A simulation tool for dynamic contrast enhanced MRI

Abstract

The quantification of bolus-tracking MRI techniques remains challenging. The acquisition usually relies on one contrast and the analysis on a simplified model of the various phenomena that arise within a voxel, leading to inaccurate perfusion estimates. To evaluate how simplifications in the interstitial model impact perfusion estimates, we propose a numerical tool to simulate the MR signal provided by a dynamic contrast enhanced (DCE) MRI experiment. Our model encompasses the intrinsic R1 and R2 relaxations, the magnetic field perturbations induced by susceptibility interfaces (vessels and cells), the diffusion of the water protons, the blood flow, the permeability of the vessel wall to the the contrast agent (CA) and the constrained diffusion of the CA within the voxel. The blood compartment is modeled as a uniform compartment. The different blocks of the simulation are validated and compared to classical models. The impact of the CA diffusivity on the permeability and blood volume estimates is evaluated. Simulations demonstrate that the CA diffusivity slightly impacts the permeability estimates (< 5% for classical blood flow and CA diffusion). The effect of long echo times is investigated. Simulations show that DCE-MRI performed with an echo time TE = 5 ms may already lead to significant underestimation of the blood volume (up to 30% lower for brain tumor permeability values). The potential and the versatility of the proposed implementation are evaluated by running the simulation with realistic vascular geometry obtained from two photons microscopy and with impermeable cells in the extravascular environment. In conclusion, the proposed simulation tool describes DCE-MRI experiments and may be used to evaluate and optimize acquisition and processing strategies.

Figure 1. Algorithm sketch of the simulation.

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. Block (a) initializes the geometry. Block (b) describes the CA behavior over time. Block (c) estimates the MR signal.

Figure 2. Illustration of the weighting lattices and .

(a) Zoom in the diffusion weighting lattice . The diffusion appears restricted near the membranes. (b) Illustration of the geometry lattices. In red, the vessel, in grey the cells. (c) Zoom in the surface weighting lattice that computes the number of contact exchange interfaces between a vessel and its periphery.

Figure 3. Illustration of the evolution of the concentration of CA.

CA concentration in the vessels (a) and the corresponding MR signal (b). is simulated for 2 echo times: (black) and (grey). The change in CA concentration , represented by the lattices, and in the magnetic field perturbations are presented at five times points labeled (1) to (5). For this longer echo time, one can observe the competition between the susceptibility effect which decreases the signal (point (2)) and the enhancement produced by the relaxation effect of the CA which extravasates into the tissue (points (3) to (5)). At the last simulation time point () (5), is lower than (not shown) and the concentration in the extravascular space begins to decrease. Note the log scale for introduced for sake of clarity.

Figure 4. Comparison between MC approach and kernel based approach for modeling the CA diffusion.

(a) Geometry used, . The white cross indicates where the CA was initially placed. (b) Spatial correlation plot between obtained via the convolution with a diffusion kernel and obtained with the MC approach after normalization. (c–d) Final maps of CA concentration, , for the MC approach () and the kernel approach (), respectively (smoothed and undersampled to a lattice).

Figure 5. Concentration profiles for various blood flows and permeabilities to CA.

(a) Concentration of CA in the vascular compartment, , as a function of time for impermeable vessel wall () and different blood flow values. (b) Time course of and for and different blood flow values. is plotted every 20s to ease readability. The plain black lines represent the fit obtained with the Tofts model (Eq.[14]). Note the difference in scale for the arterial input function, . (c) Plots of the estimated permeability coefficient and the input value for different blood flows and permeabilities to CA. A linear fit is obtained in the case of high flow (). For lower blood flows, the model failed to distinguish the flow from the permeability and is underestimated.

Figure 6. Impact of various magnetic field computations on the FID simulation.

(a) 1 vessel in 1 orientation (b) N vessels in 1 orientation (c) N vessels in 3 orientations (d) N vessels in 3D. The vessel arrangement is presented in 3D and for display, the magnetic field perturbation is only presented on each face of the cube but is computed in 3D. (e) Normalized FID for approaches (a)–(d) (averaged across the geometries for approaches (b–d)).

Figure 7. Vessel radius dependence of and .

Parameters values are , ADC = , and . across 10 geometries. The data presented here are in excellent agreement with those reported in .

Figure 8. Change in the MR signal for different and values.

(a) S(t) at for 3 values: , and with . (b) S(t) at for 7 values: , , , , , and with .

Figure 9. Error on the permeability estimate.

When modeling the outputs of blocks b and c with Eq.[14] for various and values: (a) Error on when modeling . (b) Error on when modeling S(t) for with Eqs.[16–17].

Figure 10. Impact of the echo time on the estimation of and .

(a) Evolution of the error on the parameter estimated from at different for various and various . (b) Evolution of the parameter estimated from at different , for various and for or .

Figure 11. Example of the simulation with a vascular geometry extracted from in vivo microvascular microscopy.

The simulation parameters are and . Concentration map (a) and magnetic field perturbation (b) are represented at the last simulation time point (). (c) Concentration profiles derived from the simulated MR signal using Eqs.[16–17] at 3 different . The black lines correspond to the fit obtained with the Toft model. Plane size .

Figure 12. Example of the simulation with impermeable cells placed in the extravascular space.

The simulation parameters are: and . At (a) Concentration map with vessels in black and cells in grey. (b) Magnetic field perturbation . (c) Concentration profiles derived from the simulated MR signal and using Eqs.[16–17] at 3 different . The black lines correspond to the fit obtained with the Toft model. Note the fluctuations in the concentration profiles obtained at long . This can be ascribed to the additional magnetic field perturbations induced by the cell interfaces which balance the signal enhancement. Plane size .