Disclosed herein is an example method and system for characterizing a biological structure in terms of bio-markers derived from diffusion weighted magnetic resonance imaging (DWI) data of biologic material. A first set of DWI data may be obtained using a fixed diffusion encoding gradient and a plurality of diffusion time resolutions, and a second set of DWI data may be obtained using a fixed diffusion time resolution and a plurality of diffusion encoding gradients. The first and second sets may be analytically fit with a fractional power-law diffusion model parameterized by fractional exponents each uniquely corresponding to one of a plurality of bio-markers of the biologic material. Fractional exponents may be determined from the analytical fitting of the first and second sets of DWI data, and an image of the biologic material may be generated and displayed.