Recently, we demonstrated that vessel geometry is a significant determinant of susceptibility-induced contrast in MRI. This is especially relevant for susceptibility-contrast enhanced MRI of tumors with their characteristically abnormal vessel morphology. In order to better understand the biophysics of this contrast mechanism, it is of interest to model how various factors, including microvessel morphology contribute to the measured MR signal, and was the primary motivation for developing a novel computer modeling approach called the Finite Perturber Method (FPM). The FPM circumvents the limitations of traditional fixed-geometry approaches, and enables us to study susceptibility-induced contrast arising from arbitrary microvascular morphologies in 3D, such as those typically observed with brain tumor angiogenesis. Here we describe this new modeling methodology and some of its applications. The excellent agreement of the FPM with theory and the extant susceptibility modeling data, coupled with its computational efficiency demonstrates its potential to transform our understanding of the factors that engender susceptibility contrast in MRI.