Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes
Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes
复制标题
使用随机微分方程灰盒模型进行糖尿病模型识别
DOI：
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发表时间：
2013
影响因子：
5
通讯作者：
H. Madsen
中科院分区：
文献类型：
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作者：
A. Duun;S. Schmidt;R. M. Røge;J. Møller;K. Nørgaard;J. B. Jørgensen;H. Madsen
背景：对控制算法的虚拟临床前测试的接受度正在增长，因此也需要鲁棒可靠的模型。基于常微分方程（ode）的模型很少能用标准统计工具验证。随机微分方程（SDEs）提供了建立模型的可能性，这些模型可以进行统计验证，并且不仅能够预测现实的轨迹，而且能够预测预测的不确定性。在SDE中，预测误差被分成两个噪声项。这种分离确保了错误是不相关的，并提供了查明模型缺陷的可能性。方法：以1型糖尿病（T1DM）患者血糖调节系统的可识别模型为基础，建立基于随机微分方程的灰盒模型（SDE-GB）。这些参数是根据4例T1DM患者的临床数据估计的。最优SDE-GB由似然比检验确定。最后，采用参数跟踪的方法，对“进餐反应到达峰值时间”参数的变化进行跟踪。结果：我们发现将ODE模型转换为SDE-GB后，预测误差和不相关误差显著改善。对“吸粕峰时间”参数的跟踪表明，不同种类的吸粕速率不同。结论：本研究显示了SDE-GBs在糖尿病建模中的潜力。由于预测误差的分离，得到了较好的模型预测结果。sde - gb为使用统计工具进行模型验证和模型开发提供了一个坚实的框架。
Background: The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. Methods: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the “time to peak of meal response” parameter. Results: We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the “peak time of meal absorption” parameter showed that the absorption rate varied according to meal type. Conclusion: This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development.