Magnetic Resonance in Medicine 45:397– 408 (2001)
Vessel Size Imaging
Irène Troprès, Stephan Grimault, Albert Vaeth, Emmanuelle Grillon, Cécile Julien,
Jean-François Payen, Laurent Lamalle, and Michel Décorps*
Vessel size imaging is a new method that is based on simultaneous measurement of the changes ⌬R2 and ⌬R2* in relaxation
rate constants induced by the injection of an intravascular superparamagnetic contrast agent. Using the static dephasing
approximation for ⌬R2* estimation and the slow-diffusion approximation for ⌬R2 estimation, it is shown that the ratio ⌬R2/
⌬R2* can be expressed as a function of the susceptibility difference between vessels and brain tissue, the brain water diffusion coefficient, and a weighted mean of vessel sizes.
Comparison of the results with 1) the Monte Carlo simulations
used to quantify the relationship between tissue parameters
and susceptibility contrast, 2) the experimental MRI data in the
normal rat brain, and 3) the histologic data establishes the
validity of this approach. This technique, which allows images
of a weighted mean of the vessel size to be obtained, could be
useful for in vivo studies of tumor vascularization. Magn Reson Med 45:397– 408, 2001. © 2001 Wiley-Liss, Inc.
Key words: rat brain MRI; vessel size; susceptibility contrast;
CBV; contrast agent
Magnetic resonance imaging (MRI) gives access to information on cerebral perfusion, which is of importance for
the diagnosis and therapeutic follow-up of various pathologies. Accurate mapping of cerebral blood volume (CBV),
cerebral blood flow (CBF), and mean transit time (MTT) is
an area of intense research, and CBV-, CBF- and MTTweighted imaging are beginning to be used in clinical
practice. Large vessels can be imaged; however, information on microvascular architecture is still hardly accessible.
Information on the vascular component of tissues may
be obtained by various contrast-enhanced MR methods.
Compared to bolus tracking techniques (1), steady-state
methods offer the potential of a higher signal-to-noise ratio
(SNR), and thus a higher spatial resolution. One kind of
steady-state approach for CBV imaging is based on the
measurement, in T1-weighted MR images, of changes in
signal intensity after injection of a contrast agent (2). This
method assumes that brain tissue can be modeled as two
nonexchanging compartments: intra- and extravascular.
An entirely different steady-state T1 technique for CBV
mapping is based on the analysis of changes in tissue T1
due to exchange of water between the two compartments
(3). Finally, another class of steady-state CBV imaging
techniques relies on susceptibility-induced contrast (4).
Unité mixte INSERM/Université Joseph Fourier, Hôpital Albert Michallon,
Grenoble, France.
Grant sponsor: Biomed II project; Grant number: BMH4-CT96-0861.
Albert Vaeth’s present address is Department of Neurosurgery, University of
Würzburg, Josef-Schneider-Str 11. 97080 Würzburg, Germany.
Irène Troprès’s present address is Medical Research Group, ESRF, BP 220,
38043 Grenoble, France.
*Correspondence to: Michel Décorps, INSERM U438, Hôpital Michallon, BP 217,
38043, Grenoble cédex 9, France. E-mail: [email protected]
Received 31 March 2000; revised 4 October 2000; accepted 9 October 2000.
© 2001 Wiley-Liss, Inc.
Susceptibility contrast imaging shows changes in signal
intensity related to magnetic susceptibility differences between the intra- and extravascular compartments. This
phenomenon underlies the blood oxygen level-dependent
(BOLD) contrast (5), which is the basis of functional MRI.
A similar effect is obtained with exogenous paramagnetic
or superparamagnetic contrast agents, which increase the
magnetic susceptibility differences between blood vessels
and surrounding tissues. The induced long-range magnetic
field perturbations extend to adjacent tissues and increase
the transverse relaxation rate constants R2 and R*2.
Two phenomena affect the transverse relaxation rates of
tissue water in the presence of a contrast agent in the blood
pool (6). First, magnetic field perturbations increase the
heterogeneity of the phase distribution across the voxel.
Reversible spin dephasing occurs with associated signal
loss in gradient-echo experiments (GE), resulting in an
increase ⌬R*2 in the relaxation rate. However, in the absence of diffusional motion, R2 ⫽ 1/T2 remains unchanged. Second, diffusion of water molecules in magnetic field gradients introduces two competitive effects: 1)
irreversible losses of phase coherence and signal attenuation in spin echo (SE) experiments; and 2) for rapid spatial
variations of magnetic field, possible averaging of phase
differences by motional narrowing, resulting in reduced
T*2 and T2 changes. A salient implication of these effects is
that changes ⌬R2 and ⌬R*2 in the transverse relaxation rates
depend on the size and architecture of the vascular compartment.
One topic of great interest in susceptibility contrast imaging concerns the sensitivity of MRI experiments to the
distribution of vessel sizes. On the basis of Monte Carlo
(MC) simulations, Boxerman et al. (4) suggested that information about microvascularization could be obtained by
measuring, at various TEs, the change ⌬R2 induced by
injection of an intravascular contrast agent. By combining
SE and GE BOLD MRI, Prinster et al. (7) demonstrated that
the ratio ⌬R*2/⌬R2 is related to the properties of the vascular environment. Dennie and coworkers (8) used a similar
technique to show that the ratio ⌬R*2/⌬R2 could be used as
an index of the mean vessel size to compare normal and
tumor tissues in the rat brain. To obtain information on the
vessel size distribution they compared the experimental
⌬R*2/⌬R2 ratio to that obtained from MC simulations,
which is a time-consuming technique. A vessel size index
deduced analytically from the measured changes ⌬R2 and
⌬R*2 in relaxation rates would be desirable. A relation
between ⌬R*2 and the susceptibility difference ⌬␹ between
blood and tissue has been proposed (6), and has been
successfully used to obtain information on the saturation
in oxygen of cerebral venous blood (9). More recently,
Kiselev and Posse (10,11) used a deterministic analytical
method to establish a relationship between ⌬R2 and ⌬␹, a
397
398
Troprès et al.
result which suggests that the ratio ⌬R*2/⌬R2 could be
expressed as a function of ⌬␹ and of vascular parameters.
The goal of this study was to extract quantitative information on vessel sizes from steady-state contrast-enhanced MRI. To do this, we derived ⌬R2 as a function of
⌬␹, ⌬R*2, tissue parameters and vessel size distribution.
Comparison of the results with MC simulations, experimental MRI data in the normal rat brain, and histologic
data established the validity of this approach, and we used
it to map vessel size.
very short, so blood does not contribute to the total signal.
The asymptotic form (␦␻⌻E ⬎⬎ 1) of the tissue signal in a
GE experiment given by the Yablonskiy and Haacke model
(6,10) is:
冉
s tGE ⬇ 共1 ⫺ ␰ 0兲exp ⫺
冉 冊
TE
S GE共T E兲⬀S共0兲exp ⫺ * F共TE兲
T2
[1]
where F(TE) modelizes the macroscopic field inhomogeneities and T*2 is the FID signal relaxation rate constant.
Since we use high-resolution imaging, the contribution of
macroscopic field inhomogeneities was assumed to be
very small (F(TE) ⬃ 1). For an SE experiment the signal is
simply:
冉 冊
S SE共T E兲 ⫽ S 0exp ⫺
TE
T2
[2]
where T2 modelizes irreversible signal losses.
A paramagnetic or superparamagnetic contrast agent introduced in the vascular compartment creates an additional susceptibility difference (⌬␹) between blood vessels
and surrounding tissues. The susceptibility difference
causes magnetic field distortions in the vicinity of blood
vessels, resulting in a decrease of the transverse relaxation
times of protons in the extravascular compartment.
A number of biophysical models have been developed to
describe and predict the NMR signal time course in the
presence of static magnetic field inhomogeneities
(5,6,10,11,13–15). The dephasing mechanisms that may
generate signal changes in GE and SE experiments are
related to the maximum value of the magnetic field gradient induced at the surface of a vessel (6). For vessels
modeled as infinite cylinders, the spread ␦␻ of Larmor
frequencies at the surface is given (in nonrationalized cgs
units) by:
␦␻ ⫽ 2␲␥⌬␹B 0,
[3]
for an orientation perpendicular to B0.
The phenomena which induce an increase in transverse
relaxation rates are closely related to the characteristic
diffusion time ␶D ⫽ Rv2/4D compared to the characteristic
time ␶C ⫽ ␦␻⫺1. The static regime holds if ␶C ⬍⬍ ␶D (6).
GE Experiments: ⌬R2*
In the static regime, water diffusion is assumed to be slow
enough to be neglected. In the presence of a high dose of
contrast agent, the spin-spin relaxation time of blood is
[4]
where ␰0 is the blood volume fraction in the voxel of
interest. For small ␰0, Eq. [4] may be rewritten as:
冉
THEORY AND BACKGROUND
In the absence of contrast agent in the vascular compartment, the signal in GE experiments is given by Ref. 12:
冊 冉 冊
2
TE
␦␻␰ 0T E ⫹ ␰ 0 exp ⫺ *
3
T2
s tGE共T E兲 ⬇ exp ⫺
冊 冉 冊
2
TE
␦␻␰ 0T E exp ⫺ * .
3
T2
[5]
Hence, at the long TEs (⌻E ⬎⬎ 1/␦␻) associated with this
asymptotic form, this model predicts a monoexponential
signal decay. The enhancement in the relaxation rate constants is given by:
⌬R *2 ⫽
2
␦␻␰ 0.
3
[6]
The results obtained with the Yablonskiy and Haacke (6)
model were found to be in excellent agreement with MC
simulations (4) for vessel radii larger than a limit value.
For example (see Fig. 1 of Ref. 4), for D ⫽ 10–9 m2 sec–1,
⌬␹ ⫽ 10–7, B0 ⫽ 1.5 T, the limit is about 7 ␮m. This lower
bound on vessel size decreases when ⌬␹ increases (16).
However, the static approximation cannot describe the
signal decay in an SE experiment.
SE Experiments: ⌬R2
In SE experiments, the dephasing resulting from local
differences in Larmor frequencies is refocused and diffusion effects become more visible. Recently, an analytical
treatment including both static and diffusion dephasing
has been described (10). The model assumes that during
the experiment time (TE) the diffusing water molecules
experience a constant field gradient, the value of which
depends on the initial position of the water molecules
(slow diffusion approximation). This assumption imposes
a lower bound on the vessel radius:
Rv Ⰷ
冑2DT E.
[7]
For an SE experiment, the comparison of MC simulations with the analytical model (see Fig. 6 of Ref. 10)
shows that for ⌬␹ ⫽ 10–7, D ⫽ 10–9 m2 sec–1, B0 ⫽ 1.5 T
and TE ⫽ 100 msec, the validity range of this slow diffusion model is similar to that of Yablonskiy and Haacke (6)
in GE experiments: Rv ⱖ 7 ␮m. This value is significantly
smaller than that given by Eq. [7]. Note that in GE (10) MC
simulations clearly show the influence of motional narrowing but do not show any evidence of the diffusioninduced attenuation predicted by the model of Kiselev and
Posse (10).
In an SE experiment, the asymptotic form of the signal
(␦␻⌻E ⬎⬎ 1) is given by (10):
Vessel Size Imaging
399
冉 冊
s tSE ⬇ 共1 ⫺ ␰ 0兲exp共⫺0.694␦␻ 2/3D 1/3␩ 0T E ⫹ ␰ 0兲exp ⫺
TE
,
T2
[8]
within the slow diffusion approximation. In the above
formula ␩0 ⫽ ␰0R⫺2/3, where we define the vessel size
index (VSI) R by the weighted mean
R ⫺2/3 ⫽
冕
⬁
R v⫺2/3f共R v兲 dR v,
[9]
0
and ␰0f(Rv) is the volume fraction of vessels with radius Rv
(note that 兰0⬁f(Rv)dRv ⫽ 1). For small ␰0, Eq. [8] reduces to:
s tSE ⬇ exp共⫺0.694␦␻ 2/3D 1/3␩ 0T E兲.
[10]
Thus the relaxation rate constant increase is given by:
⌬R 2 ⬇ 0.694␦␻ 2/3D 1/3␩ 0.
[11]
It should be noted that this simplified model predicts
that at long TEs (⌻E ⬎⬎ 1/␦␻), ⌬R2 depends on the blood
volume fraction and on the distribution of vessel radii but
not on the TE.
⌬R2 vs. ⌬R2*
By combining Eqs. [6] and [11] one obtains:
⌬R 2 ⬇ 0.909D 1/3␰ 01/3R ⫺2/3共⌬R *2兲 2/3
[12]
and thus, ⌬R2 ⬀ (⌬R*2)2/3. The proportionality coefficient
depends on the VSI, the diffusion coefficient, and the
vascular volume fraction (␰0), but not on the vascular concentration of the contrast agent.
Range of Validity
With ⌬␹ ⫽ 10–7, D ⫽ 10–9 m2 sec–1, B0 ⫽ 1.5 T, Eqs. [5] and
[11] should be valid for vessel radii larger than about 7 ␮m.
At smaller radii, differences between MC simulations and
Eq. [11] are due to the contribution of motional narrowing
(10,11). This contribution decreases when ␦␻ increases,
and the conditions of validity of Eqs. [5] and [11] could be
reached for capillaries when a high dose of contrast agent
is used.
Summary
Absolute measurement of R requires measurement (or
prior knowledge) of the diffusion coefficient and of the
increase in blood susceptibility due to the contrast agent
injection.
These theoretical results were first compared with MC
simulations. Then experiments were carried out on a first
group of animals to determine the increase in blood susceptibility due to the injection of the contrast agent. A
second group of animals was used to assess accurately the
relation between ⌬␹ and ⌬R*2 in the rat brain and for
absolute CBV mapping. Finally, a third group of animals
was used for simultaneous measurement of ⌬R2 and ⌬R*2 at
various doses of contrast agent and for comparison with
the theoretical findings.
MATERIALS AND METHODS
MC Simulations
MC simulations were performed using a method very similar to that described by Boxerman et al. (4). A proton was
placed initially at the origin O of a sphere of radius R0 ⫽
3公6DTE⫹60Rv, defining the range over which the proton
was allowed to diffuse. The microvasculature was modeled as a set of independent cylinders whose distribution
had to produce a uniform and isotropic volume fraction.
Writing di for the vector distance to the origin associated to
cylinder #i, the latter requirement was met by generating
random position vectors di in spherical coordinates (r, ␪, ␫)
with probability densities ␳r ⫽ 2r/R02 for r, ␳␪ ⫽ (sin␪)/2 for
␪ and ␳␫ ⫽ 1/2␲ for ␫. The orientation of each cylindrical
vessel about its distance vector di was then chosen according to a uniform random law. The magnetic field value was
set to 2.35 T and the number of protons to 16000. The
random walk proceeded by 50 ␮s time steps, with a diffusion coefficient D of 10–9 m2 sec–1. Smaller steps did not
modify the results in the explored range of vessel radii.
Only extravascular protons were considered, and they
could not pass through the cylinder (endothelial) wall.
The gradient-echo attenuation was calculated at TE ⫽ 10,
20, 30, 40, and 50 msec, while that for the spin echo was
calculated at TE ⫽ 100 msec. ⌬R*2 was calculated from a
two-parameter (A0, ⌬R*2) least-squares fit of the function:
A ⫽ A 0exp共⫺T E/⌬R *2兲
on the MC data. ⌬R2 was calculated with the formula:
⌬R 2 ⫽
The blood fraction ␰0 may be determined from ⌬R*2 measurements if the blood concentration of contrast agent (and
hence ⌬␹) is known (Eqs. [3] and [5]):
␰0 ⫽
3 ⌬R *2
.
4␲ ␥⌬␹B 0
[13]
A spin-echo experiment yields information on the vessel
size distribution. From Eqs. [12] and [13], VSI can be
written as:
R ⫽ 0.425
冉
冊冉 冊
D
␥⌬␹B 0
1/2
⌬R *2
⌬R 2
3/2
.
[14]
[15]
冋
册
A0
1
ln
,
TE
共1 ⫺ ␰ 0兲A共T E兲
[16]
where the factor (1–␰0) accounts for intravascular protons.
These simulations were carried out for various vascular
fractions, radius distributions, and susceptibility differences (detailed in the Results section). Simulations were
run on a Sparc 20® workstation (Sun Microsystems Inc.,
Mountain View, CA). A typical run with 16000 particles
required approximately 15 CPU hours.
Contrast Agent
The contrast agent used in this study (AMI-227 (trade
name Sinerem®)) belongs to the class of ultrasmall super-
400
paramagnetic iron oxide (USPIO) particles. It was obtained
from Laboratoires Guerbet (Aulnay-sous-Bois, France).
Provided that the blood brain barrier (BBB) is intact, AMI227 acts as a blood pool contrast agent. In the rat plasma,
the halflife is 4.5 hr for a dose of 200 ␮mol Fe/kg (Laboratoires Guerbet, unpublished data) and the relaxivities r1
and r2 at 37°C and 20 MHz are, respectively, 27 sec–1 mM–1
and 83 sec–1 mM–1 (17). At 100 MHz these relaxivities
should be smaller. The saturation magnetization of
AMI-227 (Laboratoires Guerbet, unpublished data) is
69.8 emu/g iron (1 emu ⫽ 1 G cm3). At the field strength
used in this study, AMI-227 is saturated (4,18). The diameter of the iron oxide core is 4 – 6 nm (electron microscopy
data), and that of the dextran-coated particle is approximately 30 nm (photon correlation spectroscopy data) (17).
Animals
Three groups of animals were prepared. Group 1 consisted
of 9 OFA rats (six males weighing 400 – 470 g, and three
females weighing 200 –270 g). To measure ⌬␹ in blood
after injection of 200 ␮mol Fe/kg, the rats were first anesthetized with 1.5% halothane and a 0.7-mm catheter was
inserted into the femoral vein to inject the contrast agent.
Five minutes after injection 3 ml of blood was taken for ⌬␹
measurement, and 0.1 ml for analyzing blood gases (pO2,
pCO2), blood pH, hematocrit (Hct), and oxygen saturation
of hemoglobin (Y) (Radiometer ABL 510, Copenhagen,
Denmark).
Group 2 consisted of 8 OFA female rats (262 ⫾ 9 g) that
were examined to evaluate the changes in ⌬R*2 with the
dose of contrast agent. The rats were anesthetized with 4%
halothane and then maintained with 1.5% halothane during surgery. They were tracheotomized and mechanically
ventilated with halothane and 70% nitrous oxide/30%
oxygen using a rodent ventilator (model 804; Edco/NEMI,
Medway, MA). Volume and respiratory frequency were
adjusted to maintain pCO2 between 30 and 40 mm Hg. The
fractional inspired oxygen (FiO2) was continuously monitored (MiniOx I analyzer; Catalyst Research Corp., Owing
Mills, MD). A neuromuscular blocking agent (normal saline containing pancuronium bromide, 0.4 mg/ml) was
infused intraperitoneally at a rate of 4 ml h–1 kg–1 throughout the study. A 0.7-mm catheter was inserted into the
femoral vein to inject the contrast agent. Another catheter
was inserted into the femoral artery to monitor the mean
arterial blood pressure (MABP) via a graphic recorder
(8000S; Gould Electronics, Balainvilliers, France). Blood
samples (⬍ 0.1 ml) were taken for analysis of arterial gases,
arterial pH, and oxygen saturation of hemoglobin. At the
end of the MRI experiments, the rats were sacrificed by
ventilation with 5% halothane and pure nitrous oxide.
Group 3 consisted of 10 Sprague-Dawley male rats
(weight 290 –360 g) in which ⌬R*2 and ⌬R2 were measured
simultaneously. The animal protocol was the same as that
described for the animals in group 1, except that the rats
were ventilated with halothane and 65% nitrous oxide/
35% oxygen. After surgery, halothane was maintained at
0.6%. Blood samples were obtained and analyzed before
and immediately after each image acquisition. The inclusion criteria in the study were: MABP ⬎ 70 mm Hg, arterial
pH ⬎ 7.30, PaO2 ⬎ 85 mm Hg, Y ⬎ 95%, 30 ⬍ pCO2 ⬍
40 mm Hg, arterial hemoglobin ⬎ 10 g/dl. When pCO2,
Troprès et al.
pO2, and Y were outside the allowed range, the respiratory
volume and frequency were adjusted. After allowing at
least 5 min for stabilization, another sample was taken to
check the blood gas parameters. At the end of the MRI
experiments, the rats were killed with 2–5 ml of chloral
hydrate injected via the venous catheter.
MRI
All MRI experiments were performed in a 2.35 T, 40-cmdiameter bore magnet (Bruker Spectrospin, Wissembourg,
France), equipped with actively shielded magnetic field
gradient coils (Magnex Scientific Ltd., Abdington, UK) and
interfaced to an SMIS console (SMIS Ltd, Guildford, UK).
The NMR probe consisted of a nonmagnetic head holder
and an elliptic surface coil (with 50-mm and 40-mm semiaxes, respectively) used for signal transmission and reception. The body temperature was maintained at 37.0 ⫾
0.5°C by a heating pad placed under the abdomen.
⌬␹ Measurements
In the following, magnetic susceptibilities are expressed in
nonrationalized cgs emu units (⌬␹SI/⌬␹emu ⫽ 4␲). Bulk
magnetic susceptibility of blood in the presence of AMI227 (animals in group 1) was measured with the following
experimental setup: two heparinized glass capillaries
(0.8-mm inner diameter, 1.6-mm outer diameter) filled
with water were placed in a 2.5-cm3 cylindrical glass recipient (14-mm diameter, 15-mm height) filled with blood
obtained from animals in group 1. One of the capillaries
was aligned with B0, while the other was orthogonal to it.
All measurements were carried out at room temperature.
The susceptibility difference ⌬␹blood⫹AMI 227 between
blood containing AMI-227 and water can be written as:
⌬␹ blood⫹AMI 227 ⫽
1
共␯ ⫺ ␯ ⬜兲,
␥B 0 㛳
[17]
where ␯⁄⁄ and ␯⬜ are the resonance frequencies of water in
capillaries parallel and orthogonal to B0, respectively. Taking into account the susceptibility of plasma and deoxyHb,
the susceptibility of blood in the presence of contrast agent
can be written as:
␹ blood⫹AMI⫺227 ⫽ Hct 䡠 关Y 䡠 ␹ oxyHb ⫹ 共1 ⫺ Y兲␹ deoxyHb兴
⫹ 共1 ⫺ Hct兲␹ plasma ⫹ 共1 ⫺ Hct兲␹ AMI⫺227
[18]
where ␹oxyHb, ␹deoxyHb, ␹plasma, and ␹AMI 227 are, respectively, the susceptibilities of oxyHb, deoxyHb, plasma, and
AMI-227. The experiment measures ⌬␹blood⫹AMI 227 ⫽
␹blood⫹AMI 227 ⫺ ␹water, but what we want to determine is
the increase ⌬␹ ⫽ (1 ⫺ Hct)⌬␹AMI 227 in blood susceptibility due to the injection of AMI-227. It is known (19) that
the susceptibility of plasma is approximately equal to that
of water. Thus
⌬␹ ⫽ ⌬␹ blood⫹AMI 227 ⫺ Hct关Y⌬␹ oxyHb ⫹ 共1 ⫺ Y兲⌬␹ deoxyHb兴,
[19]
where ⌬␹oxyHb and ⌬␹deoxyHb are the susceptibility differences of oxyHb and deoxyHb with respect to water. Given
Vessel Size Imaging
hematocrit, Y, and, from Ref. 19, the susceptibility differences ⌬␹oxyHb ⫽ – 0.26 ⫾ 0.07⫻10–7 and ⌬␹deoxyHb ⫽
1.57 ⫾ 0.07⫻10–7, the net contribution ⌬␹ of the contrast
agent to the blood susceptibility can be determined.
401
Table 1
Injected Doses of AMI-227 for the Animals in Group 3
MRI Protocol
After installation of the rat in the magnet (animals in
groups 2 and 3) and preliminary adjustments (tuning,
shimming, and acquisition of scout images for accurate
positioning), a blood sample was taken and analyzed, and
precontrast images were obtained. Immediately after acquisition of precontrast images, the first dose of AMI-227
was injected. After a 3-min delay to allow the contrast
agent to distribute homogeneously in the intravascular
pool, the images were acquired and the blood gases were
analyzed.
Measurement of ⌬R2* vs. Dose
Imaging was based on a multiple gradient-recalled echo
sequence (20). A Gaussian 90° RF pulse was applied in the
presence of a slice-selective gradient. Echoes were obtained by multiple refocusing of the readout gradient. Even
echoes were discarded. Eight odd gradient echoes were
acquired for each phase-encoding step. The matrix size
was 64 ⫻ 64, FOV 40 mm, acquisition time 3.2 msec per
echo, and the number of averages was 2. Two transverse
slices of 1-mm thickness were acquired. TR was set to
1.5 sec and the inter-echo time ⌬TE to 6 msec. Eight
injections of 25 ␮mol Fe/kg were made with a delay of
6 min between two consecutive injections.
Number
of rats
First dose
(␮mol Fe/kg)
Number of
successive dosesa
Cumulated dose
(␮mol Fe/kg)
2
4
1
2
1
0
0
0
100
125
8
5
7
6
5
200
125
175
225
225
25 ␮mol Fe/kg.
a
DATA ANALYSIS
Data were processed on workstations running software
written in IDL (Interactive Data Language™; RSI, Boulder,
CO). Image reconstruction was preceded by zero-filling up
to 128 ⫻ 128 complex points. The transverse relaxation
times T*2 were obtained pixel-by-pixel from GE data by
nonlinear least-squares fitting the signal intensity S(TE) to
an exponential function:
冉 冊
TE
S共T E兲 ⫽ S共0兲exp ⫺ * .
T2
Then ⌬R*2 maps were computed according to ⌬R*2 ⫽
1
1
⫺ * , where T*2,pre and T*2,post are the pre- and
*
T 2,post
T 2,pre
postinjection relaxation times. Changes in ⌬R2 in transverse relaxation rates were directly calculated pixel-bypixel from signal intensities pre- (Spre) and postinjection
(Spost) on the SE images:
Measurements of ⌬R2 vs. ⌬R2*
Transverse relaxation rate imaging was performed with a
multislice sequence allowing simultaneous monitoring of
T*2 images and a T2-weighted image (21). The 90° RF pulse
was followed by multiple refocusing of the readout gradient, during which five gradient echoes (three odd and two
even) were acquired. Following application of a refocusing
RF pulse, a spin-echo was acquired in the presence of a
read gradient. The imaging protocol produced five GE
images and one SE image. For the spin echo, the b factor in
the readout direction was b ⫽ 5⫻105 sec/m2. Thus signal
attenuation of the spin echo due to diffusion throughout
the imaging gradient can be neglected (TE⌬R2 ⬎⬎ bD). To
avoid T1-weighting, which may introduce errors in ⌬R2
measurements, TR was set to 6 sec. The TE values were
9.04, 17.32, 25.60, 33.88, and 42.16 msec for gradient echo
images, and 100 msec for the spin echo image. The acquisition time was 7.68 msec per image. Six contiguous transverse slices of 1-mm thickness were acquired in a nonsequential order. The matrix size was 128 ⫻ 64 for a 30-mm
FOV. The number of averages was 2 and the total acquisition time was about 12 min. The use of this sequence
allowed temporal matching of T*2 and T2 measurements.
GE and SE were acquired before and after each of five to
eight successive injections of AMI-227. As shown in Table
1, the number of injections and the first injected dose
varied from rat to rat. This was because the experiment
was stopped when pCO2, pO2, or Y were outside the allowed range. After the first injection, successive doses
were kept constant and equal to 25 ␮mol Fe/kg.
[20]
⌬R 2 ⫽
冉 冊
S pre
1
ln
.
TE
S post
[21]
VSI images were then calculated using Eq. [14]. A uniform diffusion coefficient D ⫽ 697 ␮ m2 sec–1 was assumed
in the whole brain (22).
To obtain averaged information, regions of interest
(ROIs) were drawn on the transverse slices, in the cortex,
and the corpus striatum. Pixels with blood fraction ⌬R*2 ⱖ
250 s⫺1 were excluded from the averaging process. All
results are expressed as mean ⫾ standard deviation.
RESULTS
Analytical Model vs. MC Simulations
Figure 1 shows for GE experiments typical attenuation
data from an MC simulation as a function of the TE for
various ⌬␹ (Rv ⫽ 3 ␮m, ␰0 ⫽ 2%, D ⫽ 10–9 m2 sec–1, MC
signal set to 1 – ␰0 at TE ⫽ 0), and the least-squares fits to
the data. The quality of the fits reflects the monoexponential behavior of S(TE) in GE experiments. However, the
intercept is systematically greater than 1 – ␰0 (1.0075 ⫾
0.0078). Figure 2 shows ⌬R2 vs. ⌬R*2 for various vessel
radii (R ⫽ 1, 2, 4, 10 ␮m). Each (⌬R2, ⌬R*2) pair was
computed at ⌬␹ ⫽ n ⌬␹ 0 (n ⫽ 1 – 8, 8 ⌬␹ 0 ⫽ 0.789 ppm)
by using either an MC simulation or the analytical formulas (parametric Eqs. [5] and [11], parameter ⌬␹ ⫽ ␦␻ / 2␲␥
B0). Figure 3a plots the normalized difference (⌬R*2AM ⫺
⌬R*2MC)/⌬R*2MC between changes in the relaxation rate
402
Troprès et al.
FIG. 1. Typical GE attenuation data from MC simulations for various
⌬␹ (Rv ⫽ 3 ␮m, ␰0 ⫽ 2%, D ⫽ 10–9 m2 sec–1, MC signal set to 1 –
␰0 ⫽ 0.98 at TE ⫽ 0) and least-squares fits with monoexponential
decays. For all curves, the correlation coefficient R was better than
0.999. The intercepts of the fitted curves are 1.0099 ⫾ 0.0029,
1.0136 ⫾ 0.0023, 1.0104 ⫾ 0.0038, 0.9961 ⫾ 0.0062 for 107⌬␹ ⫽
0.98, 1.97, 3.95 and 7.89, respectively.
constants obtained with the analytical model (⌬R*2AM, Eq.
[6]) and with MC simulations (⌬R*2MC) as a function of the
vessel diameter and for various doses of contrast agent
(␰0 ⫽ 2%). Similarly, Fig. 3b plots the normalized difference (⌬R2AM ⫺ ⌬R2MC)/⌬R2MC, where ⌬R2AM is given by Eq.
[11], as a function of the vessel diameter and for various
doses of contrast agent (␰0 ⫽ 2%). These ratios give an
information on the relative error which is introduced
when the analytical model is used instead of MC simulations. Figures 2 and 3 show that for GE, as for SE, the
difference between the two approaches increased as Rv
and/or ⌬␹ decreased. Clearly, when the dose of contrast
FIG. 2. Parametric curves in the (⌬R2, ⌬R2*) plane. All curves are
parametrized by ⌬␹ and labelled according to a particular radius Rv
⌬␹ ⫽ n ⌬␹0, n ⫽ 1 – 8, 8 ⌬␹0 ⫽ 0.789 ppm, ␰0 ⫽ 2%, D ⫽ 10–9 m2
sec–1) For each ⌬␹ value, the pair (⌬R2, ⌬R2*) was calculated using
Eqs. [5] and [13] (filled symbols) and with MC simulations (open
symbols). Above Rv ⫽ 10 ␮m, MC data and analytical results are
indistinguishable for all ⌬␹s. For high ⌬␹s, the two approaches yield
similar results for a range of vessel sizes including capillaries.
FIG. 3. The normalized difference between MC data (MC) and results obtained with the analytical model (AM), as a function of the
vessel radius Rv and for various ⌬␹ (␰0 ⫽ 2%, D ⫽ 10–9 m2 sec–1,
B0 ⫽ 2.35 T). a: Gradient-echo experiments. b: Spin-echo experiments. The difference between the two models increases as ⌬␹ or
vessel size decreases.
agent increases, the validity range of the analytical model
expands to lower radii. For Rv ⱖ 2– 4 ␮m, the difference
between analytical and MC calculations was less than 13%
as long as ⌬␹ exceeded approximately 0.4 ppm. Figure 4
plots ⌬R2 vs. ⌬R*2 as obtained from simulations and analytically (Eq. [12]) for an “equidistributed model” (4) (capillaries with Rv ⫽ 2.5 ␮m at 2% CBV, larger vessels with
Rv ⫽ 25 ␮m at 2% CBV). The two approaches were in
reasonable agreement. The curve obtained by analytical
calculation was, however, shifted to higher ⌬R2 values.
The mean offset was found to be 0.98 ⫾ 0.35 sec–1.
MC simulations probably give results closer to the in
vivo situation than does the analytical model. Figure 5
shows the vessel size index calculated (Eq. [14]) from the
MC data as a function of dose for the equidistributed
model (⌬␹ ⬃ 0.571 ⫾ 0.03 ppm at 200 ␮mol Fe/kg). At high
doses, the vessel size index was close to the theoretical one
(R ⫽ 5.28 ␮m), but the error increased when the dose
decreased.
Vessel Size Imaging
403
pairs (⌬R*2, ⌬R2) were obtained in the ROIs drawn in the
cortex and the corpus striatum plotted on Fig. 8a and b,
respectively. These graphs show a nonlinear relation between ⌬R2 and ⌬R*2. The solid line represents the leastsquares nonlinear regression of the curve ⌬R2 ⫽ k(⌬R*2)2/3
to the data. The data points are gathered round the leastsquares line with a high correlation coefficient (R ⫽ 0.970).
We found k ⫽ 0.96 sec1/3 in the cortex and k ⫽ 0.92 sec1/3
in the corpus striatum. From these results and using the
volume fractions ␰0 determined previously, the typical D
values found in the literature (22) (D ⫽ 657 ⫾ 53 ␮m2 sec–1
in the cortex and 697 ⫾ 53 ␮m2 sec–1 in the corpus striatum), and Eq. [12], we obtained R ⫽ 4.77 ␮m in the cortex
and R ⫽ 4.39 ␮m in the corpus striatum. Figure 7c shows
a VSI image obtained by assuming a uniform diffusion
coefficient in the whole brain (D ⫽ 697 ␮m2 sec–1).
FIG. 4. ⌬R2 vs. ⌬R2* for a vasculature composed of 2% capillaries
(R ⫽ 2.5 ␮m) and 2% macrovessels (R ⫽ 25 ␮m) for MC simulations
(open symbols) and analytical analysis (filled symbols). Each pair
(⌬R2, ⌬R2*) was obtained for a particular ⌬␹ (⌬␹ ⫽ n ⌬␹0, n ⫽ 1 – 8,
8 ⌬␹0 ⫽ 0.789 ppm). The other parameters were D ⫽ 10–9 m2 sec–1,
B0 ⫽ 2.35 T. For all ⌬␹s, the difference between the two approaches
was found to be approximately constant (⌬R2AM – ⌬R2MC ⫽ 0.98 ⫾
0.35 sec–1).
⌬␹ Measurements
Blood gas measurements from the animals in group
1 yielded the following results: pO2 ⫽ 40.3 ⫾ 4.7 mm Hg,
pCO2 ⫽ 52.6 ⫾ 6.1 mm Hg, Y ⫽ 48.7 ⫾ 12.8%, Htc ⫽
42.5 ⫾ 3%. Blood samples from animals which received
200 ␮mol Fe/kg body weight were placed in the experimental setup. A frequency shift of 3.77 ⫾ 0.18 ppm between the two water peaks was found for a linewidth of
0.15 ppm. Equation [19] leads to ⌬␹blood⫹AMI-227 ⫽
0.600 ⫾ 0.029 ppm. The net contribution of the contrast
agent was obtained after correction for the susceptibility
difference induced by the presence of Hb and deoxyHb
(Eq. [19]). Using Y ⫽ 48.7% and Htc ⫽ 42.5%, the increase
in blood susceptibility due to the contrast agent was ⌬␹ ⫽
0.571 ⫾ 0.03 ppm at the dose of 200 ␮mol Fe/kg.
DISCUSSION
Relaxation Rate Measurements
In many studies (7–9,16,23,24), changes in R*2 induced by
the contrast agent were obtained with a two-point technique, i.e., from the ratio of the signal intensities measured, at time TE, before (Spre) and after (Spost) injection of
contrast agent:
⌬R *2 ⫽ ⫺
冉 冊
S post
1
ln
TE
S pre
[22]
In the present study, ⌬R*2 was obtained from the difference of the R*2 relaxation rates measured before and after
contrast agent injection. R*2 was determined by leastsquares fitting of the GE signal decay S(TE) to a monoexponential function. This technique was used for both MC
and experimental data. It assumes the exponential decay
predicted by Eq. [5].
⌬R2* vs. Dose: CBV Measurements
The physiological parameters for animals in group 2 are
summarized in Table 2. Figure 6 plots ⌬R*2 in the cerebral
cortex and the corpus striatum, as a function of the injected dose, for the animals in group 2. In both regions the
data points lie along a straight line with a high correlation
coefficient (R ⫽ 0.999). The slope of the ⌬R*2 vs. dose linear
regression is greater in the cortex (⌬R*2 ⫽ 0.295 ⫻ dose ⫹
2.102, where iron dose is given in ␮mol.kg–1) than in the
corpus striatum (⌬R*2 ⫽ 0.210 ⫻ dose ⫹ 1.133). Both
curves show a small intercept. The blood volume fraction
␰0 was obtained using Eq. [13], from the measured susceptibility of AMI-227 and the ⌬R*2/Dose ratio. We found a
blood volume fraction ␰0 of 4.07% in the cortex and 2.87%
in the corpus striatum.
⌬R2 vs. ⌬R2*: VSI Measurements
Figure 7a and b shows ⌬R2 and ⌬R*2 transverse maps for
one animal in group 3. For each animal and each dose, the
FIG. 5. Vessel size index (R) calculated with Eq. [14] from the MC
data as a function of ⌬␹ (⌬␹ ⫽ 0.571 ⫾ 0.03 ppm at the dose of
200 ␮mol Fe/kg) for a vasculature composed of 2% capillaries (R ⫽
2.5 ␮m) and 2% macrovessels (R ⫽ 25 ␮m). The dashed line
represents the theoretical vessel size index (5.28 ␮m) for this vessel
size distribution. At high ⌬␹s, the vessel size index is close to the
theoretical one, but the error increases when ⌬␹ decreases.
404
Troprès et al.
Table 2
Physiological Parameters for the Animals in Groups 2 and 3
Group 2
PaCO2 (mmHg)
PaO2 (mmHg)
MABP (mmHg)
Arterial pH
Temperature (°C)
Hemoglobin (g/dl)
Hct (%)
SaO2 (%)
Group 3
Before MRI
After MRI
Before MRI
After MRI
34.9 ⫾ 1.6
160 ⫾ 17
91 ⫾ 13
7.41 ⫾ 0.03
36.7 ⫾ 0.6
13.6 ⫾ 0.6
41.7 ⫾ 1.6
100
36.0 ⫾ 5.4
154 ⫾ 9
94 ⫾ 11
7.40 ⫾ 0.03
37.2 ⫾ 0.7
13.0 ⫾ 1.1
39.8 ⫾ 1.5
100
34.7 ⫾ 2.6
153.0 ⫾ 23.5
90.5 ⫾ 23.3
7.41 ⫾ 0.04
37.1 ⫾ 0.4
12.8 ⫾ 0.5
39.5 ⫾ 1.5
100
34.4 ⫾ 2.2
151.8 ⫾ 13.1
93.0 ⫾ 22.6
7.35 ⫾ 0.06
37.2 ⫾ 0.2
11.5 ⫾ 1.7
35.3 ⫾ 5.0
100
For TE ⫽ 10 msec, MC simulations indeed showed an
exponential decay of the signal with TE (Fig. 1). In these
simulations the intravascular signal was neglected and the
signal at TE ⫽ 0 was set to 1 – ␰0 (0.98 for the data shown
in Fig. 1). The intercept of the monoexponential fit to the
data points obtained with the MC simulation is close to
1 (1.0075). This is in agreement with theoretical predictions and experimental results (6,12).
Due to the change in cerebral tissue T1 after injection (3),
any T1 weighting of the signal introduces TE-dependent
errors if ⌬R*2 is measured with a two-point technique. With
a GE technique the error in ⌬R*2 can be written as:
ε⫽⫺
再 冋
1 ⫺ exp共⫺T R/T 1post兲
1
ln
TE
1 ⫺ exp共⫺T R/T 1pre兲
⫹ ln
冋
册
1 ⫺ cos ␣ exp共⫺T R/T 1pre兲
1 ⫺ cos ␣ exp共⫺T R/T 1post兲
册冎
[23]
where ␣ is the excitation pulse angle. Thus a T1 effect leads
to underestimation of ⌬R*2 changes. It was previously
shown that at 7 T (3), T1 decreases from about 1.75 sec
before injection to 1.55 sec after injection of a contrast
agent which decreases blood T1 to about 80 –90 msec, a
value similar to that expected at high concentrations of
AMI-227. For T1pre ⫽ 1.75 sec, T1post ⫽ 1.55 sec, the error in
⌬R*2 is ε ⫽ –2.10 sec–1 when TR ⫽ 1 sec, TE ⫽ 20 msec, and
FIG. 6. ⌬R2* as a function of the injected dose measured in the
cerebral cortex (open symbols) and in the corpus striatum (filled
symbols). The solid lines represent the least-squares fits to the data
(y ⫽ ax ⫹ b).
␣ ⫽ 45° (4); the error is ε ⫽ –2.77 sec–1 when TR ⫽ 0.06 sec,
TE ⫽ 35 msec, and ␣ ⫽ 30° (24). In contrast, the analysis of
transverse decay by least-squares fit is clearly insensitive
to T1 changes.
In SE experiments, ⌬R2 was determined as usual from
the attenuation ratio (Eq. [22]). The analytical model predicts that a contrast agent induces an exponential decay
(Eq. [10]). Thus, ⌬R2 measured with a two-point technique
yields the effective decay constant. If the T2 effect of the
contrast agent on intravascular protons had not been taken
into account, the decay would have taken the form a ⫹
R2
bexp(⫺ ) and the result of the two-point technique would
TE
have been TE dependent. As for GE, ⌬R2 measured with a
two-point technique is T1 sensitive. The error can still be
estimated using Eq. [23] and ␣ ⫽ 90°. With T1pre ⫽ 1.75 sec,
T1post ⫽ 1.55 sec, one finds ε ⫽ – 4.41 sec–1 when TR ⫽
1 sec, TE ⫽ 20 msec (4), ε ⫽ –2.13 sec–1 when TR ⫽ 3 sec,
TE ⫽ 20 msec (8), ε ⫽ – 0.72 sec–1 when TR ⫽ 1.9 sec, TE ⫽
90 msec (24) and ε ⫽ – 0.12 sec–1 when TR ⫽ 6 sec, TE ⫽
100 msec (this work). Here again, the error induced by a
change in T1 is TE dependent and results in an underestimation of changes in relaxation rates. Thus ⌬R2 measurements should be carried out with long repetition times.
MC Simulations vs. Analytical Models
It is generally well accepted that the Yablonskiy and
Haacke (6) analytical model (static dephasing approximation) yielded ⌬R*2 values close to those obtained with MC
simulations, in particular for high ⌬␹ (4,10). Figure
2 shows that for relatively large vessels (Rv ⫽ 4 ␮m), the
agreement between MC simulations and analytical predictions is excellent for all ⌬␹s. For smaller vessels, the agreement between ⌬R*2 calculated analytically and by MC simulation is still very good at large ⌬␹s.
Figure 2 shows that in SE experiments the difference
between the two approaches is larger. The analytical
model of Kiselev and Posse (10) is based on the assumption of a diffusion length during the TE that is short compared to the vessel size (motional narrowing effects are
neglected). This assumption introduces a lower bound,
Rv ⫽ 10 ␮m, on the vessel size (10). Thus, due to motional
narrowing, ⌬R2 obtained with Eq. [11] is overestimated
and the error increases when the vessel size decreases.
However, as expected in the slow motion approximation,
the contribution of motional narrowing to ⌬R2 does not
depend on the width of the frequency distribution (i.e. ⌬␹).
Vessel Size Imaging
405
FIG. 7. Representative images of (a) relative CBV (⌬R2*
map), (b) ⌬R2, and (c) vessel size index, obtained with the
hybrid pulse sequence allowing simultaneous acquisition of
multiple gradient echoes and one spin echo (group 3). The
injected dose was 200 ␮mol Fe/kg.
406
FIG. 8. ⌬R2 vs. ⌬R2* in the cortex (a) and in the corpus striatum (b).
For each animal (N ⫽ 10) and each dose (see Table 1), the pairs
(⌬R2*, ⌬R2) were obtained in the ROIs drawn in the cortex (two ROIs)
and the corpus striatum (four to eight ROIs). The solid line represents the least-squares fit for ⌬R2 ⫽ k (⌬R2*)2/3.
Figure 3 indeed shows that the absolute error in ⌬R2 due to
motional narrowing remains roughly independent of ⌬␹.
In consequence, the relative error introduced with the
slow diffusion approximation decreases when the contrast
agent concentration increases. Thus, at high doses of contrast agent, the range of validity of the analytical approach
includes capillaries. Figure 4 shows that for the equidistributed model (2% 2.5 ␮m capillaries, 2% 25 ␮m vessels,
R ⫽ 5.28 ␮m), the curves ⌬R2 vs. ⌬R*2 obtained with the
two approaches are in excellent agreement. The two
curves differ however by a translation which reflects the
contribution of motional narrowing which is not taken
into account in the analytical approach. Figure 5 shows
that for a large dose of contrast agent, the vessel size index
calculated with Eq. [14], on the basis of the results obtained with MC data, is overestimated. However, the error
remains smaller than 20% if the contrast agent dose is
greater than about 100 ␮mol Fe/kg (⌬␹ ⬎ 0.28 ppm). Given
the limited accuracy of measurements of changes in relaxation rates, we conclude that the combination of the static
dephasing approximation for ⌬R*2 estimation (6) with the
slow-diffusion approximation for ⌬R2 estimation (10,11)
can be used for analyzing experimental data.
Troprès et al.
Blood Visibility
In previous models, the intravascular water proton magnetization was generally assumed to be either perfectly
refocused or partly defocused under the combined influence of two effects: diffusion in the overlapping field from
neighboring vessels, and dependence of the intravascular
magnetic field on vessel orientation (4,6,10,15,25). Other
mechanisms intervene, however. The transverse relaxation of blood is predominantly due to diffusion of water
protons through field gradients arising from the susceptibility difference between red blood cells and plasma
(16,26 –29). This effect is not visible when the relaxivity of
a contrast agent is measured with a short interpulse delay.
Thus, injection of a superparamagnetic agent in the blood
compartment induces T*2 and T2 decreases much larger
than expected from the r2 relaxivity data (as measured
with a CPMG sequence with short interpulse delay). We
assumed in this work that the transverse relaxation time of
blood water after contrast agent injection was very small,
resulting in a complete suppression of signal from the
blood compartment. The smallest TE used in the experiments was 6 msec (measurement of ⌬R*2 vs. dose). Using a
mean total blood volume in the rat of 60 ml kg–1 (4,30) and
the r2 relaxivity of AMI-227 (83 sec–1 mM–1 (17)), one can
estimate that blood T2 should be smaller than 3.60 msec at
the dose of 200 ␮mol Fe/kg, and than 28.8 msec at the
smallest dose (25 ␮mol Fe/kg). The difference in susceptibility between plasma and red blood cells should further
increase the transverse relaxation rate of blood. It was
shown (28) that a susceptibility difference between the
intra- and extracellular environments of 0.4255 ⫻ 10– 6
produces an increase of 100 sec–1 in the transverse relaxation rate constant (B0 ⫽ 2.35 T). Assuming a quadratic
dependence in ⌬␹ (26, 27), an increase in R2 of about
400 –500 sec–1 is expected for the highest dose of contrast
agent. As a result, the blood signal is not visible in spin
echo experiments (TE ⫽ 100 msec) whatever the dose. In
GE experiments, however, the black blood assumption
may have induced some errors at short TEs and lower
doses in both MC simulations and analytical predictions.
⌬␹ Measurements
The increase in blood susceptibility at B0 ⫽ 2.35 T was
found to be ⌬␹ ⬃ 0.571 ⫾ 0.03 ppm at the dose of 200 ␮mol
Fe/kg, corresponding to a magnetization M ⫽ B0 ⌬␹ ⫽
13.42 ⫾ 0.7 mG. Using a total blood volume of about
60 cm3 kg–1, and given the molecular weight of iron
(55.8 g), the calculated specific magnetization of AMI-227
is ⌬Mg ⫽ 72.04 G cm3 g–1, a value close to that given by
Laboratoires Guerbet (69.8 G cm3 g–1) but significantly
lower than that (⌬Mg ⫽ 94.8 G cm3 g–1) reported in a
previous work (18). These and other published results are
summarized in Table 3, which shows that the reported
susceptibility values of AMI-227 vary widely. The magnetic susceptibility of a superparamagnetic agent depends
closely on the size of the iron oxide core (31) and could
vary from one lot to another. This underlines the importance of accurate measurements of molar susceptibilities
for each new stock solution (23).
⌬R2* vs. Dose: CBV Measurements
It has been suggested that the variation of the GE relaxation
rate with susceptibility is quadratic (4,14,32). MC simula-
Vessel Size Imaging
407
Table 3
Magnetization of AMI-227
Reference
Field strength
(T)
Magnetization
(G cm3 g⫺1)
This work
Laboratories GUERBETa
(35)b
(18)
(19)
2.35
—
2
5
1.5
72.04
69.8
56.0
94.8
91.4
a
Saturation magnetization.
Value extracted from the Fig. 2 of Does et al. (35) which shows that
⌬␹ ⬇ 0.5 ppm at the cumulated dose of 192 ␮mol Fe/kg (average of
the 10 data points showing the largest shift).
tained with this technique could be overestimated. It is
known that hematocrit is smaller in the brain tissue than
in large vessels (36,37). The increase in plasma fraction in
small vessels results in an increased blood-tissue susceptibility difference, leading to CBV overestimation. Correction for Hct by a factor 0.83 gives blood volume fractions of
3.37% and 2.38% in the cerebral cortex and the corpus
striatum, respectively. Note that the same correction
should be applied to steady-state techniques based on T1
measurements (2,9).
b
tions indeed show a quadratic concentration dependence
at small blood tissue susceptibility difference, but this
evolves to a linear dependence at large ⌬␹ (4,25). The
range of ⌬␹ over which a quadratic regime exists decreases
as the vessel size increases. In contrast, the experimental
results show that the relationship between ⌬R*2 and the
dose of contrast agent is linear (Fig. 6). A similar linear
dependence of ⌬R*2 with ⌬␹ for relatively low ⌬␹ values
was found in rat brain (4,32) and recently in human
brain (33).
It should be noted that ⌬␹ is the increase in blood
susceptibility due to contrast agent injection rather than
the difference between blood and tissue susceptibilities.
The effective blood-tissue susceptibility difference after
injection is ⌬␹blood⫹AMI 227. Thus the measured change in
⌬R*2 should be written as:
⌬R *2共⌬␹兲 ⫽ ⌬R *2共⌬␹ blood⫹AMI 227兲 ⫺ ⌬R *2共⌬␹ blood兲.
[24]
Since the quadratic behavior occurs at low blood-tissue
susceptibility differences, the ⌬R*2(⌬␹) curve is shifted toward linear regions. This is applicable to the BOLD effect
as well.
The linearity of the ⌬R*2(⌬␹) curve suggests that the
Yablonskiy and Haacke model (6) applies and can be used
for studying brain microcirculation. This linearity, which
follows from Eqs. [3] and [6], has been used successfully
even for relatively low susceptibility differences
(7,9,33,34). The ⌬R*2/Dose ratios found in this work,
0.210 sec–1 per ␮mol Fe/kg in the corpus striatum and
0.295 sec–1 per ␮mol Fe/kg in the cortex, are quite consistent with the data given by Does et al. (35) but larger than
the value (0.106 sec–1 per ␮mol Fe/kg), which can be
extracted from the data given by Boxerman et al. (4). The
discrepancy could be due to differences in magnetic susceptibility of stock solutions, to errors in the injected dose,
or to an influence of the limited halflife of the contrast
agent in the blood compartment. Moreover, as pointed out
above, the use of T1-weighted sequences introduces an
underestimation of the ⌬R*2 changes. The blood volume
fractions ␰0 found in the cortex (4.07%) and in the corpus
striatum (2.87%) are significantly larger than that found by
Boxerman et al. (4) and Schwarzbauer et al. (3), but they
are in better agreement with Lin et al. (2,9), who obtained
a rCBV in the range of 2.40 –2.90% for the whole brain
using another MRI technique. Steady-state susceptibility
contrast imaging was recently used for absolute measurements of CBV in the human brain (33). CBV results ob-
⌬R2 vs. ⌬R2*: VSI Measurement
An important result of the MC simulations carried out by
Boxerman et al. (4) was the prediction, for large ⌬␹ values,
of a sublinear dependence of ⌬R2 on contrast agent concentration. Since ⌬R*2 was found to depend linearly on
concentration, the ⌬R2(⌬R*2) curves shown in Fig. 8 can be
analyzed as plots of ⌬R2 vs. ⌬␹. These experiments demonstrate for the first time the sublinear regime previously
predicted in Ref. 4.
Using the histogram of vessel radii reported in Ref. 8 for
the deep gray matter, one finds R ⫽ 3.84 ␮m, which is in
reasonable agreement with our findings. Similarly, from
the histogram of vessel diameters in the rat brain (whole
brain) reported in Ref. 38, a VSI of R ⫽ 3.31 ␮m is calculated. It should be noted that both histograms concern
capillaries only. Exclusion of large vessels could explain
that the VSI calculated with the histograms is smaller than
that found with the NMR data.
The contrast of the vessel size image shown in Fig. 7c is
low, suggesting that the difference in vessel size between
the different brain regions is relatively small. However, a
greatest mean vessel size can be detected in the white
matter (corpus callosum and ventral hippocampal commissure), as previously shown in the human brain white
matter (39,40). Note that this finding could be hardly extracted from the direct observation of the ⌬R2 and ⌬R*2
images.
In conclusion, we have shown that a combination of the
static dephasing approximation for ⌬R*2 estimation (6)
with the slow-diffusion approximation for ⌬R2 estimation
(10,11) can be used successfully for analyzing changes in
transverse relaxation rates due to injection of a superparamagnetic agent in the blood pool. We have demonstrated
experimentally a nonlinear dependence of ⌬R2 on ⌬R*2 and
introduced a new imaging modality.
ACKNOWLEDGMENTS
The authors thank Jonathan Coles for his critical revision
of the manuscript, Valery Kiselev for very helpful correspondence regarding the analytical analysis, Chantal
Remy and Hana Lahrech for useful discussions, Blanche
Koenisberg for technical assistance, and Laboratoires
Guerbet (Aulnay sous Bois, France) for providing the contrast agent. These studies were supported by Région
Rhône-Alpes, Ligue Nationale Contre le Cancer, and ARC.
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