Bulletin of Mathematical Biology

, Volume 73, Issue 11, pp 2731–2747

From Blood Oxygenation Level Dependent (BOLD) Signals to Brain Temperature Maps

Original Article

DOI: 10.1007/s11538-011-9645-5

Cite this article as:
Sotero, R.C. & Iturria-Medina, Y. Bull Math Biol (2011) 73: 2731. doi:10.1007/s11538-011-9645-5


A theoretical framework is presented for converting Blood Oxygenation Level Dependent (BOLD) images to brain 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 bioheat equation describing the rate of temperature changes in the brain, we obtain a nonautonomous ordinary differential equation that depends on the BOLD response, which is solved numerically for each brain voxel. Temperature maps obtained from a real BOLD dataset registered in an attention to visual motion experiment were calculated, obtaining temperature variations in the range: (−0.15, 0.1) which is consistent with experimental results. The statistical analysis revealed that significant temperature activations have a similar distribution pattern than BOLD activations. An interesting difference was the activation of the precuneus in temperature maps, a region involved in visuospatial processing, an effect that was not observed on BOLD maps. Furthermore, temperature maps were more localized to gray matter regions than the original BOLD maps, showing less activated voxels in white matter and cerebrospinal fluid.


BOLD signalBrain temperatureCerebral blood flowOxygen consumptionLambert W function

Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  1. 1.National Bioinformatics Center (BIOINFO), InSTECHavanaCuba
  2. 2.Montreal Neurological Institute, Brain Imaging Centre, Depts. of Neurology and Neurosurgery and Biomedical EngineeringMcGill UniversityMontrealCanada
  3. 3.Cuban Neuroscience CenterHavanaCuba