A four-dimensional model was built to mimic the cross-talk among plasma glucose, plasma insulin, intracellular glucose and cytoplasmic calcium of a cardiomyocyte. A time delay was considered to represent the time required for performing various cellular mechanisms between activation of insulin receptor and subsequent glucose entry from extracellular region into intracellular region of a cardiac cell. We analysed the delay-induced model and deciphered conditions for stability and bifurcation. Extensive numerical computations were performed to validate the analytical results and give further insights. Sensitivity study of the system parameters using LHS-PRCC method reveals that some rate parameters, which represent the input of plasma glucose, absorption of glucose by noncardiac cells and insulin production, are sensitive and may cause significant change in the system dynamics. It was observed that the time taken for transportation of extracellular glucose into the cell through GLUT4 plays an important role in maintaining physiological oscillations of the state variables. Parameter recalibration exercise showed that reduced input rate of glucose in the blood plasma or an alteration in transportation delay may be used for therapeutic targets in diabetic-like condition for maintaining normal cardiac function.

中文翻译：

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糖尿病条件下细胞外葡萄糖转运至心肌细胞延迟的影响：通过数学模型的研究


建立了一个四维模型来模拟心肌细胞的血浆葡萄糖、血浆胰岛素、细胞内葡萄糖和细胞质钙之间的串扰。时间延迟被认为代表在胰岛素受体的激活和随后的葡萄糖从心肌细胞的细胞外区域进入细胞内区域之间执行各种细胞机制所需的时间。我们分析了延迟引起的模型并破译了稳定性和分岔的条件。进行了大量的数值计算以验证分析结果并提供进一步的见解。使用LHS-PRCC方法对系统参数进行敏感性研究表明，一些代表血浆葡萄糖输入、非心肌细胞吸收葡萄糖和胰岛素产生的速率参数是敏感的，可能会引起系统动力学的显着变化。据观察，细胞外葡萄糖通过 GLUT4 运输到细胞内所需的时间在维持状态变量的生理振荡中起着重要作用。参数重新校准练习表明，降低血浆中葡萄糖的输入速率或改变运输延迟可用于糖尿病样病症的治疗目标，以维持正常的心脏功能。