Contreras Sebastián, Medina-Ortiz David, Conca Carlos, Olivera-Nappa Álvaro
Centre for Biotechnology and Bioengineering (CeBiB), University of Chile, Santiago, Chile.
Department of Chemical Engineering, Biotechnology and Materials, Faculty of Physical and Mathematical Sciences, University of Chile, Santiago, Chile.
Front Bioeng Biotechnol. 2020 Mar 13;8:195. doi: 10.3389/fbioe.2020.00195. eCollection 2020.
Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.
现有的葡萄糖 - 胰岛素（G - I）动力学数学模型通常涉及不易直接测量的变量。用于测量G - I水平以诊断潜在疾病的标准临床测试简单且相对便宜，但很少能提供足够信息以在具有生物学意义的范围内识别模型参数，从而在数学建模与任何可能的生理学解释或临床解释之间产生差距。在本研究中，我们提出了一个综合数学模型来表示口服葡萄糖耐量试验（OGTT）中的G - I动力学，这是首次在与OGTT相关的模型中涉及延迟微分方程。我们的模型可以表示在407名血糖正常患者的研究队列中观察到的截然不同的行为（这是迄今为止在参数拟合实验中分析的最大队列），所有这些行为在当前基于阈值的正常标准下都被掩盖了。我们还提出了一种新颖的方法来解决参数拟合反问题，该方法涉及对不同G - I曲线进行聚类、基于模拟的可行集探索以及基于临床记录、实验不确定性和生理学标准构建重塑可行集的信息函数。这种方法允许直接使用小尺寸OGTT数据（5次测量）以个体方式识别我们模型的参数，而无需修改常规程序或需要特殊的临床设置。因此，我们的方法可以很容易地应用于获取参数见解，以补充现有的用于诊断G - I失调的工具。我们测试了个体受试者的参数稳定性和敏感性，并发现了这些指标与曲线形状之间的经验关系。由于根据我们的模型，不同的G - I曲线与不同的生理机制相关，本方法提供了一种用于个性化诊断和治疗以及更好地定义新健康标准的工具。
