Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125, USA.
Division of Endocrinology, Metabolism and Diabetes, Department of Medicine, School of Medicine, University of Colorado Anschutz Medical Campus, Aurora, Colorado 80045, USA.
Chaos. 2023 Jul 1;33(7). doi: 10.1063/5.0146808.
Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.
用常规收集的数据预测血糖 (BG) 水平对于血糖管理很有用。BG 动态是非线性、复杂且非平稳的，可以用非线性模型来表示。然而，当使用高保真度的复杂模型时，常规收集的数据稀疏性会导致参数可识别性问题，从而导致预测不准确。人们可以使用具有较低生理保真度的模型来进行稳健且准确的参数估计和稀疏数据预测。为此，我们通过线性随机微分方程来近似 BG 调节的非线性动态：我们开发了一种线性随机模型，它可以针对不同的设置进行专门化：2 型糖尿病 (T2DM) 和重症监护病房 (ICU)，并选择适当的模型函数。该模型包括定量描述血糖通过血糖调节系统从血液中去除的确定性项，并代表营养和外部给予的胰岛素的作用。随机项包含 BG 振荡。模型输出以伴随该值周围的带的形式给出。模型参数是针对特定患者进行估计的，从而产生个性化模型。预测包括 BG 均值和变化的值，量化可能的高和低 BG 水平。这些预测有可能作为控制系统的一部分用于血糖管理。我们展示了 T2DM 和 ICU 环境中的参数估计和预测的实验结果。我们将该模型的预测能力与为 T2DM 和 ICU 上下文构建的两个不同的非线性模型进行了比较，以了解该模型实现的预测水平。
