Mapping vascular parameters using contrast agents

Exogenous contrast agents (CA) include intravenously administered substances that modify the contrast of blood and organs. CA are not directly visible but are imaged because they shorten the relaxation times T1 and T2 or because they increase the magnetic susceptibility differences between blood vessels and surrounding tissues. In this last case, the induced long-range magnetic field perturbations extend to adjacent tissues and increase the transverse relaxation rates R2 and R^∗₂. Therefore, a CA is characterized by its magnetic susceptibility and its relaxivities (r₁ and r₂), i.e. its ability to locally modify the magnetic field and the relaxation times of the molecule around, and also by its size, charge, or hydrophilicity that determines the locations where it goes. We used two main classes of CA (main characteristics given in Table2.3):

• superparamagnetic iron oxide particles, used for their susceptibility effect and in particular result in a decrease T^∗₂-weighted signal.

• gadolinium chloride, paramagnetic, with the principal effect of signal enhancement in T1-weighted imaging.

Currently, gadolinium-based CAs are the most commonly used in MRI and particularly in clinical MRI, whereas ultrasmall superparamagnetic iron oxides (USPIO) are rather limited to a pre-clinical application.

Contrast agent Relaxivities(s⁻¹.mM⁻¹) Hydrodynamic

r₁ r₂ size(nm)

Gd-Dota (Gadolinium) 3.3 4.1 1

P904 (USPIO) 4.0 92.0 25-30

Table 2.3 – Superparamagnetic iron oxide particle and gadolinium chloride contrast agents characteristics. Given for 37 °C, 4 % human albumin serum and 4.7 T [127,128].

2.3.4.1 Ultrasmall superparamagnetic iron oxide

The first contrast agent presented induces magnetic susceptibility and relaxivity effects.

When such a CA is compartmentalized within a voxel, these effects result in a decrease of the MR signal in an inhomogeneous magnetic field. This is what happens at vessel-tissue interfaces, since CA is distributed only in the vascular compartment. This paramagnetic substance acquires, in the magnetic field, a magnetization different from that of the surrounding environment: on each vessel surface, and over few microns, a magnetic field gradient appears [129]. This increase in the heterogeneity in the magnetic field of the voxel yield a decrease in signal intensity due to an increased spin-spin dephasing (T2

relaxation). In a first approximation and when the blood volume fraction is small, the decrease of the signal observed in a voxel depends on the concentration of the tracer in vessels (i.e. the blood volume fraction), and on the fraction of blood in the volume.

Going a little further, we can also show that this signal decrease depends on the number of vessels and their diameter [130]. Figures 2.22(b, c) show an example of T^∗₂-weighted images before and after the injection of USPIO. On these images, it is easy to distinguish (in black because of signal decrease) the important vascular structures.

Using a multiple gradient echo sampling of the free induction decay and spin echo (MGEFIDSE) sequence (cf. below), it is possible to directly evaluate two parameters: the blood volume fraction (BVf) and the vessel size index (VSI), which are the proportion of blood in the volume imaged in % and a weighted mean vessel radius [131], respectively.

VSI is computed as:

where r_i is the radius of thei^th vessel, and R the total number of vessels in the voxel.

MGEFIDSE sequence is composed of a first 90° RF pulse and then a 180° RF pulse.

Gradient echos collected after the first pulse capture information about the relaxation rate R^∗₂ (inverse of T^∗₂) while the information acquired around twice the time between the two pulses capture information about the relaxation rate R₂ (inverse of T₂). The theory for determining BVf and VSI is presented in [132]. The changes in relaxation rates ∆R^∗₂ and ∆R2 induced by the injection of USPIO are computed using gradient echo (GE) and spin echo (SE) signal intensities, respectively. The pre- and post-injection relaxation times T^∗_2,preand T^∗_2,postare obtained by fitting the GE signal intensities to an exponential function, see section 2.3.1. It allows to compute ∆R^∗₂, while ∆R2 is directly calculated

from the two SE signal intensities (pre-injection: S_SE,pre; and post-injection: S_SE,post):

Then, these changes in relaxation rates are used to compute BVf and VSI using the following equations:

where ∆χ_USPIO is the increase in blood susceptibility due to USPIO. Note that VSI depends on the diffusion parameter ADC introduced in section 2.3.2.

(a) MGEFIDSE sequence

(b) T^∗2-weighted pre-injection image

2 mm

(c) T^∗2-weighted post-injection image

0 20 40 60

Figure 2.22 – Vascular structure MRI using USPIO.

Example of T^∗₂-weighted images of a mouse brain (a) before and (b) 1 minute after the 200 µmol Fe.kg⁻¹ body weight injection of USPIO. Data were acquired at 9.4 T on an adult mouse: spatial resolution of 136×136×700 µm³ and spin echo at 50 ms. The average MR signals for the 3 regions (rectangles) are provided in (c). Each point of the curves correspond to one‘Acq’ on the chronogram represented in (a) (the blank corresponds to the 180° pulse).

The tissue oxygen saturation (StO₂) parameter is estimated using the quantitative approach described in [133]. First, the relaxation time T2 is computed, see section2.3.1.

Equation (2.30) is then fitted to the MR signal decay of the mutli gradient echo sequence (MGE), which is given by:

S_MGE(t) = S₀ exp− 1 T₂ t− 4

3π γB0∆χ₀HctBVf (1−StO2)t

, (2.30) where ∆χ₀ is the difference between the magnetic susceptibilities of fully oxygenated and fully deoxygenated hemoglobin, which is set to 3.32 ppm (SI unit), and Hct is the microvascular hematocrit, which is set to 0.357 (see [134]). S₀ is a constant.

2.3.4.2 Gadolinium

Dynamic contrast enhanced (DCE) imaging measures changes in relaxation time T1

over time following an injection of Gadolinium. Immediately after the CA injection, gadolinium circulates throughout organs and extravasates (i.e. leaks out of the vessels into the surrounding area) in most of them with the exception of the healthy brain.

Indeed, Gadolinium does not cross the BBB except in pathological conditions where it may be damaged. In this case, there is an extravasation of the CA, which reduces the T1

of tissues. In practice, acquisition starts before the injection in order to observe changes induced by CA over time. The figure 2.23(a, b) shows T₁-weighted images during the acquisition and three examples of typical curves that can be observed.

There are two main groups of approaches to quantitatively analyze DCE MRI, namely, parametric (analytical) techniques and nonparametric (model-free). Parametric approaches aim to quantify kinetic parameters directly by fitting pharmacokinetic models to the concentration curves. Pharmacokinetic models are based on different assumptions and simplifications, see [135]. The advantage is that parameters are physiologically interpretable but the underlying model assumptions may not be applicable to all tissues or to damaged tissue. In addition, these approaches require the preliminary quantification of the arterial input function and the conversion of signal evolution into the CA concentration

evolution. Nonparametric approaches, on the other hand, derive empirical parameters that characterize directly the shape of signal evolution. All these steps add noise and can reduce reliability of the estimates. Empirical parameters correlate with physiological pharmacokinetic parameters [136] but it is difficult to estimate the tissue’s physiological quantities, such as vascular permeability. Examples of such parameters are shown in figure2.23(c) and computed from signalS_DCE(t) by:

• Signal enhancement (∆S) is the difference between the maximum signal intensity S_max and the baselineS₀: ∆S =S_max−S₀ .

• Time-to-peak (TTP) is the delay between the CA arrival and the peak, i.e. signal intensity reaches its maximum value: S_DCE(t= TTP) = S_max .

• Area-under-curve (AUCT) for a time T in seconds (typically, 180):

AUCT =^{Z T}

0 (S_DCE(t)−S₀) dt. (2.31) In chapter 5, the term BBB permeability (BBBp) is used for AUC600, for sake of clarity.

Figure 2.23 – Dynamic contrast enhanced MRI using gadolinium injection.

(a) Example of T₁-weighted images of a mouse brain at 5 different times after the beginning of the acquisition. The gadolinium (200 µmol.kg⁻¹) was injected at 60 seconds. Data were acquired at 9.4 T on an adult mouse, using a spatial resolution of 136×136×700 µm³. The average MR signals over time for the 3 regions (colored rectangles) are provided in (b). The markers on curves indicate the values corresponding to the weighted images in (a). This mouse presents an edema in the cortex (red rectangle). (c) Nonparametric parameters: time-to-peak (TTP), signal enhancement (∆S) and area-under-curve (AUC_T).