Mathematical modeling of gastrointestinal starch digestion-blood glucose-insulin interactions

A Fractional‐Order Kinetics Approach for Modeling Enzymatic Starch Multiscale Digestion

“…and Γ is the gamma function (i.e., an extension of the factorial function for nonintegers). It is noted that the structure of Equation ( 12) is like that of the exponential model (1). Such a similar structure is because the Mittag-Leffler function is a generalization of the standard exponential function.…”

“…where X(t) is the time-dependent starch conversion, X ∞ is the maximal starch conversion and k H is the hydrolysis rate constant. Equation (1) states that…”

“…Essentially, the above differential equation is consistent with the simple kinetics scheme S K H → P (5) which states that the conversion of the starch S into products P follows a first-order kinetics. Given its simplicity and easy interpretation of the parameters, the exponential model given by Equation (1) is the most widely model employed to describe starch digestograms. [4] Despite its widespread usage, the exponential model (1) exhibits some important limitations, with the prediction of a unique time scale being the main limitation.…”

“…has shown to be an alternative for the accurate fitting of starch digestograms. [12] For 0 < a < 1, Weibull's model corresponds to a stretched-time version of the conventional exponential model (1). Intuitively, Equation (7) recasts the variations in time of the hydrolysis mechanisms by tacitly assuming a nonconstant rate parameter:…”

“…An accurate fitting of digestograms accompanied by the model's parameters with a reliable physical interpretation is an important issue for, e.g., assessing the impact of starchy food matrices in the dynamical behavior of blood insulin-glucose interactions. [1] The present work explores the use of fractional-order kinetics for the modeling of starch digestograms. The aim is to show that a) the fractional-order framework offers a framework for capturing multiscale patterns observed, and b) to show that the increasingly used Weibull and Peleg models are particular cases of a model expressed in terms of a generalized exponential function (i.e., Mittag-Leffler function).…”