Conscious awareness of the world fluctuates, either through variation in the quality with which we perceive the environment, or, when attention switches to information generated using imagination rather than the external environment. Our study combined individual differences in experience sampling, psychophysical reports of perception, and neuroimaging descriptions of structural connectivity, to better understand these changes in conscious awareness. In particular, we (a) examined if aspects of ongoing thought, as measured by multi-dimensional experience sampling during a sustained attention task, are associated with the white matter fibre organization of the cortex as reflected by their relative degree of anisotropic diffusion, and (b) whether these neuro-cognitive descriptions of ongoing experience are related to a more constrained measure of visual consciousness provided by the analysis of bistable perception during binocular rivalry. Individuals with greater fractional anisotropy (FA) in right hemisphere white matter regions involving the inferior fronto-occipital fasciculus, the superior longitudinal fasciculus and the cortico-spinal tract, described their ongoing thoughts as lacking external details. Subsequent analysis indicated that the combination of low FA in these right hemisphere regions, with reports of high level external details, was associated with the shortest periods of dominance during binocular rivalry. Since variation in binocular rivalry reflects differences between bottom-up and top-down influences on vision, our study suggests that reports of ongoing thoughts with vivid external details may occur when conscious precedence is given to bottom-up representation of perceptual information and that this may partly be rooted in the white matter fibre organization of the cortex.Word count: 248.