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 spin-echo (SE) or gradient-echo (GE) protocols. In contrast to GE technique, the SE sequence uses an additional refocusing pulse during image acquisitionthat 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*:
[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.
Inconventional 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):
[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 ofcontrast agent or by rigorous post-processing routines.S7–S10
Vessel-calibre imaging by DSC-MRI
Unlike small vessels in whichdiffusion effects dominate, the magnitude of the MRI signal in large vessels is determined by so-called intra-voxel dephasing, whenthe 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.S12used the quotient of GE (∆R2*) and SE (∆R2) blood volume to obtain a dimensionless measure coined the mean vessel diameter (mVD):
[3]
This relationship holds true for standard clinical contrast agent dosages, where TE under normal conditions is dependent on χ as follows:
[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 onexperimental data that the magnitudes of the GE and SE MRI signals (relaxivities) for small vessels (radius <10µm) increase in a similar exponentially fashion because proton diffusion is so fast that the SE refocusing pulse has limitedor no effect.S17,S18 For larger vessels (radius >10µm), 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,S19Expanding onthe work by Dennie and colleagues,S12in 2000, Jensen and ChandraS20 proposed an alternative use of the GE to SE relationship that wasshown to correlate with the mean vessel density of tissue, denoted Q:
[5]
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:
[6]
Furthermore, a steady-state image acquisition method has been proposed as an alternative to dynamic MRI routines.S13,S21,S16For 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,S23Because of the relatively large size of suchmolecules (ferumoxytol ~30nm at a concentration of 80µmolFe/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 describedin equation [2] can beused for single echoes, shown by the following equation for SE:
[7]
Alternatively, a multi-GE, single/multi-SE sequence can be used, withthe MRI signal decay fitted to a monoexponential curve. A benefit of the steady-state approach compared withhigh-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 onintravascular 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 challengesowing to theuptake 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 canalso 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.S15After 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 (~1.5sec). In patients, after approximately 10 baseline scans, a total of 0.1–0.2mmol/kg of a gadolinium-based contrast agent is injected.S7 In addition to the pre-injection baseline scan and the subsequent first-pass 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 Turbofast low angle shot (TurboFLASH) sequence for body vessel-calibre MRI. Animal imaging at higher field strengthsS16 (animal scanners at around 4.7Tesla) will require shorter temporal resolutions (~0.5sec). 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,S36and 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 (3–4sec), and the post-contrast-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 usinga standard Gaussian filter.S32 For high resolution, highfield strength (~4.7Tesla) animal imaging, temporal resolution can be as long as 6 seconds.
Additional technical considerations forvessel-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, S37However, this model might underestimate the contribution ofcapillaries,S38as well asatortuous 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.S39Also, the traditional monoexponential decay of the GE and SE signal mightbe over-simplistic in regions with local variations in magnetic field susceptibility, and also for geometric imperfections.S40–S42In 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,S26as such drugsmightchange the cellularity of the tissue.
Vessel-calibre MRI is valid for the static dephasing protocols,S43in whichspin diffusion is slow and canbe ignored; the SE pulse is assumed to completely refocus the phase accumulation of the spins. This approximation is fair in clinical MRI, but mighthave to be refined for certain values of ∆χ according to equation [4].S38In mesoscopic tissues,S44the magnetic field has local variations, especially in the venous aspect of the vasculature andfollowinga paramagnetic contrast-agent injection, for example.S14 Mesoscopic-tissue effectsare 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 withthe 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*/∆R2has been reported to bein better agreement with histological findingsin a glioma model than estimates based on this 3/2-power dependence,S49 whereas another study in abreast 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 usingMRI compared withhistological 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 ± 10µmS14 and 38 ± 12µm,S36values 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 (>0.1mmol/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 estimatesusingmore 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 vessel-calibre 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-by-point GE and SE relaxation rate curves (ΔR2* and ΔR23/2, respectively) in a scatter plot representative of the image voxel.S14,S34A gamma-variate function is fitted to the GE and SE curves for better visualization of vessel vortex effects and scaled with corresponding slice-specific 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 thedirection 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 best-fit (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,S34in whicharterioles aberrantly connect to venulesbypassing 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 vessel-vortex area reflects the different magnetic susceptibility states ofoxygenated (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 SO2 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
References
S1. Barbier,E.L., Lamalle,L., & Decorps,M. Methodology of brain perfusion imaging. J. Magn Reson. Imaging13, 496-520 (2001).
S2. Covarrubias,D.J., Rosen,B.R., & Lev,M.H. Dynamic magnetic resonance perfusion imaging of brain tumors. Oncologist.9, 528-537 (2004).
S3. van Osch,M.J., Vonken,E.J., Bakker,C.J., & Viergever,M.A. Correcting partial volume artifacts of the arterial input function in quantitative cerebral perfusion MRI. Magn Reson. Med.45, 477-485 (2001).
S4. Rosen,B.R., Belliveau,J.W., Vevea,J.M., & Brady,T.J. Perfusion imaging with NMR contrast agents. Magn Reson. Med.14, 249-265 (1990).
S5. Ostergaard,L., Weisskoff,R.M., Chesler,D.A., Gyldensted,C., & Rosen,B.R. High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. Part I: Mathematical approach and statistical analysis. Magn Reson. Med.36, 715-725 (1996).