A model of glucose-insulin-pramlintide pharmacokinetics and pharmacodynamics in type I diabetes

Abstract

Type 1 diabetes mellitus (T1DM) complications are significantly reduced when normoglycemic levels are maintained via intensive therapy. The artificial pancreas is designed for intensive glycemic control; however, large postprandial excursions after a meal result in poor glucose regulation. Pramlintide, a synthetic analog of the hormone amylin, reduces the severity of postprandial excursions by reducing appetite, suppressing glucagon release, and slowing the rate of gastric emptying. The goal of this study is to create a glucose-insulin-pramlintide physiological model that can be employed into a controller to improve current control approaches used in the artificial pancreas. A model of subcutaneous (SC) pramlintide pharmacokinetics (PK) was developed by revising an intravenous (IV) pramlintide PK model and adapting SC insulin PK from a glucose-insulin model. Gray-box modeling and least squares optimization were used to obtain parameter estimates. Pharmacodynamics (PD) were obtained by choosing parameters most applicable to pramlintide mechanisms and then testing using a proportional PD effect using least squares optimization. The model was fit and validated using 27 data sets, which included placebo, PK, and PD data. SC pramlintide PK root mean square error values range from 1.98 to 10.66 pmol/L. Pramlintide PD RMSE values range from 10.48 to 42.76 mg/dL. A new in silico model of the glucose-insulin-pramlintide regulatory system is presented. This model can be used as a platform to optimize dosing of both pramlintide and insulin as a combined therapy for glycemic regulation, and in the development of an artificial pancreas as the kernel for a model-based controller.

Keywords: artificial pancreas; physiology model; postprandial hyperglycemia; pramlintide; type 1 diabetes mellitus.

Figure 1.

Compartment model of glucose–insulin-pramlintide system. G₁ and G₂ represent masses in accessible (plasma) and nonaccessible compartments, Plasma_I represents plasma insulin; I_i represents insulin action on glucose transport, disposal, and endogenous glucose production; Plasma_P represents plasma pramlintide; P_i represents hypothetical compartments that affect Plasma_P; P_eff represents the effective pramlintide compartment that is used for pramlintide mechanisms on glucose. For more details, see the text.

Figure 2.

Comparison of intravenous pramlintide kinetics 3-compartment model to experimental data. The top represents intravenous bolus and the bottom represents intravenous infusion, where the left, middle, and right represent pramlintide dosages of 30, 100, and 300 mcg, respectively, where the model prediction is represented by the solid line and experimental data points are represented by the dotted line.

Figure 3.

Comparison of intravenous pramlintide kinetics 3-compartment model to experimental data. The top represents intravenous bolus and the bottom represents intravenous infusion where the left, middle, and right represent pramlintide dosages of 30, 100, and 300 mcg respectively, where the model prediction is represented by the solid line and experimental data points are represented by the dotted line.

Figure 4.

(a) Meal error (left) shows cumulative glucose consumed after a step change at t = 20 min of $t_{max,G}$ from 40 to 30 min (line with pluses), $t_{max,G}$ remaining at 40 min (line with asterisks), and $t_{max,G}$from 40 to 50 min (line with dots). (b) A gap is created when a change in $t_{max,G}$ occurs (middle). (c) Meal correction (right) compensates for the gap created by a change in $t_{max,G}$ by using difference of the total meal consumed at previous time point and total meal consumed at current time point.

Figure 5.

Fitting of pramlintide pharmacodynamics to experimental data, the top shows the placebo fit followed by pramlintide doses of 60 mcg given and t = −15, t = 0, t = 15 and t = 30 min. Model fit is represented by the solid line, experimental data points are represented by the dotted line, and the standard deviation of the experimental data is represented by the dashed line.

Figure 6.

Fitting of pramlintide subcutaneous pharmacokinetics and prediction of pramlintide pharmacodynamics to experimental data. The top shows pharmacodynamics predictions and the bottom shows pharmacokinetic fits. The left graph shows placebo fits followed by 30, 60, and 90 mcg pramlintide doses. Our model fit/prediction is represented by the solid line, experimental data points are represented by the dotted line, and the standard deviation of the experimental data is represented by the dashed line.

Figure 7.

Prediction of pramlintide pharmacodynamics and subcutaneous pharmacokinetics to experimental data. The top shows the placebo fits, the middle shows pharmacodynamics predictions, and the bottom shows pharmacokinetics predictions of 30, 100, and 300 mcg pramlintide doses, left, middle, and right, respectively. Model prediction is represented by the solid line, experimental data points are represented by the dotted line, and the standard deviation of the experimental data is represented by the dashed line.

Figure 8.

Prediction of pramlintide pharmacodynamics to experimental data. The top shows the placebo fits and the bottom shows pharmacodynamics predictions of 10, 30, and 100 mcg pramlintide doses, left middle, and right, respectively. Model prediction is represented by the solid line, experimental data points are represented by the dotted line, and the standard deviation of the experimental data is represented by the dashed line.

Figure 9.

Prediction of pramlintide pharmacodynamics and intravenous pharmacokinetics to experimental data. The top shows the pharmacodynamics predictions and the bottom shows pharmacokinetic predictions of 30, 100, and 300 mcg pramlintide doses, left, middle, and right, respectively. Model prediction is represented by the solid line, experimental data points are represented by the dotted line, Fang et al’s predicted pharmacodynamics are represented by the line with asterisks, and the standard deviation of the experimental data is represented by the dashed line.