List of modifications and replies to referee comments We are very grateful for your concern and highly valuable comments and advice. The following are our responses (blue text) to the comments of referee 3 (black text). All indications are identified by appending consecutive numbers. The modifications and additions have been indicated in blue font in the revised manuscript. Responses to Referee 3 3-1 First, apparently, no core size distribution was implemented in the analysis. Second, from the papers by Eberbeck and Yoshida et al., it is known that there is a bimodal distribution of magnetic moments and effective core diameters, respectively. As can be seen from Fig. 4, the fit of the measured quasi-static magnetization curves with the Langevin functions is not perfect, and consequently provides a very rough guess for the effective core diameter. The obtained sample parameters are summarized in Table 1. Here it does not get clear how the individual numbers were determined. In comparing the magnetic susceptibility values, did the authors make sure that all samples have the same iron oxide content? The physical properties of the magnetic nanoparticle within the ferucarbotran’s fractionation sample were evaluated in detail by D. Eberbeck and your group, as you pointed out, and the knowledge obtained by those studies greatly contributed to MPI. In contrast, the descriptions provided in our paper were insufficient. Therefore, we provided explanations by suitably quoting these other studies (P.6 in the 2nd revised manuscript). In addition, because the explanation of Da and Dv in Table 1 was insufficient, details of the valuation method were added (P.11 in the 2nd revised manuscript). In response to your final question, we have already indicated that the Fe concentration of each sample, as well as that of the Resovist sample, was adjusted to 28 [mg/mL]. 3-2 The comparison of their correlation-based reconstruction algorithms with the fundamental one (which is applied my most other groups working on MPI) suffers from two points: First, in contrast to the original version of the manuscript, the description of the fundamental mode was completely omitted. To compare both reconstruction methods, some description of the fundamental approach is necessary. Second, the description of the authors’ time-correlation method has been published in detail elsewhere, i.e., it is not new. Because our redundant description was already pointed out by the previous two referees, the explanation of the image reconstruction method based on a fundamental method was deleted (although when we asked the Editorial Board how we should correspond when the 3rd referee’s comment differed from the previous referees’ directions for our “revised manuscript,” there was no reply from the Editorial Board)*. The principle of the time-correlation method and the results of a numerical simulation have already been published, as you pointed out. In addition, if a nanoparticle with a large diameter is used, the image resolution is also expected to improve. However, it was important to determine the influence of the difference in particle diameter on the reconstructed images by the time-correlation method, and the characteristics using an experiment with a prototype system have not been clarified previously. In addition, because it was thought that the point regarding the relation with the particle diameter of magnetic nanoparticles and the hardware ability evaluated from these reconstructed images had novelty, the article was changed to emphasize these points (P.6 in the 2nd revised manuscript). *Although we genuinely express our gratitude for your polite refereeing, there are many questions about this peer review process. Based on the previous two referees' comments, we corrected our manuscript faithfully and submitted it on November 10, 2012. After that, the manuscript was referred to you as the 3rd reviewer, and we received these refereeing results on April 26, 2013. During this period, we asked the Editorial Board why the 3rd reviewer was requested after the revised version was submitted. Usually, in the peer review process for an academic journal, if the opinions of two referees differ, an editor would ask a 3rd reviewer for another opinion before sending all of the referees’ comments to the author. However, such a procedure was not followed this time (The Editorial Board also admitted that this process differed from usual.). It is unsuitable to add directions for corrections from a different reviewer's viewpoint to an already corrected manuscript, and it must be said that fairness was missing. We asked for information about the delay in the review process, and the reason why the 3rd referee was needed. However, the Editorial Board has not provided any details except to say that the 2nd referee has given up refereeing. If the Editorial Board allows such a situation, it will become difficult for the authors and the referee to discuss MPI in the same study field in the future because this journal reveals the referee's name to the authors. 3-3 Summarizing the first two points, neither the facts that there are certain fractions from Resovist having a better MPI performance than Resovist and that magnetic nanoparticles having a steeper M-H curve allow one to achieve a better spatial resolution, nor the application of the proposed time-correlation reconstruction algorithm are new. Their conclusion (p. 16 last paragraph) that magnetic tracers with steeper M-H curves relax the requirements on the magnetic field gradient while having the same spatial resolution is trivial and ignores the important issue or particle dynamics: As shown in the papers by Yoshida and Ludwig (see above) the requirement of marge magnetic moments, i.e., steep M-H curves is not sufficient for getting a good MPI performance. The only new contribution of the paper is that they directly demonstrate - applying their reconstruction technique - that the spatial resolution of sample 3 is indeed better than that achievable with Resovist using the same hardware. As you pointed out, only the particle diameter had no effect on the image resolution. We believe that the influence of the factor that your group is evaluating on the reconstructed images by the time-correlation method should be considered in the future. For this reason, an explanation of that point was added, quoting your studies (P.18 in the 2nd revised manuscript). 3-4 p. 4, 4th line: The authors say that “clinical trials (of cancer treatment) have now started”. The referenced paper, however, is from 2001. We changed this expression to indicate that clinical trials are continuing (P.4 in 2nd revised manuscript). 3-5 p. 10: Equations (2) and (3) are not clear, presumably a formatting problem. Please check! The signal observed as a time function at each FFP scanned in two-dimensional space is expressed by the one-dimensional sequence of numbers. Because this is an expression commonly used in the field of signal and image processing, we did not change it. 3-6 p. 12, last paragraph and p. 13, last two paragraphs: First they say that a gradient field of 1.5 T/m at the center was used. On the next page, they quote a value of 1.9 T/m. Why did the authors use a different value in the numerical analysis? Because the experimental condition differed from the conditions of the numerical analysis, an unsuitable expression was deleted (P.12 in the 2nd revised manuscript). *Although it is necessary to perform the experiment under essentially the same conditions, our research-and-development organization has been changed after submitting our revised manuscript, and we have not been able to carry out further experiments under the same conditions. 3-7 P. 14, middle paragraph: The authors say that “magnetization curves were normalized by the maximum magnetization”. However, for the investigated field range, there is no maximum. Please correct! Because the ranges in consideration of normalization used different theoretical and measurement values, we standardized the definitions of normalization (Figure 4 in the 2nd revised manuscript). 3-8 p. 15, 1st paragraph: The authors conclude that the saturation magnetization of the MNP accompanies an increase in particle diameter. First, this is against the general tendency for magnetite MNP reported in numerous papers. Second, the referee cannot follow the authors’ argumentation. They say that the induced EMF for sample 3 was about a factor of 3 higher than that of pure Resovist. The induced EMF depends on a number of points: on the mean magnetic moment of the MNP, on the iron oxide content of the given sample, of the percentage of MNP with large moments etc. Thus, their argumentation should be a more detailed. Although we are concerned about the possibility of not understanding your suggestions correctly, because the saturation magnetization becomes large when the diameters of the particles that compose a magnetic fluid become large, we believe that there was no error from the perspective of physical properties in our experimental findings. 3-9 p. 15, middle: Please specify the location of the MNP sample! Because the magnetic nanoparticle was arranged at the central pixel of the image, we specified it in each figure (Figures 5 and 7, and P.15 in the 2nd revised manuscript). 3-10 In the title and in the conclusions, the authors stress the excellent biocompatibility of their tracer materials. However, there is no obvious own contribution to improve the biocompatibility. The statement is just based on the biocompatibility of the coating of Resovist. As you pointed out, the biocompatibility of the ferucarbotran samples was restricted to the range guaranteed by the drug trial data for Resovist. For example, because the nanoparticles with large diameters in internal organs might differ in behavior from Resovist, we added a note about that point (title and P.18 in the 2nd revised manuscript). 3-11 Captions of Figs. 5, 6, and 7: It should be explicitly said that (a) refers to fundamental and (b) to correlation-based reconstruction. We added a caption to the figure as requested (Figures 5 and 7 in the 2nd revised manuscript). 3-12 p. 17, first paragraph: The positions of L20, C and R20 are not totally clear. Do these numbers refer to the z axis position? In the caption, we added text stating that those symbols indicated the distance in the z-axial direction (P.17 and 23 in the 2nd revised manuscript). 3-13 Fig. (c): A log axis for S would be helpful to make differences clearer. We changed it to the log scale as suggested (Figure 8 in the 2nd revised manuscript).