Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes

Sabrina Lyngbye Wendt; Ajenthen Ranjan; Jan Kloppenborg Møller; Signe Schmidt; Carsten Boye Knudsen; Jens Juul Holst; Sten Madsbad; Henrik Madsen; Kirsten Nørgaard; John Bagterp Jørgensen

doi:10.1177/1932296817693254

Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes

Sabrina Lyngbye Wendt^*, Ajenthen Ranjan, Jan Kloppenborg Møller, Signe Schmidt, Carsten Boye Knudsen, Jens Juul Holst, Sten Madsbad, Henrik Madsen, Kirsten Nørgaard, John Bagterp Jørgensen

^*Corresponding author for this work

Department of Clinical Medicine

9 Citations (Scopus)

Abstract

Background: Currently, no consensus exists on a model describing endogenous glucose production (EGP) as a function of glucagon concentrations. Reliable simulations to determine the glucagon dose preventing or treating hypoglycemia or to tune a dual-hormone artificial pancreas control algorithm need a validated glucoregulatory model including the effect of glucagon. Methods: Eight type 1 diabetes (T1D) patients each received a subcutaneous (SC) bolus of insulin on four study days to induce mild hypoglycemia followed by a SC bolus of saline or 100, 200, or 300 µg of glucagon. Blood samples were analyzed for concentrations of glucagon, insulin, and glucose. We fitted pharmacokinetic (PK) models to insulin and glucagon data using maximum likelihood and maximum a posteriori estimation methods. Similarly, we fitted a pharmacodynamic (PD) model to glucose data. The PD model included multiplicative effects of insulin and glucagon on EGP. Bias and precision of PD model test fits were assessed by mean predictive error (MPE) and mean absolute predictive error (MAPE). Results: Assuming constant variables in a subject across nonoutlier visits and using thresholds of ±15% MPE and 20% MAPE, we accepted at least one and at most three PD model test fits in each of the seven subjects. Thus, we successfully validated the PD model by leave-one-out cross-validation in seven out of eight T1D patients. Conclusions: The PD model accurately simulates glucose excursions based on plasma insulin and glucagon concentrations. The reported PK/PD model including equations and fitted parameters allows for in silico experiments that may help improve diabetes treatment involving glucagon for prevention of hypoglycemia.

Original language	English
Journal	Journal of Diabetes Science and Technology
Volume	11
Issue number	6
Pages (from-to)	1101-1111
Number of pages	11
ISSN	1932-2968
DOIs	https://doi.org/10.1177/1932296817693254
Publication status	Published - 1 Nov 2017

Keywords

cross-validation
glucagon
glucoregulatory model
parameter estimation
simulation model
type 1 diabetes

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Wendt, S. L., Ranjan, A., Møller, J. K., Schmidt, S., Knudsen, C. B., Holst, J. J., Madsbad, S., Madsen, H., Nørgaard, K., & Jørgensen, J. B. (2017). Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes. Journal of Diabetes Science and Technology, 11(6), 1101-1111. https://doi.org/10.1177/1932296817693254

Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes. / Wendt, Sabrina Lyngbye; Ranjan, Ajenthen; Møller, Jan Kloppenborg et al.

In: Journal of Diabetes Science and Technology, Vol. 11, No. 6, 01.11.2017, p. 1101-1111.

Research output: Contribution to journal › Journal article › Research › peer-review

Wendt, SL, Ranjan, A, Møller, JK, Schmidt, S, Knudsen, CB, Holst, JJ , Madsbad, S, Madsen, H, Nørgaard, K & Jørgensen, JB 2017, 'Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes', Journal of Diabetes Science and Technology, vol. 11, no. 6, pp. 1101-1111. https://doi.org/10.1177/1932296817693254

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abstract = "Background: Currently, no consensus exists on a model describing endogenous glucose production (EGP) as a function of glucagon concentrations. Reliable simulations to determine the glucagon dose preventing or treating hypoglycemia or to tune a dual-hormone artificial pancreas control algorithm need a validated glucoregulatory model including the effect of glucagon. Methods: Eight type 1 diabetes (T1D) patients each received a subcutaneous (SC) bolus of insulin on four study days to induce mild hypoglycemia followed by a SC bolus of saline or 100, 200, or 300 µg of glucagon. Blood samples were analyzed for concentrations of glucagon, insulin, and glucose. We fitted pharmacokinetic (PK) models to insulin and glucagon data using maximum likelihood and maximum a posteriori estimation methods. Similarly, we fitted a pharmacodynamic (PD) model to glucose data. The PD model included multiplicative effects of insulin and glucagon on EGP. Bias and precision of PD model test fits were assessed by mean predictive error (MPE) and mean absolute predictive error (MAPE). Results: Assuming constant variables in a subject across nonoutlier visits and using thresholds of ±15% MPE and 20% MAPE, we accepted at least one and at most three PD model test fits in each of the seven subjects. Thus, we successfully validated the PD model by leave-one-out cross-validation in seven out of eight T1D patients. Conclusions: The PD model accurately simulates glucose excursions based on plasma insulin and glucagon concentrations. The reported PK/PD model including equations and fitted parameters allows for in silico experiments that may help improve diabetes treatment involving glucagon for prevention of hypoglycemia.",

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AU - Wendt, Sabrina Lyngbye

AU - Ranjan, Ajenthen

AU - Møller, Jan Kloppenborg

AU - Schmidt, Signe

AU - Knudsen, Carsten Boye

AU - Holst, Jens Juul

AU - Madsbad, Sten

AU - Madsen, Henrik

AU - Nørgaard, Kirsten

AU - Jørgensen, John Bagterp

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N2 - Background: Currently, no consensus exists on a model describing endogenous glucose production (EGP) as a function of glucagon concentrations. Reliable simulations to determine the glucagon dose preventing or treating hypoglycemia or to tune a dual-hormone artificial pancreas control algorithm need a validated glucoregulatory model including the effect of glucagon. Methods: Eight type 1 diabetes (T1D) patients each received a subcutaneous (SC) bolus of insulin on four study days to induce mild hypoglycemia followed by a SC bolus of saline or 100, 200, or 300 µg of glucagon. Blood samples were analyzed for concentrations of glucagon, insulin, and glucose. We fitted pharmacokinetic (PK) models to insulin and glucagon data using maximum likelihood and maximum a posteriori estimation methods. Similarly, we fitted a pharmacodynamic (PD) model to glucose data. The PD model included multiplicative effects of insulin and glucagon on EGP. Bias and precision of PD model test fits were assessed by mean predictive error (MPE) and mean absolute predictive error (MAPE). Results: Assuming constant variables in a subject across nonoutlier visits and using thresholds of ±15% MPE and 20% MAPE, we accepted at least one and at most three PD model test fits in each of the seven subjects. Thus, we successfully validated the PD model by leave-one-out cross-validation in seven out of eight T1D patients. Conclusions: The PD model accurately simulates glucose excursions based on plasma insulin and glucagon concentrations. The reported PK/PD model including equations and fitted parameters allows for in silico experiments that may help improve diabetes treatment involving glucagon for prevention of hypoglycemia.

AB - Background: Currently, no consensus exists on a model describing endogenous glucose production (EGP) as a function of glucagon concentrations. Reliable simulations to determine the glucagon dose preventing or treating hypoglycemia or to tune a dual-hormone artificial pancreas control algorithm need a validated glucoregulatory model including the effect of glucagon. Methods: Eight type 1 diabetes (T1D) patients each received a subcutaneous (SC) bolus of insulin on four study days to induce mild hypoglycemia followed by a SC bolus of saline or 100, 200, or 300 µg of glucagon. Blood samples were analyzed for concentrations of glucagon, insulin, and glucose. We fitted pharmacokinetic (PK) models to insulin and glucagon data using maximum likelihood and maximum a posteriori estimation methods. Similarly, we fitted a pharmacodynamic (PD) model to glucose data. The PD model included multiplicative effects of insulin and glucagon on EGP. Bias and precision of PD model test fits were assessed by mean predictive error (MPE) and mean absolute predictive error (MAPE). Results: Assuming constant variables in a subject across nonoutlier visits and using thresholds of ±15% MPE and 20% MAPE, we accepted at least one and at most three PD model test fits in each of the seven subjects. Thus, we successfully validated the PD model by leave-one-out cross-validation in seven out of eight T1D patients. Conclusions: The PD model accurately simulates glucose excursions based on plasma insulin and glucagon concentrations. The reported PK/PD model including equations and fitted parameters allows for in silico experiments that may help improve diabetes treatment involving glucagon for prevention of hypoglycemia.

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KW - simulation model

KW - type 1 diabetes

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SN - 1932-2968

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JO - Journal of diabetes science and technology

JF - Journal of diabetes science and technology

IS - 6

ER -

Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation Using Data From Patients With Type 1 Diabetes

Abstract

Keywords

UN SDGs

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