| Journal: | Visión electrónica |
| Database: | PERIÓDICA |
| System number: | 000461816 |
| ISSN: | 1909-9746 |
| Authors: | Duitama Leal, Alejandro1 González Galeano, Andrei Alan1 Gil Gómez, Javier Hernán1 |
| Institutions: | 1Universidad El Bosque, Bogotá. Colombia |
| Year: | 2016 |
| Season: | Jul-Dic |
| Volumen: | 10 |
| Number: | 2 |
| Pages: | 190-194 |
| Country: | Colombia |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Prospectivo |
| Spanish abstract | Debido a la importancia que actualmente tiene la diabetes como enfermedad que se perfilaser una pandemia a nivel mundial, se hace necesario estudiar y comprender, desde diferentesdisciplinas, los procesos que se involucran para una mejor identificación y tratamiento de lamisma. El presente art ́ıculo describe el modelamiento matem ́atico de los niveles de glucosa einsulina presentes en el cuerpo basado en el trabajo de Ackerman realizando una modificaci ́ondel sistema de ecuaciones diferenciales acopladas (SEDA) en el modelo m ́ınimo incluyendo unaumento gradual ex ́ogeno para considerar variaciones ex ́ogenas de tales niveles. A partir dela curva experimental se consideraron diferentes casos, de manera que cada familia de curvascorrespondiente se analiz ́o en funci ́on de la cantidad de glucosa e insulina, respectivamente. Lasoluci ́on aproximada del SEDA se obtuvo usando el m ́etodo de Runge Kutta de cuarto orden yse compar ́o con resultados experimentales reportados. Se encontr ́o que peque ̃nos aumentos en lacantidad de Glucosa produce un incremento en la Insulina debido a que el cuerpo aumenta suproducción para regularla a niveles normales |
| English abstract | Due to the importance that diabetes is nowadays, a disease that is worldwide nominated as apandemic, it is necessary to study and understand from different disciplines the processes thatare involved in a better identification and treatment of it. Thus the mathematical modeling ofthe glucose and insulin levels present in the body was done making a modification of the minimalmodel, to consider exogenous variations of the glucose and insulin levels. For that, the studywas based on the work done by Ackerman and the minimal model, and the system of differentialequations connected (SDEC) was modified in order to include a gradual exogenous increase ofthe glucose and insulin amount. The approximate solution of the SDEC was obtained usingthe Runge Kutta method of fourth order and it was compared with the reported experimentalresults, finding a good behavior. Based on the experimental curve, different cases were modeledwhere the insulin and glucose amount varies, and for each case, the group of correspondingcurves was analyzed according to the insulin and glucose amount respectively. It was found thatsmall increases of the glucose amount causes an increase of the insulin production and this isbecause the body increases the insulin production to regulate it to the normal levels |
| Disciplines: | Medicina, Matemáticas |
| Keyword: | Matemáticas aplicadas, Diabetes, Ecuaciones diferenciales, Glucosa, Modelación matemática |
| Keyword: | Applied mathematics, Diabetes, Differential equations, Glucose, Mathematical modelling, Runge Kutta method |
| Full text: | https://revistas.udistrital.edu.co/index.php/visele/article/view/11739/12455 |
