We propose a novel method to simultaneously trace brain white matter (WM) fascicles and estimate WM microstructure characteristics. Recent advancements in diffusion-weighted imaging (DWI) allow multi-shell acquisitions with b-values of up to 10,000 s/mm2 in human subjects, enabling the measurement of the ensemble average propagator (EAP) at distances as short as 10 μm. Coupled with continuous models of the full 3D DWI signal and the EAP such as Mean Apparent Propagator (MAP) MRI, these acquisition schemes provide unparalleled means to probe the WM tissue in vivo. Presently, there are two complementary limitations in tractography and microstructure measurement techniques. Tractography techniques are based on models of the DWI signal geometry without taking specific hypotheses of the WM structure. This hinders the tracing of fascicles through certain WM areas with complex organization such as branching, crossing, merging, and bottlenecks that are indistinguishable using the orientation-only part of the DWI signal. Microstructure measuring techniques, such as AxCaliber, require the direction of the axons within the probed tissue before the acquisition as well as the tissue to be highly organized. Our contributions are twofold. First, we extend the theoretical DWI models proposed by Callaghan et al. to characterize the distribution of axonal calibers within the probed tissue taking advantage of the MAP-MRI model. Second, we develop a simultaneous tractography and axonal caliber distribution algorithm based on the hypothesis that axonal caliber distribution varies smoothly along a WM fascicle. To validate our model we test it on insilico phantoms and on the HCP dataset.