Modeling Diabetes Progression Factors

The culprits of diabetes may vary for different subgroups of diabetic patients, which implies the distinction of possible interference factors to the glucose regulation system. Nevertheless, the underlying mechanisms through which the factors lead to dysglycemia are common. Numerous studies indicate that glycemia is primarily attributed to excess hepatic glucose output and abnormal insulin secretion and utilization [35 (link)]. Of note, beta-cell function is regulated by various mechanisms, not limited to glucose utilization [12 (link)]. Thus, confining the model for beta-cell function only with the variables of glucose and insulin may impede the study of beta-cell dysfunction. We aim to test through an in-silico approach how the T2D progression is affected by certain pathological factors. Here we propose a general form of diabetes progression model with a pathological factor X that is to be specified:
$$\begin{array}{c}{\displaystyle \frac{\mathrm{d}G}{\mathrm{d}t}}=G_{in}+p_1\left(X\right)-f_2\left(G\right)-C\left(I\right)GI,\hfill \end{array}$$
$$\begin{array}{c}{\displaystyle \frac{\mathrm{d}I}{\mathrm{d}t}}=f_1\left(G\right)p_2\left(X\right)\beta -kI,\hfill \end{array}$$
$$\begin{array}{c}{\displaystyle \frac{\mathrm{d}\beta }{\mathrm{d}t}}=(f_3\left(I\right)+p_3\left(X\right))\beta ,\hfill \end{array}$$
where X is a bounded variable with a real value; all the variables in the system are in the time scale of days: p₁(X) is incorporated into Eq (1) to stand for the increased hepatic glucose production caused by the pathological factor; p₂(X) integrated into Eq (2) symbolizes the impact of the factor on the insulin secretion rate; p₃(X) is incorporated to Eq (3) to describe the abnormal response of beta-cells to a hostile environment that develops in a slow time scale. The exact forms of the influence functions p_i(X) (i = 1, 2, 3) will be determined with X being an obesity-related factor in Section. We assume that p₁(X) = 0, p₂(X) = 1, and p₃(X) = 0 when X = 0 so the model is in accordance with the undisturbed glucose-insulin regulatory model when no diabetogenic factors exist in normal subjects.