**Author details**

dephasing signal calculation by a linear approximation. The fast Bloch simulation method is good for MR phase image simulation, but not good for MR magnitude simulation due to an accentuated edge effect. Moreover, the IV and EV signal separation and the diffusion simula‐

We conclude our numerical BOLD fMRI simulations by the following findings (albeit quali‐

**1.** Both the MR magnitude and the phase images are spatially different from the predefined magnetic susceptibility distribution. This image-source distortion is due to the inevitable

**2.** By numerical simulation, we can separate the intravascular (IV) signal from the extrava‐ scular (EV) signal in a voxel signal. The IV signal is much stronger than the EV signal as a result of a BOLD χ change. However, the drastic IV signal evolution is usually greatly suppressed in a voxel signal by a small proportion of blood volume fraction (*bfrac* ≈ [0.02,

**3.** As voxel size decreases, the voxel signals evolve more drastically and turbulently inside

**4.** The proton diffusion effect due to nonstationary water molecules in brain tissues incurs more MR magnitude signal decays in a low field than in a high field. In comparison, the

**5.** The numerical simulation on 4D BOLD fMRI for task-evoked functional mapping shows that the functional activity extraction by a task correlation technique is sensitive to data

Overall, the numerical simulations on BOLD fMRI allow us to look into the insights of a singlevoxel signal, a multivoxel image, and a video of brain functional BOLD activity with respect to various parameter settings. The finding in source-image mismatch inspires us to seek for the underlying magnetic source of BOLD fMRI for more accurate brain functional mapping. The finding in the noise sensitiveness of task-correlated fmap raises a caveat to the correlation-

1D: one dimensional; 2D: two dimensional; 3D: three dimensional (spatial); 4D: four dimen‐ sional (spatiotemporal); BOLD: blood oxygenation level dependent; MR: magnetic resonance; MRI: magnetic resonance imaging; fMRI: functional MRI; FFT: fast Fourier transform; NAB: neuroactive blob; VOI: volume of interest; IV: intravascular; EV: extravascular; gridel: grid

tions are not implementable by the Bloch method.

24 Numerical Simulation - From Brain Imaging to Turbulent Flows

data transformations associated with MRI data.

proton diffusion has little effect on MR phase signals.

**5. Conclusion**

0.04]).

noise.

based functional mapping.

**Abbreviations:**

and around the large vessels.

tative):

Zikuan Chen1\* and Vince Calhoun1,2

\*Address all correspondence to: zchen@mrn.org

1 The Mind Research Network and LBERI, Albuquerque, New Mexico, USA

2 University of New Mexico, ECE Department, Albuquerque, New Mexico, USA
