Time of arrival (TOA) of a bolus of contrast agent to the tissue voxel is a reference time point critical for the Early Time Points Perfusion Imaging Method (ET) to make relative cerebral blood flow (rCBF) maps. Due to the low contrast to noise (CNR) condition at TOA, other useful reference time points known as relative time of arrival data points (rTOA) are investigated. Candidate rTOA's include the time to reach the maximum derivative, the maximum second derivative, and the maximum fractional derivative. Each rTOA retains the same relative time distance from TOA for all tissue flow levels provided that ET's basic assumption is met, namely, no contrast agent has a chance to leave the tissue before the time of rTOA. The ET's framework insures that rCBF estimates by different orders of the derivative are theoretically equivalent to each other and monkey perfusion imaging results supported the theory. In rCBF estimation, maximum values of higher order fractional derivatives may be used to replace the maximum derivative which runs a higher risk of violating ET's assumption. Using the maximum values of the derivative of orders ranging from 1 to 1.5 to 2, estimated rCBF results were found to demonstrate a gray-white matter ratio of approximately 3, a number consistent with flow ratio reported in the literature.