## 5 Conclusions  
In the present work, a step-by-step analysis scheme using a spectral analysis (SA) approach was introduced. The present scheme determines the 3D spatial distribution of positron emitting radioisotopes, namely \({}^{11}\)C, \({}^{15}\)O and \({}^{13}\)N. All the developed numerical tools that are essential for the present scheme have been made open-source and freely available. The present scheme was tested using proton irradiation experiments and measurements from the PEMGRAPH system. The employed water-gel phantom was irradiated with an 80 MeV monoenergetic pencil-like beam. The results obtained from the present scheme showed the formation of a \({}^{13}\)N peak near the Bragg peak, which was found to be in a good agreement with previous investigations. The present scheme and developed tools would be useful for the 3D visualization of positron emitting radioisotopes and in turn for proton range monitoring and verification.  
The movie clips, source codes and raw data can be downloaded at: [[https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_ammography_system/17171093](https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_ammography_system/17171093)]([https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_ammography_system/17171093](https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_ammography_system/17171093)).  
Conceptualization, M.R.I. and H.W.; methodology, M.R.I, H.W. and M.S.B.; software, M.S.B. and H.W.; validation, M.R.I, M.S.B., T.Y. and H.W.; formal analysis, M.R.I., M.S.B., S.I, S.G. and H.W.; investigation, M.R.I, M.S.B. and H.W.; resources, S.I., S.G. and H.W.; data curation, M.R.I, M.S.B. and H.W.; writing--original draft preparation, M.R.I.; writing--review and editing, M.S.B. and H.W.; visualization, M.R.I; supervision, H.W.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research work was funded by Japan Agency for Medical Research and Development (AMED) under Grant Number 20 he2202004h0402 and Ministry of Education, Culture, Sports, Science and Technology (MEXT) under the grant number 21F21103.  
**Institutional Review Board Statement:** All involved institutes were informed about the work done.  
**Informed Consent Statement:** Informed consent is not applicable.  
**Data Availability Statement:** [[https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_mammography_system/17171093](https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_mammography_system/17171093)]([https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_mammography_system/17171093](https://figshare.com/articles/software/An_analysis_scheme_for_3D_visualization_of_positron_emitting_radioisotopes_using_positron_emission_mammography_system/17171093)) (accessed on: 11 January 2022).  
**Acknowledgments:** The authors thank the Cyclotron and Radioisotopes Center (CYRIC) for the technical support.  
**Conflicts of Interest:** All authors declare that have no conflict of interest.