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White matter tract integrity (WMTI) can characterize brain microstructure in areas with highly aligned fiber bundles. Several WMTI biomarkers have now been validated against microscopy and provided promising results in studies of brain development and aging, and in a number of brain disorders. Currently, WMTI is mostly used in dedicated animal studies and clinical studies of slowly progressing diseases but has not yet emerged as a routine clinical tool. To this end, a less data intensive experimental method would be beneficial by enabling high resolution validation studies, and ease clinical applications by speeding up data acquisition compared to typical diffusion kurtosis imaging (DKI) protocols utilized as part of WMTI imaging. Here, we evaluate WMTI based on recently introduced axially symmetric DKI which has lower data demand than conventional DKI. We compare WMTI parameters derived from conventional DKI to those calculated analytically from axially symmetric DKI. We employ numerical simulations, as well as data from fixed rat spinal cord (1) and in vivo human (3) and rat brain (4). Our analysis shows that analytical WMTI based on axially symmetric DKI with sparse data sets (19 images) produces WMTI metrics that correlate strongly with estimates based on traditional DKI data sets (60 images or more). We demonstrate the preclinical potential of the proposed WMTI technique in in vivo rat brain (300 {\mu}m isotropic resolution with whole brain coverage). WMTI parameter estimates are subject to a duality leading to two solution branches dependent on a sign choice which is currently debated. Results from both of these branches are presented and discussed throughout our analysis. The proposed fast WMTI approach may be useful for preclinical research and e.g. clinical evaluation of patients with traumatic white matter injuries or symptoms of neurovascular or neuroinflammatory disorders., Comment: 41 pages, 8 figures, 1 table, 3 supplementary figures