Early time points perfusion imaging: theoretical analysis of correction factors for relative cerebral blood flow estimation given local arterial input function

If local arterial input function (AIF) could be identified, we present a theoretical approach to generate a correction factor based on local AIF for the estimation of relative cerebral blood flow (rCBF) under the framework of early time points perfusion imaging (ET). If C(t), the contrast agent bolus concentration signal time course, is used for rCBF estimation in ET, the correction factor for C(t) is the integral of its local AIF. The recipe to apply the correction factor is to divide C(t) by the integral of its local AIF to obtain the correct rCBF. By similar analysis, the correction factor for the maximum derivative (MD1) of C(t) is the maximum signal of AIF and the correction factor for the maximum second derivative (MD2) of C(t) is the maximum derivative of AIF. In the specific case of using normalized gamma-variate function as a model for AIF, the correction factor for C(t) (but not for MD1) at the time to reach the maximum derivative is relatively insensitive to the shape of the local AIF.