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. CPT: Pharmacometrics & Systems Pharmacology (2013) developing glucose controllers, understanding disease progression, and predicting risks for complications. Nonclinical/knowledge-based models are more complex in nature and account for the mechanistic description of the biological systems, eventually aimed at being used for clinical purposes. Within clinical and nonclinical categories, models can be subclassified further based on the biological processes and purpose for which they are proposed. Figure 3 provides a complete picture of models and their relationship to each other (see figure legend for details), for each subclassification. Classification of models describing systemic diseases cannot be definitive due to their complex nature, and hence, some models fit into multiple classes. Moreover, as certain subclasses include a plethora of models, only representative models are presented here. A wide range of clinical diabetes models focusing on predicting and understanding different stages of the disease, such as diagnostics, control, progression, and complication are being developed. These models are discussed in this section. Figure 1 General overview of the glucose homeostasis mechanism under normal and diabetic condition. Plasma glucose level is maintained within a narrow range through the combined antagonistic action of two pancreatic hormones: insulin and glucagon. (a) In normal individuals, high plasma glucose level induces the release of insulin from pancreatic β-cells, which enables the muscle and other cells to take up glucose for energy or to store it as glycogen in liver. On the other hand, at low plasma glucose level, glucagon secreted from α-cells counterregulates the glucose level by inducing the breakdown of glycogen into glucose. (b) In diabetic individuals, the synchronized mechanism between insulin and glucagon secretion is disrupted. Insufficient or lack of insulin production by β-cells, or insulin sensitivity in muscle and other cells, leads to persistent high plasma glucose level (hyperglycemia). This condition is often accompanied by absolute or relative excess level of glucagon, which causes a higher rate of hepatic glucose production than utilization, favoring hyperglycemia (S123-S125). Another defect that is seen in diabetic patients is the impaired secretory response of α-cells to release glucagon when the plasma glucose level drops, leading to the risk of episodes of severe hypoglycemia (S126). This often occurs due to exposure to excess insulin during treatment or to extreme physical activities carried out as part of self-management, accompanied with compromised glucose counterregulation (see Supplementary Data online, for details).  To evaluate the diabetic and prediabetic condition in an individual, different glucose tolerance tests, such as intravenous glucose tolerance test (IVGTT), oral glucose tolerance test (OGTT), and meal glucose tolerance test have been devised. The aim of these tests is to obtain an estimate of insulin sensitivity (S I ), glucose effectiveness (S G ), insulin secretion, and β-cell function. Insulin sensitivity (S I ) and glucose effectiveness (S G ). Earlier models for insulin-glucose systems are mainly focused at evaluating different diagnostics tests. Following the pioneering model of Bolie, 2 a series of mathematical models illustrating insulin-glucose dynamics were developed (S6-S9). However, a major breakthrough in diabetes modeling occurred with the development of the physiological model 3 for glucose disappearance following IVGTT. Being parsimonious and simple, this model is generally known as the "minimal model." This classical model was developed as two parts, namely, the glucose minimal model 4 and the insulin minimal model (S10), which account for glucose uptake and insulin release, respectively. The comparison between the assessment of S I using the glucose clamp technique (S11) and minimal models is discussed by Bergman et al. 5 The structural simplicity and ability to evaluate significant physiological parameters has led to more than 1,000 publications related to minimal model. 6 Despite their extensive usage, there are several limitations in the use of minimal models including overestimation of S G and underestimation of S I (S12, S13). To overcome these limitations, an additional compartment for glucose kinetics was incorporated into the model along with labeled IVGTT (S14-S18) experiments. Although these bicompartment models allow precise estimation of S I and S G , the additional cost and technology involved in using labeled IVGTT make it impractical to be applied to the general population. To overcome this, Bayesian approaches were employed in the bicompartmental model (S19 Silber et al. 8 proposed an integrated insulin-glucose model to describe IVGTT data from healthy as well as diabetic individuals, using a bidirectional insulin-glucose feedback mechanism. As OGTT closely resembles the physiological condition, this model was extended further by incorporating the description for glucose absorption and incretin effects following a meal (S21). Further extensions were made to (S21), by including data from healthy individuals (S22). Subsequently, Jauslin et al. (S23) developed a model describing the whole-day insulin-glucose profiles following multiple meal tests. Unlike IVGTT, OGTT accounts for slow glycemic changes that correspond to the rate of glucose appearance in systemic circulation. To gain a more realistic view of glucose dynamics, mixed meal and oral glucose minimal models were extended upon IVGTT minimal models by parametrically defining the rate of glucose appearance in the plasma (S24-S26). The oral glucose test and meal test are increasingly being used for their experimental simplicity and for generating the explicit measure of S I under physiological conditions (S26-S28). Subsequently, a minimal model for labeled MOGTT was proposed (S29). To incorporate different physiological processes associated with insulin-glucose dynamics, different variations and extensions of the classical minimal model have been developed. 9,10 Besides these, there are several physiology-based paradigm models available for diagnosis, such as HOMA, 11 CIGMA (S30), MATSUDA (S31), and QUICKI (S32). Insulin secretion and β-cell function. Since the liver degrades more than a half of the secreted insulin before it is utilized by other body tissues, accurate estimation of prehepatic insulin secretion, hepatic insulin extraction, and clearance are essential for evaluating insulin secretion and β-cell function under normal and diseased conditions. Plasma C-peptide, a part of preproinsulin peptide and therefore secreted in equimolar amounts as insulin by β-cell, acts as an indicator for insulin secretion. However, peripheral C-peptide has a longer half-life and can limit the accurate estimation of insulin secretion. To address this problem, several mathematical models and model-based methods are proposed and reviewed. The most commonly used methods/models for estimating the rate of insulin secretion include the deconvolution method 13 (S33) and combined models assuming single-(S34) and double-(S35) compartmental disappearance kinetics of both the peptides. In addition, to quantify β-cell activity under different pathological conditions, Thomseth et al. (S36) developed a model to determine the peripheral concentrations of insulin, C-peptide, and islet amyloid polypeptide during OGTT. Later, Hovorka et al. (S37) formulated a computational method, namely, Insulin SECretion, by implementing a constrained regularization method of deconvolution. Furthermore, the Van Cauter algorithm was applied in Insulin   Figure 2 Modeling approaches vs. the number of models in relation to diabetes and associated complications, over the past five decades. There has been a significant increase in the number of models, as well as in the diversity of the modeling approaches applied toward addressing diabetes. ANNs, artificial neural networks; DDEs, delay differential equations; IDEs, integrodifferential equations; ODEs, ordinary differential equations; PDEs, partial differential equations; SDEs, stochastic differential equations. 1961 -1970 1971 -1980 1981 -1990 Decades 1991 2001 -2010 /2013 CPT: Pharmacometrics & Systems Pharmacology Understanding diabetes via mathematical modeling Ajmera et al.
There are several models produced by academia and industries that incorporate different physiological processes associated with insulinglucose dynamics and different variations REF .
The impact of mathematical modeling on the understanding of diabetes and related complications
CPT: Pharmacometrics & Systems Pharmacology
CPT: Pharmacometrics & Systems Pharmacology
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