Non-calibrated Equations for Quantification of Local fMRI Signal Changes with Hemodynamic Oxygen Metabolism (CBF and CMRO2)

Conventional CO₂ calibration for quantification functional changes of CMRO2 may be sensitive to the experimental conditions. We derive a nonlinear coupling relationship of CMRO2 and CBF as simple as (CMRO2/CMRO2₀)=(CBF/CBF₀)^0.25, when α=0.38, β=1.5, where M-value from calibration is not necessary, from Davis model. Nonlinearity between percentage changes of δ(CMRO2)=CMRO2/CMRO2₀-1 and δ(CBF)=CBF/CBF₀-1, in our equation is shown comparable to two classical models. Calculations of δ(CMRO2), based on our equation, are approximately consistent with previous results from both PET and MRI. Additionally, we prove that when desired, M can be measured directly from BOLD and CBF functional changes instead of CO₂ calibration.