Optimal Blood Glucose Control Through Continuous Insulin Infusion
In this paper, we formulate the problem of the insulin supply regimen in a diabetic patient as an optimal control problem, so that there is no overdose or insufficiency of the hormonal drug under different feeding styles. The interaction between glucose and insulin is modeled as a nonlinear syste...
| Main Authors: | , |
|---|---|
| Format: | Online |
| Language: | spa |
| Published: |
Universidad Pedagógica y Tecnológica de Colombia
2022
|
| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/14173 |
| _version_ | 1801706354368315392 |
|---|---|
| author | Panqueba Moreno, Edwar Fabián Ruiz Vera, Jorge Mauricio |
| author_facet | Panqueba Moreno, Edwar Fabián Ruiz Vera, Jorge Mauricio |
| author_sort | Panqueba Moreno, Edwar Fabián |
| collection | OJS |
| description |
In this paper, we formulate the problem of the insulin supply regimen in a diabetic patient as an optimal control problem, so that there is no overdose or insufficiency of the hormonal drug under different feeding styles. The interaction between glucose and insulin is modeled as a nonlinear system of ordinary differential equations. We prove the existence and global uniqueness of the solution of the system, as well as for the optimal control. The optimal control problem is solved directly by using the quadratic sequential programming method. The numerical results suggest setting, according to the patient’s dietary style, the prescribed glucose concentration level to be maintained during the day. The analytical and numerical study of this proposal is expected to be helpful in future insulin pump developments.
|
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-14173 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2022 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-141732023-06-26T20:43:15Z Optimal Blood Glucose Control Through Continuous Insulin Infusion Control óptimo de la glucosa en la sangre mediante infusión continua de insulina Panqueba Moreno, Edwar Fabián Ruiz Vera, Jorge Mauricio Control óptimo programación no lineal dinámica glucosa-insulina diabetes biología matemática Optimal control Nonlinear programming lucose-insulin dynamic diabetes mathematical biology In this paper, we formulate the problem of the insulin supply regimen in a diabetic patient as an optimal control problem, so that there is no overdose or insufficiency of the hormonal drug under different feeding styles. The interaction between glucose and insulin is modeled as a nonlinear system of ordinary differential equations. We prove the existence and global uniqueness of the solution of the system, as well as for the optimal control. The optimal control problem is solved directly by using the quadratic sequential programming method. The numerical results suggest setting, according to the patient’s dietary style, the prescribed glucose concentration level to be maintained during the day. The analytical and numerical study of this proposal is expected to be helpful in future insulin pump developments. En este trabajo se plantea el problema del régimen de suministro de insulina en un paciente diabético como un problema de control óptimo, de tal manera que no se genere sobredosis o insuficiencia del medicamento hormonal bajo diferentes estilos de alimentación. La interacción entre la glucosa e insulina se modela como un sistema no lineal de ecuaciones diferenciales ordinarias. Se prueba la existencia y unicidad global de la solución de dicho sistema, al igual que la del control óptimo. El problema de control óptimo se resuelve de manera directa empleando el método de programación cuadrática secuencial. Los resultados numéricos sugieren establecer, según el estilo de alimentación del paciente, el nivel de concentración de glucosa prescrito a mantener durante el día. Se espera que el estudio analítico y numérico de esta propuesta sea de ayuda en futuros desarrollos en bombas de insulina. Universidad Pedagógica y Tecnológica de Colombia 2022-07-12 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/14173 10.19053/01217488.v13.n2.2022.14173 Ciencia En Desarrollo; Vol. 13 No. 2 (2022): Vol. 13 Núm. 2 (2022): Vol. 13 Núm. 2 (2022): Vol 13, Núm.2 (2022): Julio-Diciembre; 49-67 Ciencia en Desarrollo; Vol. 13 Núm. 2 (2022): Vol. 13 Núm. 2 (2022): Vol. 13 Núm. 2 (2022): Vol 13, Núm.2 (2022): Julio-Diciembre; 49-67 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/14173/12646 |
| spellingShingle | Control óptimo programación no lineal dinámica glucosa-insulina diabetes biología matemática Optimal control Nonlinear programming lucose-insulin dynamic diabetes mathematical biology Panqueba Moreno, Edwar Fabián Ruiz Vera, Jorge Mauricio Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title | Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title_alt | Control óptimo de la glucosa en la sangre mediante infusión continua de insulina |
| title_full | Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title_fullStr | Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title_full_unstemmed | Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title_short | Optimal Blood Glucose Control Through Continuous Insulin Infusion |
| title_sort | optimal blood glucose control through continuous insulin infusion |
| topic | Control óptimo programación no lineal dinámica glucosa-insulina diabetes biología matemática Optimal control Nonlinear programming lucose-insulin dynamic diabetes mathematical biology |
| topic_facet | Control óptimo programación no lineal dinámica glucosa-insulina diabetes biología matemática Optimal control Nonlinear programming lucose-insulin dynamic diabetes mathematical biology |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/14173 |
| work_keys_str_mv | AT panquebamorenoedwarfabian optimalbloodglucosecontrolthroughcontinuousinsulininfusion AT ruizverajorgemauricio optimalbloodglucosecontrolthroughcontinuousinsulininfusion AT panquebamorenoedwarfabian controloptimodelaglucosaenlasangremedianteinfusioncontinuadeinsulina AT ruizverajorgemauricio controloptimodelaglucosaenlasangremedianteinfusioncontinuadeinsulina |
