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Cerebral ATP metabolic rates and fluxes can be measured in vivo using 31P MRS in combination with magnetization transfer (MT) techniques, such as saturation transfer (ST) 2, inversion transfer 9, and two‐dimensional chemical exchange spectroscopy 11. The ST method is the most commonly used in vivo, due to its high efficiency and methodological simplicity 12. The tightly‐coupled ATPase and CK reactions can be modeled as a three‐pool 31P‐spin chemical exchange kinetic network involving ATP, PCr, and Pi 2:JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM1/v/2017-12-21T175206Z/r/image-png where k1, k–1, k2, k–2 are the forward and reverse reaction rates; JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM2/v/2017-12-21T175206Z/r/image-png , JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM3/v/2017-12-21T175206Z/r/image-png , JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM4/v/2017-12-21T175206Z/r/image-png , JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM5/v/2017-12-21T175206Z/r/image-png are the associated fluxes of CK and ATPase reactions; and [ATP], [PCr] and [Pi] are the concentrations of the three phosphate metabolites. Based on this model, the 31P MRS‐observable changes in the PCr, ATP, and Pi magnetizations ( JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM6/v/2017-12-21T175206Z/r/image-png ) with saturation time (tsat) can be described by the modified Bloch equations 13. For the progressive saturation of γ‐ATP (with boundary condition of JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM7/v/2017-12-21T175206Z/r/image-png at all saturation times), these equations can be simplified to: JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM8/v/2017-12-21T175206Z/r/image-pngJOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM9/v/2017-12-21T175206Z/r/image-png where the apparent relaxation rates and longitudinal relaxation times are given by JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM10/v/2017-12-21T175206Z/r/image-pngJOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM11/v/2017-12-21T175206Z/r/image-png , JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM12/v/2017-12-21T175206Z/r/image-png are the intrinsic longitudinal relaxation times of PCr and Pi, respectively, corresponding to the relaxation rate in the absence of any exchange. In the steady‐state condition, with complete saturation of γ‐ATP, the Bloch equations can be further simplified with the boundary conditions of JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM13/v/2017-12-21T175206Z/r/image-png and JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM14/v/2017-12-21T175206Z/r/image-png to give: JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM15/v/2017-12-21T175206Z/r/image-pngJOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM16/v/2017-12-21T175206Z/r/image-png where JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM17/v/2017-12-21T175206Z/r/image-png and JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM18/v/2017-12-21T175206Z/r/image-png are the steady‐state magnetizations of PCr and Pi. Previous animal and human studies have shown that the intrinsic T1s of PCr and Pi are insensitive to changes in physiology 3. To the best of our knowledge, there are no previous reports of the values of the intrinsic T1s of PCr and Pi in the human brain at 3 T. Therefore, in this study, JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM19/v/2017-12-21T175206Z/r/image-png and JOURNAL/mrim/04.02/01445475-201801000-00003/math_3MM20/v/2017-12-21T175206Z/r/image-png values were measured at rest and were then assumed to be unchanged during activation.

The chemical shift between PCr and γ‐ATP is only ∼2.5 ppm, which means that it is difficult to saturate γ‐ATP without partially suppressing the PCr peak 16.