We previously developed (CMRO2/CMRO20)=(CBF/CBF0)(1-α/β)(1-1/β)as special power relation (SPR) for brain activation. In this work, based on different perspective of SPR, we derive that functional activity induces general power relation (GPR) (CMRO2/CMRO20)=(CBF/CBF0)α/β. When α=0.38,β=1.5, both powers (SPR and GPR) are calculated to be 0.25,which is approximately equivalent to inverse of conventional coupling constant of 4. By equalizing two powers, the relationship of α and β parameters can be established. We also show that any coupling pairs between changes of CMRO2,CBF,CBV and OEF can be reduced into power laws. Finally, we propose the power law for quantification CMRO2 changes during CO2 calibration.
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