A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data

Abstract

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.

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“…To obtain reliable values for the selected parameters, Monte Carlo simulations [35] were performed according to the methodology described in Contreras et al. [14] ( ). In these simulations, we induce a white noise in the input data, and fit the parameters using this mildly noisy signal.…”

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“… 114 , 128 Therefore, to help resolve the heterogeneity in glucose curve shape, various statistical and epidemiological modeling techniques have been employed. 114 , 135 , 136 One example, functional data analysis, utilizes the entire glucose curve to identify typical temporal morphologies instead of single glucose measurements at specific time points. Compared to simple shape classifications, functional component analysis improved risk classification for GDM in their first trimester of pregnancy.…”

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“…(2). Using their curves and the model of Contreras et al (23), we obtain their physiological parameters and non-dimensional numbers. (3).…”

“…Mathematical modelling has long been used to quantify the G-I function. We recently presented a model ( 23 ) representing G-I dynamics as a set of separate coordinated subsystems, each characterised by quantitative physiological parameters. Parameters are obtained in a patient-wise manner from a low-cost, non-invasive, routine Oral Glucose Tolerance Test (OGTT) with insulinemia measurements at 5-time points, instead of the standard 2 points (cf.…”

“…Different colours represent selected individual subjects in the healthy (A,B) and non-healthy (C,D) cohorts whose glycemia curves are similar, but having different insulinemia curves (subjects 370/402 and 94/406), or similar insulinemia curves but different glycemia curves (subject 251/377 and 784/715). (E) G-I dynamics during an OGTT can be represented by a compact compartmental mathematical model ( 23 ), where the main physiological processes in G-I dynamics are represented as subsystems. Compartments are represented by coloured boxes (orange for glucose pools in the lumen of the digestive system, magenta for blood concentrations and green for the liver compartment).…”