Abstract :
Mathematical models make it possible to quantitatively simulate clinical situations and to test various hypotheses. The determination of insulin doses and sensitivity in type 1 diabetic patients is made on the basis of calculations after the fasting test and after estimation of the carbohydrate ratios. The objective of our study is to build a mathematical model describing the doses of basal and prandial insulin and the sensitivity to insulin, in order to propose a therapeutic scheme adapted to the needs of the diabetic patient and this through a mathematical model describing type 1 diabetes. The study focused on the files of diabetic patients followed up in the endocrinology department between 2015 - 2021, and who benefited from functional insulin therapy. The variables analyzed relate to patient age, sex, duration of diabetes, HbA1c, weight, BMI, total insulin dose, prandial insulin dose, basal insulin dose, the number of daily 10g serving, insulin sensitivity. A mathematical analysis was performed which allows to numerically estimate the dose of basal insulin, rapid insulin and K sensitivity for each new patient. The results of the analysis were then tested on an Excel spreadsheet, then used to build a web-based calculator application. We included 105 patients in the study. The set {V_1,V_2,⋯,V_105 } constitutes the table of the database considered in this study. Let P be a patient who is not from the database: P∈{P_i | i∈{1,⋯,105}}. Therefore, to determine basal insulin IB, rapid insulin IR and sensitivity Ksensitivity, we find the closest patient in the database according to the chosen factors. These patients are found by minimizing the cartesian distance between the factor vectors, these distances are defined as: d_1 (i)=√(〖(〖Age〗_i-Age)〗^2+〖(〖Weight〗_i-Weight)〗^2+〖(〖HbA1c〗_i-HbA1c)〗^2 ) for the Basal Insulin. d_2 (i)=√(〖(〖Age〗_i-Age)〗^2+〖(〖Weight〗_i-Weight)〗^2+〖(〖NS〗_i-NS)〗^2 ) for the Rapid Insulin Once we found the minimal distances and best values for Rapid and Basal Insulin dose, we can calculate the Total Insulin IT and deduce the K-Sensitivity defined as: K_sensibilité=I_T/I_Th These formulas were tested on an Excel spreadsheet, then used to build a Web-based Calculator application. The model obtained from this mathematical simulation will make it possible to reliably estimate the doses of basal and prandial insulin and the sensitivity in T1D patients.
