Much attention has been devoted in the last few decades to mathematical models of insulin secretion, in order to better understand the regulation of glycemia and its derangements. The glucose-insulin homeostatic mechanism is so complex and gives rise to such diverse behavior following perturbations that different models had been published, which reproduced the results of single experiments. More recently, a unifying model of pancreatic insulin secretion was proposed, which is able to account, with a single value of the (meta)parameters, for the wide array of clinically observed behavior. This model explicitly represented the pulsatile nature of the many pancreatic hormone-secreting firing units: the price to pay for its flexibility and performance is the very high dimensionality (hundreds of thousand equations) of the corresponding dynamical system. Clearly, it would be desirable to reduce this model to a much simpler form while retaining its power to reproduce heterogeneous phenomena. The present work reviews the qualitative behavior of this pancreas pulsatile model and offers some insight into its reduction in equilibrium and quasi-equilibrium conditions, also considering single-shot (non-repeated) glucose jumps from an approximately resting condition (such as would occur in standard Intra-Venous bolus dosing of glucose during diabetes diagnostic maneuvers). The resulting quasi-steady-state model can be further endowed with additional lower-order dynamics to also approximate transient behavior. Although a more accurate reduction of the original pulsatile model is left to further investigation, numerical results confirm the biomedical applicability of the formulation already obtained.

在过去的几十年中，人们对胰岛素分泌的数学模型投入了很多注意力，以便更好地了解血糖的调节及其紊乱。葡萄糖-胰岛素稳态机制如此复杂，并且在扰动后产生了如此多种多样的行为，以至于已经发布了不同的模型，从而再现了单个实验的结果。最近，有人提出了一种统一的胰腺胰岛素分泌模型，该模型能够用（meta）参数的单个值来解释各种临床观察到的行为。该模型明确表示了许多分泌胰腺激素的点火单元的搏动性质：为其灵活性和性能付出的代价是相应动力学系统的很高维度（数十万个方程）。显然，希望将此模型简化为更简单的形式，同时保留其再现异质现象的能力。本工作回顾了这种胰腺的定性行为脉动模型，并为它在平衡和准平衡条件下的减少提供了一些见识，还考虑了单次（非重复）葡萄糖从近似静止状态跳跃（例如在糖尿病期间标准的静脉内推注葡萄糖时会发生）诊断演习）。所得的准稳态模型可进一步赋予其他低阶动力学特性，以近似瞬态行为。尽管对原始脉动模型的更精确还原尚待进一步研究，但数值结果证实了已经获得的制剂的生物医学适用性。