Bayesian Learning Based Optimization of Meal Bolus Dosage for Intelligent Glucose Management
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摘要: 餐前胰岛素剂量精准决策是改善糖尿病患者血糖管理的关键. 临床治疗中胰岛素剂量调整一般在较短时间内完成, 具有典型的小样本特征; 数据驱动建模在该情形下无法准确学习患者餐后血糖代谢规律, 难以确保胰岛素剂量的安全和有效决策. 针对这一问题, 设计一种临床经验辅助的餐前胰岛素剂量自适应优化决策框架, 构建高斯过程血糖预测模型和模型有效性在线评估机制, 提出基于历史剂量和临床经验决策约束的贝叶斯优化方法, 实现小样本下餐后血糖轨迹的安全预测和餐前胰岛素注射剂量的优化决策. 该方法的安全性和有效性通过美国食品药品监督管理局接受的UVA/Padova T1DM平台测试结果和1型糖尿病患者实际临床数据决策结果充分验证. 可为餐前胰岛素剂量智能决策及临床试验提供方法基础和技术支持, 也为中国糖尿病患者血糖管理水平的有效改善, 提供了精准医学治疗手段.Abstract: Precise decision of preprandial insulin bolus is of crucial importance to achieving enhanced glucose management for patients with diabetes. Insulin dosage adjustment in current clinical practice normally needs to be completed in a relatively short period of time and thus the data size is typically small. It would be consequently challenging to accurately learn the postprandial glucose metabolism through data-driven modelling techniques and to further ensure the safe and efficient insulin dosage decision. For this problem, a clinical-experience-assisted adaptive preprandial insulin bolus decision framework is proposed in this work. To achieve safe prediction of the postprandial glucose traces and optimal decision of the preprandial insulin dosage with limited training data, a Gaussian process based glucose prediction model and an online model efficiency assessment mechanism are constructed, and a Bayesian optimization method with historical data exploitation and clinical-experience guided decision constraints is proposed. The safety and effectiveness of the proposed method are extensively validated through in silico results of the US Food and Drug Administration accepted UVA/Padova T1DM simulator and advisory mode analysis based on clinical data from a subject with type 1 diabetes. The obtained results provide methodological and technical support for intelligent meal bolus decision and the forthcoming clinical studies, and introduce a precision medicine solution to effectively improved glucose management for Chinese patients with diabetes mellitus.
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图 1 餐前胰岛素剂量贝叶斯学习优化方法框架图
Fig. 1 Block diagram of the Bayesian learning based optimization method for meal bolus
图 4 前期剂量正常$r=1$情形下, 餐后血糖调节和剂量决策比较结果
Fig. 4 Comparison of postprandial glucose regulation and dosage decision in the case of normal boluses in the early stage when$r=1$
图 5 前期餐前剂量偏少$ r = 0.5 $情形下, 餐后血糖调节和剂量决策比较结果
Fig. 5 Comparison of postprandial glucose regulation and dosage decision in the case of under-estimated boluses in the early stage when$ r = 0.5 $
图 6 前期餐前剂量偏多$ r = 1.5 $情形下, 餐后血糖调节和剂量决策比较结果
Fig. 6 Comparison of postprandial glucose regulation and dosage decision in the case of over-estimated boluses in the early stage when$ r = 1.5 $
图 7 膳食扰动下, 本文方法与R2R方法餐后血糖调节和剂量决策比较结果
Fig. 7 Comparison of postprandial glucose regulation and dosage decision in the case of meal disturbance between the proposed method and the R2R method
图 9 基于临床数据的餐前剂量决策评估结果
Fig. 9 The evaluation results for the meal bolus decision based on the clinical data
表 1 方法参数
Table 1 The parameters of the proposed method
变量 含义 值 $ \gamma $ 风险敏感参数 −2 $ R $ 权重系数 10 $ u_{\max} $ 最大剂量约束值 20 $ M $ 最大优化次数 25 $ {Q\mathit{\boldsymbol{}}}_b $ 基准惩罚矩阵 $\rm{diag}\{0.0025,\cdots, 0.0025,$ $0.005,0.005\}$ $ \Gamma $ 不对称惩罚强度 $ \{1,10,5,1\} $ $ {G\mathit{\boldsymbol{}}}_r $ 餐后血糖控制目标 $[110,130,150,170, 160,$ $150,150,150]^{\rm{T} }$ $ \Delta u $ 评估增量 $ 2 $ $ G_h $ 餐后血糖高阈值 $ 120 $ $ G_l $ 餐后血糖低阈值 $ 80 $ $ \Delta G $ 餐前血糖均值增量 $ 30 $ 
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表 2 前期餐前剂量正常情形下$r = 1 $血糖控制评估结果 (%)
Table 2 Evaluation results of the glucose control in the case of normal boluses in the early stage when$r=1 $ (%)
评价指标 标准方法 本文方法 $ p $ 值 < 54 mg/dL (%) 0 (0) 0 (0) 1.000 < 70 mg/dL (%) 0 (0) 0 (0) 1.000 70 ~ 180 mg/dL (%) 93.6 (7.5) 92.3 (6.6) 0.188 > 250 mg/dL (%) 0 (0) 0 (0) 1.000 血糖平均值(mg/dL) 133.2 (9.4) 132.5 (14.0) 1.000 标准差(mg/dL) 30.2 (7.0) 30.3 (4.4) 0.037 7:00血糖平均值(mg/dL) 109.8 (11.0) 109.3 (8.0) 0.195
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表 3 前期餐前剂量偏少/偏多情形下血糖控制评估结果(%)
Table 3 Evaluation results of the glucose control in the case of under-estimated/over-estimated boluses in the early stage (%)
评价指标 前期餐前剂量偏少($ r = 0.5 $) 前期餐前剂量偏多($ r = 1.5 $) 标准方法 本文方法 $ p $ 值 标准方法 本文方法 $ p $ 值 < 54 mg/dL (%) 0 (0) 0 (0) 1.000 1.6 (3.8) 0 (0) 0.031 < 70 mg/dL (%) 0 (0) 0 (0) 1.000 6.5 (7.8) 0 (1.4) 0.008 70 ~ 180 mg/dL (%) 64.8 (23.6) 77.1 (18.4) 0.004 91.6 (6.9) 95.6 (2.6) 0.232 > 250 mg/dL (%) 1.0 (4.5) 0 (0) 0.031 0 (0) 0 (0) 1.000 血糖平均值 (mg/dL) 162.1 (29.2) 148.7 (16.8) 0.004 114.9 (9.0) 125.6 (10.5) 0.002 标准差 (mg/dL) 37.9 (7.6) 35.8 (5.6) 0.010 29.4 (6.2) 30.9 (5.3) 0.049 7:00血糖平均值 (mg/dL) 118.0 (20.0) 113.0 (9.5) 0.008 104.8 (10.0) 108.0 (12.5) 0.039
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表 4 膳食扰动下血糖控制评估结果(%)
Table 4 Evaluation results of the glucose control in the case of meal disturbance (%)
评价指标 R2R 本文方法 $ p $ 值 $< $54 mg/dL (%) 0 (0.7) 0 (0) 0.250 $< $70 mg/dL (%) 3.6 (8.3) 0 (0) 0.016 70 ~ 180 mg/dL (%) 87.7 (13.0) 89.1 (5.6) 0.625 $>$250 mg/dL (%) 0 (0) 0 (0) 1.000 血糖平均值(mg/dL) 123.8 (10.6) 131.3 (7.0) 0.006 标准差(mg/dL) 36.0 (9.4) 34.9 (7.5) 0.432 7:00血糖平均值(mg/dL) 102.8 (12.0) 103.8 (8.5) 0.004
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