Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.