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.