The human brain undergoes age-related microstructural alterations across the lifespan. Soma and Neurite Density Imaging (SANDI), a novel biophysical model of diffusion MRI, provides estimates of cell body (soma) radius and density, and neurite density in gray matter. The goal of this cross-sectional study was to assess the sensitivity of high-gradient diffusion MRI toward age-related alterations in cortical microstructure across the adult lifespan using SANDI. Seventy-two cognitively unimpaired healthy subjects (ages 19-85 years; 40 females) were scanned on the 3T Connectome MRI scanner with a maximum gradient strength of 300mT/m using a multi-shell diffusion MRI protocol incorporating 8 b-values and diffusion time of 19 ms. Intra-soma signal fraction obtained from SANDI model-fitting to the data was strongly correlated with age in all major cortical lobes (r = -0.69 to -0.60, FDR-p < 0.001). Intra-soma signal fraction (r = 0.48-0.63, FDR-p < 0.001) and soma radius (r = 0.28-0.40, FDR-p < 0.04) were significantly correlated with cortical volume in the prefrontal cortex, frontal, parietal, and temporal lobes. The strength of the relationship between SANDI metrics and age was greater than or comparable to the relationship between cortical volume and age across the cortical regions, particularly in the occipital lobe and anterior cingulate gyrus. In contrast to the SANDI metrics, all associations between diffusion tensor imaging (DTI) and diffusion kurtosis imaging metrics and age were low to moderate. These results suggest that high-gradient diffusion MRI may be more sensitive to underlying substrates of neurodegeneration in the aging brain than DTI and traditional macroscopic measures of neurodegeneration such as cortical volume and thickness.