A theoretical framework is presented for converting Blood Oxygenation Level Dependent (BOLD) images to temperature maps, based on the idea that disproportional local changes in cerebral blood flow (CBF) as compared with cerebral metabolic rate of oxygen consumption (CMRO2) during functional brain activity, lead to both brain temperature changes and the BOLD effect. Using an oxygen limitation model and a BOLD signal model we obtain a transcendental equation relating CBF and CMRO2 changes with the corresponding BOLD signal, which is solved in terms of the Lambert W function. Inserting this result in the dynamic bio-heat equation describing the rate of temperature changes in the brain, we obtain a non autonomous ordinary differential equation that depends on the BOLD response, which is solved numerically for each brain voxel. In order to test the method, temperature maps obtained from a real BOLD dataset are calculated showing temperature variations in the range: (-0.15, 0.1) which is consistent with experimental results. The method could find potential clinical uses as it is an improvement over conventional methods which require invasive probes and can record only few locations simultaneously. Interestingly, the statistical analysis revealed that significant temperature variations are more localized than BOLD activations. This seems to exclude the use of temperature maps for mapping neuronal activity as areas where it is well known that electrical activity occurs (such as V5 bilaterally) are not activated in the obtained maps. But it also opens questions about the nature of the information processing and the underlying vascular network in visual areas that give rise to this result
