摘要
本文研究了利用外部辅助设备来治疗糖尿病的生理模型,其中存在着两个时滞:辅助设备的技术时滞τ1和肝脏的生理时滞τ2。发现由于技术时滞τ1的出现,使模型存在着共振和非共振的双Hopf分岔。应用非线性动力学理论,对由此产生的非共振分岔的动力学行为进行了分类。结果表明,随着技术时滞τ1和糖尿病人患病程度α的变化,利用该模型可以预测不同的医疗结果:血糖稳定(康复)、简单的和复杂的血糖波动。结果对分析、预测、优化糖尿病治疗方案的医疗结果、评估该方案的医疗风险和可行性等有着潜在的应用价值。本文结果的意义在于针对糖尿病患者患病的不同程度,可以定性的调节辅助设备的技术时滞τ1,以达到更好的治疗效果。
The physiological model of the diabetic treatment with external auxiliary system was considered. There are two delays, i.e., the technological delay τ1 and the liver＇s physiological delay τ2 in this model. The resonant double Hopf bifurcations and the nonresonant ones exist due to the technological delay τ1. The classification and unfolding of the nonresonant double Hopf bifurcation were done by the theory of nonlinear dynamics. The obtained results show that this model can be employed to predict the external system＇s different efficiency with the variance of the technological delay τ1 and the affection degree α, i. e. , the diabetic patients can recover or be still tormented by the simpler or complex glucose fluctuation. The results have promising applications on analyzing, predicting and optimizing the medical outcome of the treatment, evaluating the medical risk and feasibility of the treatment. The physiological meaning is for the different affection degrees α, the technological delay τ1 can be regulated qualitatively to achieve the better medical outcomes.
出处
《力学季刊》
CSCD
北大核心
2005年第3期448-450,共3页
Chinese Quarterly of Mechanics
基金
国家自然科学基金资助项目(NO:10472083)
关键词
双Hopf分岔
糖尿病
时滞
血糖稳定
血糖波动
double Hopf bifurcation
diabetes
delay
stability of blood-glucose quantity
fluctuation of blood-glucose quantity
