Advertisement

Journal of Pharmacokinetics and Pharmacodynamics

, Volume 44, Issue 5, pp 477–489 | Cite as

Evaluation of pharmacokinetic model designs for subcutaneous infusion of insulin aspart

  • Erin J. Mansell
  • Signe Schmidt
  • Paul D. Docherty
  • Kirsten Nørgaard
  • John B. Jørgensen
  • Henrik Madsen
Original Paper

Abstract

Effective mathematical modelling of continuous subcutaneous infusion pharmacokinetics should aid understanding and control in insulin therapy. Thorough analysis of candidate model performance is important for selecting the appropriate models. Eight candidate models for insulin pharmacokinetics included a range of modelled behaviours, parameters and complexity. The models were compared using clinical data from subjects with type 1 diabetes with continuous subcutaneous insulin infusion. Performance of the models was compared through several analyses: R2 for goodness of fit; the Akaike Information Criterion; a bootstrap analysis for practical identifiability; a simulation exercise for predictability. The simplest model fit poorly to the data (R2 = 0.53), had the highest Akaike score, and worst prediction. Goodness of fit improved with increasing model complexity (R2 = 0.85–0.92) but Akaike scores were similar for these models. Complexity increased practical non-identifiability, where small changes in the dataset caused large variation (CV > 10%) in identified parameters in the most complex models. Best prediction was achieved in a relatively simple model. Some model complexity was necessary to achieve good data fit but further complexity introduced practical non-identifiability and worsened prediction capability. The best model used two linear subcutaneous compartments, an interstitial and plasma compartment, and two identified variables for interstitial clearance and subcutaneous transfer rate. This model had optimal performance trade-off with reasonable fit (R2 = 0.85) and parameterisation, and best prediction and practical identifiability (CV < 2%).

Keywords

Pharmacokinetic modelling Continuous subcutaneous insulin infusion Type 1 diabetes Parameter identification Goodness of fit Practical identifiability 

Notes

Acknowledgements

Clinical data collection was funded by the Danish Council for Strategic Research (NABIIT Project 2106-07-0034).”

References

  1. 1.
    Rasmussen CH, Røge RM, Ma Z, Thomsen M, Thorisdottir RL, Chen JW, Mosekilde E, Colding-Jørgensen M (2014) Insulin aspart pharmacokinetics: an assessment of its variability and underlying mechanisms. Eur J Pharm Sci 62:65–75. doi: 10.1016/j.ejps.2014.05.010 CrossRefPubMedGoogle Scholar
  2. 2.
    Lindholm A, Jacobsen LV (2001) Clinical pharmacokinetics and pharmacodynamics of insulin aspart. Clin Pharmacokinet 40(9):641–659CrossRefPubMedGoogle Scholar
  3. 3.
    Home PD, Barriocanal L, Lindholm A (1999) Comparative pharmacokinetics and pharmacodynamics of the novel rapid- acting insulin analogue, insulin aspart, in healthy volunteers. Eur J Clin Pharmacol 55(3):199–203. doi: 10.1007/s002280050618 CrossRefPubMedGoogle Scholar
  4. 4.
    Kang S, Brange J, Burch A, Volund A, Owens DR (1991) Subcutaneous insulin absorption explained by insulin’s physicochemical properties. Evidence from absorption studies of soluble human insulin and insulin analogues in humans. Diabetes Care 14(11):942–948CrossRefPubMedGoogle Scholar
  5. 5.
    Brems DN, Alter LA, Beckage MJ, Chance RE, DiMarchi RD, Green LK, Long HB, Pekar AH, Shields JE, Frank BH (1992) Altering the association properties of insulin by amino acid replacement. Protein Eng 5(6):527–533CrossRefPubMedGoogle Scholar
  6. 6.
    Wilinska ME, Chassin LJ, Schaller HC, Schaupp L, Pieber TR, Hovorka R (2005) Insulin kinetics in type-1 diabetes: continuous and bolus delivery of rapid acting insulin. IEEE Trans Biomed Eng 52(1):3–12. doi: 10.1109/TBME.2004.839639 CrossRefPubMedGoogle Scholar
  7. 7.
    Wong J, Chase JG, Hann CE, Shaw GM, Lotz TF, Lin J, Le Compte AJ (2008) A subcutaneous insulin pharmacokinetic model for computer simulation in a diabetes decision support role: model structure and parameter identification. J Diabetes Sci Technol 2(4):658–671CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Wong J, Chase JG, Hann CE, Shaw GM, Lotz TF, Lin J, Le Compte AJ (2008) A subcutaneous insulin pharmacokinetic model for computer simulation in a diabetes decision support role: validation and simulation. J Diabetes Sci Technol 2(4):672–680CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Li J, Johnson JD (2009) Mathematical models of subcutaneous injection of insulin analogues: a mini-review. Discrete Continuous Dyn Syst Ser B 12(2):401–414. doi: 10.3934/dcdsb.2009.12.401 CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Lehmann ED, Tarín C, Bondia J, Teufel E, Deutsch T (2009) Incorporating a generic model of subcutaneous insulin absorption into the aida v4 diabetes simulator 3. Early plasma insulin determinations. J Diabetes Sci Technol 3(1):190–201CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Nilam Alexander ME, Mathur R, Moghadas SM, Shivakumar PN (2007) Modelling the effect of csii on the control of glucose concentration in type 1 diabetes. Appl Math Comput 187(2):1476–1483. doi: 10.1016/j.amc.2006.09.105 Google Scholar
  12. 12.
    Li J, Kuang Y (2009) Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes. Math Biosci Eng 6(1):41–58PubMedPubMedCentralGoogle Scholar
  13. 13.
    Song X, Huang M, Li J (2014) Modeling impulsive insulin delivery in insulin pump with time delays. SIAM J Appl Math 74(6):1763–1785. doi: 10.1137/130933137 CrossRefGoogle Scholar
  14. 14.
    Schmidt S, Finan DA, Duun-Henriksen AK, Jorgensen JB, Madsen H, Bengtsson H, Holst JJ, Madsbad S, Norgaard K (2012) Effects of everyday life events on glucose, insulin, and glucagon dynamics in continuous subcutaneous insulin infusion-treated type 1 diabetes: collection of clinical data for glucose modeling. Diabetes Technol Ther 14(3):210–217. doi: 10.1089/dia.2011.0101 CrossRefPubMedGoogle Scholar
  15. 15.
    Docherty PD, Chase JG, Lotz TF, Desaive T (2011) A graphical method for practical and informative identifiability analyses of physiological models: A case study of insulin kinetics and sensitivity. Biomed Eng Online 10(1):39CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923–1929. doi: 10.1093/bioinformatics/btp358 CrossRefPubMedGoogle Scholar
  17. 17.
    Saccomani MP Structural vs practical identifiability in system biology. In: Rojas I, Guzman FMO (eds) IWBBIO, Granada, 2013. Copicentro Editorial, pp 305–313Google Scholar
  18. 18.
    Duun-Henriksen AK, Schmidt S, Nørgaard K, Madsen H (2013) Clinical data for advanced glucose modeling. Technical University of Denmark, LyngbyGoogle Scholar
  19. 19.
    Eaton RP, Allen RC, Schade DS, Erickson KM, Standefer J (1980) Prehepatic insulin production in man: kinetic analysis using peripheral connecting peptide behavior. J Clin Endocrinol Metab 51(3):520–528CrossRefPubMedGoogle Scholar
  20. 20.
    Fisk LM, Docherty PD, Pretty CG, Chase JG (2016) Incorporating bolus and infusion parmacokinetics into the icing insulin model. Math Biosci 281(11):1–8. doi: 10.1016/j.mbs.2016.08.005 CrossRefPubMedGoogle Scholar
  21. 21.
    Lin J, Razak NN, Pretty CG, Le Compte A, Docherty P, Parente JD, Shaw GM, Hann CE, Geoffrey Chase J (2011) A physiological intensive control insulin-nutrition-glucose (icing) model validated in critically ill patients. Comput Methods Programs Biomed 102(2):192–205. doi: 10.1016/j.cmpb.2010.12.008 CrossRefPubMedGoogle Scholar
  22. 22.
    Petersen SB, Lovmand JM, Honoré L, Jeppesen CB, Pridal L, Skyggebjerg O (2010) Comparison of a luminescent oxygen channeling immunoassay and an elisa for detecting insulin aspart in human serum. J Pharm Biomed Anal 51(1):217–224. doi: 10.1016/j.jpba.2009.08.008 CrossRefPubMedGoogle Scholar
  23. 23.
    Baker SM, Poskar CH, Schreiber F, Junker BH (2015) A unified framework for estimating parameters of kinetic biological models. BMC Bioinform 16(1):1–21. doi: 10.1186/s12859-015-0500-9 CrossRefGoogle Scholar
  24. 24.
    Pironet A, Dauby PC, Chase JG, Docherty PD, Revie J, Desaive T (2016) Structural identifiability of a cardiovascular system model. Med Eng Phys 38(5):433–441CrossRefPubMedGoogle Scholar
  25. 25.
    Pironet A, Docherty PD, Dauby PC, Chase JG, Desaive T (2017) Practical identifiability analysis of a minimal cardiovascular system model. Comput Methods Programs in Biomed. doi: 10.1016/j.cmpb.2017.01.005 Google Scholar
  26. 26.
    Audoly S, Bellu G, D’Angio L, Saccomani MP, Cobelli C (2001) Global identifiability of nonlinear models of biological systems. IEEE Trans Biomed Eng 48(1):55–65CrossRefPubMedGoogle Scholar
  27. 27.
    Audoly S, D’Angio L, Saccomani MP, Cobelli C (1998) Global identifiability of linear compartmental models: a computer algebra algorithm. IEEE Trans Biomed Eng 45(1):36–47CrossRefPubMedGoogle Scholar
  28. 28.
    Bellu G, Saccomani MP, Audoly S, D’Angio L (2007) Daisy: a new software tool to test global identifiability of biological and physiological systems. Comput Methods Programs Biomed 88(1):52–61CrossRefPubMedPubMedCentralGoogle Scholar
  29. 29.
    Mansell EJ, Docherty PD, Fisk LM, Chase JG (2015) Estimation of secondary effect parameters in glycaemic dynamics using accumulating data from a virtual type 1 diabetic patient. Math Biosci 266(8):108–117. doi: 10.1016/j.mbs.2015.06.002 CrossRefPubMedGoogle Scholar
  30. 30.
    Docherty PD, Chase JG, Lotz T, Hann CE, Shaw GM, Berkeley JE, Mann JI, McAuley KA (2009) Distq: an iterative analysis of glucose data for low-cost real-time and accurate estimation of insulin sensitivity. Open Med Inform J 3:65–76CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Lotz TF, Chase JG, McAuley KA, Shaw GM, Docherty PD, Berkeley JE, Williams SM, Hann CE, Mann JI (2010) Design and clinical pilot testing of the model-based dynamic insulin sensitivity and secretion test (disst). J Diabetes Sci Technol 4(6):1408–1423CrossRefPubMedPubMedCentralGoogle Scholar
  32. 32.
    Kang S, Creagh FM, Peters JR, Brange J, Volund A, Owens DR (1991) Comparison of subcutaneous soluble human insulin and insulin analogs (aspb9, glub27-aspb10-aspb28) on meal-related plasma-glucose excursions in type-i diabetic subjects. Diabetes Care 14(7):571–577CrossRefPubMedGoogle Scholar
  33. 33.
    Nucci G, Cobelli C (2000) Models of subcutaneous insulin kinetics. A critical review. Comput Methods Programs Biomed 62(3):249–257CrossRefPubMedGoogle Scholar
  34. 34.
    Potocka E, Baughman RA, Derendorf H (2011) Population pharmacokinetic model of human insulin following different routes of administration. J Clin Pharmacol 51(7):1015–1024. doi: 10.1177/0091270010378520 CrossRefPubMedGoogle Scholar
  35. 35.
    Yáñez JA, Remsberg CM, Sayre CL, Forrest ML, Davies NM (2011) Flip-flop pharmacokinetics–delivering a reversal of disposition: challenges and opportunities during drug development. Ther Deliv 2(5):643–672CrossRefPubMedPubMedCentralGoogle Scholar
  36. 36.
    Sheiner LB, Beal SL (1980) Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: routine clinical pharmacokinetic data. J Pharmacokinet Biopharm 8(6):553–571. doi: 10.1007/bf01060053 CrossRefPubMedGoogle Scholar
  37. 37.
    Beal SL, Sheiner LB, Boeckmann AJ (1994) NONMEM IV user’s guide. Parts I–VI, NONMEM Project Group, University of California, San FranciscoGoogle Scholar
  38. 38.
    Juhl R, Møller JK, Jørgensen JB, Madsen H (2016) Modeling and prediction using stochastic differential equations. In: Kirchsteiger H, Jørgensen BJ, Renard E, del Re L (eds) Prediction methods for blood glucose concentration: design, use and evaluation. Springer International Publishing, Cham, pp 183–209. doi: 10.1007/978-3-319-25913-0_10 CrossRefGoogle Scholar
  39. 39.
    Kristensen NR, Madsen H, Ingwersen SH (2005) Using stochastic differential equations for pk/pd model development. J Pharmacokinet Pharmacodyn 32(1):109–141. doi: 10.1007/s10928-005-2105-9 CrossRefPubMedGoogle Scholar
  40. 40.
    Duun-Henriksen AK, Schmidt S, Røge RM, Møller JB, Nørgaard K, Jørgensen JB, Madsen H (2013) Model identification using stochastic differential equation grey-box models in diabetes. J Diabetes Sci Technol 7(2):431–440CrossRefPubMedPubMedCentralGoogle Scholar
  41. 41.
    Madsen H, Thyregod P (2010) Introduction to general and generalized linear models. CRC Press, Taylor & Francis Group, Boca RatonGoogle Scholar
  42. 42.
    Pories WJ, Dohm GL (2012) Diabetes: have we got it all wrong?: hyperinsulinism as the culprit: Surgery provides the evidence. Diabetes Care 35(12):2438–2442. doi: 10.2337/dc12-0684 CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Centre for BioengineeringUniversity of CanterburyChristchurchNew Zealand
  2. 2.Department of EndocrinologyHvidovre University HospitalHvidovreDenmark
  3. 3.Danish Diabetes AcademyOdense CDenmark
  4. 4.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations