Journal of Magnetic Resonance 149, 282–286 (2001) doi:10.1006/jmre.2001.2286, available online at http://www.idealibrary.com on On Neglecting Chemical Exchange When Correcting in Vivo 31 P MRS Data for Partial Saturation: Commentary on: “Pitfalls in the Measurement of Metabolite Concentrations Using the One-Pulse Experiment in in Vivo NMR” 1 Ronald Ouwerkerk 2 and Paul A. Bottomley Division of MR Research, Department of Radiology, Johns Hopkins University, School of Medicine, Baltimore, Maryland 21287 Received December 8, 2000; revised January 3, 2001 This article replies to Spencer et al. (J. Magn. Reson. 149, 251– 257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo 31 P NMR, we employ differential anal- ysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis con- tradicts Spencer et al.’s broad claim that chemical exchange results in a strong dependence of saturation factors upon M 0 ’s and T 1 and exchange parameters. For Spencer et al.’s example of a dynamic 31 P NMR experiment in which phosphocreatine varies 20-fold, we show that ourstrategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates. C  2001 Academic Press In an article in this issue (1), Spencer et al. misrepresent our conclusion that chemical exchange has a negligible effect on partial saturation corrections made with saturation factors (2) by stating that it is based on the approximately monoexponen- tial dependence of the saturation factor (SF) on the repetition time. Our conclusions (2) are in fact based on the small errors in the SFs found over a wide range of experimental conditions input to the same equations used by Spencer et al. (3–5). More- over, Spencer et al.’s broad claim that “saturation factors in the presence of chemical exchange are strongly dependent upon all M 0 ’s, T 1 and chemical exchange parameters” (1) is not substan- tiated and is not, in general, valid. In order to illustrate their case, Spencer et al. limit their analy- sis to the “dynamic” case where creatine kinase (CK) metabolite concentrations vary during the experiment and where informa- tion about the saturation factors is incomplete (1), a situation which Binzoni and Cerretelli (6) and ourselves (2) had already addressed. 1 Supported by NIH Grants R01 HL56882-01, R01-HL61912-01, and R21 HL62332-01. 2 To whom correspondence should be addressed at Department of Radiology, Johns Hopkins University, JHOC Room 4250, 601 N. Caroline Street, Baltimore, MD 21287-0845. Fax: (410) 614-1977. E-mail: rouwerke@mri.jhu.edu. In this response, we first demonstrate, using differential anal- ysis, the existence of a broad range of operating conditions over which the saturation factors are both minimally sensitive to M 0 ’s and exchange rates, and which yield near-optimum phosphorus ( 31 P) SNR/unit time. Second, we show that the application of our interpolation strategy (2) to the specific dynamic experiment posed in Spencer et al.’s commentary (1) reduces errors in sat- uration corrections for PCr, ATP, and the ratios thereof to less than 2%, although the error in quantities involving P i is higher (≤13%). Finally, we show that a fully relaxed experiment could accomplish Spencer et al.’s dynamic experiment with <1% er- rors in all metabolite ratios, with only a 40% increase in the acquisition time required to achieve the same SNR as that pro- vided by the optimum Ernst angle condition. Sensitivity of SFs to k’s and M 0 ’s. To address Spencer et al.’s broad claim directly, the sensitivity of SF to the k ’s and M 0 ’s in the three-site exchange model described in their Refs. (2, 5) was computed by expanding the derivative of SF in terms of its partial derivatives with respect to the various independent variables, as routinely used for determining error propagation (7). The root mean square fractional uncertainty in SF for species A is δSF( A) SF( A) = 1 SF( A)  ∂ SF ∂ M 0A δ M 0A  2 +  ∂ SF ∂ M 0A δ M 0A  2 +  ∂ SF ∂ M 0C δ M 0C  2 +  ∂ SF ∂ k AB δk AB  2 +  ∂ SF ∂ k BC δk BC  2  1/2 [1] = [SF( M 0A ) 2 + SF( M 0B ) 2 + SF( M 0C ) 2 + SF(k AB ) 2 + SF(k BC ) 2 ] 1/2 , [2] where δSF,δ M 0 ,δk , etc., are the variations standard deviations (SDs) in the corresponding variables, and the SF are fractional errors in each of the composite variables as defined by the re- spective terms in Eq. [1]. Similar expressions can be written for 282 1090-7807/01 $35.00 Copyright C  2001 by Academic Press All rights of reproduction in any form reserved.