Supplementary Methods
Dynamic susceptibility contrast MRI
In perfusion MRI, the paramagnetic effect of a blood tracer (such as a gadolinium-based
contrast agent) changes the biophysical properties of the tissue by increasing the proton
relaxation rates, and a linear relationship is assumed between the observed MRI signal
change and the concentration of the contrast agent. S1,S2 This assumption holds true if the
contrast agent is distributed in the intravascular space. The echo-planar imaging technique
used in dynamic T2-weighted perfusion MRI is particularly sensitive to the accelerated T2
relaxation times (with a relaxation rate R2) following a contrast agent injection, a
phenomenon known as the magnetic susceptibility effect (χ). The magnetic susceptibility
effect describes the degree of magnetization induced in a medium when exposed to a
magnetic field, and this effect causes large local variations in the magnetic field across
different tissues.S3 Consequently, this imaging technique is referred to as dynamic
susceptibility contrast (DSC)-MRI.
Two different echo-planar imaging techniques are used in DSC-MRI, either based on a spinecho (SE) or gradient-echo (GE) protocols. In contrast to GE technique, the SE sequence uses
an additional refocusing pulse during image acquisition that reverses an inherent dephasing
of proton spins that immediate start to go out of phase after the initial proton excitation. As
a result, the SE sequence is predominantly T2-sensitive, whereas the GE sequence, in reality,
experiences a T2* effect with a relaxation rate R2*:
R2 
*
1
1
  γΔB 0
*
T2
T2
[1]
where ∆B0 is the bulk inhomogeneity of the magnetic field causing the dephasing of proton
spins and γ is the gyromagnetic ratio unique for each isotope possessing a spin.
In conventional DSC-MRI protocols, the resulting voxel-wise signal-versus-time curve S(t)
following administration of contrast agent is converted into a concentration-versus-time
curve C(t) by assuming a monoexponential signal decay as a function of the increase in
relaxation rate ΔR2 (or ΔR2* for GE sequences):
C(t)  
k
S(t)
ln(
)  ΔR2 (t)
TE S(0)
[2]
where k is an unknown proportionality constant, TE is the image sampling time known as
echo-time and T1-effects are assumed negligible or corrected for.S4 Using the central volume
principle, blood volume is proportional to the integral of C(t), but in order to derive
quantitative estimates this integral needs to be normalized to the corresponding C(t) curve
of a feeding artery, known as the arterial input function. Another benefit of the arterial
input function is the ability to measure the tissue residue function, describing the amount of
blood remaining in the tissue per unit time.S5 For practical purposes, the tissue residue
function can be expressed as a monoexponential function and the mean transit time
corresponds to the area of the residue function. Values of blood flow are derived from the
central volume principle once the blood volume and mean transit time are known.
In practice, the arterial input function is typically assumed to be a constant resulting in
relative values of perfusion. This simplification assumes that the contrast agent inflow
originates from a common site (that is, the injection site). Furthermore, in permeable
vessels or in cerebral regions with severe blood–brain barrier disruption,S6 the C(t) curve
needs to be corrected for T1 shortening effects. This correction is a research topic of much
interest and debate, but usually contrast-agent extravasation correction is performed by
saturating the tissue using an additional ‘pre-dose’ injection of contrast agent or by rigorous
post-processing routines. S7–S10
Vessel-calibre imaging by DSC-MRI
Unlike small vessels in which diffusion effects dominate, the magnitude of the MRI signal in
large vessels is determined by so-called intra-voxel dephasing, when the proton spins
immediately start to go out of phase following the initial proton excitation that forms the
basis for all clinical MRI. MRI-based vessel calibres can be estimated in a number of ways, all
of which estimate information on average vessel diameters and structure well below the
spatial resolution of the MR image (~100 µm for small animal scanners).S11–S16 Dennie et
al.S12 used the quotient of GE (∆R2*) and SE (∆R2) blood volume to obtain a dimensionless
measure coined the mean vessel diameter (mVD):
mVD 
R *2
R 2
[3]
This relationship holds true for standard clinical contrast agent dosages, where TE under
normal conditions is dependent on χ as follows:
TE 
1
2B 0
[4]
where ∆χ is the difference in magnetic susceptibility between the intravascular and the
extravascular space, and the blood volume fraction (Vf) is <<100%. It has been shown both
in theory, using mathematical modelling, and based on experimental data that the
magnitudes of the GE and SE MRI signals (relaxivities) for small vessels (radius <10 µm)
increase in a similar exponentially fashion because proton diffusion is so fast that the SE
refocusing pulse has limited or no effect.S17,S18 For larger vessels (radius >10 µm), diffusion
becomes unimportant because intra-voxel dephasing of the proton spins dominate the MRI
signals. Consequently, the SE relaxivity will decrease exponentially with increasing vessel
calibres, whereas the GE relaxivity remains constant and independent of large vessel
calibres. An alternative to the mVD estimate described above is the direct assessment of the
point-by-point difference in the GE and SE concentration-versus-time curves (±5 points
around the peak height of the GE curve).S12,S19 Expanding on the work by Dennie and
colleagues,S12 in 2000, Jensen and ChandraS20 proposed an alternative use of the GE to SE
relationship that was shown to correlate with the mean vessel density of tissue, denoted Q:
Q
R2
[5]
2
* 3
2
(R )
For sufficiently high contrast-agent-induced values of ∆χ compared to native tissue, the Q
parameter is appreciated by its independence of the contrast-agent concentration.S20
A quantitative measure of vessel calibre, often referred to as the vessel size index (VSI), has
also been proposed.S20,S13,S14 This measure is a weighted average of the vessel calibres, also
including the water diffusion coefficient in the tissue (D) and Vf:
VSI  k Vf D 
1/2
ΔR *2
3
ΔR 2 2
[6]
Furthermore, a steady-state image acquisition method has been proposed as an alternative
to dynamic MRI routines.S13,S21,S16 For this approach, GE and SE images are acquired before
and after injection of a contrast agent, most often super-paramagnetic iron-oxide (SPIO)
nanoparticles or monocrystalline iron-oxide nanoparticles (MION).S22,S23 Because of the
relatively large size of such molecules (ferumoxytol ~30 nm at a concentration of
80 µmolFe/kg–1),S24 SPIO agents remain within the vasculature and are, therefore,
particularity favourable in permeable vessels outside the central nervous system. For image
acquisition, the standard protocol described in equation [2] can be used for single echoes,
shown by the following equation for SE:
ΔR2 
S
1
ln( SE, pre )
TE S SE, post
[7]
Alternatively, a multi-GE, single/multi-SE sequence can be used, with the MRI signal decay
fitted to a monoexponential curve. A benefit of the steady-state approach compared with
high-temporal resolution dynamic imaging is capacity of the former to use longer acquisition
times, thereby resulting in higher spatial resolution. Even in extravasating tumours, direct
comparisons between estimates of vessel calibres based on intravascular to extravascular
gadolinium-chelates and intravascular SPIO agents yield similar results.S16 However,
although not assumed to be toxic in the long-term, SPIO nanoparticles present challenges
owing to the uptake of these agents in the liver and lymph nodes, among others
organs.S25,S23 This characteristic makes repeated injection of such contrast agents over short
periods of time difficult, and unlike gadolinium-based chelates, iron-oxide based contrast
agents are currently restricted to off-label use.S26,S27 SPIO–based agents can also cause
signal voids from ultrashort image sampling times.S28,S29
Finally, the blood-oxygenation-level-dependent (BOLD) effectS30,S31 can also be used to
estimate vessel calibres in the brain.S15 After triggering changes in venous blood oxygen by
brain stimuli or gas challenges, vessel calibres can be estimated according to equations [3]
and [7].S32 Although data show good agreement with other methods for vessel-calibre
estimations, it should be noted that BOLD vessel-calibre estimates suffers from low signal-
to-noise ratios (<5% signal change) and that BOLD only enables measurement of the venous
vasculature.S32
Scan parameters for vessel-calibre MRI
For a standard DSC-MRI data acquisition during injection of a gadolinium-based contrast
agent,S14,S16,S33,S34 image resolution should be as high as possible and cover the entire
tumour region while maintaining sufficient temporal resolution (~1.5 sec). In patients, after
approximately 10 baseline scans, a total of 0.1–0.2 mmol/kg of a gadolinium-based contrast
agent is injected.S7 In addition to the pre-injection baseline scan and the subsequent firstpass imaging period of the initial passage of the contrast agent bolus, the dynamic scan
should also image a sufficiently long tail after this first-pass (>30 scans) for contrast agent
extravasation correction.S9 Alternatively, Lüdemann and colleaguesS35 reported using an
inversion-prepared dual-contrast Turbo fast low angle shot (TurboFLASH) sequence for body
vessel-calibre MRI. Animal imaging at higher field strengthsS16 (animal scanners at around
4.7 Tesla) will require shorter temporal resolutions (~0.5 sec). It should also be noted that
efforts have been made to assess the value of combining separate GE and SE echo-planar
imaging (EPI) examinations for institutions without access to a combined GE/SE sequence
MRI setup.S36 Computer simulations suggested a 8% error in the vessel-calibre estimates
using this method, which was dependent on the temporal resolution,S36 and exploratory
data in human brain tumours in this study also showed reasonable vessel-calibre values.
Although care must be taken for correct spatial and temporal coregistration and correction
of potentially alternating contrast agent effects, this approach might also be applicable to
relative measures of vessel architectural imaging (VAI).S34
For steady-state vessel-calibre MRI,S13,S32,S21 imaging is typically performed using a combined
multi-GE and single-SE setup with longer temporal resolutions (3–4 sec), and the postcontrast-agent scan is performed 3–5 min after intravenous SPIO or MION injection. The
acquired data should be motion-corrected and are usually also smoothened using a
standard Gaussian filter.S32 For high resolution, high field strength (~4.7 Tesla) animal
imaging, temporal resolution can be as long as 6 seconds.
Additional technical considerations for vessel-calibre MRI
Traditional vessel-calibre estimates assume that the vascular network consists of a randomly
distributed set of perfect cylinders of infinite length and with diameters considerable
smaller than the voxel size.S18, S37 However, this model might underestimate the contribution
of capillaries,S38 as well as a tortuous and chaotic tumour vasculature with high blood
volumes.S11 More precise models of the vessel geometry have been proposed and will
probably result in higher accuracy vessel-calibre estimates.S39 Also, the traditional
monoexponential decay of the GE and SE signal might be over-simplistic in regions with local
variations in magnetic field susceptibility, and also for geometric imperfections.S40–S42 In
addition, accurate determination of D in equation [6] is particularly important in
interventional studies of certain vascular disrupting agents such as combretastatin A-4
disodium phosphate,S26 as such drugs might change the cellularity of the tissue.
Vessel-calibre MRI is valid for the static dephasing protocols,S43 in which spin diffusion is
slow and can be ignored; the SE pulse is assumed to completely refocus the phase
accumulation of the spins. This approximation is fair in clinical MRI, but might have to be
refined for certain values of ∆χ according to equation [4].S38 In mesoscopic tissues,S44 the
magnetic field has local variations, especially in the venous aspect of the vasculature and
following a paramagnetic contrast-agent injection, for example.S14 Mesoscopic-tissue effects
are dependent on the magnetic field strength and image sequence used, and imaging might,
therefore, become imperfect with slow refocusing pulses. A practical consequence of
mesoscopic tissue effects is overestimation of the vessel-calibre estimate at 3 Tesla.S45 This
effect, however, will be smaller at higher field strengthsS45 (small-bore animal scanners), and
can also be corrected for analytically.S46
The GE signal has been shown to have a linear relationship with the contrast-agent
concentration, whereas the SE signal, which is assumed independent of GE, has a nonlinear
relationship with contrast-agent concentration.S42,S47,S48 In equations [5] and [6], this
nonlinear relationship is adjusted for by the 1/(R2/3) dependence of ∆R2.S47, S20 However, a
linear ratio ∆R2*/∆R2 has been reported to be in better agreement with histological findings
in a glioma model than estimates based on this 3/2-power dependence,S49 whereas another
study in a breast cancer xenograft model showed no significant difference between the two
estimates.S50 In human vessel-calibre MRI, the 3/2-power is most commonly used. S13,S14,S41
Because of the issues described above, authors using data from theoretical simulations,S13
animal models,S22 and studies in humansS14 all report a slight systematic overestimation of
absolute measures of vessel calibres determined using MRI compared with histological
findings and literary evidence. Compared with CD31-stained cryosections, Zwick et al.S51
found a twofold overestimation of vessel calibres in HaCaT-ras-A-5RT3 human skin
squamous-cell carcinomas. However, care should be taken when comparing in vivo
measures with thick ex vivo histologic sections because cryosectioning or similar methods
may result in collapsed vessels leading to underestimation of vessel diameters.S11,S51 In
humans, the average vessel diameter of normal-appearing grey matter tissue in patients
with gliomas or meningiomas was found to be in the order of 36 ± 10 µmS14 and 38 ±
12 µm,S36 values in good agreement with vascular casts examined by scanning electron
microscope.S52 Furthermore, simulations by Kiselev and colleaguesS14 suggested a 20–40%
overestimation, which is in agreement with data using contrast-agent dosages
(>0.1 mmol/kg) and field strengths (>1.5 Tesla) representative of those used in most
institutions at present.S13,S18,S39 It should also be noted that efforts have been made to
mathematically reduce potential overestimations of vessel-calibre estimates using more
rigorous calculations of D, ∆R2* and ∆R2.S53
In conclusion, the accuracy of the absolute vessel-calibre estimate in the abnormal
vasculature of cancer should be used with care. However, the validity of relative vesselcalibre MRI for most cancers in vivo has been investigated and confirmed in many studies
(Supplementary Table 3).
Vessel architectural imaging
The VAI technique stems from a parametric vortex curve formed by combining the point-bypoint GE and SE relaxation rate curves (ΔR2* and ΔR23/2, respectively) in a scatter plot
representative of the image voxel.S14,S34 A gamma-variate function is fitted to the GE and SE
curves for better visualization of vessel vortex effects and scaled with corresponding slicespecific mean, normal-tissue reference curves to account for potential global systemic
effects.S10,S34 From the resulting vessel-vortex curves, a set of parameters can be derived
that describes the microvasculature.S34,S54 The vessel-vortex direction is defined by the
direction in which the point-by-point scatter plot propagates.S14 In healthy tissue, a
clockwise vortex direction corresponds to an image voxel representing vessels with
predominantly fast inflow and early arrival of the contrast agent, typical of arterioles. A
counter-clockwise vortex direction corresponds to areas of slow-inflow, late arrival of the
contrast agent, typical of venules. At similar calibres, owing to the difference in oxygen
saturation (SO2) levels between arterioles and venules, the vessel vortex will transverse in a
counter-clockwise direction if both vessel types are included.S34 If all vessels in a vascular
system (that is, the image voxel) have identical calibres and SO2 levels, or are of the same
vessel type, no vortex is observed.S34
The long axis of the vessel-vortex curve is found by a linear fit of the vortex curve. This can
be performed using least squares estimation or other similar methods estimating the bestfit (that is, the minimum error) of a straight line. In normal tissue, an increase in the long
axis is proportional to an increase in the area under the concentration-versus-time rate
curve, which is the traditional measure of blood volume. The gradient of the long axis, or
the slope value, is under normal conditions assumed proportional to the vessel calibre and
tilted towards the gradient-echo axis for larger average vessel calibres.S14 It should be noted
that this slope value is also dependent on blood volume and the average SO2 level in the
tissue.S34 Interestingly, regardless of vessel calibre, the highest theoretical slope values have
been observed for shunting vessels,S34 in which arterioles aberrantly connect to venules
bypassing capillary vessels. Finally, the corrected vessel-vortex area is calculated by dividing
the vessel-vortex area by the length of the long axis. This corrects for systemic and local,
tissue-specific variations in volume fractions. Adjusted for variations in the average vessel
calibres and vessel types (determined based on vortex direction), the corrected vesselvortex area reflects the different magnetic susceptibility states of oxygenated (arterioles)
and deoxygenated (capillaries or venules) blood, and corresponds to a relative measure of
SO2.S34,S55,S56 For example, in a system with arterioles and capillaries only, a relative
reduction in the corrected vessel-vortex area is observed for reduced capillary SO2 levels,
whereas a relative increase is observed for a subsequent reduction in arteriole SO 2 levels.
Another potential benefit of the VAI technique is the apparent reduced sensitivity of this
approach to contrast-agent extravasation into tumour tissues. Although pre-load saturation
routinesS7 and rigorous post-processing corrections are recommended for both brainS8,S9
and body imaging,S10,S57 extravasation effects are presumably of less importance in VAI
because calculations are performed during the up-slope and down-slope of the contrast
bolus first-pass and well before most extravasation effects occur.S9, S54 Indeed, VAI with and
without analytic contrast agent correction in the brain produced only minor variations.S34
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