The goal of this paper is to develop a method for assessment of microstructural properties of the fornix in conventional (low resolution, single non-zero b-value) diffusion-weighted magnetic resonance imaging (DW-MRI) data. For this purpose, a bi-tensor model, comprising of an isotropic and an anisotropic diffusion compartment, was fitted to the diffusion-weighted images. Two subject-specific constraints were studied to solve the ill-posedness of the parameter estimation at a single (non-zero) b-value, namely by fixating the mean diffusivity (MD) or the axial diffusivity (AxD) of the anisotropic compartment. The bi-tensor statistics were compared to conventional diffusion statistics using simulated fiber bundles with different diameters and using fornix segmentations of 577 elderly subjects. Based on simulated fiber bundles, the anisotropy (FA) estimated by the bi-tensor model did not become biased with decreasing fiber bundle diameter, unlike conventional diffusion statistics such as FA and MD estimated by the single tensor model. In the population-based study, the bi-tensor tissue fraction decreased significantly with age, suggesting an increase of free water. The FA estimated by the bi-tensor model decreased with age, but this relation was not significant when the subject-specific values to which MD or AxD were constrained were added as covariates in the regression analysis. The distinction of an isotropic and an anisotropic diffusion compartment may allow a more sophisticated analysis of the fornix based on conventional DW-MRI data.