In the last three decades, several models relevant to the subcutaneous injection of insulin analogues have appeared in the literature. Most of them model the absorption of insulin analogues in the injection depot and then compute the plasma insulin concentration. The most recent systemic models directly simulate the plasma insulin dynamics. These models have been and/or can be applied to the technology of the insulin pump or to the coming closed-loop systems, also known as the artificial pancreas. In this paper, we selectively review these models in detail and at point out that these models provide key building blocks for some important endeavors into physiological questions of insulin secretion and action. For example, it is not clear at this time whether or not picomolar doses of insulin are found near the islets and there is no experimental method to assess this in vivo. This is of interest because picomolar concentrations of insulin have been found to be effective at blocking beta-cell death and increasing beta-cell growth in recent cell culture experiments.

中文翻译：

---

胰岛素类似物皮下注射的数学模型：小型回顾。

在过去的三十年中，文献中出现了几种与皮下注射胰岛素类似物相关的模型。他们中的大多数模拟注射库中胰岛素类似物的吸收，然后计算血浆胰岛素浓度。最新的系统模型直接模拟血浆胰岛素动力学。这些模型已经和/或可以应用于胰岛素泵技术或即将到来的闭环系统，也称为人工胰腺。在本文中，我们有选择地详细回顾这些模型，并指出这些模型为胰岛素分泌和作用的生理问题的一些重要努力提供了关键的构建模块。例如，目前尚不清楚胰岛附近是否发现皮摩尔剂量的胰岛素，并且没有实验方法可以在体内评估这一点。这很有趣，因为在最近的细胞培养实验中，皮摩尔浓度的胰岛素被发现可以有效阻止 β 细胞死亡并增加 β 细胞生长。