This paper describes a method for removing 2H signal from extracranial lipids without affecting the brain lactate 2H signal based on 1H MRI-based spatial prior knowledge of brain and skull regions.  Magnetic field heterogeneity was accounted for by using surrogate B1 and B0 maps based on the 2H water shift and signal intensity respectively in each pixel across a 2D slice and by dividing the skull region into smaller compartments.  Although the lipid signal from subcutaneous lipid is very low this is enhanced by proximity to the receiver elements of the coil and the benefits of removing this signal are illustrated by the images shown in figure 3 D & E.  The method gave a 91% suppression of the skull lipid signal in the human brain images while retaining essentially 100% of the brain glucose and glutamate/glutamine signals albeit with greater standard deviations when compared to simulations.

The paper is well written and the presentation of the approach very clear.  Not clear to me that this will be widely adopted since the correction is small and only necessary for regions close to the skull (see figure 3 C).  Nevertheless, a useful method for 2H MRSI of the human brain.

General comments

The authors present a clever and practical application of the SLIM method for lipid suppression in DMI scans. The problem is well-motivated as the described artifact potentially impacts all DMI scans of the brain, and the proposed solution is well-justified. This work has immediate potential impact that is easily accessible to the DMI research community given its open-source implementation. The results on the in vivo  dataset are qualitatively impressive and highlight the promise of this technique. Simulations assessing the impact of B0 and B1 inhomogeneities are thorough and accompanied by a well-reasoned discussion. Some additional simulation results assessing SLIM’s ability to disambiguate lipids from Lac in superficial lesions could give further confidence that the proposed technique is robust across a variety of DMI scenarios.

Specific comments

1. Pages 5-6: The author describes the challenge of non-homogenous ROIs, and several techniques (magnetic field heterogeneity correction; smaller regions) to address this issue. However, subsequent experiments assign the entire non-skull brain a single ROI, despite the expected heterogeneity in the true metabolic DMI signal across brain tissue. This seems to violate a major assumption made by SLIM of compartment homogeneity, and is a deviation from previously cited works using SLIM (e.g. Dong & Hwang 2006 where fat is also subdivided into micro-compartments, but muscle is sub-divided into medium-sized compartments). While simulation results seem to indicate that this choice does not hinder algorithm performance, I think the paper may benefit from further explanation as this result is not necessarily intuitive given the provided explanation of SLIM and its assumptions. In particular, even though the skull-only compartments are subtracted leaving the brain spectra untouched, would the violation of the homogenous compartment assumption in the brain have any non-local effects on the skull quantification due to its spatial response function?

2.  Page 7, Line 6: Are scenarios considered where the pathological ROI position results in partial-voluming with skull lipids in the DMI dataset? This would seem to be the most challenging, as well as most clinically useful, application of SLIM, as it could directly disambiguate lipids from Lac and therefore impact clinical assessment of the Lac fraction of a lesion. Such an experiment would further give confidence in using SLIM in scenarios where a superficial lesion is present and partial-voluming with the skull is strongly suspected. For this reason, I think this scenario may be deserving of special consideration within the simulation analysis.

3. Page 7, Line 20: How are DMI datasets generated from the given simulated brain ROIs? In particular, what DMI metabolite values are assigned to each tissue type? And what noise level(s) are chosen?

4. Page 8, line 7: How are the anatomical MRIs spatially registered to the DMI datasets? Are the MR scans taken with the DMI coil in-place, or is the patient re-positioned between scans? I would anticipate that SLIM may be sensitive to registration errors, so I think this is worth mentioning.

5. Page 8, Line 16: The author states that “the brain ROI was not divided into tissue-specific compartments (e.g. GM, WM, CSF) as simulations (see Results) demonstrated that this step did not affect lipid suppression and metabolite retention”However, I do not see this experiment in the results section. While the Appendix shows metabolite retention  for each brain tissue type, I do not see the impact of sub-dividing the brain into distinct compartments on algorithm performance. I think this result would help shed light on Point 1.

6. Page 8, Line 27: The author states that “only pure brain pixels are considered for metabolite retention”.  In the case of partial-voluming of lipids with a glycolytic lesion, however, it would be interesting to see metabolite retention in this scenario as a special case (see Point 2).

7. Page 12, Line 8: Signal retention for Glc and Glx are shown, but signal retention for Lac would also be of interest (see Point 2, 6).

Technical correction

1. Page 4, Line 12: First use of the acronym ROI, spell out “region of interest”.

2. Page 4, Line 20: “a N_enc xN_ROI encoding matrix” should be “an N_enc xN_ROI encoding matrix”.

3. Page 8, Line 28: “…partial skull pixels are also considered even though can lead to an underestimation...” should be “…partial skull pixels are also considered even though they can lead to an underestimation...”

This is a very nice manuscript describing the use of a SVD-based isolation of lipid signals in deuterium metabolic imaging. The technique is potentially important, since there could be significant signal contamination in the head, especially in the vicinity of lipids, which would lead to incorrect metabolic profiling. While I do find the topic and the manuscript interesting, I feel that the authors are not up-front with providing the reviewer with the central result, or the central issue, namely the partial volume effects. Although the strategy taken with the use of prior spatial knowledge seems to work well, as demonstrated, the authors do not provide a simple statement about the partial volume effects, which would summarize the work and its value succinctly. One would normally expect such a statement in the Conclusion and perhaps also in the abstract, and I strongly suggest that this should be done as a service to the reader.