Mathematical expansion and clinical application of chronic kidney disease stage as vector field

• Eiichiro Kanda ,

  Roles Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

  * E-mail: kms.cds.kanda@gmail.com

  ¶☯ All these authors are contributed equally to this work.

  Affiliation Medical Science, Kawasaki Medical School, Kurashiki, Okayama, Japan

  https://orcid.org/0000-0003-0676-096X

  ⨯
• Bogdan I. Epureanu ,

  Roles Conceptualization, Formal analysis, Methodology, Project administration, Resources, Software, Supervision, Validation, Writing – review & editing

  ¶☯ All these authors are contributed equally to this work.

  Affiliation College of Engineering, University of Michigan, Ann Arbor, Michigan, United states of America

  ⨯
• Taiji Adachi ,

  Roles Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – review & editing

  ¶☯ All these authors are contributed equally to this work.

  Affiliation Institute for Life and Medical Sciences, Kyoto University, Sakyo, Kyoto, Japan

  ⨯
• Tamaki Sasaki ,

  Roles Data curation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – review & editing

  ¶☯ All these authors are contributed equally to this work.

  Affiliation Department of Nephrology and Hypertension, Kawasaki Medical School, Kurashiki, Okayama, Japan

  ⨯
• Naoki Kashihara

  Roles Conceptualization, Data curation, Formal analysis, Methodology, Project administration, Supervision, Validation, Writing – review & editing

  ¶☯ All these authors are contributed equally to this work.

  Affiliation Kawasaki Geriatric Medical Center, Kita, Okayama, Japan

  ⨯