The mechanism of blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) lies in the detection of blood-induced magnetic field disturbance during brain activity. A magnetic dipole induces a magnetic field in 3D space, which is represented by a 3D kernel that shows orientation-dependent decay in space (with a radial distant decay factor of 1/r3), bipolar values, and revolution symmetry. By representing the intravascular blood space with a pack of magnetic dipoles, we can use the 3D kernel to calculate the BOLD fieldmap by a 3D convolution. In our implementation, a vasculature-laden voxel of interest (VOI) is represented by a matrix at a grid resolution(~1micron), and the intravascular space is filled with macroscopic blood magnetic dipoles (each is defined for a matrix element sitting in the blood space). Based on the magnetic dipole model of blood magnetization and the convolution algorithm, we calculate the effect of exterior vasculature (from nearest neighborhood as well as from farther or remote surrounding) on the BOLD fieldmap at the VOI. Our results show that only vessels at the VOI boundary region impose a noticeable influence, and this effect increases slightly with vessel size. The effect of remote vasculature (sitting in voxels outside the nearest neighborhood) is ignorable. We also discuss the case of asymmetrical surroundings.