Islam Rafiqul, Yang Junyuan, Li Miao, Mokshagundam Sri Prakash, Cai Lu, Li Jiaxu
Department of Mathematics, University of Louisville, Louisville, KY, USA; Department of Mathematics, Khulna University of Engineering & Technology, Khulna, Bangladesh.
Complex Systems Research Center, Shanxi University, Taiyuan, China.
J Theor Biol. 2025 Aug 21;611:112188. doi: 10.1016/j.jtbi.2025.112188. Epub 2025 Jun 16.
Existing mathematical models investigating the progression of type 2 diabetes (T2D) over time primarily focus on glucose, insulin, β-cell mass, and other related factors, while often omitting fatty acids (FA) as an explicit variable-despite FA being a major energy source for the body. There exists a complex network of dynamical interactions among glucose, insulin, FA, and β-cell mass. To gain deeper insights into the metabolic dynamics and pathophysiology of T2D, it is essential to incorporate FA into such models. In this paper, we extend the classic Topp's GIβ model by explicitly incorporating FA and exploring its interactions with glucose, insulin, and β-cell mass. A new formula for insulin sensitivity (S) is proposed to better capture the impaired effect of FA on S, enabling the exploration of diabetes development pathways and strategies for prevention or delay. Model simulations align well with clinical data and successfully replicate key characteristics of T2D progression, including declining S, reduced β-cell mass, a sedentary lifestyle, and excessive dietary intake. Our results demonstrate a strong positive correlation between glucose and FA levels, indicating that elevated FA is associated with increased glucose concentrations. Model analysis shows that FA levels in diabetic subjects rise significantly as a result of T2D development. Numerical analyses indicate that maintaining adequate physical activity or reducing dietary excess effectively preserves S and β-cell mass, thereby reducing the risk of developing T2D. Most notably, our detailed simulations reveal a striking pattern: in healthy and non-diabetic individuals, FA levels consistently remain below glucose levels across their lifespan. In contrast, in individuals with T2D, FA levels initially remain lower but begin to increase sharply and tangle with glucose levels, and then surpass glucose concentrations near the time of β-cell failure. These patterns suggest that elevated FA may play a contributory role in increasing glucose levels, reducing insulin sensitivity, and ultimately leading to hyperglycemia. Our findings support the notion that glucotoxicity and lipotoxicity accelerate β-cell decline, impair insulin secretion, and drive T2D progression. Elevated FA thus emerges not only as a contributing pathway but also as a potential biomarker for monitoring disease development. Furthermore, the observed relationship between glucose and FA levels seems suggesting a quantitative marker that could be used to track progression toward T2D.
现有的研究2型糖尿病（T2D）随时间进展的数学模型主要关注葡萄糖、胰岛素、β细胞质量及其他相关因素，却常常忽略脂肪酸（FA）这一明确变量——尽管FA是人体的主要能量来源。葡萄糖、胰岛素、FA和β细胞质量之间存在着复杂的动态相互作用网络。为了更深入地了解T2D的代谢动态和病理生理学，将FA纳入此类模型至关重要。在本文中，我们通过明确纳入FA并探索其与葡萄糖、胰岛素和β细胞质量的相互作用，扩展了经典的托普斯GIβ模型。提出了一种新的胰岛素敏感性（S）公式，以更好地捕捉FA对S的损害作用，从而能够探索糖尿病的发展途径以及预防或延缓策略。模型模拟与临床数据吻合良好，并成功复制了T2D进展的关键特征，包括S下降、β细胞质量减少、久坐不动的生活方式和过度饮食摄入。我们的结果表明葡萄糖和FA水平之间存在很强的正相关，表明FA升高与葡萄糖浓度增加有关。模型分析表明，糖尿病患者的FA水平会因T2D的发展而显著升高。数值分析表明，保持足够的身体活动或减少饮食过量可有效维持S和β细胞质量，从而降低患T2D的风险。最值得注意的是，我们的详细模拟揭示了一个显著模式：在健康和非糖尿病个体中，FA水平在其一生中始终低于葡萄糖水平。相比之下，在T2D患者中，FA水平最初较低，但随后开始急剧上升并与葡萄糖水平交织在一起，然后在β细胞衰竭时超过葡萄糖浓度。这些模式表明，FA升高可能在增加葡萄糖水平、降低胰岛素敏感性并最终导致高血糖方面起作用。我们的研究结果支持了糖毒性和脂毒性加速β细胞衰退、损害胰岛素分泌并推动T2D进展的观点。因此，升高的FA不仅成为一种促成途径，还成为监测疾病发展的潜在生物标志物。此外，观察到的葡萄糖和FA水平之间的关系似乎暗示了一种可用于追踪向T2D进展的定量标志物。
