motion can be amplified, with
a motion-sensitive MRI sequence, as a phase incoherence of the spins that causes
a loss of intensity of image. The blood flow-driven motion is several times higher
than Brownian motion; therefore, the intensity attenuation contains a separate
fast and slow component. The fast component correlates to the pseudorandom
microcirculation. The slower component corresponds to Brownian motion.
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15.4 Blood Oxygenation Level-Dependent (BOLD) Contrast 373
The dependence of the MR signal S
IVIM
on the diffusion-weighting b-value
8)
can
be approximated as a biexponential relation: S
IVIM
/S
0
= (1 − f )exp(−bD) + f ×
exp[−b(D +D
∗
)], where S
0
is the signal intensity for b = 0, f is the vascular volume
fraction, D is the molecular diffusion coefficient, and D* is the flow index. This
allows both forms of movement to be measured in all three spatial directions.
15.3.4
Perfusion Imaging with Tracers
This approach uses ultrafast imaging techniques with high temporal solution to
measure a tracer bolus flowing through the tissue. An administered bolus of tracer
defines the AIF, which is the time-dependent function of the trace at the supply
artery. The AIF can be estimated by measuring signal changes in and around a
major blood vessel [51]. Measurement of both the AIF and the time course of tracer
concentration in the tissue allows the quantification of cerebral blood volume
(CBV) and CBF using the Meier and Zierler indicator-dilution method [42, 52,
53].
15.3.5
Applications
In 1991, Belliveau et al. [3] used an MRI contrast method to demonstrate for the
first time that MRI has the ability to image functional activation in the brain.
Edelman et al. [36] (for PASL) and Kerskens et al. [25] (for CASL) showed that
ASL can provide results as accurate as contrast techniques. Recently, Kelly et al.
[47] used a new ASL technique that enabled them to quantify blood flow-related
parameters during brain activation (Figure 15.9a) [54]. In clinical application, it
has been found that ASL measurements are highly accurate in detecting lesion
laterality in temporal lobe epilepsy, stenotic–occlusive disease, and brain tumors.
At the moment, conclusions about the utility of ASL in clinical routine are limited
by the small sample sizes of studies currently in the literature [55].
15.4
Blood Oxygenation Level-Dependent (BOLD) Contrast
Blood oxygenation level–dependent (BOLD) contrast [56 –58] is derived from the
fact that deoxyhemoglobin is paramagnetic while the brain tissue is diamagnetic.
Changes in the local concentration of deoxyhemoglobin within the brain lead to
alterations in the MR signal. The contrast mechanism is similar to those discussed
for contrast agents.
8) The b-value includes the sequence-specific
parameter of spin-echo diffusion experi-
ment [51].
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374 15 Imaging Blood Circulation Using Nuclear Magnetic Resonance
15.4.1
BOLD Contrast Mechanism
BOLD contrast has become very important as the contrast changes during brain
stimulation. It allows the use of MRI in noninvasively mapping of areas with
increased neuronal activity in the human brain without resorting to an exogenous
contrast agent [59–61]. This revolutionary development of the past two decades
is called functional magnetic resonance imaging (fMRI). The contrast mechanism is
based on the fact that neuronal activation induces an increase in regional blood
flow without a commensurate increase in the regional oxygen consumption rate
(CMRO
2
) [62]. Therefore, the amount of oxygenated hemoglobin that is delivered
to the tissue is greater than the oxygen extracted by the activated neurons. The net
effect is a local increase in oxyhemoglobin (diamagnetic) and a local decrease in
deoxyhemoglobin (paramagnetic). Consequently, the decrease in paramagnetism
leads to an increase in transversal relaxation rate T
2
∗
and T
2
, which can be detected
with optimized MRI sequences. The optimum TE
opt
to detect changes in the
transversal relaxation is given by
TE
opt
= ln
T
2c
T
2a
1
T
2a
−
1
T
2c
−1
(15.20)
where T
2a
and T
2c
denote the relaxation time during activation and control, respec-
tively. For small changes in T
2
/T
2
∗
, the optimum TE to maximize signal changes is
found to be equal toT
2
/T
2
∗
[5]. The assumption of smallactivation-induced changes
in T
2
/T
2
∗
might generally be true for the EV compartment, but, for example, the
T
2
of venous blood can change significantly during activation. The consequence of
this is that at lower field strengths, the T
2
of venous blood is longer than that of
the tissue and its contribution to the BOLD signal change will be overweighted. At
very high-field strengths, T
2
is very short, and at the optimum TE for tissue, the
intravascular signal may be neglected [5].
For cognitive science, it is desirable to have a high sensitivity and specificity of
the activation map. Since the BOLD contrast is an indirect measurement of the
neuronal response, a discussion about the origin of signal changes is important.
First, one can divide the signal contributions into extravascular (ev) and in-
travascular (iv) components and, secondly, into dynamic and static dephasing
of magnetization in the susceptibility gradient of the magnetic dipole of the
hemoglobin iron complex [5, 63]. The static case is detectable with GE sequences
sensitive to local frequency offsets, while SE sequences refocus this offset. In the
dynamic case, the frequency offset becomes dependent on motion and diffusion.
These dynamic effects are detectable with both GE and SE sequences. Static de-
phasing is the dominant extravascular mechanism for vessels of a diameter greater
than about 20 µm [64], while dynamic dephasing is the most important mechanism
for capillaries and smaller postcapillary vessels.
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15.4 Blood Oxygenation Level-Dependent (BOLD) Contrast 375
15.4.2
fMRI
The BOLD contrast has been extensively used to investigate questions within
classic cognitive neuroscience, including issues pertaining perception, attention,
and memory. The rationale of most of those studies is that the BOLD signal
shows localized levels of neuronal activity, which, in turn, reflects cognitive pro-
cesses. To circumvent the fact that the entire brain is always active to some
degree, the subtraction paradigm has been applied. For the subtraction paradigm,
a participant performs a task with two very similar conditions. One condition
has exactly one feature (or putative process) more than the other, the process
one wants to investigate. Subtracting brain activity in one condition from the
other (called a contrast) produces a map of activity reflecting the process of
interest. Using the subtraction paradigm, Downing and colleagues [65] estab-
lished the existence of a cortical area specific to visual processing of the human
body. Their participants viewed images of bodies and body parts in one con-
dition and other objects and object parts in one of the control conditions. The
difference between the conditions was particularly large in a part of the ven-
tral visual stream of the cortex, in what they termed the extrastriate body area
(EBA).
In such experiments, the conditions can principally be arranged in two ways.
One condition can be repeated many times over, before a break, after which the
next condition is repeated many times. Clustering events of the same kind in this
manner is referred to as a block design. Then, the analysis involves comparing
brain activity across blocks. Such designs are relatively simple and statistically
powerful; that is, they are sensitive to detect activity. On the other hand, they
are susceptible to confounding factors, such as drifts or movements, related
to time. Crucially, they can only be used to investigate processes that can be
repeated many times in sequence: any process related to novelty will be dif-
ficult to study with a block design. The alternative to it is to mix trials of
different conditions in a nonpredictable, often random, way. The analysis then
involves averaging single trials specific to one condition. Such studies are called
event-related design and offer great experimental flexibility but sacrifice statistical
power.
15.4.2.1 The fMRI Setup
A person participating in an experiment is located on a tray in the bore of an
MRI magnet. The participant’s head is gently fixed within an RF coil, a device
that resembles a helmet. To perform the tasks necessary for a given experiment,
participants can see a computer screen (through goggles or a mirror system), which
displays instructions and stimuli; they can hear stimuli through headphones, and
smell or taste stimuli through tubes. Robotic devices can be introduced to produce
tactile sensations and record motor actions. Participants typically respond with
small, handheld keyboards (Figure 15.10).
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