**BOLD fMRI Simulation**

Zikuan Chen and Vince Calhoun

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63313

#### **Abstract**

**Background:** Brain functional magnetic resonance imaging (fMRI) is sensitive to changes in blood oxygenation level dependent (BOLD) brain magnetic states. The fMRI scanner produces a complex-valued image, but the calculation of the original BOLD magnetic source is not a mathematically tractable problem. We conduct numeric simulations to understand the BOLD fMRI model.

**Methods:** A brain cortex volume of interest (VOI) is configured with vasculatures (vessels or beads). Brain activity results in a local vascular blood magnetic susceptibil‐ ity change in VOI (denoted by χ(**r**,*t*)), manifesting as a dynamic magnetic source for BOLD fMRI. The MRI scanner produces a timeseries of complex-valued images reflecting the dynamic source χ(**r**,*t*). A voxel BOLD fMRI signal is simulated by calculating the intravoxel spin precession dephasing signal, a 3D BOLD fMRI by a multivoxel image of voxel signals for a 3D χ source distribution, and a 4D BOLD fMRI by a timeseries of 3D multivoxel images. The simulation data are subject to pattern analysis and statistical parametric mapping.

**Results**: Both MR magnitude and phase signals (images) are different from a prede‐ fined χ source due to data transformations inherent in the MRI scanning process. The 3D BOLD fMRI simulation shows the spatial distortions between the χ source and the MR image. The 4D BOLD fMRI simulation shows that the reconstructed source map is different from the original image and also that the task-correlation-based functional mapping method is susceptible to noise.

**Conclusion**: BOLD fMRI simulation offers a means to understand the single-voxel MR magnitude and phase signals, 3D multivoxel images, and 4D functional movies for a predefined BOLD χ source with respect to various parameter settings. It also allows us to separate the intravascular/extravascular signals and numerically characterize spin diffusion effect. The 3D BOLD fMRI simulation shows the source-image mismatch, which motivates the benefits of χ source reconstruction by solving an inverse MRI problem. The 4D BOLD fMRI simulation shows the noise dependence of the taskcorrelated functional map extraction.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Keywords:** magnetic resonance imaging (MRI), blood oxygenation level dependence (BOLD), magnetic susceptibility source, dipole effect, voxelization, complex-valued magnetic resonance signal (image), intravoxel dephasing signal, multivoxel image, BOLD fMRI simulation, task correlation
