One contribution of 15 to a Theo Murphy meeting issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'. LG, 0000-0001-7202-5176Hypercapnic-calibrated fMRI allows the estimation of the relative changes in the cerebral metabolic rate of oxygen (rCMRO 2 ) from combined BOLD and arterial spin labelling measurements during a functional task, and promises to permit more quantitative analyses of brain activity patterns. The estimation relies on a macroscopic model of the BOLD effect that balances oxygen delivery and consumption to predict haemoglobin oxygenation and the BOLD signal. The accuracy of calibrated fMRI approaches has not been firmly established, which is limiting their broader adoption. We use our recently developed microscopic vascular anatomical network model in mice as a ground truth simulator to test the accuracy of macroscopic, lumped-parameter BOLD models. In particular, we investigate the original Davis model and a more recent heuristic simplification. We find that these macroscopic models are inaccurate using the originally defined parameters, but that the accuracy can be significantly improved by redefining the model parameters to take on new values. In particular, we find that the parameter a that relates cerebral blood-volume changes to cerebral blood-flow changes is significantly smaller than typically assumed and that the optimal value changes with magnetic field strength. The results are encouraging in that they support the use of simple BOLD models to quantify BOLD signals, but further work is needed to understand the physiological interpretation of the redefined model parameters. This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.