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, Sten Madsbad, Henrik Madsen, Kirsten Nørgaard, John Bagterp Jørgensen

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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.
Original languageEnglish
JournalJournal of Diabetes Science and Technology
Volume11
Issue number6
Pages (from-to)1101-1111
ISSN1932-2968
DOIs
Publication statusPublished - 2017

Keywords

  • Cross-validation
  • Glucagon
  • Glucoregulatory model
  • Parameter Estimation
  • Simulation model
  • Type 1 diabetes

Cite this

Wendt, Sabrina Lyngbye ; Ranjan, Ajenthen ; Møller, Jan Kloppenborg ; Schmidt, Signe ; Boye Knudsen, Carsten ; Holst, Jens Juul ; Madsbad, Sten ; Madsbad, Sten ; Madsen, Henrik ; Nørgaard, Kirsten ; Jørgensen, John Bagterp. / Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation using Data from Patients with Type 1 Diabetes. In: Journal of Diabetes Science and Technology. 2017 ; Vol. 11, No. 6. pp. 1101-1111.
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title = "Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation using Data from Patients with Type 1 Diabetes",
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.",
keywords = "Cross-validation, Glucagon, Glucoregulatory model, Parameter Estimation, Simulation model, Type 1 diabetes",
author = "Wendt, {Sabrina Lyngbye} and Ajenthen Ranjan and M{\o}ller, {Jan Kloppenborg} and Signe Schmidt and {Boye Knudsen}, Carsten and Holst, {Jens Juul} and Sten Madsbad and Sten Madsbad and Henrik Madsen and Kirsten N{\o}rgaard and J{\o}rgensen, {John Bagterp}",
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volume = "11",
pages = "1101--1111",
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issn = "1932-2968",
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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; Schmidt, Signe; Boye Knudsen, Carsten; Holst, Jens Juul; Madsbad, Sten; Madsbad, Sten; Madsen, Henrik; Nørgaard, Kirsten; Jørgensen, John Bagterp.

In: Journal of Diabetes Science and Technology, Vol. 11, No. 6, 2017, p. 1101-1111.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Cross-Validation of a Glucose-Insulin-Glucagon Pharmacodynamics Model for Simulation using Data from Patients with Type 1 Diabetes

AU - Wendt, Sabrina Lyngbye

AU - Ranjan, Ajenthen

AU - Møller, Jan Kloppenborg

AU - Schmidt, Signe

AU - Boye Knudsen, Carsten

AU - Holst, Jens Juul

AU - Madsbad, Sten

AU - Madsbad, Sten

AU - Madsen, Henrik

AU - Nørgaard, Kirsten

AU - Jørgensen, John Bagterp

PY - 2017

Y1 - 2017

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.

KW - Cross-validation

KW - Glucagon

KW - Glucoregulatory model

KW - Parameter Estimation

KW - Simulation model

KW - Type 1 diabetes

U2 - 10.1177/1932296817693254

DO - 10.1177/1932296817693254

M3 - Journal article

C2 - 28654314

VL - 11

SP - 1101

EP - 1111

JO - Journal of Diabetes Science and Technology

JF - Journal of Diabetes Science and Technology

SN - 1932-2968

IS - 6

ER -