**3.2. Volumetric BOLD fMRI simulations**

60] ms) and for a range of field strength (*B*0=[1.5, 3, 4, 7, 9] Tesla). It is seen in **Figure 7** that the IV signal changes quickly with a long echo time. However, the drastic IV signal changes are greatly suppressed in the voxel signals by the dominant EV signals. In particular, the IV signal may be developed into phase wrapping phenomenon for a long echo time (see **Figure 7(b2)**). With the dominance of EV signals in a large voxel, a voxel signal remains as a linear phase

As a voxel size decreases, the voxel space contains less (or none) vessels, and there is less voxel average effect. In **Figure 8**, the four-level voxel subdivision and multiresolution voxel signal behaviors are demonstrated. At level =1, the parent voxel contains a clutter of vessels where the complex voxel signal appears as a short line-segment trajectory (with respect to *TE*). As the voxel is decomposed into an 8 × 8 × 8 array at level = 4, the subvoxel only contains a single vessel, and the voxel signal becomes turbulent due to the high field values for rapid Larmor

**Figure 8.** Multiresolution complex-valued voxel signals due to voxel subdivision. As the voxel size is dyadically re‐ duced, the smaller voxels contain less vessels, and the voxel signal may become turbulent at vessel boundary (Adapted

The numerical simulations on the diffusion effect on MR magnitude and phase are presented in **Figure 9** for a span of *TE* = [0, 60] ms with different field strengths (in terms of Δχ*B*0 = [0.1, 3] ppmT). The results show that the diffusion has more effect on low field magnitude than on high field magnitude [20]. Nevertheless, the diffusion has little effect on MR phase signals.

accrual with echo time (see **Figure 7(b3)**).

16 Numerical Simulation - From Brain Imaging to Turbulent Flows

*3.1.2. Multiresolution voxel signal behavior*

precession [14, 23].

from [23]).

*3.1.3. Diffusion effects on magnitude and phase signals*
