The impact of mathematical modeling on the understanding of diabetes and related complications

Abstract

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

A Simple Mathematical Model for Wound Closure Evaluation

“…Wound shape evolution during this study has been documented by the S c calculation through equation (6). As previously mentioned, S c is a parameter that does not depend on the size of the analyzed figure, but on its shape.…”

“…Data obtained from planimetric measurements have been treated introducing A, P, and t in equations (1), (5) and (6). D values obtained from equation (1) for the healing process of the 15 patients are shown in Fig.…”

“…5 Mathematical modeling may also aid in identifying potential methods for disease control and management if wound closure results can be correlated with the wound and the patient's condition. 6 Few mathematical models in the literature deal with the complications associated with diabetes due to their complexity. 6 The literature reveals great diversity in the procedures employed to compare wound-healing rates, including variables such as periods of study, type, size and shape of the analyzed lesions, closing rate definition, calculation methods, mechanisms, etc.…”

“…6 Few mathematical models in the literature deal with the complications associated with diabetes due to their complexity. 6 The literature reveals great diversity in the procedures employed to compare wound-healing rates, including variables such as periods of study, type, size and shape of the analyzed lesions, closing rate definition, calculation methods, mechanisms, etc. 3,[7][8][9][10][11][12][13] However, controversy exists in the selection of the adequate indicative parameter of the wound closure rate.…”

Mixed Meal Model in Type 1 Diabetes

“…To assist T1DM patients with their BG management, recent technologies-several of them relying on mathematical modeling of glucose-insulin metabolism -include diabetes diagnostics, decision support systems for insulin dosing and smart BG sensors [2]. In recent years, BG control systems that maintain normoglycemia automatically by closed-loop continuous infusion of insulin have taken particularly large strides towards its commercial development.…”