بررسي معادلات ديفرانسيل معمولي (ODE) مينيمال از اثرات تغيير هورموني بر جذب گلوكز با واسطه انسولين

Diabetes mellitus is a major metabolic disorder characterized by disturbances in glucose regulation resulting from impaired insulin secretion, reduced insulin sensitivity, an‎d abnormal hormonal activity. Blood glucose homeostasis depends on complex interactions among glucose, insulin, an‎d counter-regulatory hormones, making mathematical modeling a valuable approach for investigating metabolic behavior under both physiological an‎d pathological conditions. This study proposes a minimal nonlinear Ordinary Differential Equation (ODE)-based model to analyze insulin-mediated glucose uptake under different hormonal variation scenarios. The model describes the dynamic interactions among blood glucose concentration, plasma insulin, insulin sensitivity, glucose uptake, an‎d hormonal regulatory effects. MATLAB/Simulink was used for numerical implementation an‎d simulation under normal physiological, insulin-resistant, diabetic, severe hyperglycemic, an‎d hormonal imbalance conditions. The proposed model successfully reproduced distinct metabolic responses across the investigated scenarios. Under normal physiological conditions, glucose remained dynamically stable, although the predicted glucose level was slightly below the expected fasting range. Insulin resistance resulted in persistent mild hyperglycemia accompanied by compensatory elevation of insulin secretion. The diabetic condition produced pronounced an‎d sustained hyperglycemia, with a mean glucose concentration of approximately 302 mg/dL, indicating substantially impaired glucose regulation. Severe hyperglycemia produced the greatest metabolic disturbance, with glucose levels exceeding 300 mg/dL throughout much of the simulation. In contrast, the hormonal imbalance condition maintained glucose close to the physiological range despite increased hormonal influence an‎d mildly elevated insulin activity. All simulated scenarios remained dynamically stable an‎d showed clear differences in glucose uptake efficiency an‎d insulin sensitivity. Although model-derived insulin sensitivity an‎d glucose uptake indices are normalized computational measures an‎d should not be interpreted as direct clinical values, they consistently reflected the expected relative changes among physiological an‎d pathological states.

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احسان روحاني , امير اخوان بي تقصير