Vascular MRF

Christen et al. have shown the possibility of applying MRF to directly quantify BVf, mean vessel radius and StO2 [147]. The authors called this framework vascular magnetic resonance fingerprinting. We propose to reproduce the previous figure 2.25 for vascular MRF in figure2.26 in order to illustrate similarities and differences.

2.4.2.1 Acquisition sequence

In this work, the full MGEFIDSE signal samples were exploited compared to the classic CEF approach introduced in section2.3.4, which only used the samples before the 180°

RF pulse and the spin echo sample. Authors proposed to use the ratio of the pre- and post-USPIO injection MGEFIDSE signal evolutions (section 2.3.4) as the fingerprint, which reduced the effect of B0 inhomogeneities and T2’s effect on signals (figure 2.26A).

For the moment, no other sequences have been used in vascular MRF.

The MRF implementation to vascular signals required more sophisticated simulation tools than Bloch’s equations that are used for relaxation times related works.

2.4.2.2 Simulations

Using Bloch’s equations as a simulation model, the magnetization is homogeneous within the voxel since the voxel itself is characterized by a single T1 and a single T2 values, and placed into a constant magnetic field (figure2.27(a)). For vascular MRF applications, the voxel needs to be segmented into a vascular compartment and an extravascular compartment, which results in an inhomogeneous magnetization through the voxel

Figure 2.26 –Illustration of the vascular MRF method, inspired by [138] and composed with images from [147].

The flowchart shows an overview of the vascular MRF framework as used for MGEFIDSE pre-and post-USPIO contrast agent acquisitions. (A) MGEFIDSE sequence. (B) Three images acquired in different TE and pre/post-USPIO injection. (C) Typical virtual voxel used for simulation of the dictionary signals. (D) Pattern matching of the voxel fingerprint with the closest entry in the dictionary, which allows to retrieve the tissue features represented by that voxel. (E) Normalized intensity variation of two ROI across the images. (F) Parameter maps obtained by repeating the matching process for each voxel.

(figure2.27(b)). The complexity of the task calls for more sophisticated simulation tools than those based on Bloch’s equations only.

Such a tool has been developed by Pannetier et al. [152]. This particularly complete tool accounts for the intrinsic relaxations, the magnetic field perturbations induced by susceptibility interfaces (vessels), the diffusion of the water protons and the compartmen-talization of the contrast agent within the vessels (figure2.27(c)). The resulting model can be used to produce signals considering a large number of input parameters. Some of the input parameters of the model are reported in figure2.27(c). This simulation tool opens the possibility of simultaneously quantifying T1, T2, ADC, BVf, VSI and StO2

but this would probably require the optimization of a new sequence sensitive to all these parameters.

(a)

(b)

(c)

Figure 2.27 – Sketch of the simulation algorithm, adapted from [152].

(a) Typical magnetization in a pixel using Bloch’s equations. (b) Typical magnetization in a pixel using the vascular simulation tool. (c) Sketch of the simulation algorithm. In (c), only the most important parameters have been represented. Data on the left of the gray boxes are inputs to the model. Data on the right are outputs of the simulation. The simulation is organized in three blocks. Geometry block initializes the geometry. Physiology block describes the contrast agent behavior over time. NMR block estimates the MR signal.

In this version of vascular MRF, a dictionary was designed based on relatively simplistic models for blood vessels and oxygen distribution (figure 2.26C). Specifically, the authors modeled the blood vessels as straight cylinders, with no preferential directions, and with uniform oxygenation across the network, similar to those used in classic approach’s mathematical models. In addition, the image volume is reduced to a 2-dimensional plane.

A major improvement on vascular MRF can be to take greater heterogeneity into account to increase the vascular characterization in a 3-dimensional volume. This process would

certainly even overcome the proposed vascular MRF implementation as it has been shown by [153]. In this work, authors used real mouse angiograms and physiological values as the substrate for the MR simulations. However, the generation of a dictionary for each mouse angiogram took 70 hours on a computer cluster [153].

The consequence of using this simulation tool is that the simulation times are considerably increased compared to Bloch simulation. For vascular MRF, authors report that a single signal simulation took about 2.5 seconds on a desktop computer and the largest dictionary of the study, composed of about 1 150 000 entries, was generated on a 30-node cluster in about 24 hours [154] (about 8-9 days with a 4-core computer).

Compared to the CPU implementation of the PnP-MRF tool on a desktop computer, it took about 75 times longer on a cluster. The processing of this amount of data is already almost impossible on a desktop computer and the addition of a single parameter would make the study impossible even on high-performance hardware.

At this point, we understand that the simulation constraints are very different between the two MRF applications. For simple simulations, the stakes of standard MRF only consist in managing the large volume of data simulated during quantification (i.e. time and memory), whereas in vascular MRF, the simulation time is already a concern.

2.4.2.3 Quantification

Concerning quantification, the procedure remains the same as the one of standard MRF.

The parameter values that generate the vascular signal that minimizes the equation (2.32) is used as estimate (figure 2.26D).

While it has not been clearly shown that the vascular MRF method can improve estimates on BVf and mean radius, this is mainly due to the lack of a validation solution.

It is most likely that the use of all signal samples should provide this improvement. What is certain is that the method allows, in addition to BVf and mean radius, the quantification of StO₂, which is achieved by acquiring other sequences using CEF method. This results in a reduction of the scan time. The main limit to be addressed to extend the vascular MRF and quantify more parameters and/or acquire longer sequences, is the extensive simulation times. An acceleration of the simulation tool can be considered (out of the scope of this work) but one could also investigate the optimization of the reconstruction methods in order to reduce the need for dictionary entries, i.e. for simulations.