Mathematical analysis of a model for glucose regulation
Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding gl...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2015-09-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.83 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590135515938816 |
|---|---|
| author | Kimberly Fessel Jeffrey B. Gaither Julie K. Bower Trudy Gaillard Kwame Osei Grzegorz A. Rempała |
| author_facet | Kimberly Fessel Jeffrey B. Gaither Julie K. Bower Trudy Gaillard Kwame Osei Grzegorz A. Rempała |
| author_sort | Kimberly Fessel |
| collection | DOAJ |
| description | Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding glucose-insulin interactions. Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). In this study we present an explicit solution to the minimal model which allows for separating the glucose and insulin dynamics of the minimal model and for identifying patient-specific parameters of glucose trajectories from IVGTT. As illustrated with patient data, our approach seems to have an edge over more complicated methods currently used. Additionally, we also present an application of our method to prediction of the time to baseline recovery and calculation of insulin sensitivity and glucose effectiveness, two quantities regarded as significant in diabetes diagnostics. |
| format | Article |
| id | doaj-art-9fca00e86c574d2ba3a52357f2660f9b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9fca00e86c574d2ba3a52357f2660f9b2025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-01131839910.3934/mbe.2016.13.83Mathematical analysis of a model for glucose regulationKimberly Fessel0Jeffrey B. Gaither1Julie K. Bower2Trudy Gaillard3Kwame Osei4Grzegorz A. Rempała5Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210College of Public Health, The Ohio State University, Columbus, OH 43210Department of Medicine, The Ohio State University, Columbus, OH 43210Department of Medicine, The Ohio State University, Columbus, OH 43210Mathematical Biosciences Institute and College of Public Health, The Ohio State University, Columbus, OH 43210Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding glucose-insulin interactions. Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). In this study we present an explicit solution to the minimal model which allows for separating the glucose and insulin dynamics of the minimal model and for identifying patient-specific parameters of glucose trajectories from IVGTT. As illustrated with patient data, our approach seems to have an edge over more complicated methods currently used. Additionally, we also present an application of our method to prediction of the time to baseline recovery and calculation of insulin sensitivity and glucose effectiveness, two quantities regarded as significant in diabetes diagnostics.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.83parameter estimationglucose tolerance testinsulin sensitivity.diabetesminimal model |
| spellingShingle | Kimberly Fessel Jeffrey B. Gaither Julie K. Bower Trudy Gaillard Kwame Osei Grzegorz A. Rempała Mathematical analysis of a model for glucose regulation Mathematical Biosciences and Engineering parameter estimation glucose tolerance test insulin sensitivity. diabetes minimal model |
| title | Mathematical analysis of a model for glucose regulation |
| title_full | Mathematical analysis of a model for glucose regulation |
| title_fullStr | Mathematical analysis of a model for glucose regulation |
| title_full_unstemmed | Mathematical analysis of a model for glucose regulation |
| title_short | Mathematical analysis of a model for glucose regulation |
| title_sort | mathematical analysis of a model for glucose regulation |
| topic | parameter estimation glucose tolerance test insulin sensitivity. diabetes minimal model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.83 |
| work_keys_str_mv | AT kimberlyfessel mathematicalanalysisofamodelforglucoseregulation AT jeffreybgaither mathematicalanalysisofamodelforglucoseregulation AT juliekbower mathematicalanalysisofamodelforglucoseregulation AT trudygaillard mathematicalanalysisofamodelforglucoseregulation AT kwameosei mathematicalanalysisofamodelforglucoseregulation AT grzegorzarempała mathematicalanalysisofamodelforglucoseregulation |