The traumatic brain injury (TBI) presents several challenges to a mechanician. First, there is a need to translate the MRI information on the human head-brain system into a composite model with heterogeneous material properties (scalp, skull, CSF, white and gray matter). Given the MRI with one cubic milimeter voxel mesh, we construct a 3D finite element (FE) model. To validate this model, a previous cadaver experiment of frontal impact is simulated. The model is run under either of two extreme assumptions concerning the head-neck junction - either free or fixed - and the experimental measurements are well bounded by the computed pressures from the two boundary conditions. In both cases the impact gives rise not only to a fast pressure wave but also to a slow and spherically convergent shear stress wave, which is potentially more damaging to brain tissues. Such heretofore unknown wave patterns are also discovered in other head impacts. However, this rather conventional continuum-computational mechanics approach has to be contrasted with the random fractal geometry of brain. Given the material spatial randomness, the separation of scales does not hold. Here we note that the human brain surface has a fractal dimension of about 2.7-2.8, while the entire cardiovascular system has a fractal structure, and so does the pulmonary system. A possible way to deal with these challenges is to adapt a recently begun extension of continuum mechanics of fractal porous media which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution length scale R. That theory is based on a dimensional regularization, in which D is also the order of fractional integrals employed to state global balance laws. In effect, the governing equations are cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing coefficients involving D, d and R. This procedure allows a specification of geometry configuration of continua by 'fractal metric' coefficients, on which the continuum mechanics is subsequently constructed, with micropolar effects arising naturally. While all the derived relations depend explicitly on D, d and R, upon setting D=3 and d=2, they reduce to conventional forms of governing equations for continuous media with Euclidean geometries. Our formulation is based on a product measure, making it capable of grasping local material anisotropy, and assuring consistency of the mechanical approach to continuum mecahnics with that based on energy principles.