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Effect of magnetization transfer on the measurement of cerebral blood flow using steady‐state arterial spin tagging approaches: A theoretical investigation

A simple four‐compartment model for magnetization transfer was used to obtain theoretical expressions for the relationship between regional cerebral blood flow and ΔM, the change in longitudinal magnetization of brain water spins when arterial water spins are perturbed. The theoretical relationship can be written in two forms, depending on the approach used to normalize ΔM. Using the first approach, the calculation of cerebral blood flow requires a knowledge of R1 (ω1, Δω), the longitudinal relaxation rate observed in the presence of continuous off‐resonance RF irradiation. Using the second approach, the calculation of cerebral blood flow requires a knowledge of ℛ1(ω1, Δω), where ℛ1(ω1, Δω) is given by the product of R1(ω1, Δω) and the fractional steady‐state longitudinal water magnetization in the presence of off‐resonance RF irradiation. If the off‐resonance RF irradiation used for arterial tagging does not produce appreciable magnetization transfer effects, ℛ1, (ω1, Δω) can be approximated by the longitudinal relaxation rate measured in the absence of offresonance RF irradiation, R1obs. Theoretical expressions obtained by using the four‐component model for magnetization transfer are compared with equivalent expressions obtained by using two‐compartment models.