Computational anatomy studies typically use T1-weighted magnetic resonance imaging contrast to look at local differences in cortical thickness or grey matter volume across time or subjects. This type of analysis is a powerful and non-invasive tool to probe anatomical changes associated with neurodevelopment, aging, disease or experience-induced plasticity. However, these comparisons could suffer from biases arising from vascular and metabolic subject- or time-dependent differences. Differences in blood flow and volume could be caused by vasodilation or differences in vascular density, and result in a larger signal contribution of the blood compartment within grey matter voxels. Metabolic changes could lead to differences in dissolved oxygen in brain tissue, leading to T1 shortening. Here, we analyze T1 maps and T1-weighted images acquired during different breathing conditions (ambient air, hypercapnia (increased CO2) and hyperoxia (increased O2)) to evaluate the effect size that can be expected from changes in blood flow, volume and dissolved O2 concentration in computational anatomy studies. Results show that increased blood volume from vasodilation during hypercapnia is associated with an overestimation of cortical thickness (1.85%) and grey matter volume (3.32%), and that both changes in O2 concentration and blood volume lead to changes in the T1 value of tissue. These results should be taken into consideration when interpreting existing morphometry studies and in future study design. Furthermore, this study highlights the overlap in structural and physiological MRI, which are conventionally interpreted as two independent modalities.