Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Abstract

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Fixed‐ratio combination of insulin glargine plus lixisenatide (iGlarLixi) improves ß‐cell function in people with type 2 diabetes

“…The model also yields an estimate of early insulin response (termed rate sensitivity, or response to plasma glucose rate of change) and a potentiation parameter, reflecting potentiation of insulin secretion by glucose and incretins. 11 The fasting insulin secretion rate and total insulin output (insulin secretion during 2 h post-MMTT) were also calculated. Modelling analysis did not yield reliable results in 32 tests (19 in the iGlarLixi group, 13 in the GLP-1RA group), as meal glucose excursions were minimal and not concordant with those of C-peptide.…”

“…The mean slope of the insulin secretion/plasma glucose dose‐response function is taken to represent β‐cell glucose sensitivity (in pmol/min/m 2 /mM). The model also yields an estimate of early insulin response (termed rate sensitivity, or response to plasma glucose rate of change) and a potentiation parameter, reflecting potentiation of insulin secretion by glucose and incretins 11 . The fasting insulin secretion rate and total insulin output (insulin secretion during 2 h post‐MMTT) were also calculated.…”

Unraveling the Factors Determining Development of Type 2 Diabetes in Women With a History of Gestational Diabetes Mellitus Through Machine-Learning Techniques

“…A more traditional approach with respect to metabolomics and lipidomics in the field of T2DM research consists of the extraction, sometimes with sophisticated mathematical modeling methodologies, of features describing parameters of physiological interest from raw data measured during standard clinical tests ( Mari et al, 2020 ). However, to the best of our knowledge, the application of machine-learning techniques to analyze data set containing this kind of features has never been performed in women with a history of GDM and at risk of developing T2DM.…”

Mahalanobis distance, a novel statistical proxy of homeostasis loss is longitudinally associated with risk of type 2 diabetes

“…The impact of homeostasis loss in the development of T2D has included the role of the pancreas [8], skeletal muscle [9], adipose tissue [10], and more recently the gut microbiota [11]. Although the interconnection of such systems in health and disease has been recognized, analyzes of their related biomarkers has largely been confined to individual biomarkers to date.…”