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Mathematical modelling of disease progression

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Mathematical modelling of disease progression

  1. 1. A mechanism-based disease progression model to analyse long-term treatment effects on disease processes underlying type 2 diabetes Workshop Yvonne Rozendaal y.j.w.rozendaal@tue.nl “The interplay of fat and carbohydrate metabolism with application in Metabolic Syndrome and Type 2 Diabetes” December 12th 2013
  2. 2. Introduction • Disease progression – multi-scale problem – how to assess/measure? • Treatment interventions – effect of treatment on disease progression? short-term vs long-term • How to simulate adaptations & interventions? 2
  3. 3. Type 2 Diabetes Mellitus (T2DM) • Impaired beta-cell function • Reduced insulin sensitivity chronic loss of glycemic control • Monitoring glycemic control: biomarkers – FPG: fasting plasma glucose secondary – FSI: fasting serum insulin glycemic markers – HbA1c: glycosylated hemoglobin primary glycemic marker how to derive disease status? 3
  4. 4. T2DM treatment • hypoglycemic effect: short-term – immediate symptomatic effects on glycemic control • inhibitory effect on disease progression: long-term – protect against T2DM progression 4
  5. 5. Objective disease progression progressive loss of beta-cell function and insulin sensitivity metabolic biomarkers adaptations in biological network FPG FSI HbA1c treatment interventions pharmacological therapy computational model: description and quantification of inputs minimal model disease progression model test functionality of method on minimal model:  human vs. mouse  glucose vs. lipid metabolism introduction to ADAPT application of ADAPT 5
  6. 6. Modelling disease progression (1) • Disentangle treatment effects – long-term loss of beta-cell function and insulin sensitivity – short-term anti-hyperglycemic effects • Computational model: study & quantify time-course effects de Winter et al. (2006) J Pharmacokinet Pharmacodyn,33(3):313-343 disease progression model introduction to ADAPT application of ADAPT 6
  7. 7. PK/PD modelling • PharmacoKinetic-PharmacoDynamic modelling • Simple kinetics are modelled using minimal/macroscopic models • e.g. absorption profiles disease progression model introduction to ADAPT application of ADAPT 7
  8. 8. T2DM disease progression model (1) glucose – insulin – HbA1c • Model components – FPG: fasting plasma glucose – FSI: fasting serum insulin – HbA1c: glycosylated hemoglobin • Physiological FPG-FSI homeostasis: – feedback between FSI and FPG FPG stimulates FSI production: FSI production rate ∝ FPG concentration – feed-forward between FPG and HbA1c HbA1c production rate ∝ to FSI concentration disease progression model introduction to ADAPT application of ADAPT 8
  9. 9. T2DM disease progression model (2) model structure B: beta-cell function (disease status) k in EFB: treatment effect on insulin secretion S: insulin sensitivity (disease status) k in EFS: insulin sensitizing effect of treatment k in disease progression model FSI k out homeostatic feed-backs FPG k out feed-forward HbA1c introduction to ADAPT k out application of ADAPT 9
  10. 10. T2DM disease progression model (3) model equations treatment specific factor of insulinsecretogogues d FSI disease status: fraction of remaining beta-cell function EF B B ( FPG dt d FPG k in FPG dt EF S S FSI d HbA 1c dt FPG k in HbA treatment specific factor of insulinsensitizers disease progression model 3 . 5 ) k in FSI FSI k out FSI FPG k out FPG HbA 1c 1c k out HbA 1c disease status: fraction of remaining insulin sensitivity introduction to ADAPT application of ADAPT 10
  11. 11. T2DM disease progression model (1) disease status • Beta-cell function 1 B fraction of remaining beta-cell function 1 exp( b 0 shift of disease progression curve • Insulin sensitivity fraction of remaining hepatic insulin-sensitivity S 1 1 exp( s 0 rB t ) slope of disease progression curve rS t ) • Assumption: asympotically decrease over time disease progression model introduction to ADAPT application of ADAPT 11
  12. 12. Model comparison with data (1) • Long-term (1y) follow-up of treatment-naïve T2DM patients • 3 treatment arms: monotherapy with different hypoglycemic agents – pioglitazone: insulin sensitizer • enhances peripheral glucose uptake • reduces hepatic glucose production – metformin: insulin sensitizer • decreases hepatic glucose production – gliclazide: insulin secretogogue • stimulates insulin secretion by the pancreatic beta-cells disease progression model introduction to ADAPT application of ADAPT 12
  13. 13. FPG [mmol/L] Model comparison with data (2) disease progression model introduction to ADAPT application of ADAPT 13
  14. 14. Reproduction of results (1)  Metabolic biomarkers over time although initial decrease, glycemic control still gradually decreases over time disease progression model introduction to ADAPT application of ADAPT 14
  15. 15. Reproduction of results (2)  Disease status gliclazide: insulin secretogogue pioglitazone & metformin: insulin sensitizers however, morphology of disease progression curves unknown... disease progression model introduction to ADAPT application of ADAPT 15
  16. 16. Introduction to ADAPT (1) • Phenotype transition over time treatment interventions medication, surgery, ... disease progression phenotype A phenotype B which adaptations occur? • Analysis of Dynamic Adaptations in Parameter Trajectories Tiemann et al. (2011). BMC Syst Biol,26(5):174 Tiemann et al. (2013). PLoS Comput Biol,9(8):e1003166 disease progression model introduction to ADAPT application of ADAPT 16
  17. 17. Introduction to ADAPT (2) • Phenotype transition: – gradual, long-term processes – measurements at metabolome level • Adaptation at proteome and transcriptome level • Model at metabolome level • Time-dependency implemented using timevarying parameters disease progression model introduction to ADAPT application of ADAPT 17
  18. 18. Modelling phenotype transition (1)  long-term discrete data: different phenotypes treatment disease progression disease progression model introduction to ADAPT application of ADAPT 18
  19. 19. Modelling phenotype transition (2)  long-term discrete data: different phenotypes  estimate continuous data: cubic smooth spline introduce artificial intermediate phenotypes disease progression model introduction to ADAPT application of ADAPT 19
  20. 20. Modelling phenotype transition (3)  long-term discrete data: different phenotypes  estimate continuous data: cubic smooth spline  incorporate uncertainty in data: multiple describing functions disease progression model introduction to ADAPT application of ADAPT 20
  21. 21. Parameter estimation (1)  steady state model disease progression model introduction to ADAPT application of ADAPT 21
  22. 22. Parameter estimation (2)  steady state model  iteratively calibrate model to data: estimate parameters over time minimize difference between data and model simulation disease progression model introduction to ADAPT application of ADAPT 22
  23. 23. Parameter estimation (2)  steady state model  iteratively calibrate model to data: estimate parameters over time disease progression model introduction to ADAPT application of ADAPT 23
  24. 24. Parameter estimation (2)  steady state model  iteratively calibrate model to data: estimate parameters over time disease progression model introduction to ADAPT application of ADAPT 24
  25. 25. Parameter estimation (2)  steady state model  iteratively calibrate model to data: estimate parameters over time disease progression model introduction to ADAPT application of ADAPT 25
  26. 26. Estimated parameter trajectories  effect of parameter adaptations on underlying processes? down-regulation up-regulation stochastic behaviour... unaffected physiologically unrealistic disease progression model introduction to ADAPT application of ADAPT 26
  27. 27. Possible applications for ADAPT • Unravel which processes in network might be responsible for phenotype transition • Guide new experiment design • Define possible pharmacological targets disease progression model introduction to ADAPT application of ADAPT 27
  28. 28. Application of ADAPT in disease progression model fraction of beta-cell function: time-dependent parameter d FSI B ( FPG dt d FPG k in FPG dt S FSI d HbA dt 1c 3 . 5 ) k in FSI FSI k out FSI time-constant parameters FPG k out FPG FPG k in HbA HbA1c 1c k out HbA 1c fraction of insulin sensitivity: time-dependent parameter disease progression model introduction to ADAPT application of ADAPT 28
  29. 29. Disease progression model vs. application of ADAPT (1)  Metabolic biomarkers over time treatment with pioglitazone FPG & FSI: ADAPT reproduces model predictions HbA1c: performance ADAPT disease progression model introduction to ADAPT application of ADAPT 29
  30. 30. Disease progression model vs. application of ADAPT (2)  Parameter trajectories: disease status treatment with pioglitazone ADAPT suggests dynamic disease progression curves rather than pre-defined mathematical functions by de Winter et al. disease progression model introduction to ADAPT application of ADAPT 30
  31. 31. Disease progression model vs. application of ADAPT (2)  Parameter trajectories: disease status treatment with pioglitazone ADAPT suggests dynamic disease progression curves rather than pre-defined mathematical functions by de Winter et al. disease progression model introduction to ADAPT application of ADAPT 31
  32. 32. Conclusions & Future work • Disease progression model & ADAPT approach both useful for monitoring disease status • ADAPT – applicable to both mice/human, glucose/lipoprotein metabolism and multiscale models – more dynamically correct representation of beta-cell function and insulin sensitivity using ADAPT • However; – How to disentangle disease progression effects from hypoglycemic effects? – How to estimate time-varying parameters in conjunction with time-constant parameters? 32
  33. 33. Acknowledgements

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