Abstract
To support decision-making around diet selection choices to manage glycemia following a meal, a novel mechanistic model of intermittent gastric emptying and plasma glucose-insulin dynamics was developed. Model development was guided by postprandial timecourses of plasma glucose, insulin and the gastric emptying marker acetaminophen in infant calves fed meals of 2 or 4 L milk replacer. Assigning a fast, slow or zero first-order gastric emptying rate to each interval between plasma samples fit acetaminophen curves with prediction errors equal to 9% of the mean observed acetaminophen concentration. Those gastric emptying parameters were applied to glucose appearance in conjunction with minimal models of glucose disposal and insulin dynamics to describe postprandial glycemia and insulinemia. The final model contains 20 parameters, 8 of which can be obtained by direct measurement and 12 by fitting to observations. The minimal model of intestinal glucose delivery contains 2 gastric emptying parameters and a third parameter describing the time lag between emptying and appearance of glucose in plasma. Sensitivity analysis of the aggregate model revealed that gastric emptying rate influences area under the plasma insulin curve but has little effect on area under the plasma glucose curve. This result indicates that pancreatic responsiveness is influenced by gastric emptying rate as a consequence of the quasi-exponential relationship between plasma glucose concentration and pancreatic insulin release. The fitted aggregate model was able to reproduce the multiple postprandial rises and falls in plasma glucose concentration observed in calves consuming a normal-sized meal containing milk components.
Highlights
The mathematical simulation of glucose-insulin dynamics in response to a meal is of great value for decision support related to management of plasma glucose in animals under our care, including domestic species and human patients
Upon consumption of a meal, the ability to dispose of the absorbed glucose, and minimize postprandial hyperglycemia and its potentially negative consequences, is dependent on the subject’s pancreatic responsiveness, insulin sensitivity and glucose effectiveness
Dt In MINMOD, PIn is a linear function of cGlP above a certain threshold [12]. This structure accommodates, with 2 parameters, the quasi-exponential relation between cGlP and pancreatic insulin release at the lower end of its sigmoidal relationship [17] but it introduces a breakpoint around the threshold cGlP value that causes the first derivative to be discontinuous, which we considered undesirable for continuous simulations that may cross this threshold several times in one run
Summary
The mathematical simulation of glucose-insulin dynamics in response to a meal is of great value for decision support related to management of plasma glucose in animals under our care, including domestic species and human patients. Tlag,SP affected peak times without altering other characteristics of the glycemic response (Fig 5) According to these simulations, each of the parameters exerted unique effects on the postprandial responses, except for similarities between KGl,PIn and expPIn, and kIs,UGl and VPIn. Gastric emptying is under neural and hormonal controls that regulate delivery of nutrients to the periphery for metabolism. Parameters that affected AUCGl the most (Table 2) were those related to pancreatic response (KGl,PIn and expPIn), followed by insulin sensitivity (kIs,UGl, Tlag,IS) and gastric emptying (kSP). The remaining parameters of glucose-insulin dynamics (kGl,UGl, kIn,UGl, Tlag,SP and Tlag,IS in eqs 7 to 9, and VPIn, KGl,PIn, expPIn, and iInP in eqs 11, 12 and 14) were estimated with a differential evolution algorithm [21] to minimize the sum of residual sums of squares between predicted and observed cGlP, and predicted and observed cInP. Percentage rMSPE for cGlP curves were 9.1% on average with the original iGlS values and 9.5% with the higher iGlS values, indicating little effect on curve fits
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