Calibrated functional MRI was developed to tease apart the hemodynamic and metabolic contributions to the blood oxygenation level-dependent (BOLD) signal using simultaneous measurements of the BOLD signal and cerebral blood flow. While calibrated fMRI has substantially improved our ability to image and understand aspects of brain physiology, it has not been widely adopted due to the need for specialized gas delivery equipment and biophysical confounds associated with the calibration measurements. One such confound is the magnetic susceptibility of dissolved oxygen, which, like deoxyhemoglobin, is paramagnetic. In this talk, I will present work on modelling and measuring the susceptibility and relaxation rates of dissolved oxygen in blood and what impact they have on the hyperoxic BOLD signal and calibration. I will also discuss recent efforts towards improving the accuracy of gas-free BOLD calibration. This work could greatly increase the appeal of calibrated fMRI by eliminating the gas challenge completely. In all, I hope these studies underscore the role that analytical modelling and simulations can play in improving our understanding of the biophysics of the BOLD signal and in guiding imaging strategies to probe brain physiology.